A method is proposed to easily reduce the number of energy evaluations required to compute numerical gradients when constraints are imposed on the system, especially in connection with rigid fragment optimization. The method is based on the separation of the coordinate space into a constrained and an unconstrained space, and the numerical differentiation is done exclusively in the unconstrained space. The decrease in the number of energy calculations can be very important if the system is significantly constrained. The performance of the method is tested on systems that can be considered as composed of several rigid groups or molecules, and the results show that the error with respect to conventional optimizations is of the order of the convergence criteria. Comparison with another method designed for rigid fragment optimization proves the present method to be competitive. The proposed method can also be applied to combine numerical and analytical gradients computed at different theory levels, allowing an unconstrained optimization with numerical differentiation restricted to the most significant degrees of freedom. This approach can be a practical alternative when analytical gradients are not available at the desired computational level and full numerical differentiation is not affordable. © 2015 Wiley Periodicals, Inc.

Geometry optimization, a central problem in computational chemistry, is ideally performed using analytical gradients. However, for many high-level methods such gradients are not available and one has to resort to more expensive numerical differentiation. In this work, it is shown how constraints used to simplify the optimization problem can also be used to speed-up an underlying numerical gradient calculation. In addition, a method to combine numerical and analytical differentiation is proposed, allowing efficient, unconstrained optimization.

Selecting the saturated graphene fragment as a model of graphene, we have investigated seven popular density functionals, including *ω*B97X-D, B97-D, B-LYP-D3, M05-2X, M06-2X, M11-L, and N12, for their performance in describing the adsorption of aromatic molecules on graphene. The best performing functionals are B97-D, B-LYP-D3, and *ω*B97X-D. M05-2X, M06-2X, and M11-L significantly underestimate the adsorption strengths, while N12 fails completely in this respect. The effects of the basis sets and size of the saturated graphene fragments on the geometries, energies, and properties for the adsorption of aromatic molecules on graphene have also been studied. It was found that the small basis sets such as 6–31G(d) and jun-cc-pVDZ are not suitable for the accurate description of the adsorption of aromatic molecules on graphene. The size of selected graphene fragments has a little effect on both the *ω*B97X-D and SCS-SAPT0 interaction energies, but the effects of the size of selected graphene fragments on the energy components are significant in some cases of the adsorption of aromatic molecules on graphene. The surprising weakness of electrostatic interactions by F substitution for the adsorption of F-substituted benzenes on graphene was explained using the energy component analysis. © 2015 Wiley Periodicals, Inc.

M05-2X, M06-2X, M11-L, and N12 significantly underestimate the strengths of the adsorption of aromatic molecules on graphene. The best performing functionals are B97-D, B-LYP-D3, and *ω*B97X-D. The combination of SCS-SAPT0 and aug-cc-pVDZ performs very well for the energy component analysis of the adsorption of aromatic molecules on graphene.

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.

A versatile high-accuracy computational scheme for the ^{77}Se nuclear magnetic resonance (NMR) chemical shifts of the medium-sized organoselenium compounds is suggested within a framework of a full four-component relativistic density functional theory (DFT). The main accuracy factors (DFT functionals, relativistic geometry, vibrational corrections, and solvent effects) are addressed. The best result is achieved with NMR-oriented KT2 functional of Keal–Tozer characterized by a fairly small error of only 30 ppm for the span of about 1700 ppm (<2%). © 2015 Wiley Periodicals, Inc.

A versatile high-accuracy computational scheme for the ^{77}Se NMR chemical shifts of the medium-sized organoselenium compounds is suggested within a framework of a full four-component relativistic density functional theory. The main accuracy factors (functionals, basis sets, relativistic geometry, vibrational corrections, and solvent effects) are addressed.

The mechanism of enzymatic peptide hydrolysis in matrix metalloproteinase-2 (MMP-2) was studied at atomic resolution through quantum mechanics/molecular mechanics (QM/MM) simulations. An all-atom three-dimensional molecular model was constructed on the basis of a crystal structure from the Protein Data Bank (ID: 1QIB), and the oligopeptide Ace-Gln-Gly∼Ile-Ala-Gly-Nme was considered as the substrate. Two QM/MM software packages and several computational protocols were employed to calculate QM/MM energy profiles for a four-step mechanism involving an initial nucleophilic attack followed by hydrogen bond rearrangement, proton transfer, and CN bond cleavage. These QM/MM calculations consistently yield rather low overall barriers for the chemical steps, in the range of 5–10 kcal/mol, for diverse QM treatments (PBE0, B3LYP, and BB1K density functionals as well as local coupled cluster treatments) and two MM force fields (CHARMM and AMBER). It, thus, seems likely that product release is the rate-limiting step in MMP-2 catalysis. This is supported by an exploration of various release channels through QM/MM reaction path calculations and steered molecular dynamics simulations. © 2015 Wiley Periodicals, Inc.

