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Keywords:

  • absolute configuration;
  • conformational analysis;
  • X-ray diffractometry;
  • TDDFT calculations;
  • exciton-coupled CD;
  • KCl pellet

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED

In this review article we examine state-of-the-art techniques for the structural elucidation of organic compounds isolated from natural sources. In particular, we focus on the determination of absolute configuration (AC), perhaps the most challenging but inevitable step in the whole process, especially when newly isolated compounds are screened for biological activity. Among the many methods employed for AC assignment that we review, special attention is paid to electronic circular dichroism (CD) and to the modern tools available for quantum-mechanics CD predictions, including TDDFT. In this context, we stress that conformational flexibility often poses a limit to practical CD calculations of solution CD spectra. Many crystalline natural products suitable for X-ray analysis do not contain heavy atoms for a confidential AC assignment by resonant scattering. However, their CD spectra can be recorded in the solid state, for example with the KCl pellet technique, and analyzed possibly by nonempirical means to provide stereochemical information. In particular, solid-state CD spectra can be compared with those calculated with TDDFT or other high-level methods, using the X-ray geometry as input. The solid-state CD/TDDFT approach, described in detail, represents a quick and reliable tool for AC assignment of natural products. Chirality 21:E181–E201, 2009. © 2009 Wiley-Liss, Inc.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED

Chirality is of prime importance in the interaction of living matter with the environment. One of the most immediate and essential consequences of chirality is seen in pharmaceutical science. All receptors in the human body are chiral and thus interact in a different manner with the two enantiomers of any chiral drug, which can have distinct biological and pharmacological effects.1 Currently, pharmaceutical regulatory authorities have recognized the essential role played by stereochemistry, and applicants are now prescribed to identify the absolute structure of new drugs, and to attempt to separate and determine the activity of all stereoisomers.2–4 As a consequence, an increasingly larger portion of chiral drugs is patented as a single enantiomer (about 90% between 2004 and 2006 in the United States).5, 6

A great number of drugs are directly or indirectly derived from natural products (ca. 40% of drugs marketed in the last 25 years),7 and the search for lead structures, notably for anticancer drugs, still heavily depends on natural product chemistry. As a consequence, isolation and identification of new natural products is a vital field of research, which necessarily includes the assignment of their absolute stereochemistry.

Structure Elucidation of Natural Products

The complete structure elucidation of a newly isolated natural compound may require a considerable effort and involve many different spectroscopic and, sometimes, computational techniques. In the next sections, we outline the various steps of what can be considered a common strategy followed to tackle this challenging task. Our attention will be especially devoted to the assessment of absolute stereochemistry, a purpose for which the use of computations has become decisive. In particular, this review focuses on the quantum-mechanics prediction of solid-state circular dichroism spectra, an option that recently drew our attention as a quick and reliable tool for determining absolute configurations of natural products.

Determine constitution

Generally, the first step in natural product chemistry is the determination of constitution, i.e., the network of chemical connections between all atoms in a molecule; for that purpose, the major role is played by nuclear magnetic resonance (NMR). In favorable cases, the structural elucidation of compounds in mixtures is also possible with NMR; however, a prior purification by chromatography and/or crystallization makes structure elucidation much easier.

Assistance from other spectroscopic and spectrometric techniques is also important. Mass spectrometry (MS) provides the molecular formula from high-resolution mass spectra (HRMS),8 and if FAB or ESI ionization techniques are employed, it also indicates the presence of “dimeric” structures. Those molecules composed by two equivalent covalently-linked fragments are in fact not directly appreciated from NMR spectra. Combination of NMR and MS also affords the number of unsaturations and/or rings present in the molecule under investigation. IR and UV/VIS spectroscopies provide information on the presence and nature of functional groups such as carbonyl, conjugated double bonds, and aromatic or hetero-aromatic systems.8, 9

With the proper atomic composition in hand, the structural assignment proceeds through the detection of molecular fragments, often composed around functional groups, by using several sophisticated modern NMR techniques, which usually include the measurement of H,H coupling constants (JHH) and of 1H-1H COSY spectra. Among the many existing excellent textbooks devoted to the topic, only our favourite choices are quoted here.8, 10–12 The next step requires the assembly of the various fragments, which is often realized by the help of two-dimensional HMQC and HMBC spectra. When hydrogen atoms are missing, for instance at vicinal tertiary carbon atoms, the connection between fragments must be deduced indirectly. Often a number of different structures that seem to fit NMR data can be constructed, which need to be distinguished also by the help of computer routines.13

Finally, the proposed “planar” or “gross” structures (constitutional isomers) can be substantiated by measuring selective Overhauser effects (NOE) or NOESY spectra, although the main use of NOE is in the conformational analysis.

