As an extension of the Outlier FLOODing (OFLOOD) method [Harada et al., J. Comput. Chem. 2015, 36, 763], the sparsity of the outliers defined by a hierarchical clustering algorithm, FlexDice, was considered to achieve an efficient conformational search as sparsity-weighted “OFLOOD.” In OFLOOD, FlexDice detects areas of sparse distribution as outliers. The outliers are regarded as candidates that have high potential to promote conformational transitions and are employed as initial structures for conformational resampling by restarting molecular dynamics simulations. When detecting outliers, FlexDice defines a rank in the hierarchy for each outlier, which relates to sparsity in the distribution. In this study, we define a lower rank (first ranked), a medium rank (second ranked), and the highest rank (third ranked) outliers, respectively. For instance, the first-ranked outliers are located in a given conformational space away from the clusters (highly sparse distribution), whereas those with the third-ranked outliers are nearby the clusters (a moderately sparse distribution). To achieve the conformational search efficiently, resampling from the outliers with a given rank is performed. As demonstrations, this method was applied to several model systems: Alanine dipeptide, Met-enkephalin, Trp-cage, T4 lysozyme, and glutamine binding protein. In each demonstration, the present method successfully reproduced transitions among metastable states. In particular, the first-ranked OFLOOD highly accelerated the exploration of conformational space by expanding the edges. In contrast, the third-ranked OFLOOD reproduced local transitions among neighboring metastable states intensively. For quantitatively evaluations of sampled snapshots, free energy calculations were performed with a combination of umbrella samplings, providing rigorous landscapes of the biomolecules. © 2015 Wiley Periodicals, Inc.

Biologically rare events play important roles in understanding functions. To computationally reproduce them, Outlier FLOODing (OFLOOD) method is powerful, in which sparse distributions of biological states are detected as outliers and intensively resampled by MD simulations. As an extension, sparsity-weighted OFLOOD method is newly proposed, in which a hierarchical clustering defines ranks of outliers. Accordingly to the ranks, the confirmational resampling from outliers is performed, accerlarating the conformational sampling of bio-molecules.

The UV-induced photochemistry of HCFC-132b (CF_{2}ClCH_{2}Cl) was investigated by computing excited-state properties with time-dependent density functional theory (TDDFT), multiconfigurational second-order perturbation theory (CASPT2), and coupled cluster with singles, doubles, and perturbative triples (CCSD(T)). Excited states calculated with TDDFT show good agreement with CASPT2 and CCSD(T) results, correctly predicting the main excited-states properties. Simulations of ultrafast nonadiabatic dynamics in the gas phase were performed, taking into account 25 electronic states at TDDFT level starting in two different spectral windows (8.5 ± 0.25 and 10.0 ± 0.25 eV). Experimental data measured at 123.6 nm (10 eV) is in very good agreement with our simulations. The excited-state lifetimes are 106 and 191 fs for the 8.5 and 10.0 eV spectral windows, respectively. Internal conversion to the ground state occurred through several different reaction pathways with different products, where 2Cl, C-Cl bond breakage, and HCl are the main photochemical pathways in the low-excitation region, representing 95% of all processes. On the other hand, HCl, HF, and C-Cl bond breakage are the main reaction pathways in the higher excitation region, with 77% of the total yield. © 2015 Wiley Periodicals, Inc.

HCFC-132b is an important industrial compound, with a strong impact on health and environment. Upon UV irradiation, it decomposes into dozens of different photoproducts. In this article, nonadiabatic dynamics simulation is used to explain how photo-decomposition takes place through the competition between diverse reaction pathways in the subpicosecond time scale.

We present new algorithms to improve the performance of ENUF method (F. Hedman, A. Laaksonen, Chem. Phys. Lett. 425, 2006, 142) which is essentially Ewald summation using Non-Uniform FFT (NFFT) technique. A *NearDistance* algorithm is developed to extensively reduce the neighbor list size in real-space computation. In reciprocal-space computation, a new algorithm is developed for NFFT for the evaluations of electrostatic interaction energies and forces. Both real-space and reciprocal-space computations are further accelerated by using graphical processing units (GPU) with CUDA technology. Especially, the use of CUNFFT (NFFT based on CUDA) very much reduces the reciprocal-space computation. In order to reach the best performance of this method, we propose a procedure for the selection of optimal parameters with controlled accuracies. With the choice of suitable parameters, we show that our method is a good alternative to the standard Ewald method with the same computational precision but a dramatically higher computational efficiency. © 2015 Wiley Periodicals, Inc.

By using graphical processing units and developing new algorithms both for real-space and reciprocal-space computations, the computational efficiency of the ENUF method used to evaluate electrostatic interactions in particle-based simulations is extraordinarily improved. A procedure for the selection of the optimal parameters with controlled accuracies is proposed. With this method, the same computational precision as the standard Ewald method is achieved, but with dramatically higher computational efficiency.

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three-dimensional reference interaction site model (3D-RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D-RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.

Although the hydration free energy (HFE) is one of the most important factors in studies on the structural stability of a protein, its calculation is significantly difficult in computational cost and accuracy. We develop a new method for calculating the HFE by combining the generalized Born model and the morphometric approach. Our method gives almost the same result as that from the three-dimensional reference interaction site model (3D-RISM) theory with drastic reduction of computational cost.

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ∼330,000 (∼5600) eigenvalues and eigenfunctions are obtained in ∼190 (∼5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. A parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated. © 2015 Wiley Periodicals, Inc.

Massively parallel supercomputers can extend the size of systems that we can study with quantum chemistry methods. However, the eigenvalue problem remains the bottleneck of scalability for density-functional based tight-binding (DFTB) or semi-empirical molecular orbital methods. We present a sparse eigensolver that enables DFTB calculations for systems with more than 100,000 atoms utilizing more than 200,000 CPU cores.

A number of model Diels-Alder (D-A) cycloaddition reactions (H_{2}CCH_{2} + cyclopentadiene and H_{2}CCHX + 1,3-butadiene, with X = H, F, CH_{3}, OH, CN, NH_{2}, and NO) were studied by static (transition state - TS and IRC) and dynamics (quasiclassical trajectories) approaches to establish the (a)synchronous character of the concerted mechanism. The use of static criteria, such as the asymmetry of the TS geometry, for classifying and quantifying the (a)synchronicity of the concerted D-A reaction mechanism is shown to be severely limited and to provide contradictory results and conclusions when compared to the dynamics approach. The time elapsed between the events is shown to be a more reliable and unbiased criterion and all the studied D-A reactions, except for the case of H_{2}CCHNO, are classified as synchronous, despite the gradual and quite distinct degrees of (a)symmetry of the TS structures. © 2015 Wiley Periodicals, Inc.

Model Diels-Alder cycloaddition reactions were studied by static and dynamics approaches to establish the (a)synchronous character of the concerted mechanism. The use of static criteria, such as the asymmetry of the TS geometry, for classifying and quantifying the (a)synchronicity of the concerted reaction mechanism provides contradictory results and conclusions when compared to the dynamics approach.

Fragment-based linear scaling quantum chemistry methods are a promising tool for the accurate simulation of chemical and biomolecular systems. Because of the coupled inter-fragment electrostatic interactions, a dual-layer iterative scheme is often employed to compute the fragment electronic structure and the total energy. In the dual-layer scheme, the self-consistent field (SCF) of the electronic structure of a fragment must be solved first, then followed by the updating of the inter-fragment electrostatic interactions. The two steps are sequentially carried out and repeated; as such a significant total number of fragment SCF iterations is required to converge the total energy and becomes the computational bottleneck in many fragment quantum chemistry methods. To reduce the number of fragment SCF iterations and speed up the convergence of the total energy, we develop here a new SCF scheme in which the inter-fragment interactions can be updated concurrently without converging the fragment electronic structure. By constructing the global, block-wise Fock matrix and density matrix, we prove that the commutation between the two global matrices guarantees the commutation of the corresponding matrices in each fragment. Therefore, many highly efficient numerical techniques such as the direct inversion of the iterative subspace method can be employed to converge simultaneously the electronic structure of all fragments, reducing significantly the computational cost. Numerical examples for water clusters of different sizes suggest that the method shall be very useful in improving the scalability of fragment quantum chemistry methods. © 2015 Wiley Periodicals, Inc.

Fragment-based, linear-scaling, quantum chemistry methods hold great potential for application in accurate simulations of complex molecular systems. Because of the coupled inter-fragment interactions, however, conventional fragment methods often employ a dual-layer SCF scheme to converge both the intra- and inter-fragment interactions. The total number of fragment SCF iterations displays a size-dependence to the target molecule. A new global SCF scheme developed here shows excellent performance over a broad range of molecular sizes and is applicable to other fragment methods.

We show that the empirical 18-electron rule of transition metal chemistry corresponds to an intrinsic *saturation limit* for the 3c/4e hyperbonding interactions that are a ubiquitous feature of D-block aggregation phenomena. Such a “rule” therefore requires no “p-orbital participation,” “d^{2}sp^{3} hybridization,” “valence shell expansion,” or other p-type intrusions into the *Aufbau* orbital filling sequence. Instead, 18e stability corresponds to the natural terminus of post-Lewis 3c/4e resonance-type stabilizations that lead to successive ligand additions (and formal increments of electron count) at a transition metal center, all within the normal (s + 5d) confines of D-block valence space. © 2015 Wiley Periodicals, Inc.

Electronic iconography of the 18e rule, illustrating how a normal-valent (12e) transition metal MX_{3} species (using s and d orbitals at M to accommodate three MX bonds, blue dots, and three lone pairs, red dots) achieves the maximally stabilizing *e*_{M} = 18 “count” (all dots) by adding three L donor ligands (green dots) that participate in all possible 3c/4e hyperbonding interactions (*n*_{L}σ*_{MX}) with MX bonds.

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas–Kroll–Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization. © 2015 Wiley Periodicals, Inc.

The Molcas quantum chemistry program package has a long history, and with the release of Molcas 8 in 2014, it continues to offer state-of-the-art tools for computational chemistry. This article summarizes some of the most significant additions and improvements included in the package in the last 6 years. There are sections on electron correlation methods, relativistic features, molecular dynamics, gradients and optimizations, and technical features.

The conformational dynamics of a macromolecule can be modulated by a number of factors, including changes in environment, ligand binding, and interactions with other macromolecules, among others. We present a method that quantifies the differences in macromolecular conformational dynamics and automatically extracts the structural features responsible for these changes. Given a set of molecular dynamics (MD) simulations of a macromolecule, the norms of the differences in covariance matrices are calculated for each pair of trajectories. A matrix of these norms thus quantifies the differences in conformational dynamics across the set of simulations. For each pair of trajectories, covariance difference matrices are parsed to extract structural elements that undergo changes in conformational properties. As a demonstration of its applicability to biomacromolecular systems, the method, referred to as DIRECT-ID, was used to identify relevant ligand-modulated structural variations in the β_{2}-adrenergic (β_{2}AR) G-protein coupled receptor. Micro-second MD simulations of the β_{2}AR in an explicit lipid bilayer were run in the apo state and complexed with the ligands: BI-167107 (agonist), epinephrine (agonist), salbutamol (long-acting partial agonist), or carazolol (inverse agonist). Each ligand modulated the conformational dynamics of β_{2}AR differently and DIRECT-ID analysis of the inverse-agonist vs. agonist-modulated β_{2}AR identified residues known through previous studies to selectively propagate deactivation/activation information, along with some previously unidentified ligand-specific microswitches across the GPCR. This study demonstrates the utility of DIRECT-ID to rapidly extract functionally relevant conformational dynamics information from extended MD simulations of large and complex macromolecular systems. © 2015 Wiley Periodicals, Inc.