QM/MM calculations on oligopeptide proteolysis in the active site of matrix metalloproteinase MMP-2 predict fast chemical steps and a rate-limiting product release.

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.

An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library is able to evaluate arbitrary integral expressions on top of *p*, *r* and *σ* operators with one-electron overlap and nuclear attraction, two-electron Coulomb and Gaunt operators for segmented contracted and/or generated contracted basis in Cartesian, spherical or spinor form. Using a symbolic algebra tool, new integrals are derived and translated to C code programmatically. The generated integrals can be used in various types of molecular properties. To demonstrate the capability of the integral library, we computed the analytical gradients and NMR shielding constants at both nonrelativistic and 4-component relativistic Hartree–Fock level in this work. Due to the use of kinetically balanced basis and gauge including atomic orbitals, the relativistic analytical gradients and shielding constants requires the integral library to handle the fifth-order electron repulsion integral derivatives. The generality of the integral library is achieved without losing efficiency. On the modern multi-CPU platform, Libcint can easily reach the overall throughput being many times of the I/O bandwidth. On a 20-core node, we are able to achieve an average output 8.3 GB/s for C_{60} molecule with cc-pVTZ basis. © 2015 Wiley Periodicals, Inc.

Integral evaluation can be as simple as building toy bricks. In this spirit, an open source library Libcint was developed to automatically implement integrals for Gaussian type basis functions. Libcint library is able to handle arbitrary integral expressions on top of *p*, *r* operators and Pauli matrices for various integral types (one-electron overlap, nuclear attraction, two-electron Coulomb, and Gaunt operators) for various basis types (Cartesian, spherical, and spinor), without loss of computational efficiency.

Three different H/D isotope effect in nine H_{3}XH(D)^{…}YH_{3} (X = C, Si, or Ge, and Y = B, Al, or Ga) hydrogen-bonded (HB) systems are classified using MP2 level of multicomponent molecular orbital method, which can take account of the nuclear quantum nature of proton and deuteron. First, in the case of H_{3}CH(D)^{…}YH_{3} (Y = B, Al, or Ge) HB systems, the deuterium (D) substitution induces the usual H/D geometrical isotope effect such as the contraction of covalent *R*(CH(D)) bonds and the elongation of intermolecular *R*(H(D)^{…}Y) and *R*(C^{…}Y) distances. Second, in the case of H_{3}XH(D)^{…}YH_{3} (X = Si or Ge, and Y = Al or Ge) HB systems, where H atom is negatively charged called as charge-inverted hydrogen-bonded (CIHB) systems, the D substitution leads to the contraction of intermolecular *R*(H(D)^{…}Y) and *R*(X^{…}Y) distances. Finally, in the case of H_{3}XH(D)^{…}BH_{3} (X = Si or Ge) HB systems, these intermolecular *R*(H(D)^{…}Y) and *R*(X^{…}Y) distances also contract with the D substitution, in which the origin of the contraction is not the same as that in CIHB systems. The H/D isotope effect on interaction energies and spatial distribution of nuclear wavefunctions are also analyzed. © 2015 Wiley Periodicals, Inc.

Geometrical isotope effect, which is induced by isotope-substitution of hydrogen, in various H_{3}XH^{…}YH_{3} (X = C, Si, or Ge, and Y = B, Al, or Ga) hydrogen-bonded systems are systematically analyzed using the multicomponent MO method. Isotope effects of interaction energies and spatial distribution of nuclear wavefunctions are also analyzed. The GIEs in these HB systems can be classified into three types.