Assign relative stereochemistry

Determination of the relative configuration of chirality elements is strictly related to the determination of the overall molecular conformation. Both are normally accomplished by means of NMR, by recording data sensitive to three-dimensional structure such as scalar J-couplings (especially 3JHH and 3JCH) and NOE effects.14 The coupling constant of vicinal and sometimes more distant nuclei is directly correlated to their reciprocal dihedral angle, which can be quantified through Karplus-type equations.15 Free rotations around single bonds connecting two fragments may render NOE interactions difficult to interpret because, due to sixth-power scaling with distance, a relatively nonpopulated conformation may be responsible for an apparent NOE. Especially in these difficult cases, assistance by molecular modeling may become indispensable.

Nowadays, fast computational procedures exist, based on Monte Carlo or molecular dynamics approaches, for efficient conformational analyses at various levels of theory, ranging from molecular mechanics (MM), to semi-empirical methods like AM1 or PM3, to ab initio methods (at least for small molecules).16 Conformational search routines provide a set of structures, which are then optimized at a higher level of theory, usually density functional theory (DFT) or other ab initio methods. Geometry optimizations afford structures with respective energies, thereafter used to estimate the population at the operating temperature of each conformer concurring to the observed property. Calculated geometries must be checked against NMR data by considering H[BOND]H distances versus observable NOEs, and H/H and C/H dihedrals versus measured J-couplings, with the help of Js predictors.15 When necessary, 13C chemical shifts may be calculated and compared with the experimental set.14

A typical example of difficulties encountered in the structure elucidation of a natural product is offered by blennolides D and E (1 and 2, Scheme 1).17 Blennolides are a family of compounds with unusual chromanone skeleton, isolated from Blennoria sp., an endophytic fungus from Carpobrotus edulis. Blennolides D and E, in particular, are rearrangement products of linearly condensed tetrahydroxanthones. From analysis of J-couplings and NOEs, it was possible to elucidate the relative configuration of the chirality centers of the five-membered ring. However, the observed NOE interactions between H-3 protons of the chromanone part with H-9 and H-10 protons of the lactone ring were ambiguous, because they could equally be justified by different conformations of the two stereoisomers. The overall relative stereochemistry of blennolides D and E could only be established by a concomitant use of spectroscopic (NOESY, heteronuclear 3JC-H couplings) and computational techniques (MM conformational searches, DFT geometry optimizations), which allowed the conformational situation around C-2/C-9 bond to be defined.17

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Scheme 1. Natural compounds discussed as examples of relative configuration assignments.

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Quite often, the relative configuration of endocyclic chirality centers can be assigned easily, whereas the stereochemistry of the long-chain substituents remains undetermined. In these situations, the last resort is either chemical correlation to a fragment with known configuration or X-ray single-crystal analysis. The structure elucidation of fusidilactone B (3, Scheme 1), obtained from an endophytic Fusidium sp. isolated from the leaves of Mentha arvensis, is an example demonstrating a solution to that kind of problem.18 In 2002, some of us published the structure showing the relative configuration of the cyclic core elucidated by NMR, but it was not possible to assign the relative configuration of the chirality centers of the side-chain (starred in Scheme 1).19 Later in 2008, suitable single crystals could be obtained and X-ray analysis became possible. The relative configuration of all chirality centers was then determined, while the assignment of absolute configuration was achieved by using the solid-state CD/TDDFT approach described later (section “TDDFT Calculations: The Solid-State CD/TDDFT Approach”).18