Characterizing changes in conformational dynamics of a macromolecule is important for understanding its function. To rapidly quantify the change and identify structural features that contribute most significantly to the conformational changes, a covariance matrix-based method, called DIRECT-ID, is presented. Ligand-modulated conformational changes in the β2-adrenergic GPCR are quantified using DIRECT-ID and both previously known and new ligand-specific microswitches are identified using the method.

Implicit solvent models for biomolecular simulations have been developed to use in place of more expensive explicit models; however, these models make many assumptions and approximations that are likely to affect accuracy. Here, the changes in free energies of solvation upon folding of several fast folding proteins are calculated from previously run μs–ms simulations with a number of implicit solvent models and compared to the values needed to be consistent with the explicit solvent model used in the simulations. In the majority of cases, there is a significant and substantial difference between the values calculated from the two approaches that is robust to the details of the calculations. These differences could only be remedied by selecting values for the model parameters—the internal dielectric constant for the polar term and the surface tension coefficient for the nonpolar term—that were system-specific or physically unrealistic. We discuss the potential implications of our findings for both implicit and explicit solvent simulations. © 2015 Wiley Periodicals, Inc.

We compare changes in solvation free energy upon folding provided by several implicit solvent models and the TIP3P explicit solvent model. Inconsistencies of an unexpected magnitude were found across the models, which could only be corrected by using settings that were nonphysical or system-specific.

We present a low rank moment expansion of the linear density-density response function. The general interacting (fully nonlocal) density-density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well-defined moments. This transformation generates the irreducible representations of the density-density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density-density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.

Intermolecular interactions lead to changes of the electronic charge density. We provide an efficient scheme to express these changes for an arbitrary interaction with an universal yet low-rank tensor. To that extend, we transform the linear density–density response function from its spectral decomposition to a more condensed representation, separating the contributions to the electronic response density from different multipole moments of the perturbation.

Molecular docking is a computational approach for predicting the most probable position of ligands in the binding sites of macromolecules and constitutes the cornerstone of structure-based computer-aided drug design. Here, we present a new algorithm called *Attracting Cavities* that allows molecular docking to be performed by simple energy minimizations only. The approach consists in transiently replacing the rough potential energy hypersurface of the protein by a smooth attracting potential driving the ligands into protein cavities. The actual protein energy landscape is reintroduced in a second step to refine the ligand position. The scoring function of Attracting Cavities is based on the CHARMM force field and the FACTS solvation model. The approach was tested on the 85 experimental ligand–protein structures included in the Astex diverse set and achieved a success rate of 80% in reproducing the experimental binding mode starting from a completely randomized ligand conformer. The algorithm thus compares favorably with current state-of-the-art docking programs. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

A new algorithm called Attracting Cavities, which allows molecular docking to be performed by only simple energy minimizations, is presented. The approach consists in transiently replacing the rough protein potential energy landscape by a smooth attracting landscape driving the ligands into protein cavities. The actual protein energy landscape is ultimately reintroduced to refine the ligand pose. The approach achieved a success rate of 80% on the Astex diverse set starting from completely randomized ligand conformers.

The extensibility of force field is a key to solve the missing parameter problem commonly found in force field applications. The extensibility of conventional force fields is traditionally managed in the parameterization procedure, which becomes impractical as the coverage of the force field increases above a threshold. A hierarchical atom-type definition (HAD) scheme is proposed to make extensible atom type definitions, which ensures that the force field developed based on the definitions are extensible. To demonstrate how HAD works and to prepare a foundation for future developments, two general force fields based on AMBER and DFF functional forms are parameterized for common organic molecules. The force field parameters are derived from the same set of quantum mechanical data and experimental liquid data using an automated parameterization tool, and validated by calculating molecular and liquid properties. The hydration free energies are calculated successfully by introducing a polarization scaling factor to the dispersion term between the solvent and solute molecules. © 2015 Wiley Periodicals, Inc.

A hierarchical definition of atom type is proposed to solve the problem of “missing parameters”. The extensible atom type definitions make the force field extensible. Two general force fields are parameterized for some common organic molecules. Parameters are derived from ab initial data and experimental liquid data. Calculation results show good accuracy of the parameters.

This article describes a revised version 56A6_{CARBO_R} of the GROMOS 56A6_{CARBO} force field for hexopyranose-based carbohydrates. The simulated properties of unfunctionalized hexopyranoses are unaltered with respect to 56A6_{CARBO}. In the context of both O_{1}-alkylated hexopyranoses and oligosaccharides, the revision stabilizes the regular ^{4}C_{1} chair for α-anomers, with the opposite effect for β-anomers. As a result, spurious ring inversions observed in α(14)-linked chains when using the original 56A6_{CARBO} force field are alleviated. The ^{4}C_{1} chair is now the most stable conformation for all d-hexopyranose residues, irrespective of the linkage type and anomery, and of the position of the residue along the chain. The methylation of a d-hexopyranose leads to a systematic shift in the ring-inversion free energy (^{4}C_{1} to ^{1}C_{4}) by 7–8 kJ mol^{−1}, positive for the α-anomers and negative for the β-anomers, which is qualitatively compatible with the expected enhancement of the anomeric effect upon methylation at O_{1}. The ring-inversion free energies for residues within chains are typically smaller in magnitude compared to those of the monomers, and correlate rather poorly with the latter. This suggests that the crowding of ring substituents upon chain formation alters the ring flexibility in a nonsystematic fashion. In general, the description of carbohydrate chains afforded by 56A6_{CARBO_R} suggests a significant extent of ring flexibility, i.e., small but often non-negligible equilibrium populations of inverted chairs, and challenges the “textbook” picture of conformationally locked carbohydrate rings. © 2015 Wiley Periodicals, Inc.

A revised version 56A6_{CARBO_R} of the GROMOS 56A6_{CARBO} force field for hexopyranose-based carbohydrates is proposed. The revision significantly improves the description of ring-conformational properties for residues within chains. In the revised force field, the ^{4}C_{1} chair is the most stable conformation for all d-hexopyranose residues, irrespective of the linkage type and anomery, and of the position of the residue along the chain. Additionally, the influence of the functionalization type (alkylation or glycosylation) of the anomeric oxygen atom on the ring-inversion properties is discussed.

Combined quantum mechanical calculations and classical molecular dynamics simulations were conducted to investigate the hydration properties of carboxybetaine zwitterion brushes with varying separation distances between the quaternary ammonium cation and carboxylic anion. The brushes consist of zwitterion trimers and are investigated to mimic interacting zwitterion chains grafted on a substrate as well as polymers with interacting zwitterion side chains. Our results show that the values of both positive and negative charges, their separation distances as well as chain interactions appear to play a critical role in the hydration properties of the zwitterions. The overall hydration property of these zwitterions is dictated by the competition between the strong hydration of the charged groups and the dehydration of the hydrocarbon chains. The strongest hydration occurs when the CH_{2}− unit in the hydrocarbon chain reaches 6–8 for these trimers. Further increase in the hydrocarbon chain length to 10–14 leads to significant and sudden dehydration of the trimers. The water structure and the water residence time surrounding the zwitterions also demonstrate substantial alteration at this length scale. This hydrophilic-to-hydrophobic transition is induced by the hydrophobic interactions of the trimer chains. Our hydration results could explain the observed trend of the superiority of the methylated carbohydrates and poly(ethylene glycol) as antifouling materials compared to corresponding hydroxyl-terminated compounds. © 2015 Wiley Periodicals, Inc.

The average pair distribution functions (*g*(*r*)) correlates the C atoms on the hydrocarbon chains between the cationic and anionic groups and the O atoms in water as a function of the carbon spacer chain length (CSL) on a carboxybetaine trimer. The sudden decrease in the *g*(*r*) function correlates to the hydrophilic-to-hydrophobic transition when the CSL increases from 12 to 14.

When an electric field is applied to an insulating membrane, movement of charged particles through a nanopore is induced. The measured ionic current reports on biomolecules passing through the nanopore. In this work, we explored the kinetics of DNA unzipping in a nanopore using our coarse-grained model (Stachiewicz and Molski, J. Comput. Chem. 2015, 36, 947). Coarse graining allowed a more detailed analysis for a wider range of parameters than all-atom simulations. Dependence of the translocation mode (unzipping or distortion) on the pore diameter was examined, and the threshold voltages were estimated. We determined the potential of mean force, position-dependent diffusion coefficient, and position-dependent effective charge for the DNA unzipping. The three molecular profiles were correlated with the ionic current and molecular events. On the unzipping/translocation force profile, two energy maxima were found, one of them corresponding to the unzipping, and the other to the translocation barriers. The unzipping kinetics were further explored using Brownian dynamics. © 2015 Wiley Periodicals, Inc.

When an electric field is applied to an insulating membrane, movement of charged particles through a nanopore is induced. In this work, the kinetics of DNA unzipping in a nanopore is explored using a coarse-grained model. Dependence of the translocation mode on the pore diameter is examined, and the threshold voltages are estimated. The potential of mean force, position-dependent diffusion coefficient and position-dependent effective charge are determined for the DNA unzipping.

Noncovalent functionalization of buckybowls sumanene (S), corannulene (R), and coronene (C) with greenhouse gases (GGs) such as CO_{2}, CH_{4} (M), and C_{2}H_{2} (A) has been studied using hybrid density functional theory. The propensity and preferences of these small molecules to interact with the concave and convex surfaces of the buckybowls has been quantitatively estimated. The results indicate that curvature plays a significant role in the adsorption of these small molecules on the π surface and it is observed that buckybowls have higher binding energies (BEs) compared with their planar counterpart coronene. The concave surface of the buckybowl is found to be more feasible for adsorption of small molecules. BEs of small molecules towards π systems is CO_{2} > A > M and the BEs of π systems toward small molecules is S > R > C. Obviously, the binding preference is dictated by the way in which various noncovalent interactions, such as π···π, lone pair···π, and CH···π manifest themselves on carbaneous surfaces. To delineate the intricate details of the interactions, we have employed Bader's quantum theory of atoms in molecule and localized molecular orbital energy decomposition analysis (LMO-EDA). LMO-EDA, which measures the contribution of various components and traces the physical origin of the interactions, indicates that the complexes are stabilized largely by dispersion interactions. © 2015 Wiley Periodicals, Inc.

Computational studies reveal that monolayer carbonaceous surfaces, such as sumanene, corannulene and coronene, are optimal for adsorption of small gas molecules such as CO_{2}, CH_{4} and C_{2}H_{2}. The concave surface of the buckybowl is preferred over the convex alternative for the adsorption as well as the selective binding of small molecules. Dispersion is largely responsible for binding of small molecules, buckybowls and coronene.