The simulation of diffusional association (SDA) Brownian dynamics software package has been widely used in the study of biomacromolecular association. Initially developed to calculate bimolecular protein–protein association rate constants, it has since been extended to study electron transfer rates, to predict the structures of biomacromolecular complexes, to investigate the adsorption of proteins to inorganic surfaces, and to simulate the dynamics of large systems containing many biomacromolecular solutes, allowing the study of concentration-dependent effects. These extensions have led to a number of divergent versions of the software. In this article, we report the development of the latest version of the software (SDA 7). This release was developed to consolidate the existing codes into a single framework, while improving the parallelization of the code to better exploit modern multicore shared memory computer architectures. It is built using a modular object-oriented programming scheme, to allow for easy maintenance and extension of the software, and includes new features, such as adding flexible solute representations. We discuss a number of application examples, which describe some of the methods available in the release, and provide benchmarking data to demonstrate the parallel performance. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

SDA 7 is the latest release of the Simulation of Diffusional Association software, a Brownian dynamics simulation package for the modeling of biomolecular systems. This release has been fully rewritten in Fortran 90, using an object-oriented programming approach, with improved parallelization on multi-core shared memory architectures. It consolidates the previously separate versions used for simulations of bimolecular and many-molecule systems, and allows modeling of solute flexibility.

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.

For a decade, the multivariate image analysis applied to quantitative structure–activity relationship (MIA-QSAR) approach has been successfully used in the modeling of several chemical and biological properties of chemical compounds. However, the key pitfall of this method has been its exclusive applicability to congeneric datasets due to the prerequisite of aligning the chemical images with respect to the basic molecular scaffold. The present report aims to explore the use of the 2D-discrete Fourier transform (2D-DFT) as a means of opening way to the modeling, for the first time, of structurally diverse noncongruent chemical images. The usability of the 2D-DFT in QSAR modeling of noncongruent chemical compounds is assessed using a structurally diverse dataset of 100 compounds, with reported inhibitory activity against MCF-7 human breast cancer cell line. An analysis of the statistical parameters of the built regression models validates their robustness and high predictive power. Additionally, a comparison of the results obtained with the 2D-DFT MIA-QSAR approach with those of the DRAGON molecular descriptors is performed, revealing superior performance for the former. This result represents a milestone in the MIA-QSAR context, as it opens way for the possibility of screening for new molecular entities with the desired chemical or therapeutic utility. © 2015 Wiley Periodicals, Inc.

The 2D-Discrete Fourier Transform is introduced as a strategy for creating a common base to construct multivariate images for chemical structures using their magnitude spectra. Thus, for the first time, the modeling of structurally diverse noncongruent chemical images in the Multivariate Image Analysis-Quantitative Structure Activity Relationship context is possible.

Fragment-based searching and abstract representation of molecular features through reduced graphs have separately been used for virtual screening. Here, we combine these two approaches and apply the algorithm *RedFrag* to virtual screens retrospectively and prospectively. It uses a new type of reduced graph that does not suffer from information loss during its construction and bypasses the necessity of feature definitions. Built upon chemical epitopes resulting from molecule fragmentation, the reduced graph embodies physico-chemical and 2D-structural properties of a molecule. Reduced graphs are compared with a continuous-similarity-distance-driven maximal common subgraph algorithm, which calculates similarity at the fragmental and topological levels. The performance of the algorithm is evaluated by retrieval experiments utilizing precompiled validation sets. By predicting and experimentally testing ligands for endothiapepsin, a challenging model protease, the method is assessed in a prospective setting. Here, we identified five novel ligands with affinities as low as 2.08 μM. © 2015 Wiley Periodicals, Inc.

RedFrag is a fast and intuitive algorithm for similarity-based molecule screenings. It uses a reduced graph representation of molecules, with an infinite color space for each of the nodes. This makes it an evolved version of feature trees while retaining the efficiency of this concept. RedFrag is evaluated both retro- as well as prospectively, the latter leading to five novel binders of endothiapepsin.

We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual *hole* and *electron* densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge–resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed. © 2015 Wiley Periodicals, Inc.

A new methodology for the analysis of electronic excitations is introduced. The formalism, which is based on a statistical analysis of the wavefunction of the *electron-hole* pair, allows to quantify the spatial location and compactness of electronic excitations, as well as giving new insight into charge transfer and correlation effects. A special focus is laid on different ways to quantify charge separation. In the figure, the *hole* (red) and *electron* (blue) densities are shown for a Rydberg state of cytosine. The *hole* size *σ _{h}*, the

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.

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}.