Assign absolute configurations

The available techniques for assigning absolute configurations (ACs) may be divided in two large families, that is, relative and absolute. Relative methods are those based on the existence of a reference, consisting in the compound itself (if previously known and characterized), a chemically-related compound with known AC, or a molecular portion with known configuration, which can be attached to the sample to provide a suitable derivative to be further characterized. Relative methods include measurement of optical rotatory power (OR, or [α]) to be compared with that of the pure compound (or of an enantiomerically enriched sample), and stereochemical correlations, that is, chemical transformations with known stereochemical pathways that relate the sample compound with a second compound whose AC is known. A comprehensive list of other “relative” methods may be found in Eliel's textbook.20

NMR is intrinsically unable to discriminate between enantiomers. However, if the sample compound is endowed with easily derivatized functional groups, such as an amine or an alcohol, it may be reacted with a so-called chiral derivatizing agent (CDA) of known AC, e.g. a carboxylic acid, to afford a chiral derivative a portion of which has known configuration. Thereafter, NMR analysis is performed to assign the relative configuration between the various chirality elements, usually based on through-space anisotropic effects of the reagent, and then to deduce the AC of the original sample. Use of CDAs like Mosher reagent and its modern analogs is relatively simple and versatile;21, 22 its major limitation is that a proper CDA must be found on a case-by-case basis, and the necessary chemical handling may be laborious and require moderate amounts of sample.

A second very important relative method is provided by X-ray crystallography. Even in the absence of reliable anomalous scattering effects (see below), the relative configuration may still be determined by X-ray analysis; therefore, the presence of a molecular portion with known absolute configuration (X-ray internal reference or CXR) leads unambiguously to the absolute stereochemistry of the whole molecule. Again, introduction of the proper CXR that would lead to a crystalline derivative with sufficient (though not necessarily high) quality is mandatory. CXRs are based on the formation of acid–base salts, covalent bonds such as amides or esters (e.g., alcohols with chiral acids like camphorsultam dichlorophthalic acid), and, more recently, inclusion complexes.22 Although the described methods based on NMR and X-ray are in general very powerful in their application to natural products, it must be taken into account that a thorough screening for the most appropriate CDA or CXR may be prevented by the usually small amount of sample available.

Contrarily to relative methods, absolute methods for assigning AC do not rely on the existence of any reference compound and are therefore expected to be of wider scope. This is especially relevant for the investigation of new compounds such as natural or synthetic products to be screened for pharmacological properties, where hundreds of substrates of the most various kinds are discovered every year. The most important and reliable technique for assigning ACs consists in X-ray analysis of crystalline compounds exhibiting resonant scattering.

The beginning of determination of AC dates back to the diffraction experiment of Bijvoet et al.23 on NaRb (+)-tartrate in 1951, showing that the anomalous dispersion effect could be used to distinguish a structure from its mirror image on an absolute basis. The “normal” interaction of X-rays with crystals is described as elastic scattering.24 However, if an atom gets excited during this process, anomalous dispersion or anomalous scattering takes place, and the scattering factor f for this atom, which describes its scattering power and contribution to the whole scattering process, becomes f = |f | exp(iϕ) = f + if″, ϕ being the phase angle. Depending both on the wavelength used for the diffraction experiment and on the involved atoms, f′ and f″ vary significantly, but the small f″ contributions, which are independent of the scattering angle, are most important for the magnitude of the anomalous dispersion effect.

As a consequence, for non-centrosymmetric space groups, Friedel's law I(hkl) = I(-h-k-l), where I is the intensity of an X-ray reflection hkl is no longer valid, and the small but measurable Bijvoet differences of these Friedel pairs may be used to determine the absolute structure. Refining left- and right-hand image of the structure (after successful and complete structure solution) and comparing the R values of both models with the Hamilton test25 should provide the correct assignment, too. Other methods to recognize the absolute structure are refinement of Rogers' η or Flack's x parameter.26–28 The calculated structure factor for the complete structure Fc2(all) consists of contributions from the model Fc2 and from the inverted one Fic2: Fc2(all) = (1 − x) Fc2 + xFic2. If x = 0, then the correct absolute structure has been refined; otherwise, if x = 1, the model has to be inverted and refined again. It should be stressed that the Flack (and Rogers) parameter is associated with its least-squares standard uncertainty (s.u.), giving a useful measure of confidence.28 Values significantly deviating from 0 or 1 may well indicate twinning or other problems.