A zone-folding (ZF) approach is applied for the estimation of the phonon contributions to thermodynamic properties of carbon-and ZrS_{2}-based nanotubes (NTs) of hexagonal morphology with different chiralities. The results obtained are compared with those from the direct calculation of the thermodynamic properties of NTs using PBE0 hybrid exchange-correlation functional. The phonon contribution to the stability of NTs proved to be negligible for the internal energy and small for the Helmholtz free energy. It is found that the ZF approach allows us an accurate estimation of phonon contributions to internal energy, but slightly overestimates the phonon contributions to entropy. © 2015 Wiley Periodicals, Inc.

In the case of nanotubes rolled up from the layers of layered compounds (such as graphite, ZrS2, or V2O5) the phonon contributions to the heat capacity and internal energy calculated directly and estimated with using the appropriate 2D layer supercell (within the zone-folding approach) remain very close to each other for temperatures up to 600 K.

We investigated the performance of the density functional theory (DFT) functionals PBE, PBE0, M06, and M06-L for describing the molecular and dissociative adsorption of O_{2} onto pure and doped Al(111) surfaces. Adsorption of O_{2} was studied at the perfect Al(111) surface and compared with the case where an additional Al atom was present as an adatom. Additionally, we studied how these functionals perform when different dopants are present at the Al(111) surface in two distinct geometries: as an adatom or as a substitutional atom replacing an Al atom. The performance of the different functionals is greatly affected by the surface geometry. The inclusion of Hartree-Fock exchange in the functional leads to slight differences in adsorption energies for molecular adsorption of O_{2}. These differences become very pronounced for dissociative adsorption, with the hybrids PBE0 and M06 predicting more exergonic adsorption than PBE and M06-L. Furthermore, PBE0 and M06 predicted trends in adsorption energies for defective and perfect surfaces which are in line with the experimental knowledge of the effects of surface defects in adsorption energies. The predictions of the non-hybrids PBE and M06-L point in the opposite direction. The analysis of the contributions of the van der Waals (vdW) forces to the adsorption energies reveals that the PBE and PBE0 functionals have similar difficulties in describing vdW interactions for molecular adsorption of O_{2} while the M06 functional can give a description of these forces with an accuracy which is at least similar to that of the correction of the D3 type. © 2015 Wiley Periodicals, Inc.

Within density functional theory (DFT), different functionals produce very large differences in the description of the molecular and dissociative adsorption of O_{2} at pure and doped aluminum surfaces. These differences are here reported and discussed in view of the type of physical descriptors of the electron density incorporated in each functional.

A new type of reaction pathway which involves a nontotally symmetric trifurcation was found and investigated for a typical S_{N}2-type reaction, NC^{-} + CH_{3}X NCCH_{3} + X^{-} (X = F, Cl). A nontotally symmetric valley-ridge inflection (VRI) point was located along the *C*_{3}_{v} reaction path. For X = F, the minimum energy path (MEP) starting from the transition state (TS) leads to a second-order saddle point with *C*_{3}_{v} symmetry, which connects three product minima of *C _{s}* symmetry. For X = Cl, four product minima have been observed, of which three belong to

A new type of reaction pathway which involves a nontotally symmetric trifurcation was found and investigated for the S_{N}2-type reaction, NC^{-} + CH_{3}X NCCH_{3} + X^{-} (X = F, Cl). A nontotally symmetric valley-ridge inflection (VRI) point was located along the *C*_{3}_{v} reaction path. The branching path from the VRI point to the lower symmetry minima was determined. The possibility of a nontotally symmetric *n-furcation* is discussed.

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.

The amount of relativistic contribution to nuclear shielding is the same for noble gas dimers and free atoms. For Ne to Xe, the relativistic contribution is more important than both electron correlation and vibrational corrections. However, for the chemical shifts the relativistic corrections almost cancel, so that ZPVC become more important than relativistic corrections for Ne_{2}, Kr_{2}, and Ar_{2}.

A computational protein design method is extended to allow Monte Carlo simulations where two ligands are titrated into a protein binding pocket, yielding binding free energy differences. These provide a stringent test of the physical model, including the energy surface and sidechain rotamer definition. As a test, we consider tyrosyl-tRNA synthetase (TyrRS), which has been extensively redesigned experimentally. We consider its specificity for its substrate l-tyrosine (l-Tyr), compared to the analogs d-Tyr, *p*-acetyl-, and *p*-azido-phenylalanine (ac-Phe, az-Phe). We simulate l- and d-Tyr binding to TyrRS and six mutants, and compare the structures and binding free energies to a more rigorous “MD/GBSA” procedure: molecular dynamics with explicit solvent for structures and a Generalized Born + Surface Area model for binding free energies. Next, we consider l-Tyr, ac- and az-Phe binding to six other TyrRS variants. The titration results are sensitive to the precise rotamer definition, which involves a short energy minimization for each sidechain pair to help relax bad contacts induced by the discrete rotamer set. However, when designed mutant structures are rescored with a standard GBSA energy model, results agree well with the more rigorous MD/GBSA. As a third test, we redesign three amino acid positions in the substrate coordination sphere, with either l-Tyr or d-Tyr as the ligand. For two, we obtain good agreement with experiment, recovering the wildtype residue when l-Tyr is the ligand and a d-Tyr specific mutant when d-Tyr is the ligand. For the third, we recover His with either ligand, instead of wildtype Gln. © 2015 Wiley Periodicals, Inc.

A computational protein design method is extended to allow Monte Carlo simulations where two ligands are titrated into a protein binding pocket, yielding binding free energy differences. These provide a stringent test of the physical model, including the energy surface and sidechain rotamer definition. As a test, tyrosyl-tRNA synthetase and its specificity for its substrate l-Tyr, compared to d-Tyr, *p*-acetyl-, and *p*-azido-phenylalanine is considered.

Protein fold recognition is an important and essential step in determining tertiary structure of a protein in biological science. In this study, a model termed *NiRecor* is developed for recognizing protein folds based on artificial neural networks incorporated in an adaptive heterogeneous particle swarm optimizer. The main contribution of *NiRecor* is that it is a data-driven and highly-performing predictor without manually tuning control parameters for different data sets. In biological science, since evolutionary- and structure-based information of amino acid sequences is greatly important in determination of tertiary structure of a protein, accordingly, in *NiRecor* we employ two different feature sets, which involve position specific scoring matrix and secondary structure prediction matrix, to predict the structural classes of protein folds. The experimental results demonstrate the proposed method is powerful in predicting protein folds with higher precisions by improvements of 1.1 ∼7.8 percentages on three benchmark datasets by comparing with several existing predictors. © 2015 Wiley Periodicals, Inc.

As an outstanding issue in protein science, protein-fold recognition is highly important for determining the tertiary structure of a protein from its primary sequence. How to correctly recognize the protein folds from sequences? Accordingly, a swarm-optimized predictor—a data-driven predicting method—is proposed to solve this scientific problem. Without manually tuning parameters, it avoids laborious work on finding an appropriate predictor for the problem and exhibits a good performance, even on different protein datasets.

The restricted active-space (RAS) approach can accurately simulate metal L-edge X-ray absorption spectra of first-row transition metal complexes without the use of any fitting parameters. These characteristics provide a unique capability to identify unknown chemical species and to analyze their electronic structure. To find the best balance between cost and accuracy, the sensitivity of the simulated spectra with respect to the method variables has been tested for two models, [FeCl_{6}]^{3–} and [Fe(CN)_{6}]^{3–}. For these systems, the reference calculations give deviations, when compared with experiment, of ≤1 eV in peak positions, ≤30% for the relative intensity of major peaks, and ≤50% for minor peaks. When compared with these deviations, the simulated spectra are sensitive to the number of final states, the inclusion of dynamical correlation, and the ionization potential electron affinity shift, in addition to the selection of the active space. The spectra are less sensitive to the quality of the basis set and even a double-*ζ* basis gives reasonable results. The inclusion of dynamical correlation through second-order perturbation theory can be done efficiently using the state-specific formalism without correlating the core orbitals. Although these observations are not directly transferable to other systems, they can, together with a cost analysis, aid in the design of RAS models and help to extend the use of this powerful approach to a wider range of transition metal systems. © 2015 Wiley Periodicals, Inc.

With an appropriate choice of active space, basis set, and computational procedure, the restricted active space approach can be used to simulate metal L-edge X-ray absorption spectra with reasonable accuracy and computational cost. The sensitivity of the simulated results with respect to geometrical changes opens up for analysis of dynamical processes.

The free energy calculation library PLUMED has been incorporated into the OpenMM simulation toolkit, with the purpose to perform enhanced sampling MD simulations using the AMOEBA polarizable force field on GPU platform. Two examples, (I) the free energy profile of water pair separation (II) alanine dipeptide dihedral angle free energy surface in explicit solvent, are provided here to demonstrate the accuracy and efficiency of our implementation. The converged free energy profiles could be obtained within an affordable MD simulation time when the AMOEBA polarizable force field is employed. Moreover, the free energy surfaces estimated using the AMOEBA polarizable force field are in agreement with those calculated from experimental data and *ab initio* methods. Hence, the implementation in this work is reliable and would be utilized to study more complicated biological phenomena in both an accurate and efficient way. © 2015 Wiley Periodicals, Inc.

The free energy calculation library PLUMED has been incorporated into the OpenMM simulation toolkit, with the purpose to perform enhanced sampling molecular dynamics simulations using the AMOEBA polarizable force field on GPU platform. Two examples show that the implementation in the work is reliable and would be utilized to study more complicated biological phenomena in both an accurate and efficient way

Molecular docking techniques have now been widely used to predict the protein–ligand binding modes, especially when the structures of crystal complexes are not available. Most docking algorithms are able to effectively generate and rank a large number of probable binding poses. However, it is hard for them to accurately evaluate these poses and identify the most accurate binding structure. In this study, we first examined the performance of some docking programs, based on a testing set made of 15 crystal complexes with drug statins for the human 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGR). We found that most of the top ranking HMGR–statin binding poses, predicted by the docking programs, were energetically unstable as revealed by the high theoretical-level calculations, which were usually accompanied by the large deviations from the geometric parameters of the corresponding crystal binding structures. Subsequently, we proposed a new computational protocol, DOX, based on the joint use of molecular Docking, ONIOM, and eXtended ONIOM (XO) methods to predict the accurate binding structures for the protein–ligand complexes of interest. Our testing results demonstrate that the DOX protocol can efficiently predict accurate geometries for all 15 HMGR-statin crystal complexes without exception. This study suggests a promising computational route, as an effective alternative to the experimental one, toward predicting the accurate binding structures, which is the prerequisite for all the deep understandings of the properties, functions, and mechanisms of the protein–ligand complexes. © 2015 Wiley Periodicals, Inc.

The detailed knowledge of the protein–ligand binding structures is always important for the deep understanding of protein-ligand interactions. The new computational protocol DOX, which takes the advantage of molecular *D*ocking method's efficiency and QM methods' (*O*NIOM and e*X*tended ONIOM) accuracy, can be used to predict the accurate binding structures for the protein–ligand complexes of interest, as an effective alternative to the costly experimental methods.

The extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials and electron affinities from any level of theory. Although it is widely applied to ionization potentials, the EKT approach has not been applied to evaluation of the chemical reactivity. We present the first benchmarking study to investigate the performance of the EKT methods for predictions of chemical potentials (*μ*) (hence electronegativities), chemical hardnesses (*η*), and electrophilicity indices (*ω*). We assess the performance of the EKT approaches for post-Hartree–Fock methods, such as Møller–Plesset perturbation theory, the coupled-electron pair theory, and their orbital-optimized counterparts for the evaluation of the chemical reactivity. Especially, results of the orbital-optimized coupled-electron pair theory method (with the aug-cc-pVQZ basis set) for predictions of the chemical reactivity are very promising; the corresponding mean absolute errors are 0.16, 0.28, and 0.09 eV for *μ*, *η*, and *ω*, respectively. © 2015 Wiley Periodicals, Inc.

The first benchmarking study to investigate the performance of the EKT methods for predictions of chemical potentials (*μ*) (hence electronegativities), chemical hardnesses (*η*), and electrophilicity indices (*ω*) is presented.

Isomerization and transformation of glucose and fructose to 5-hydroxymethylfurfural (HMF) in both ionic liquids (ILs) and water has been studied by the reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-SEDD) method coupled with *ab initi*o electronic structure theory, namely coupled cluster single, double, and perturbative triple excitation (CCSD(T)). Glucose isomerization to fructose has been investigated via cyclic and open chain mechanisms. In water, the calculations support the cyclic mechanism of glucose isomerization; with the predicted activation free energy is 23.8 kcal mol^{−1} at experimental condition. Conversely, open ring mechanism is more favorable in ILs with the energy barrier is 32.4 kcal mol^{−1}. Moreover, the transformation of fructose into HMF via cyclic mechanism is reasonable; the calculated activation barriers are 16.0 and 21.5 kcal mol^{−1} in aqueous and ILs solutions, respectively. The solvent effects of ILs could be explained by the decomposition of free energies and radial distribution functions of solute-solvent that are produced by RISM-SCF-SEDD. © 2015 Wiley Periodicals, Inc.

A combination of quantum mechanics and statistical mechanics, called reference interaction site model self-consistent field spatial electron density distribution, is used to investigate the transformation reaction of glucose to 5-hydroxymethylfurfural in aqueous and ionic liquids (ILs). The cyclic mechanism is more favorable in the aqueous solutions. Conversely, open chain mechanism is preferable in ILs.

A comprehensive theoretical treatment is presented for the electronic excitation spectra of ca. 50 different mono-, di-, and tetrasubstituted naphthalenediimides (NDI) using time-dependent density functional theory (TDDFT) at ZORA-CAM-B3LYP/TZ2P//ZORA-BP86/TZ2P with COSMO for simulating the effect of dichloromethane (DCM) solution. The substituents XH_{n} are from groups 14–17 and rows 2–5 of the periodic table. The lowest dipole-allowed singlet excitation (S_{0}–S_{1}) of the monosubstituted NDIs can be tuned from 3.39 eV for F to 2.42 eV for TeH, while the S_{0}–S_{2} transition is less sensitive to substitution with energies ranging between 3.67 eV for CH_{3} and 3.44 eV for SbH_{2}. In the case of NDIs with group-15 and −16 substituents, the optical transitions strongly depend on the extent to which XH_{n} is planar or pyramidal as well as on the possible formation of intramolecular hydrogen bonds. The accumulative effect of double and quadruple substitution leads in general to increasing bathochromic shifts, but the increased steric hindrance in tetrasubstituted NDIs can lead to deformations that diminish the effectiveness of the substituents. Detailed analyses of the Kohn–Sham orbital electronic structure in monosubstituted NDIs reveal the mesomeric destabilization of the HOMO as the primary cause of the bathochromic shift of the S_{0}–S_{1} transition. © 2015 Wiley Periodicals, Inc.

It is shown through TDDFT explorations that naphthalenediimide's (NDI's) strong S_{0}–S_{1} transition offers excellent opportunities for tuning its absorption frequency through substituents. Kohn–Sham MO analyses reveal that the S_{0}–S_{1} gap can be reduced by pushing the overall HOMO up in energy using a more electropositive substituent. The S_{0}–S_{1} transition can be pushed beyond the “700 nm barrier” which is crucial for developing antenna molecules absorbing near-infrared photons in the solar spectrum.

Density functional theory computations (B3LYP) have been used to explore the chemistry of titanium–aromatic carbon “edge complexes” with 1,3-metal-carbon (1,3-MC) bonding between Ti and planar tetracoordinate C_{β}. The titanium-coordinated, end-capping chlorides are replaced with OH or SH groups to afford two series of difunctional monomers that can undergo condensation to form oxide- and sulfide-bridged oligomers. The sulfide-linked oligomers have less molecular strain and are more exergonic than the corresponding oxide-linked oligomers. The HOMO–LUMO gap of the oligomers varies with their composition and decreases with growing oligomer chain. This theoretical study is intended to enrich 1,3-MC bonding and planar tetracoordinate carbon chemistry and provide interesting ideas to experimentalists. Organometallic complexes with the TiE_{2} (E = OH and SH) decoration on the edge of aromatic hydrocarbons have been computationally designed, which feature 1,3-metal-carbon (1,3-MC) bonding between titanium and planar tetracoordinate β-carbon. Condensation of these difunctional monomers by eliminating small molecules (H_{2}O and H_{2}S) produce chain-like oligomers. The HOMO–LUMO gaps of the oligomers decreases with growing oligomer chain, a trend that suggests possible semiconductor properties for oligomers with longer chains. © 2015 Wiley Periodicals, Inc.

Organometallic complexes with the TiE_{2} (E=OH and SH) decoration on the edge of aromatic hydrocarbons have been computationally designed, which feature 1,3-metal-carbon (1,3-MC) bonding between titanium and planar tetracoordinate β-carbon. Condensation of these di-functional monomers by eliminating small molecules (H_{2}O and H_{2}S) produce chain-like oligomers. The HOMO-LUMO gaps of the oligomers decreases with growing oligomer chain, a trend that suggests possible semi-conductor properties for oligomers with longer chains.

Density functional theory is used to study the mechanism of the title reaction, one of the first catalytic asymmetric 6*π*-electrocyclizations observed experimentally. The benzylideneacetone-derived phenyl hydrazone is chosen as model substrate for the cyclization reaction, both in the protonated (**A**) and unprotonated (**B**) form, while the isoelectronic carbon analogue, 1,5-diphenylpentadienyl anion (**C**), serves as a reference for comparisons. The barrier to cyclization is computed to be more than 15 kcal/mol lower in **A** compared with **B**, in line with the observed acid catalysis. The relevant transition states to cyclization are characterized for **A** and **C** using orbital inspection, natural bond orbital analysis, nucleus independent chemical shifts, and stereochemical indicators. The cyclization of **C** is confirmed to be pericyclic, while that of **A** can be described as pseudopericyclic ring closure involving an intramolecular nucleophilic addition. © 2015 Wiley Periodicals, Inc.

Density functional theory is used to answer the question whether the cyclization of the unsaturated hydrazone proceeds in a pericyclic or pseudopericyclic manner. As reference for a 6*π*-electrocyclization, the isoelectronic pentadienyl anion is taken into account as well.

Open Shell organic radicals are principal species involved in many diverse areas such as combustion, photochemistry, and polymer chemistry. Computational studies of such species with an accurate method like coupled-cluster with single and double and perturbative triple (CCSD(T)) may be restricted to systems of modest size due to the steep computational scaling of the method. Herein, we assess the accuracy of extrapolated CCSD(T) energies determined using the connectivity-based hierarchy (CBH) method on medium to large sized radicals. In our method, an MP2 calculation on the target radical is coupled with CCSD(T) energies of fragments determined uniquely by our hierarchy to perform accurate extrapolations. A careful assessment is done with a robust CBH-rad49 test set comprising of 49 diverse cyclic and acyclic radicals with a variety of functional groups. We demonstrate that the extrapolation method with CBH-2 or CBH-3 is sufficient to obtain sub-kcal accuracy. ROMP2 and PMP2 calculations with both Pople-style and Dunning-style basis-sets resulted in mean absolute errors for CCSD(T) extrapolation (full CCSD(T)—extrapolated CCSD(T)) within 0.5 kcal/mol. Further speedup for such CCSD(T) extrapolations are obtained with ROHF-based RI-MP2 calculations. Challenging systems with (a) high ring strain, (b) delocalized character, and (c) spin contamination are identified and analyzed in detail. Finally, we apply our extrapolation method on 10 larger radicals containing 10−15 heavy atoms, where accurate CCSD(T) energies are obtained at a fractional cost of full CCSD(T) calculations. © 2015 Wiley Periodicals, Inc.

Highly accurate extrapolated coupled-cluster with single and double and perturbative triple (CCSD(T)) energies were obtained using the Connectivity-Based Hierarchy method for medium to large sized radicals. A careful assessment was performed with a robust test set comprised of 49 diverse radicals including challenging systems with high ring strain and spin contamination. The most expensive calculation is MP2 on the entire radical, thereby breaking the existing bottleneck for calculating CCSD(T) energies of large open-shell organic molecules.

The Continuum in the variation of the X-Z bond length change from blue-shifting to red-shifting through zero- shifting in the X-Z---Y complex is inevitable. This has been analyzed by *ab-initio* molecular orbital calculations using Z= Hydrogen, Halogens, Chalcogens, and Pnicogens as prototypical examples. Our analysis revealed that, the competition between negative hyperconjugation within the donor (X-Z) molecule and Charge Transfer (CT) from the acceptor (Y) molecule is the primary reason for the X-Z bond length change. Here, we report that, the proper tuning of X- and Y-group for a particular Z- can change the blue-shifting nature of X-Z bond to zero-shifting and further to red-shifting. This observation led to the proposal of a continuum in the variation of the X-Z bond length during the formation of X-Z---Y complex. The varying number of orbitals and electrons available around the Z-atom differentiates various classes of weak interactions and leads to interactions dramatically different from the H-Bond. Our explanations based on the model of anti-bonding orbitals can be transferred from one class of weak interactions to another. We further take the idea of continuum to the nature of chemical bonding in general. © 2015 Wiley Periodicals, Inc.

Red- and blue- shift in the X-Z bonds during the X-Z---Y complex formation has been analyzed. A continuum in the X-Z bond length is observed for various classes of weak bonds such as H-bonds, halogen-bonds, chalcogen-bonds, and pnicogen-bonds. The balance between negative hyperconjugation within the X-Z molecule and charge transfer from Y-group provides a working model to explain the observations. The definition of the continuum in the weak (X-Z---Y) interactions is profitably extended to include strong (Z-Y) chemical bonds as well.

We investigated by computational means the kinetics and stationary behavior of stochastic dynamics on an ensemble of rough two-dimensional energy landscapes. There are no obvious separations of temporal scales in these systems, which constitute a simple model for the behavior of glasses and some biomaterials. Even though there are significant computational challenges present in these systems due to the large number of metastable states, the Milestoning method is able to compute their kinetic and thermodynamic properties exactly. We observe two clearly distinguished regimes in the overall kinetics: one in which diffusive behavior dominates and another that follows an Arrhenius law (despite the absence of a dominant barrier). We compare our results with those obtained with an exactly-solvable one-dimensional model, and with the results from the rough one-dimensional energy model introduced by Zwanzig. © 2015 Wiley Periodicals, Inc.

We compute, using the Milestoning method, the stationary flux (shown), the mean first passage time of Brownian trajectories, and the free energy (not shown) on a large ensemble of random energy landscapes with varying degrees of roughness and at a wide range of temperatures. We find two different behaviors: a diffusive regime for high temperatures and an Arrhenius-like regime for low temperatures.