CYP19A1 aromatase is a member of the Cytochrome P450 family of hemeproteins, and is the enzyme responsible for the final step of the androgens conversion into the corresponding estrogens, via a three-step oxidative process. For this reason, the inhibition of this enzyme plays an important role in the treatment of hormone-dependent breast cancer. The first catalytic subcycle, corresponding to the hydroxilation of androstenedione, has been proposed to occur through a first hydrogen abstraction and a subsequent oxygen rebound step. In present work, we have studied the mechanism of the first catalytic subcycle by means of hybrid quantum mechanics/molecular mechanics methods. The inclusion of the protein flexibility has been achieved by means of Free Energy Perturbation techniques, giving rise to a free energy of activation for the hydrogen abstraction step of 13.5 kcal/mol. The subsequent oxygen rebound step, characterized by a small free energy barrier (1.5 kcal/mol), leads to the hydroxylated products through a highly exergonic reaction. In addition, an analysis of the primary deuterium kinetic isotopic effects, calculated for the hydrogen abstraction step, reveals values (∼10) overpassing the semiclassical limit for the CH, indicating the presence of a substantial tunnel effect. Finally, a decomposition analysis of the interaction energy for the substrate and cofactor in the active site is also discussed. According to our results, the role of the enzymatic environment consists of a transition state stabilization by means of dispersive and polarization effects. © 2015 Wiley Periodicals, Inc.

CYP19A1 aromatase is a Cytochrome P450 responsible for the final step of the androgens conversion into the corresponding estrogens, and thus can play a significant role in the hormone-dependent breast cancer development. The first of three oxidative subcycles of this enzyme consists of an initial hydrogen abstraction followed by an oxygen rebound step, giving place to a hydroxylated form of the androstenedione substrate via two possible electronic spin pathways.

The normal and reverse Perlin effect is usually explained by the redistribution of electron density produced by hyperconjugative mechanisms, which increases the electron population within axial or equatorial proton in normal or reverse effect, respectively. Here an alternative explanation for the Perlin effect is presented on the basis of the topology of the induced current density, which directly determines the nuclear magnetic shielding. Current densities around the CH bond critical point and intra-atomic and interatomic contributions to the magnetic shielding explain the observed Perlin effect. The balance between intra-atomic and interatomic contributions determines the difference in the total atomic shielding. Normal Perlin effect is dominated by intra-atomic part, whereas reverse effect is dominated by interatomic contribution. © 2015 Wiley Periodicals, Inc.

Differing behavior of geminal hydrogen atoms of a cyclic structure is known as Perlin effect. In this article, the local and integrated properties of induced current density (which directly determines nuclear magnetic shielding) are used to understand the normal and reverse Perlin effect in several diheterocyclic structures.

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.

As the sophistication of reactive force fields for molecular modeling continues to increase, their use and applicability has also expanded, sometimes beyond the scope of their original development. Reax Force Field (ReaxFF), for example, was originally developed to model chemical reactions, but is a promising candidate for modeling fracture because of its ability to treat covalent bond cleavage. Performing reliable simulations of a complex process like fracture, however, requires an understanding of the effects that various modeling parameters have on the behavior of the system. This work assesses the effects of time step size, thermostat algorithm and coupling coefficient, and strain rate on the fracture behavior of three carbon-based materials: graphene, diamond, and a carbon nanotube. It is determined that the simulated stress-strain behavior is relatively independent of the thermostat algorithm, so long as coupling coefficients are kept above a certain threshold. Likewise, the stress-strain response of the materials was also independent of the strain rate, if it is kept below a maximum strain rate. Finally, the mechanical properties of the materials predicted by the Chenoweth C/H/O parameterization for ReaxFF are compared with literature values. Some deficiencies in the Chenoweth C/H/O parameterization for predicting mechanical properties of carbon materials are observed. © 2015 Wiley Periodicals, Inc.

The Reactive Force Field was originally developed to model chemical reactions in a molecular dynamics framework. However, it is a promising candidate for modeling fracture in carbon-based materials because of its ability to treat covalent bond cleavage. This work assesses the effects of time step size, thermostat algorithm and coupling coefficient, and strain rate on the predicted fracture behavior of graphene, diamond, and a carbon nanotube.