Although the determination of absolute structure by X-ray analysis is in principle straightforward, there are some pitfalls to be taken into account. As already pointed out, the anomalous dispersion effect is rather small. Thus excellent data collection should be performed with well-defined single crystals at low temperatures, measuring at least a full set of Friedel pairs and proper absorption correction. Inclusion of a strong anomalous scatterer (a heavy atom, usually halogen or P or S for organic compounds, but for real careful work, F or even O will suffice) in the structure (by salt formation or covalent functionalization with a proper chemical group, e.g., a p-bromobenzoate for alcohols and amines) and, in most cases, use of CuKα rather than MoKα radiation will improve the f″ contributions. Finally, wrong determination and/or consideration of space group and resulting symmetry information, although rare, may lead to misinterpreted results.29 In 1982, a detailed inspection by Jones30 of the then 102 entries in the Cambridge Structural Database31, 32 bearing the “absolute configuration” flag revealed “many unsatisfactory features in the original publications”. The situation of today with 6982 correspondingly flagged structures has possibly improved, but paying attention to Jones' comments30, 33 is still strongly recommended.

Because the technique of AC assignment by X-ray analysis is not universally applicable, alternative methods have been developed in years.20Chiroptical spectroscopic techniques, based on the differential interaction (transmission or emission) between the sample and left- and right-circularly polarized light, represent a wide class of versatile tools purposely designed for analyzing chiral nonracemic samples. They include several different techniques such as electronic circular dichroism (ECD or simply CD, on which we will focus in the following), vibrational CD (VCD), Raman optical activity (ROA), and fluorescence-detected CD (FDCD).34 Two enantiomers of any chiral substance are characterized by chiroptical spectra perfectly matching in shape, position, and intensity of bands but being the mirror image of each other. A CD spectrum contains all the necessary information about the absolute configuration (and, more in general, the absolute structure) of the investigated compound, and if proper means of interpretation are available, i.e., the spectrum-structure relationship is established,35 the AC can be assigned. For example, if the CD of the compound is already known and assigned, comparison with the CD spectrum of the sample provides its AC, in analogy with [α]; alternatively, the spectrum of a strictly analogous compound may be used in the comparison. Such empirical correlations have drawbacks35 and fall back in the category of relative methods. Some of them, for examples based on the formation of a Cottonogenic (CD-active) transition-metal complex, are more robust and applicable to specific classes of substrates, such as 1,2-diols.36

A common approach in interpreting ECD spectra relies on dividing the molecule into separate portions according to their chromophoric or nonchromophoric nature. Then, chromophores are further classified into intrinsically chiral and achiral and thought to be surrounded by nonchromophoric perturbers belonging to spheres of increasing order.37 This independent system approximation (ISA) is the basis for so-called semi-empirical sector and helicity rules, which relate the inherent shape of a chromophore, or the position of a perturber with respect to it, to the sign of a specific ECD band (or Cotton effect, CE) allied with a chromophore transition.20, 37, 38 Sector rules like the celebrated octant rule for saturated ketones39 are still quite popular despite known limitations and exceptions.

One step forward, in terms of reliability and firm theoretical foundation, lies the exciton chirality (ECCD) approach.35, 40, 41 It applies to molecules endowed with two or more separate chromophores giving rise to electric-dipole allowed transitions and properly arranged with respect to each other, that is, not related by roto-reflection elements of symmetry. The through-space exciton coupling between, e.g., two equivalent transitions on two equal chromophores gives rise to a so-called ECD exciton couplet, that is, two bands of opposite sign and similar intensity, centered around the chromophore UV maximum. The sign of the exciton couplet depends on the absolute angle of twist (clockwise or counter-clockwise) between the two transition dipoles, while its intensity is related to the overall arrangement, including the interchromophoric distance. The exciton chirality rule permits assigning the absolute configuration of a bis-chromophoric compound in a straightforward way, provided that a single, well-established conformation is prevailing. Application of the exciton chirality method may require chemical derivatization of the sample compound with one or two properly chosen chromophores; standard microscale procedures exist for various classes of substrates.35, 40 Alternatively, methods based on supramolecular chemistry have been developed where an achiral chromophoric host interacts with a chiral guest and acquires a diagnostic ECCD spectrum, which reports guest chirality.42 In particular, Zn bis-porphyrin tweezers by Berova et al.35, 40, 43 have been employed as chirality probes for establishing the AC of some natural products.44, 45 A single site of derivatization is required to append a suitable linker and form a multi-functional conjugate capable of double binding to the metal porphyrins.