Intrinsically disordered regions of proteins can gain structure by binding to a partner. This process, of coupled folding and binding (CFaB), is a fundamental part of many important biological processes. Structure-based models have proven themselves capable of revealing fundamental aspects of how CFaB occurs, however, typical methods to enhance the sampling of these transitions, such as replica exchange, do not adequately sample the transition state region of this extremely rare process. Here, we use a variant of Umbrella Sampling to enforce sampling of the transition states of CFaB of HdeA monomers at neutral pH, an extremely rare process that occurs over timescales ranging from seconds to hours. Using high resolution sampling in the transition state region, we cluster states along the principal transition path to obtain a detailed description of coupled binding and folding for the HdeA dimer, revealing new insight into the ensemble of states that are accessible to client recognition. We then demonstrate that exchanges between umbrella sampling windows, as done in previous work, significantly improve relaxation in variables orthogonal to the restraints used. Altogether, these results show that Window-Exchange Umbrella Sampling is a promising approach for systems that exhibit flexible binding, and can reveal transition state ensembles of these systems in high detail. © 2015 Wiley Periodicals, Inc.

Intrinsically disordered proteins often fold in conjunction with binding to their partner. Sampling configurations corresponding to the transition between unfolded and bound conformational ensembles presents a complex sampling problem. A two-dimensional sampling method, Window-Exchange Umbrella Sampling using contact fractions, is developed to address this issue.

The *opposed* and *parallel* structures for the binuclear bis(azulene) “submarine” sandwiches (C_{10}H_{8})_{2}M_{2} (M = Ti, V, Cr, Mn, Fe, Co, Ni) have been optimized using density functional theory. The lowest energy (C_{10}H_{8})_{2}M_{2} structures of the early transition metals Ti, V, Cr, and Mn have the azulene units functioning as bis(pentahapto) ligands to each metal atom similar to the azulene ligand in the long-known molybdenum carbonyl complex (η^{5},η^{5}-C_{10}H_{8})Mo_{2}(CO)_{6}. The metal–metal bonds in these early transition metal structures have distances and Wiberg bond indices consistent with the formal bond orders required to give each metal atom an 18-electron configuration for the singlet structures and a 17-electron configuration for the triplet structures. For the later transition metals Fe, Co, and Ni, the lowest energy (C_{10}H_{8})_{2}M_{2} structures contain pentahapto-trihapto azulene ligands with an uncomplexed CC double bond, similar to that in the long-known iron carbonyl complex (η^{5},η^{3}-C_{10}H_{8})Fe_{2}(CO)_{5}. The parallel (η^{5},η^{3}-C_{10}H_{8})_{2}M_{2} (M = Fe, Co, Ni) structures contain metallocene subunits with their metal atoms at long nonbonding distances of 3.5–3.9 Å from the other metal atom, which is located between the azulene C_{7} rings. Higher energy opposed (C_{10}H_{8})_{2}Fe_{2} structures contain an unprecedented distorted η^{6},η^{4}-azulene ligand using six carbon atoms for bonding to one iron atom as a hexahapto fulvene ligand and the remaining four carbon atoms for bonding to the other iron atom as a tetrahapto diene ligand. © 2015 Wiley Periodicals, Inc.

The lowest energy (C_{10}H_{8})_{2}M_{2} submarine sandwich structures of the early transition metals Ti, V, Cr, and Mn have the azulene units functioning as bis(pentahapto) ligands to each metal atom. For the later transition metals Fe, Co, and Ni the lowest energy (C_{10}H_{8})_{2}M_{2} structures contain pentahapto-trihapto azulene ligands with an uncomplexed CC double bond

This computational study identifies the rhombic *D*_{2}* _{h}* C

*D*_{2}* _{h}* C

The complex absorbing potential (CAP)/symmetry-adapted cluster-configuration interaction (SAC-CI) method has been combined with a smooth Voronoi potential, which was recently introduced in the extrapolation procedure, to locate π* resonance states of small- to medium-size molecules. Here, the projected CAP/SAC-CI method is combined with this potential and used to calculate the double-bond and heteroaromatic π* resonances of acetaldehyde, butadiene, glyoxal, pyridine, pyrazine, and furan. As observed in the pilot applications, the corrected *η*-trajectories provide a stable resonance energy and width or lifetime regardless of the size parameter (*r*_{cut}) of the smooth Voronoi potential. However, in general, the stabilization behavior of the trajectories is clearer for larger *r*_{cut} values, which implies that the interaction of the CAP with the valence electrons is more advantageously addressed by a larger “cavity” size. © 2015 Wiley Periodicals, Inc.

The complex absorbing potential (CAP)/symmetry-adapted cluster-configuration interaction method with a smooth Voronoi potential (example shown in the inset of the figure) has been developed. The method is applied to the π* resonance states of small- to medium-size molecules with double-bond and heteroaromatic structures. The corrected *η*-trajectory provides a stable resonance energy and width for all the resonances studied. Generally, the stabilization of the trajectories is clearer for the CAPs with relatively large cavity size.

Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the *NVT* and *NPT* ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc.

Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the molecular system. To eliminate the need of reweighting, the SGLD-generalized Langevin equation (GLE) method is proposed, which samples exact ensemble distribution and has enhanced conformational sampling. Using an alanine dipeptide and liquid argon, SGLD-GLE can produce correct *NVT* and *NPT* ensemble distributions while achieving enhanced conformational sampling.

The noncatalytic bromination of benzene is shown experimentally to require high 5–14 M concentrations of bromine to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (<2%) amounts of addition products such as tetra and hexabromocyclohexanes. The kinetic order in bromine at these high concentrations is 4.8 ± 0.06 at 298 K and 5.6 ± 0.11 at 273 K with a small measured inverse deuterium isotope effect using D_{6}-benzene of 0.97 ± 0.03 at 298 K. These results are rationalized using computed transition states models at the B3LYP+D3/6-311++G(2d,2p) level with an essential continuum solvent field for benzene applied. The model with the lowest predicted activation free energies agrees with the high experimental kinetic order in bromine and involves formation of an ionic, concerted, and asynchronous transition state with a Br_{8} cluster resembling the structure of the known Br_{9}^{−}. This cluster plays three roles; as a Br^{+} donor, as a proton base, and as a stabilizing arm forming weak interactions with two adjacent benzene CH hydrogens, these aspects together combining to overcome the lack of reactivity of benzene induced by its aromaticity. The computed inverse kinetic isotope effect of 0.95 agrees with experiment, and arises because CBr bond formation is essentially complete, whereas CH cleavage has not yet commenced. The computed free energy barriers for the reaction with 4Br_{2} and 5Br_{2} for a standard state of 14.3 M in bromine are reasonable for an ambient temperature reaction, unlike previously reported theoretical models involving only one or two bromines. © 2015 Wiley Periodicals, Inc.

The noncatalytic bromination of benzene is shown experimentally to require high concentrations of bromine, proceeding at ambient temperatures to form predominantly bromobenzene and exhibiting a measured inverse deuterium isotope effect. Computed transition states models reveal an ionic concerted but asynchronous transition state involving a Br_{7}^{−} or Br_{9}^{−} cluster which acts as a Br^{+} donor, as a proton base and as a stabilizing arm forming weak dispersion interactions with benzene CH hydrogens.

The atomic mechanisms of isomerization of ATP-Mg^{2+} in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg^{2+} complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg^{2+} ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.

The mechanisms of isomerization of ATP-Mg^{2+} in solution are examined with three complementary enhanced-sampling simulation methods. The recently developed String Method with Optimal Molecular Alignment is used to identify and characterize the minimum free-energy paths for the major conformational transitions of the complex, in a 48-dimensional space. This analysis reveals the driving forces controlling these isomerization mechanisms at single-atom resolution.

It has been analyzed at the MP2/def2-QZVPPD level whether
(E = C-Pb; X = H, F-Br) can bind noble gas atoms. Geometrical and electronic structures, dissociation energy values, thermochemical parameters, natural bond order, electron density, and energy decomposition analyses highlight the possibility of such noble gas bound
compounds. Except He and Ne, the other heavier congeners of this family make quite strong bonds with E. In fact, the dissociations of Ar-Rn bound analogues turn out to be endergonic in nature at 298 K, except in the cases of ArGe
,
, and
.
and
(E = Ge-Pb) can even bind two Ng atoms with reasonably high dissociation energy. As the p_{z} orbital of the E center in
plays a crucial role in its binding with the noble gas atoms, the effect of the π back-bonding causing X E electron transfer ought to be properly understood. Due to the larger back-donation, the Ng binding ability of
gradually decreases along F to Br.
and the global minimum HE^{+…}H_{2} (E = Sn, Pb) complexes are also able to bind Ar-Rn atoms quite effectively. The NgE bonds in Ar-Rn bound
,
, and
(E = Ge-Pb) and Xe/RnE bonds in
and
(E = Ge, Sn) are mainly of covalent type. © 2015 Wiley Periodicals, Inc.

**Making a bond**:
(E = C-Pb; X = H, F-Br) could bind noble gas atoms, particularly Ar to Rn, quite effectively. The π back-bonding causing X E electron transfer plays an important role in deciding their noble gas binding ability.

In this study, we explore the effect of supplementing the DuT spin-component-scaled double-hybrid density functional method with post-second-order Møller–Plesset-type theory (MP2) correlation terms. We find that the inclusion of additional MP3 correlation energies has almost no effect on the performance. Further addition of correlation effects from MP4 generally leads to a small improvement in the performance. However, we find that the inclusion of the higher-order perturbative correlation effects does not rectify some major shortcomings of DuT for more challenging systems, and the use of MP4, in fact, leads to a significant deterioration in the performance in some cases. We also find that the use of correlation energies from CCSD(T) instead of those from MP3 and MP4 does not lead to a substantial improvement over the MP4-based method, both in general and in some difficult cases that we have examined. An additional observation is that, for large systems that are dominated by noncovalent interactions, DuT and the two MP*n*-based post-MP2 double-hybrid density functional theory (DFT) procedures all benefit from the inclusion of dispersion corrections. Overall, our investigation suggests that the current generation of MP2-based double-hybrid DFT methods may already be providing close to the optimal performance that can be achieved with the double-hybrid methodology paired with spin-component-scaling. Development of even better double hybrids is an active research field, and we hope that our study provides valuable insights. We recommend the continuing use of existing MP2-based double-hybrid methods as a bridging level between hybrid density functional procedures and high-level wave-function-based procedures. © 2015 Wiley Periodicals, Inc.

Double-hybrid density functionals (DHDFs) use MP2-type correlation to significantly improve the accuracy of DFT approximations. The inclusion of higher-order MP3, MP4, CCSD, and CCSD(T) terms is explored. DHDFs are not as systematically improvable as their wave-function counterparts, and the use of MP2 represents a near-optimal balance of accuracy and efficiency. These findings provide valuable insights for future research in DHDF development.