The interaction between polyelectrolytes and counterions in confined situations and the mutual relationship between chain conformation and ion condensation is an important issue in several areas. In the biological field, it assumes particular relevance in the understanding of the packaging of nucleic acids, which is crucial in the design of gene delivery systems. In this work, a simple coarse-grained model is used to assess the cooperativity between conformational change and ion condensation in spherically confined backbones, with capsides permeable to the counterions. It is seen that the variation on the degree of condensation depends on counterion valence. For monovalent counterions, the degree of condensation passes through a minimum before increasing as the confining space diminishes. In contrast, for trivalent ions, the overall tendency is to decrease the degree of condensation as the confinement space also decreases. Most of the particles reside close to the spherical wall, even for systems in which the density is higher closer to the cavity center. This effect is more pronounced, when monovalent counterions are present. Additionally, there are clear variations in the charge along the concentric layers that cannot be totally ascribed to polyelectrolyte behavior, as shown by decoupling the chain into monomers. If both chain and counterions are confined, the formation of a counterion rich region immediately before the wall is observed. Spool and doughnut-like structures are formed for stiff chains, within a nontrivial evolution with increasing confinement. © 2015 Wiley Periodicals, Inc.

The effect of spherical confinement on conformation and counterion release is addressed. The condensation of monovalent and trivalent ions shows distinct trends, as space decreases. Different charge layers are found along the confining radius, which cannot be simply explained by polyelectrolyte electrostatic persistence. Regular structures were found for stiffer chains, even in the presence of monovalent counterions.

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.

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.

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.

Carbon is the most widely studied material today because it exhibits special properties not seen in any other materials when in nano dimensions such as nanotube and graphene. Reduction of material defects created during synthesis has become critical to realize the full potential of carbon structures. Molecular dynamics (MD) simulations, in principle, allow defect formation mechanisms to be studied with high fidelity, and can, therefore, help guide experiments for defect reduction. Such MD simulations must satisfy a set of stringent requirements. First, they must employ an interatomic potential formalism that is transferable to a variety of carbon structures. Second, the potential needs to be appropriately parameterized to capture the property trends of important carbon structures, in particular, diamond, graphite, graphene, and nanotubes. Most importantly, the potential must predict the crystalline growth of the correct phases during direct MD simulations of synthesis to achieve a predictive simulation of defect formation. Because an unlimited number of structures not included in the potential parameterization are encountered, the literature carbon potentials are often not sufficient for growth simulations. We have developed an analytical bond order potential for carbon, and have made it available through the public MD simulation package LAMMPS. We demonstrate that our potential reasonably captures the property trends of important carbon phases. Stringent MD simulations convincingly show that our potential accounts not only for the crystalline growth of graphene, graphite, and carbon nanotubes but also for the transformation of graphite to diamond at high pressure. © 2015 Wiley Periodicals, Inc.

A new parameterization of Pettifor's bond order potential has been performed for carbon. The method captures the property trends of important carbon phases and passes stringent molecular dynamics simulation tests: not only allowing for the crystalline growth of graphene, graphite, and carbon nanotubes, but also the transformation of graphite to diamond at high pressure.

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.

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.

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 **1**, where they can amount to stabilizations around about 1 kcal mol, however, they are not strong enough to dominate conformational preferences in organofluorine derivatives such as **2 - 4**.

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.

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}.

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

Application of density functional theory to molecules containing thousands of atoms is hindered by significant memory demands of the density fitting approximation. On page 1521 (DOI: 10.1002/jcc.23961), Lukáš Grajciar introduces a new low-memory iterative density fitting formulation that circumvents this problem using a combination of a continuous fast multipole method and a preconditioned conjugate gradient solver. The potential of the method implemented within the TURBOMOLE program package is demonstrated by performing density functional theory calculations for pure-silica zeolite chabazite fragment with 2592 atoms, 37 632 basis, and 121 248 auxiliary basis functions on a single processor workstation.

A novel enhanced conformational sampling method, virtual-system-coupled adaptive umbrella sampling (V-AUS), was proposed to compute 300-K free-energy landscape for flexible molecular docking, where a virtual degrees of freedom was introduced to control the sampling. This degree of freedom interacts with the biomolecular system. V-AUS was applied to complex formation of two disordered amyloid-β (Aβ_{30–35}) peptides in a periodic box filled by an explicit solvent. An interpeptide distance was defined as the reaction coordinate, along which sampling was enhanced. A uniform conformational distribution was obtained covering a wide interpeptide distance ranging from the bound to unbound states. The 300-K free-energy landscape was characterized by thermodynamically stable basins of antiparallel and parallel β-sheet complexes and some other complex forms. Helices were frequently observed, when the two peptides contacted loosely or fluctuated freely without interpeptide contacts. We observed that V-AUS converged to uniform distribution more effectively than conventional AUS sampling did. © 2015 Wiley Periodicals, Inc.