On a quantitative ground, a full prediction of exciton-coupled spectra, and in general of ECD spectra interpreted through the ISA,46 is possible by means of “classical” calculation approaches based on matrix methods,47, 48 which—in addition to the molecular conformation—require the electronic properties of all chromophores involved to be already known.

In principle, any chiral compound endowed with even a weak chromophore or group absorbing in the commonly accessible regions (185–700 nm, ECD; 750–1200 nm, near-infrared CD; 800–3200 cm–1, VCD; 100–3200 cm–1, ROA) is liable to CD measurement and AC assignment without the need for chemical derivatization. Nowadays, the direct calculation of chiroptical spectra (ECD, VCD, and ROA, but also OR) is possible by means of quantum-mechanics methods for moderately complex molecular systems,49, 50 without the need for any previous knowledge of chromophore properties or any assumption about the origin of the observed optical activity. The actual output of such calculations is a list of rotational strengths at discrete frequencies, computed (for ECD) by both dipole-length (DL) and dipole-velocity (DV) gauge formulations.49 Apart from gauge-origin independent implementations, DL and DV are consistent only when employing sufficiently large basis sets, but DL converges faster toward the basis-set limit.50, 51 Next, a full CD spectrum is generated by associating to each rotational strength a band shape, normally of Gaussian or Lorentzian type, with proper band width.52, 53 The sum of all bands affords a calculated spectrum to be compared with the experimental one to deduce for instance the AC.

In the context of VCD and ROA spectroscopies, density functional theory (DFT) calculations are the option of choice and represent a powerful and extremely efficient tool for studying the stereochemistry of molecules in the solution state with some degree of conformational freedom.53–56 ECD and OR calculations involve prediction of electronic excited states which, at least for high-level calculation methods, may be extremely demanding.57 With respect to VCD, ECD requires the presence of at least one chromophoric group, but this is not a severe limitation in the field of natural products which commonly contain at least one or more unsaturations. On the other hand, measurement of VCD spectra usually requires larger amounts of sample and the number of possible solvents is limited. Moreover, ECD instruments are still much more widespread than VCD. This is even more true for optical rotation measurements, and prediction of OR is a concise, though less reliable way of assigning ACs.58 Obviously, simulation of one chiroptical property does not necessarily exclude the others, and simultaneous use of two or more methods is beneficial in ambiguous cases.59

Several different levels exist for ECD calculations with a great variability in the computational time and the expected accuracy;49, 52, 60 many of them, relevant to the present review, will be described more in detail later (sections “Semi-Empirical Quantum-Mechanical Methods,” “TDDFT Calculations: The Solid-State CD/TDDFT Approach,” and “Conformational Studies by TDDFT and Ab Initio Calculations”). Simulation of CD spectra requires both electric and magnetic transition moments to be predicted with very high precision, because a small error in their relative orientation may revert the sign of rotational strength. Interestingly enough, it is in general not true that the less sophisticated methods are necessarily the less precise as well. Thanks to the computer technology development, ECD calculations on medium-size molecules are now possible at a reasonable computational cost even by using ab initio or time-dependent DFT (TDDFT) methods. Nowadays, this computational approach represents one of the most powerful and versatile options for stereochemical studies, as it will be widely demonstrated in the discussion below.