Hydrogen sulfide (H_{2}S), a commonly known toxic gas compound, possesses unique chemical features that allow this small solute molecule to quickly diffuse through cell membranes. Taking advantage of the recent orthogonal space tempering (OST) method, we comparatively mapped the transmembrane free energy landscapes of H_{2}S and its structural analogue, water (H_{2}O), seeking to decipher the molecular determinants that govern their drastically different permeabilities. As revealed by our OST sampling results, in contrast to the highly polar water solute, hydrogen sulfide is evidently amphipathic, and thus inside membrane is favorably localized at the interfacial region, that is, the interface between the polar head-group and nonpolar acyl chain regions. Because the membrane binding affinity of H_{2}S is mainly governed by its small hydrophobic moiety and the barrier height inbetween the interfacial region and the membrane center is largely determined by its moderate polarity, the transmembrane free energy barriers to encounter by this toxic molecule are very small. Moreover when H_{2}S diffuses from the bulk solution to the membrane center, the above two effects nearly cancel each other, so as to lead to a negligible free energy difference. This study not only explains why H_{2}S can quickly pass through cell membranes but also provides a practical illustration on how to use the OST free energy sampling method to conveniently analyze complex molecular processes. © 2015 Wiley Periodicals, Inc.

The orthogonal space tempering simulation shows that hydrogen sulfide is amphipathic, and thus is favorably localized at the interface between the head-group and acyl chain regions. Because the membrane binding affinity of H_{2}S is mainly governed by its small hydrophobic moiety and the barrier height inbetween the interfacial region and the membrane center is largely determined by its moderate polarity, the trans-membrane free energy barriers to encounter by this toxic molecule are very small.

Several ring systems (Saturn systems) have been studied using DFT methods that include dispersion effects. Comparison with X-ray structures are made with three systems, and the agreement is quite good. Binding enthalpies and binding free energies in dichloromethane and toluene have been computed. The effect of an encapsulated lithium cation is accessed by comparing C_{60}@(C_{6}H_{4})_{10} and [Li@C_{60}@(C_{6}H_{4})_{10}]^{+}. The [Li@C_{60}]^{+} cation is a much better acceptor than C_{60} which leads to greater donor–acceptor interactions and larger charge transfer from the ring to [Li@C_{60}]^{+}. © 2015 Wiley Periodicals, Inc.

Nanohoops, such as cycloparaphenylenes [10]CPP, can bind to C_{60} and [Li@C_{60})]^{+} through noncovalent interactions with free energies of binding greater than 10 kcal/mol in nonpolar solvents. With the right size, the hoops bind around the equator of the fullerene and resemble the ring around Saturn. Density functional calculations can predict the binding constants and suggest new nanohoops as targets for synthesis. The graphic image is the HOMO of C_{60}@(C_{6}H_{4})_{10}.

Advances in hardware and algorithms have greatly extended the timescales accessible to molecular simulation. This article assesses whether such long timescale simulations improve our ability to calculate order parameters that describe conformational heterogeneity on ps-ns timescales or if force fields are now a limiting factor. Order parameters from experiment are compared with order parameters calculated in three different ways from simulations ranging from 10 ns to 100 μs in length. Importantly, bootstrapping is employed to assess the variability in results for each simulation length. The results of 10–100 ns timescale simulations are highly variable, possibly explaining the variation in levels of agreement between simulation and experiment in published works examining different proteins. Fortunately, microsecond timescale simulations improve both the accuracy and precision of calculated order parameters, at least so long as the full exponential fit or truncated average approximation is used instead of the common long-time limit approximation. The improved precision of these long timescale simulations allows a statistically sound comparison of a number of modern force fields, such as Amber03, Amber99sb-ILDN, and Charmm27. While there is some variation between these force fields, they generally give very similar results for sufficiently long simulations. The fact that so much simulation is required to precisely capture ps-ns timescale processes suggests that extremely extensive simulations are required for slower processes. Advanced sampling techniques could aid greatly, however, such methods will need to maintain accurate kinetics if they are to be of value for calculating dynamical properties like order parameters. © 2015 Wiley Periodicals, Inc.

This article assesses whether modern simulations accurately capture ps-ns timescales—as judged by their ability to predict order parameters—or if force fields are now a limiting factor. The results show microseconds of simulation with any of three force fields and a proper method for calculating order parameters are required for accuracy and precision. This has important implications for the extent of simulations required for slower processes and the utility of enhanced sampling methods.

In a recently developed multiscale enhanced sampling (MSES) technique, topology-based coarse-grained (CG) models are coupled to atomistic force fields to enhance the sampling of atomistic protein conformations. Here, the MSES protocol is refined by designing more sophisticated Hamiltonian/temperature replica exchange schemes that involve additional parameters in the MSES coupling restraint potential, to more carefully control how conformations are coupled between the atomistic and CG models. A specific focus is to derive an optimal MSES protocol for simulating conformational ensembles of intrinsically disordered proteins (IDPs). The efficacy of the refined protocols, referred to as MSES-soft asymptote (SA), was evaluated using two model peptides with various levels of residual helicities. The results show that MSES-SA generates more reversible helix-coil transitions and leads to improved convergence on various ensemble conformational properties. This study further suggests that more detailed CG models are likely necessary for more effective sampling of local conformational transition of IDPs. © 2015 Wiley Periodicals, Inc.

Multiscale enhanced sampling (MSES) uses efficient coarse-grained (CG) models to accelerate sampling of atomistic protein conformations. The efficacy of MSES for simulating intrinsically disordered proteins (IDPs) is investigated, and refined MSES Hamiltonian/temperature replica exchange protocols are developed that involve additional parameters in the MSES coupling restraint potential. The refined protocols drive more conformational transitions to improve the convergence of simulated ensembles. Nonetheless, further improvement of MSES for simulating IDPs likely requires more detailed CG models.

The entrance complex, transition state, and exit complex for the bromine atom plus water dimer reaction Br + (H_{2}O)_{2} HBr + (H_{2}O)OH and its reverse reaction have been investigated using the CCSD(T) method with correlation consistent basis sets up to cc-pVQZ-PP. Based on the CCSD(T)/cc-pVQZ-PP results, the reaction is endothermic by 31.7 kcal/mol. The entrance complex Br⋯(H_{2}O)_{2} is found to lie 6.5 kcal/mol below the separated reactants. The classical barrier lies 28.3 kcal/mol above the reactants. The exit complex HBr⋯(H_{2}O)OH is bound by 6.0 kcal/mol relative to the separated products. Compared with the corresponding water monomer reaction Br + H_{2}O HBr + OH, the second water molecule lowers the relative energies of the entrance complex, transition state, and exit complex by 3.0, 3.8, and 3.7 kcal/mol, respectively. Both zero-point vibrational energies and spin-orbit coupling effects make significant changes to the above classical energetics. Including both effects, the predicted energies relation to separated Br + (H_{2}O)_{2} are −3.0 kcal/mol [Br···(H_{2}O)_{2}], 28.2 kcal/mol [transition state], 26.4 kcal/mol [HBr···(H_{2}O)OH], and 30.5 kcal/mol [separated HBr + (H_{2}O)OH]. The potential energy surface for the Br + (H_{2}O)_{2} reaction is related to that for the valence isoelectronic Cl + (H_{2}O)_{2} system but radically different from the F + (H_{2}O)_{2} system. © 2015 Wiley Periodicals, Inc.

The entrance complex, transition state, and exit complex for the Br + (H_{2}O)_{2} HBr + (H_{2}O)OH reaction have been investigated using the CCSD(T) method with correlation consistent basis sets up to cc-pVQZ-PP. Both zero-point vibrational energies and spin-orbit coupling effects are found to be important. The potential energy surface for the Br + (H_{2}O)_{2} reaction is compared with the related Br + H_{2}O, Cl + (H_{2}O)_{2} and F + (H_{2}O)_{2} reactions.

The mechanism of acetonitrile and methyl benzoate catalytic hydrogenation using pincer catalysts M(H)_{2}(CO)[NH(C_{2}H_{4}P*i*Pr_{2})_{2}] (**1M**) and M(H)(CO)[N(C_{2}H_{4}P*i*Pr_{2})_{2}] (**2M**) (M = Fe, Ru, Os) has been computed at various levels of density functional theory. The computed equilibrium between **1Fe** and **2Fe** agrees perfectly with the experimental observations. On the basis of the activation barriers and reaction energies, the best catalysts for acetonitrile hydrogenation are **1Fe/2Fe** and **1Ru/2Ru**, and the best catalysts for methyl benzoate hydrogenation are **1Ru/2Ru**. The best catalysts for the dehydrogenation of benzyl alcohol are **1Ru/2Ru**. It is to note that the current polarizable continuum model is not sufficient in modeling the solvation effect in the energetic properties of these catalysts as well as their catalytic properties in hydrogenation reaction, as no equilibrium could be established between **1Fe** and **2Fe**. Comparison with other methods and procedures has been made. © 2015 Wiley Periodicals, Inc.

DFT studies on the defined pincer-type catalysts M(H)_{2}(CO)[NH(C_{2}H_{4}P*i*Pr_{2})_{2}] (**1M**) and M(H)(CO)[N(C_{2}H_{4}P*i*Pr_{2})_{2}] (**2M**) (M = Fe, Ru, Os) reveal remarkable differences in electronic structures and hydrogenation reactivity of nitriles, ester, and ketones. For acetonitrile hydrogenation, Fe- and Ru-based catalysts are best. For methyl benzoate hydrogenation and dehydrogenation of benzyl alcohol, Ru-based catalysts are best. In contrast, Os-based catalysts are least active.

Previous calculations suggested that di-tetrazine-tetroxide (DTTO), aka tetrazino-tetrazine-tetraoxide, might have a particularly large density (2.3 g/cm^{3}) and high energy release (8.8 kJ/kg), but it has not yet been synthesized successfully. We report here density functional theory (DFT) (M06, B3LYP, and PBE-ulg) on 20 possible isomers of DTTO. For the two most stable isomers, **c1** and **c2** we predict the best packings (i.e., polymorphs) among the 10 most common space groups for organic molecular crystal using the Universal force field and Dreiding force field with Monte Carlo sampling. This was followed by DFT calculations at the PBE-ulg level to optimize the crystal packing. We conclude that the **c1** isomer has the *P2 _{1}2_{1}2_{1}* space group with a density of 1.96 g/cm

The two most stable isomers of Di-tetrazine-tetroxide (DTTO), **c1** and **c2,** were used to predict the most stable polymorphs of DTTO. For the **c1** isomer, the most stable polymorph has *P2 _{1}2_{1}2_{1}* space group with a density of 1.96 g/cm

On page 78 (DOI: 10.1002/jcc.24021), Ramon Carbó-Dorca discusses aromaticity, quantummultimolecular polyhedral, and the quantumQSPR fundamental equation. First, a concise description of the Kekulé's historical origin of aromaticity and the actual state of the question is given. After this, it is argued that still room is left to the discussion about the quantummechanical foundation existence of aromaticity. In order to perform that, quantum multimolecular polyhedra (QMP) are defined: they are based onmolecular density functions sets attached to QMP vertices. Fromthere, collective QMP distances, QSPR fundamental equation and aromaticity descriptors are proposed as away to construct an equation, able to estimate aromaticity via expectation values of Hermitian operators.

The cover image shows the largestof a family of fullerenes used for extrapolating to the graphene limit, as presented by Lukas N. Wirz, Ralf Tonner, Andreas Hermann, Rebecca Sure, and Peter Schwerdtfeger on page 10 (DOI: 10.1002/jcc.23894). The structures were obtained from a newly developed force field treated subsequently by density functional theory. Our results confirm Paul von Ragué Schleyer's hypothesis that C_{60} is not especially stable – 60 is not amagic number – comparedwith other fullerenes.