A two-dimensional free-energy landscape of dimerization for two peptide (Aβ_{30–35}) chains is computed by a virtual-system-coupled adaptive umbrella sampling. The peptides are put in a periodic boundary box filled with explicit solvent. The *x*- and *y*-axes are the mutual molecular distance and the relative molecular orientation. Parallel and antiparallel β-sheets, cross-contact complexes, and α-helices are sampled as well as completely dissociated forms. Complex-labeled “N” is the parallel β-sheet observed in crystal.

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudomultidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high-dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness, and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryoelectron microscopy data, and the scale dependence of nanoparticles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace–Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti-0 invariants and the relatively global characteristics of Betti-1 and Betti-2 invariants. © 2015 Wiley Periodicals, Inc.

Persistent homology has emerged as a popular technique for the topological simplification of massive biomolecular data. Resolution-based multidimensional persistent homology is introduced to bridge the gap between traditional topology and geometry. The utility, robustness, and efficiency of the proposed topological methods for protein folding, protein flexibility analysis, the topological denoising of cryo-electron microscopy data, and the scale dependence of nanoparticles are demonstrated.

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

Density fitting (DF) approximation within the density functional theory (DFT) leads to more than a tenfold increase of computational efficiency for systems containing few hundreds of atoms. However, application of the DF approximation to even larger systems is hindered by its significant memory demands. This article introduces a new DF formulation that circumvents this problem, enabling one to perform DFT calculations on molecules with thousands of atoms on single (multicore) processor work stations.

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2–2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies. © 2015 Wiley Periodicals, Inc.

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece, and WW domain, was simulated via accelerated molecular dynamics (aMD). Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from long-timescale conventional molecular dynamics simulations. This work demonstrates the enhanced sampling power of aMD on protein folding and will provide basic references in using aMD for further studies.

Reactive force fields make low-cost simulations of chemical reactions possible. However, optimizing them for a given chemical system is difficult and time-consuming. We present a high-performance implementation of global force-field parameter optimization, which delivers parameter sets of the same quality with much less effort and in far less time than before, and also offers excellent parallel scaling. We demonstrate these features with example applications targeting the ReaxFF force field. © 2015 Wiley Periodicals, Inc.

Fitting reactive force fields to reference data is a highly complex, global optimization problem. Significant implementation advances are presented, making the task highly efficient and scalable.

A modified CHARMM force-field (ZHB potential) with low point charges for silica was previously proposed by Zimmerman et al. (J. Chem. Theory Comput. 2011, 7, 1695). The ZHB potential is advantageous for quantum mechanics/molecular mechanics simulations as it minimizes the electron spill-out problems. In the same spirit, here we propose a modified ZHB potential (MZHB) by reformulating its bonding potential, while retaining the nonbonding potential as in the ZHB force-field. We show that several structural and dynamic properties of silica, like the IR spectrum, distribution functions, mechanical properties, and negative thermal expansion computed using the MZHB potential agree well with experimental data. Further, transferability of MZHB is also tested for reproducing the crystallographic structures of several polymorphs of silica. © 2015 Wiley Periodicals, Inc.

A new potential with low point charges is proposed here for modeling siliceous zeolites.

The protein-protein docking server ClusPro is used by thousands of laboratories, and models built by the server have been reported in over 300 publications. Although the structures generated by the docking include near-native ones for many proteins, selecting the best model is difficult due to the uncertainty in scoring. Small angle X-ray scattering (SAXS) is an experimental technique for obtaining low resolution structural information in solution. While not sufficient on its own to uniquely predict complex structures, accounting for SAXS data improves the ranking of models and facilitates the identification of the most accurate structure. Although SAXS profiles are currently available only for a small number of complexes, due to its simplicity the method is becoming increasingly popular. Since combining docking with SAXS experiments will provide a viable strategy for fairly high-throughput determination of protein complex structures, the option of using SAXS restraints is added to the ClusPro server. © 2015 Wiley Periodicals, Inc.

SAXS is a high throughput experimental technique for obtaining low resolution structural data for macromolecules in solution. While it cannot be used on its own to solve the structure of complex structures, utilizing SAXS data during automated docking improves the ranking of predicted models. The option of using SAXS data as an experimental restraint has been added to the ClusPro server.