Prediction of Solid-State CD Spectra: Advantages and Limitations

A common prerequisite to the prediction of any molecular property, with any means, is the availability of a reliable molecular structure representative of that (or those) responsible for the observed property. In the context of chiroptical spectroscopies, in particular, it is important to stress that any CD spectrum is sensitive to, and contains information about, the overall molecular geometry, in terms of both conformation and absolute configuration. However, configurational and conformational factors are strictly intertwined, and it is usually very difficult to deduce both pieces of information from a single CD spectrum.35, 61 Therefore, when applied to deduce absolute configurations, CD calculations rely on an independently established conformational picture, which is in turn gained through the use of other spectroscopic and/or theoretical means, as discussed earlier (section “Assign Relative Stereochemistry”). Any solution CD spectrum amounts to the sum of contributions from all populated conformations; therefore, the set of input structures to be considered in the calculation must be representative of the whole conformational ensemble. The conformational analysis step may be very computationally demanding and prone to inaccuracy, the major sources of error lying in the prediction of relative energies, and the possible missing of one or more significant conformers. Computational results should always be checked against NMR data, which increases the length of the whole procedure. Finally, after a reliable set of input structures is available, the CD calculation must be run on each structure at the same level of theory. Therefore, flexible molecules may represent very difficult cases to handle with the above calculation scheme. A further critical point concerns the presence of solvent. A correct treatment of solute-solvent interactions, in both geometry optimization and CD calculation steps, requires inclusion of a solvent model62 which additionally increases the computational time.

One possibility of avoiding the time consumption and uncertainty related to the conformational search is offered by considering the solid crystalline state. Compounds that can be isolated as crystals amenable to X-ray analysis offer a two-fold advantage: first, in the solid state, the molecular conformation is fixed and univocal (unless polymorphs occur); second, the structure can be determined with high accuracy by X-ray single-crystal diffraction experiments. Thus, the prediction of any property related to the crystalline state, such as the solid-state CD spectrum, requires a unique and already determined conformation to be taken into account.

CD spectra of microcrystalline samples may be recorded by the procedures described in the next paragraph (from now on, we use CD as a synonym for ECD). It is then possible to compare experimental solid-state CD spectra with those calculated with different methods, using the X-ray geometry as input structure and deduce the AC. This is the essence of the solid-state CD/TDDFT and related approaches which is discussed in detail later (section “TDDFT Calculations: The Solid-State CD/TDDFT Approach”). Their main advantage, with respect to the procedure based on solution CD calculations,60, 61 is that the whole conformational analysis step is skipped. They are therefore much faster and avoid the uncertainties connected to conformational searches and geometry optimizations. A second key point is that the experimental and the calculated property (CD spectrum) refer to the very same geometry, therefore, provided that suitable and accurate means for calculating CD is chosen, a good agreement is expected between theory and experiment, and AC assignment can be performed with high confidence.

The most important limitation of the solid-state method is that it is only applicable to samples giving single crystals suitable for X-ray diffraction, although they need not to contain “heavy” elements. It must be stressed that the vast majority of natural compounds contains only H, C, O, and N atoms. The February 2009 version of the CSD Cambridge database31, 32 comprises about 7000 structures in chiral space groups that are flagged with “absolute configuration” but only 523 of these consist of H, C, O, and N atoms, and 40 of H, C, O, N, F (8% overall). The problems concerning correct assignment of absolute configuration (or absolute structure) by X-ray diffraction especially in these difficult cases30, 33 have been already outlined (section “Assign Absolute Configurations”). Considering that most interesting biologically active natural compounds contain at least one unsaturation (a chromophoric group), there is much space available for application of the solid-state CD method for assigning ACs. Clearly, the compound considered should not be polymorph or the form ofthe crystals used for CD measurement must be recognized.

A second problem associated with solid-state CD spectra is that intermolecular interactions between molecules closely packed in the crystals may give rise to non-negligible contributions to the spectrum.63, 64 It is clear that any phenomenon of this kind cannot be predicted by a calculation run on a single, isolated, molecule. The actual impact of solid-state intrinsic CD effects will be more extensively discussed in the Application section (sections “Exciton Chirality and Related Methods” and “TDDFT Calculations: The Solid-State CD/TDDFT Approach”).

Measurement of CD Spectra in the Solid State

Measurement of solid-state chirooptical spectra represents a topical area of research in connection with the recent advances in the fields of solid-phase enantioselective synthesis, spontaneous resolution, chiral recognition, and supramolecular chemistry.65–67 The measured solid-state optical parameters can be correlated with data from other solid-state methods such as single-crystal X-ray diffraction, solid-state IR, and NMR measurements. Solid-state ECD spectra can be measured by different techniques, most of which are well known for several decades, described in several reviews by Kuroda et al.63, 64, 68 and summarized in the following.