On page 18 (DOI: 10.1002/jcc.23914), the Gibbs energies of association between primary alkyl ammonium ions and crown ethers in solution are measured and calculated by Andreas J. Achazi, Larissa K. S. von Krbek, Christoph A. Schalley, and Beate Paulus.Measurementswere carried out by isothermal titration calorimetry. Calculations were done as accurate as possible for the gas phasewith DFT-D3(BJ). The Gibbs energies to transfer the educts in the gas phase and the products back in solution were calculated with the solvation model COSMO-RS in order to get the Gibbs energies of association in solution. Calculated andmeasured Gibbs energies of association in solution agreewell and reveal a strong solvent-dependent ion pair effect.

We introduce a simple but computationally very efficient harmonic force field, which works for all fullerene structures and includes bond stretching, bending, and torsional motions as implemented into our open-source code *Fullerene*. This gives accurate geometries and reasonably accurate vibrational frequencies with root mean square deviations of up to 0.05 Å for bond distances and 45.5 cm^{−1} for vibrational frequencies compared with more elaborate density functional calculations. The structures obtained were used for density functional calculations of Goldberg–Coxeter fullerenes up to C_{980}. This gives a rather large range of fullerenes making it possible to extrapolate to the graphene limit. Periodic boundary condition calculations using density functional theory (DFT) within the projector augmented wave method gave an energy difference between −8.6 and −8.8 kcal/mol at various levels of DFT for the reaction C_{60}graphene (per carbon atom) in excellent agreement with the linear extrapolation to the graphene limit (−8.6 kcal/mol at the Perdew–Burke–Ernzerhof level of theory). © 2015 Wiley Periodicals, Inc.

A general force field is introduced which works for all fullerene isomers. It leads to structures and zero-point vibrational energy contributions in very good agreement to more expensive quantum theoretical calculations. The graphene limit is well represented by the growth of Goldberg-Coxeter transforms of C_{20}.

The Gibbs energies of association between primary alkyl ammonium ions and crown ethers in solution are measured and calculated. Measurements are performed by isothermal titration calorimetry and revealed a strong solvent-dependent ion pair effect. Calculations are performed with density functional theory including Grimme's dispersion correction D3(BJ). The translational, rotational, and vibrational contributions to the Gibbs energy of association are taken into account by a rigid-rotor-harmonic-oscillator approximation with a free-rotor approximation for low lying vibrational modes. Solvation effects are taken into account by applying the continuum solvation model COSMO-RS. Our study aims at finding a suitable theoretical method for the evaluation of the host guest interaction in crown/ammonium complexes as well as the observed ion pair effects. A good agreement of theory and experiment is only achieved, when solvation and the effects of the counterions are explicitly taken into account.

Gibbs energies of association of monovalent crown/ammonium complexes in solution are calculated with DFT-D3(BJ) and the continuum solvation model COSMO-RS. For comparison, experimental data are obtained by isothermal titration calorimetry. Calculated and measured Gibbs energies of association in solution agree well.

Weak inter- and intra- molecular C^{δ+}F^{δ−}···C^{δ+}O^{δ−} interactions were theoretically evaluated in 4 different sets of compounds at different theoretical levels. Intermolecular CH_{3}F···CO interactions were stabilizing by about 1 kcal mol^{−1} for various carbonyl containing functional groups. Intramolecular CF···CO interactions were also detected in aliphatic and fluorinated cyclohexane carbonyl derivatives. However, the stabilization provided by intramolecular CF···CO interactions was not enough to govern the conformational preferences of compounds **2–4**. © 2015 Wiley Periodicals, Inc.

Prototypical inter- and intramolecular CF···CO interactions are assessed computationally at the B3LYP-D3 level. The interactions are noticeable in intermolecular complexes, where they can amount to stabilizations around 1 kcal/mol. However, they are not strong enough to dominate conformational preferences in organofluorine derivatives.

The recent σ-hole concept emphasizes the contribution of electrostatic attraction to noncovalent bonds, and implies that the electrostatic force has an angular dependency. Here a set of clusters, which includes hydrogen bonding, halogen bonding, chalcogen bonding, and pnicogen bonding systems, is investigated to probe the magnitude of covalency and its contribution to the directionality in noncovalent bonding. The study is based on the block-localized wavefunction (BLW) method that decomposes the binding energy into the steric and the charge transfer (CT) (hyperconjugation) contributions. One unique feature of the BLW method is its capability to derive optimal geometries with only steric effect taken into account, while excluding the CT interaction. The results reveal that the overall steric energy exhibits angular dependency notably in halogen bonding, chalcogen bonding, and pnicogen bonding systems. Turning on the CT interactions further shortens the intermolecular distances. This bond shortening enhances the Pauli repulsion, which in turn offsets the electrostatic attraction, such that in the final sum, the contribution of the steric effect to bonding is diminished, leaving the CT to dominate the binding energy. In several other systems particularly hydrogen bonding systems, the steric effect nevertheless still plays the major role whereas the CT interaction is minor. However, in all cases, the CT exhibits strong directionality, suggesting that the linearity or near linearity of noncovalent bonds is largely governed by the charge-transfer interaction whose magnitude determines the covalency in noncovalent bonds. © 2015 Wiley Periodicals, Inc.

The block-localized wavefunction method, which can derive hypothetical structures without the charge transfer effect and conduct intermolecular energy decomposition analysis, is used to probe the origins of the directionality of weak noncovalent bonds. While the overall steric energy exhibits certain angular dependency, in all cases the charge transfer exhibits the strongest directionality, suggesting that the linearity or near linearity of noncovalent bonds is largely governed by the charge-transfer interaction whose magnitude determines the bond covalency.

NICS(1) calculations have been performed on the 8π and 10π singlet states and the 9π triplet state of (CO)_{4}, (CS)_{4}, and (CSe)_{4}. The results show that transfer of electrons from the b_{2g} σ MO into the a_{2u} π MO decreases the NICS(1) value, indicating an increase in the diamagnetic ring current. The decreases in the calculated NICS(1) values are substantially larger in (CO)_{4} than in (CS)_{4} or (CSe)_{4}. This finding is rationalized by the larger coefficients on the carbons in the a_{2u} MO of (CO)_{4} than in the a_{2u} MOs of (CS)_{4} and (CSe)_{4}. © 2015 Wiley Periodicals, Inc.

The occupancy of the a_{2u} MOs of (CO)_{4}, (CS)_{4}, and (CSe)_{4} control the NICS(1) values that are computed for these compounds.

Hydrocarbon cages are key reference materials for the validation and parameterization of computationally cost-effective procedures such as density functional theory (DFT), semiempirical molecular orbital theory, and molecular mechanics. We obtain accurate total atomization energies (TAEs) and heats of formation (Δ* _{f}H*°

This work determines total atomization energies and heats of formation for platonic and prismatic polycyclic hydrocarbon cages by means of the W1-F12 and W2-F12 thermochemical protocols. Using these accurate reference data, the performance of computationally economical theoretical methods (e.g., density functional theory and composite *ab initio* methods) was evaluated via atomization and bond separation reactions for the calculation of these challenging thermochemical quantities.

Self-assembling building blocks like the 4-pyridone can exhibit extraordinary H-bond-aromaticity coupling effects. Computed dissected nucleus independent chemical shifts (NICS(1)* _{zz}*), natural bond orbital (NBO) charges, and energy decomposition analyses (EDA) for a series of hydrogen (H-) bonded 4-pyridone chains (4-py)

Hydrogen bonding interactions can polarize the π-systems of 4-pyridones to increase cyclic (4n+2) π-electron delocalization. The resulting H-bonded six-membered rings exhibit enhanced π-aromaticity and the corresponding NH···OC interactions are strengthened. Extended H-bonded 4-pyridone chains exhibit high degrees of such cooperativity, even when each of the neighboring 4-pyridone rings are twisted to preclude direct π-overlap between the H-bonded units.

Density functional theory shows that the lowest energy CpMoC_{3}B_{n}_{−4}H_{n}_{−1} (*n* = 8, 9, 10, 11) structures are based on *isocloso* or similar deltahedra with the molybdenum atom at a degree 6 vertex. Such deltahedra include the capped pentagonal bipyramid for the 8-vertex system. Among such geometries the lowest energy structures have the carbon atoms at the lowest degree vertices (typically degree 4 vertices), no pairs of adjacent carbon atoms (i.e., no C-C edges), and the maximum number of Mo-C edges. Optimizing these factors favoring low-energy CpMoC_{3}B_{n}_{−4}H_{n}_{−1} (*n* = 8, 9, 10, 11) structures leads to a unique lowest energy structure lying more than 10 kcal/mol below the next lowest energy structure for the 8-, 10-, and 11-vertex systems. However, the 9-vertex CpMoC_{3}B_{5}H_{8} system has three structures within 8 kcal/mol including a structure based on the *closo* tricapped trigonal prism rather than the *isocloso* 9-vertex deltahedron. © 2015 Wiley Periodicals, Inc.

The lowest energy CpMoC_{3}B_{n}_{−4}H_{n}_{−1} (*n* = 8, 9, 10, 11) structures are based on *isocloso* or similar MoC_{3}B_{n}_{−4} deltahedra with the molybdenum atom at the unique degree 6 vertex, the carbon atoms at the lowest degree vertices (typically degree 4 vertices), no pairs of adjacent carbon atoms (i.e., no C-C edges), and the maximum number of Mo-C edges.

The rearrangement pathways of the equilibrating tertiary carbocations, 2,3-dimethyl-2-butyl cation (C_{6}
, **1**), 2,3,3-trimethyl-2-butyl cation (C_{7}
, **5**) and 2,3-dimethyl-2-pentyl cation (C_{7}
, **8** and **9**) were investigated using the *ab initio*/GIAO-CCSD(T) ^{13}C NMR method. Comparing the calculated and experimental ^{13}C NMR chemical shifts of a series of carbocations indicates that excellent prediction of δ^{13}C could be achieved through scaling. In the case of symmetrical equilibrating cations (**1** and **5**) the Wagner–Meerwein 1,2-hydride and 1,2-methide shifts, respectively, produce the same structure. This indicates that the overall ^{13}C NMR chemical shifts are conserved and independent of temperature. However, in the case of unsymmetrical equilibrating cations (**8** and **9**) the Wagner–Meerwein shift produces different tertiary structures, which have slightly different thermodynamic stabilities and, thus, different spectra. At the MP4(SDTQ)/cc-pVTZ//MP2/cc-pVTZ + ZPE level structure **8** is only 90 calories/mol more stable than structure **9**. Based on computed ^{13}C NMR chemical shift calculations, mole fractions of these isomers were determined by assuming the observed chemical shifts are due to the weighted average of the chemical shifts of the static ions. © 2015 Wiley Periodicals, Inc.

The rearrangement pathways of the equilibrating tertiary carbocations such as 2,3-dimethyl-2-butyl cation were calculated by the *ab initio*/GIAO-CCSD(T) method.

A causal relation connecting aromaticity with the current aromaticity descriptors used in the literature and compliant with a quantum mechanics theoretical background is described. © 2015 Wiley Periodicals, Inc.

A concise description of Kekulé's historical origin of aromaticity and the current state of the field is given. Still, space is left for a discussion about the existence of aromaticity's quantum mechanical foundation. Quantum multimolecular polyhedra (QMP), based on density functions sets attached to QMP vertices, collective QMP distances, QSPR fundamental equation, and aromaticity descriptors are proposed as a way to construct an equation able to estimate aromaticity via expectation values of Hermitian operators.

Computational studies of organic systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chemical systems are dynamic entities where a multitude of molecular conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biological simulations, together with empirical force fields, and apply it to organic chemical problems. Replica-exchange molecular dynamics (REMD) permits thorough exploration of the PES. We combined REMD with density functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small molecular systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temperature-dependent rotational processes, and catalysis, we reveal new insights and chemistry that likely would be missed using static electronic structure computations. The REMD-DFTB methodology at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes. © 2015 Wiley Periodicals, Inc.

Replica-exchange molecular dynamics (REMD) is combined with density functional tight binding (DFTB) and applied to organic chemical problems. REMD@DFTB permits thorough exploration of the potential energy surface and reveals new insights and chemistry that likely would be missed using static electronic structure computations.

A series of paracyclophane (PC) bridged mixed-valence (MV) bis-triarylamine radical cations with different ([2.2], [3.3], [4.4]) linkers, with and without additional ethynyl spacers, have been studied by quantum-chemical calculations (BLYP35-D3/TZVP/COSMO) of ground-state structures, thermal electron-transfer barriers, hyperfine couplings, and lowest-lying excited states. Such PC-bridged MV systems are important intra-molecular model systems for inter-molecular electron transfer (ET) via π-stacked aromatics, since they allow enforcement of a more or less well-defined geometrical arrangement. Closely comparable ET barriers and electronic couplings for all [2.2] and [3.3] bridges are found for these class-II MV systems, irrespective of the use of *pseudo*-*para* and *pseudo*-*meta* connections. While the latter observation contradicts notions of quantum interference for off-resonant conduction through molecular wires, it agrees with the less intricate nodal structures of the highest occupied molecular orbitals. The ET in such MV systems may be more closely connected with hole conduction in the resonant regime. Computations on model cations, in which the [2.2] linkers have been truncated, confirm predominant through-space π-π electronic coupling. Systems with [4.4] PC bridges exhibit far more structural flexibility and concomitantly weaker electronic interactions between the redox centers. © 2015 Wiley Periodicals, Inc.

Electron transfer through the π-stacked faces of paracyclophane bridge units in bis-triarylamine mixed-valence systems has been studied using a previously established quantum-chemical protocol. Pseudo-*meta* and pseudo-*para* connected systems exhibit very similar electronic couplings and thermal electron-transfer barriers, explained by resonant hole transfer. Through-space electron transfer through the π-stack dominates over through-bond transfer through the linkers.

After the first introduction of π aromaticity in chemistry to explain the bonding, structure, and reactivity of benzene and its derivatives, this concept was further applied to many other compounds featuring other types of aromaticity (i.e., σ, δ). Thus far, there have been no reports on d-AO-based spherical σ aromaticity. Here, we predict a highly stable bare Ce_{6}O_{8} cluster of a spherical shape using evolutionary algorithm USPEX and DFT + U calculations. Natural bond orbital analysis, adaptive natural density partitioning algorithm, electron localization function, and partial charge plots demonstrate that bare Ce_{6}O_{8} cluster exhibits d-AO spherical σ aromaticity, thus explaining its exotic geometry and stability. Ce_{6}O_{8} complex plays an important role in many reactions and is known to exist in many forms, such as in NH_{4}[Ce_{6}(μ^{3}O)_{5}(μ^{3}OH)_{3}(μ^{2}-C_{6}H_{5}COO)_{9}(NO_{3})_{3}(DMF)_{3}]*DMF*H_{2}O compound, which is prepared under room temperature, and acts as an oxidizing agent. © 2015 Wiley Periodicals, Inc.

A highly stable bare Ce_{6}O_{8} cluster of a spherical shape is predicted using evolutionary algorithm and DFT + U calculations. Natural bond orbital analysis, adaptive natural density partitioning algorithm, electron localization function, and partial charge plots demonstrate that the bare Ce_{6}O_{8} cluster exhibits a unique 6c2e chemical bonding, thus, explaining its exotic geometry and stability.

The generation of 1,2-azaborine (**4**), the BN-analogue of *ortho*-benzyne, was recently achieved by elimination of *tert*-butyldimethylchlorosilane under the conditions of flash vacuum pyrolysis. The present investigation identifies by computational means pathways for the thermal isomerization and fragmentation of 1,2-azaborine. The computations were performed using single reference (hybrid/density functional, second order Møller-Plesset perturbation, and coupled cluster theories) as well as multiconfiguration methods (complete active space SCF based second order perturbation theory, multireference configuration interaction, and multiconfiguration coupled electron pair approximation) with basis sets up to polarized triple-ζ quality. The 1,2-azaborine is, despite the distortion of its molecular structure, the most stable C_{4}H_{4}BN isomer investigated. The formation of BN-endiyne isomers is highly unfavorable as the identified pathways involve barriers close to 80 kcal mol^{−1}. The concerted fragmentation to ethyne and 2-aza-3-bora-butadiyne even has a barrier close to 120 kcal mol^{−1}. The fragmentation of BN-enediynes has energetic requirements similar to enediynes. © 2015 Wiley Periodicals, Inc.

Very recently, the isolation of 1,2-azaborine was achieved in a cryogenic matrix. The possible isomerization, ring opening, and fragmentation pathways of 1,2-azaborine are investigated computationally and compared with available experimental and theoretical results for the all-carbon system.

Schleyer's discovery of hyperconjugative aromaticity and antiaromaticity in 5-substituted cyclopentadienes further expanded our understanding of the pervasive influence of aromaticity. Acceptors induce antiaromatic character by Schleyer's negative hyperconjugative aromaticity, and donors have the opposite effect. We computationally explored the Diels–Alder reactivity of 5-substituted cyclopentadienes with ethylene and maleic anhydride. The predicted billionfold difference in the computed gas phase rate constants at room temperature for the Diels–Alder reactions of 5-substituted cyclopentadienes with ethylene or maleic anhydride results from differences in the transition state distortion energies, which are directly related to the hyperconjugative aromaticity of these molecules. © 2015 Wiley Periodicals, Inc.

Quantum chemical calculations are used to investigate the effect of substituents at the 5-position of cyclopentadiene on the stabilities and the activation energies (*E*_{a}) for the Diels–Alder reactions. Acceptors induce antiaromatic character by Schleyer's negative hyperconjugative aromaticity; donors have the opposite effect. The interaction energies (red) are nearly constant, and the differences in *E*_{a} arise mainly through changes in the distortion energies of the diene (blue) and dienophile (green). (Values reported in kcal/mol.)

Molecular mechanics (MM4) studies have been carried out on the catenane (C_{13}H_{26})_{2}, specifically 13-13D2. The structure obtained is in general agreement with second-order perturbation theory. More importantly, the MM4 structure allows a breakdown of the energy of the molecule into its component classical parts. This allows an understanding of why the structure is so distorted, in terms of CC bonding and nonbonding interactions, van der Waals repulsion, CCC and CCH angle bending, torsional energies, stretch-bend, torsion-stretch, and bend–torsion–bend interactions. Clearly, the hole in 113-membered ring is too small for the other ring to fit through comfortably. There are too many atoms trying to fit into the limited space at the same time, leading to large van der Waals repulsions. The rings distort in such a way as to enlarge this available space, and lower the total energy of the molecule. While the distortions are spread around the rings, one of the nominally tetrahedral CCC bond angles in each ring is opened to 147.9° by MM4 (146.8° by MP2). The stability of the compound is discussed in terms of the strain energy. © 2015 Wiley Periodicals, Inc.

Catenanes have become important molecular units for the design of new materials for 21^{st} century technology. The origins of strain in the simplest viable saturated hydrocarbon knots is investigated here. The combination of quantum chemistry with molecular mechanics provides many new insights.

A set of 42 molecules with N-F, O-F, N-Cl, P-F, and As-F bonds has been investigated in the search for potential bond anomalies, which lead to reverse bond length–bond strength (BLBS) relationships. The intrinsic strength of each bond investigated has been determined by the local stretching force constant obtained at the CCSD(T)/aug-cc-pVTZ level of theory. N-F or O-F bond anomalies were found for fluoro amine radicals, fluoro amines, and fluoro oxides, respectively. A rationale for the deviation from the normal Badger-type inverse BLBS relation is given and it is shown that electron withdrawal accompanied by strong orbital contraction and bond shortening is one of the prerequisites for a bond anomaly. In the case of short electron-rich bonds such as N-F or O-F, anomeric delocalization of lone pair electrons in connection with lone pair repulsion are decisive whether a bond anomaly can be observed. This is quantitatively assessed with the help of the CCSD(T) local stretching force constants, CCSD(T) charge distributions, and G4 bond dissociation energies. Bond anomalies are not found for fluoro phosphines and fluoro arsines because the bond weakening effects are no longer decisive. © 2015 Wiley Periodicals, Inc.

Reverse bond length/bond strength relations have been reported in the literature, in particular for chemical bonds between electron rich atoms, e.g. NF or OF bonds. In this work, a comprehensive rational is derived covering all electronic and electrostatic factors that may lead to shorter but weaker bonds. A key feature is the use of a qualified bond strength measure based on vibrational spectroscopy.

We respond to the two questions posed by Weinhold, Schleyer, and McKee (WSM) in their study of *cis-*2-butene (Weinhold et al., J Comput Chem 2014, 35, 1499), in which they solicit explanations for the relative conformational energies of this molecule in terms of the Quantum Theory of Atoms in Molecules (QTAIM). WSM requested answers to the questions: (1) why is *cis-*2-butene less stable than *trans*-2-butene despite the presence of a hydrogen-hydrogen (H⋯H) bond path in the former but not in the latter if the H⋯H bond path is stabilizing? (2) Why is the potential well of the conformational global minimum of *cis-*2-butene only 0.8 kcal/mol deep when the H⋯H bonding is stabilizing by 5 kcal/mol? Both questions raised by WSM are answered by considering the changes in the energies of *all* atoms as a function of the rotation of one of the two methyl groups from the minimum-energy structure, which exhibits the H**⋯**H bond path, to the transition state, which is devoid of this bond path. It is found that the stability gained by the H⋯H bonding interaction is cancelled by the destabilization of one of the ethylenic carbon atoms which, alone, destabilizes the system by as much as 5 kcal/mol in the global minimum conformation. Further, it is found that the 1.1 kcal/mol stability of *trans*-2-butene with respect to the *cis-*isomer is driven by the considerable destabilization of the ethylenic carbons by 11 kcal/mol, while the changes in the atomic energies of the other corresponding atoms in the two isomers account for the observed different stabilities. The error introduced into QTAIM atomic energies by neglecting the virials of the forces on the nuclei for partially optimized structures is discussed. © 2015 Wiley Periodicals, Inc.

Atomic origin of the locally stabilizing H⋯H contact in *cis*-2-butene from virial QTAIM atomic energies along the potential energy surface of methyl rotation, i.e., in terms of atomic sub-potential energy surfaces.