Microcrystalline pellet method

The microcrystalline pellet or disc method is the most frequently used solid-state ECD technique. The crystalline sample is mixed and powdered with a suitable matrix such KBr, KCl, or CsI, and the microcrystalline powder is pressed to produce a translucent glassy disc. Initially, the method was introduced and applied to study solid-state optical activity of crystals of metal complexes, and this is still one of the major field of interest.69–72 KBr can be used for ECD measurements only above 220 nm, because of its UV cutoff. The use of CsI and KCl is less common in the literature, despite the fact that KCl can be used down to 180 nm and its handling is the same as that of KBr. The short-wavelength range extension may be crucial for the solid-state CD analysis of natural products containing only chromophores such as alkene and lactone.18, 73

The KBr pellet method is well suited to follow optical activity specific to the solid state and lost during dissolution, such as achiral compounds giving spontaneous resolution,74 metal complex polymers,75 and inclusion complexes of chiral hosts with achiral chromophoric guests.76 The use of pellet technique for the secondary structure analysis of peptides and proteins is instead very rare.77 Before our recent investigations discussed later (sections “Exciton -Chirality and Related Methods,” “Semi-empirical Quantum-Mechanical Methods,” and “TDDFT Calculations: The Solid-State CD/TDDFT Approach”), pellet method had also been scarcely adopted in stereochemical studies of natural products.64, 78 A limitation of the pellet method is the rarely observed interaction of metal and halide ions with the sample,79 and, in special cases, the interference from vacuum and pressure used during the disc formulation.64, 80

Detailed procedures of pellet preparation are reported in several articles.69, 71, 77 In our solid-state CD measurements of natural products, the disc was prepared by grinding and mixing ∼180–250 mg KCl (≥99.999% Fluka, preheated at 100 °C) and 30–250 μg sample (depending on the chromophore) with the aid of a Perkin–Elmer vibrating mill equipped with a stainless steel ball for 5 min, and the mixture was then pressed under vacuum at 10 tons with a Perkin–Elmer press for 5–10 min to provide a translucent disc. To decrease diffused reflections at grain boundaries, the sample and the matrix must be finely powdered and mixed to provide homogenous distribution. Because the intensity of the scattered light is proportional to sixth power of the particle diameter, elaborated grinding is necessary. The lowest possible sample amounts providing acceptable CE were generally used to decrease the effect of absorption flattening81 and to assure linear relationship between CD and sample concentration.69 Because KCl is hygroscopic, measurements were carried out right after the preparation of the disc by mounting the KCl disc on a holder and placing it as close to the PMT detector as possible.

Artifacts from macroscopic anisotropies, contributions from linear dichroism (LD) and linear birefringence (LB), can endanger the measurement of a true solid-state CD.68, 82, 83 Macroscopic artifacts have both rotation-dependent and -independent contributions, whose presence may be ascertained by, respectively, sample rotation around the incident-light axis (or z axis) and flip (180° rotation) around the vertical y axis.82, 83 However, averaging the various spectra obtained by z-rotation and y-flip is not a proper way of obtaining artifact-free CD. Recently, Kuroda et al.68, 83 have designed Jasco J-800KCM chiroptical spectrophotometer, which is capable of measuring simultaneously CD, LB, and LD. Moreover, an analytical protocol was devised to get the true CD by application of Mueller matrix formalism. Because LD data can be recorded with the commercially available regular ECD spectrophotometers, the simultaneous recording during CD measurements is desirable whenever possible. In the case of our solid-state CD measurements of natural products, various spectra were usually recorded with 90° z-axis rotations and y-axis flip to check the presence of rotation-dependent and -independent contributions from macroscopic anisotropies. In most cases, the spectra showed negligible changes with rotation or flip, as exemplified by the four z-axis rotated KCl CD spectra of papyracillic acid methyl acetal (8, Fig. 1a).84 When minor rotation-dependent artifacts appeared, they showed periodic shifts with 90° z-axis rotations as shown for the KCl spectra of 4,5-bis(4-bromobenzoate) (9a) of palmarumycin M1 (9, Fig. 1b).84 Except for proved intermolecular ECCD interactions in the solid-state (vide infra, sections “Exciton Chirality and Related Methods” and “TDDFT Calculations: The Solid-State CD/TDDFT Approach”), solid-state KCl CD spectra corroborated well the solution ones, which is a strong indication of the absence of significant artifacts in the solid-state CD signal.

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Figure 1. Solution and solid-state CD spectra of 8 (a) and 9a (b). Solid-state spectra were measured on KCl pellets upon four rotations around the incident light z axis.

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Other solid-state CD techniques

The first single-crystal ECD measurement was carried out along the optical axis of hexagonal crystals of Λ-(+)-2[Co en3]Cl3·NaCl·6H2O (en = 1,2-ethanediamine) by McCaffery and Mason in 1963 and the single-crystal CD spectrum was compared with the microcrystalline KBr one.70, 85 The measurement of single-crystal ECD along directions different from the optical axis suffers from serious birefringence artifact, which is three orders of magnitude larger than the optical activity, and thus the measurements must be carried out along the optical axis of mainly cubic and uniaxial crystals.63 Because of experimental difficulties, only a few examples have been reported exclusively in the field of metal complexes.71 Recently, the supramolecular optical activity and arrangement of the achiral inorganic salt α-Ni(H2O)6·SO4, exhibiting optical activity only in the solid state, was studied by single-crystal CD86 and a sign inversion was detected at low temperature.87

The Nujol mull method was adopted from IR spectroscopy, and it was an option to the pellet technique whenever the matrix K+ or Br ions reacted with the microcrystalline sample. Although it is easy to perform, Nujol emulsions often suffers from dispersion effect and solute-solvent interaction between the sample and Nujol. Because of substitution of the tartrate ion by the bromide, the D-tartrate salt of a hexaaminecobalt(III) complex gave no CE in KBr disc, whereas the Nujol mull sample had the same CE as in the aqueous solution but with larger intensity.88 Use of a specific procedure renders CD measurements by the Nujol mull method quantitative.79, 89 The Nujol mull method was used to identify optically active conglomerates formed by crystallization of achiral compounds like benzophenone90 and two-component mixtures such as 4·5 and 6·7 (Scheme 2).91–93 In these cases, optical activity was specific for the crystalline state and only solid-state methods were suitable to detect and characterize it.

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Scheme 2. Two-component complexes characterized by CD spectra as Nujol mulls.

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Diffuse reflectance circular dichroism (DRCD) has recently emerged as a powerful alternative to other solid-state CD methods, which, similarly to the single-crystal method, can eliminate the disturbance of the matrix. It exploits an integrating sphere optical device, adapted to CD measurements in transmission or total/diffuse reflectance mode by Castiglioni and Albertini.94 In the DRCD method, the finely ground, microcrystalline sample is diluted with KBr and used directly for measurement without the need to press a pellet. Kuroda and coworkers recorded DRCD spectra of coordination compounds in solids, on their own and as KBr and CsI pellets, Nujol mulls and mixture of solid samples with KBr, obtaining similar ECD spectra of different quality.95 The DRCD method was found the only feasible option for the solid-state CD measurement of the microcrystals of p-benzoquinone/pyrene cluster having supramolecular chirality.80 Pellet and Nujol methods could not be used because, respectively, benzoquinone sublimed from the complex crystals during the disc preparation, and the complex dissolved in Nujol.

Finally, although not specifically related to the present context, we mention that in film-state CD measurements, a solution of the studied compound is cast on the surface of a quartz cuvette and evaporation of the solvent produces a solid film. This method was mainly reported, to give just a few examples, for the secondary structure analysis of proteins96 and polypeptides97 as well as for the characterization of the supramolecular structure of synthetic chiral polymers.98, 99

EXAMPLES OF APPLICATION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED

In the following sections, we will discuss several kinds of interpretations of solid-state CD spectra for the stereochemical analysis of organic compounds. Our discussion will especially focus on the assignment of absolute configurations of crystalline organic compounds, in particular natural products, whose solid-state structure—but not the AC—is known from X-ray analysis. Solid-state CD is comparatively much less used as a source of conformational information. However, a few examples exist of a possible application consisting in establishing a connection between the conformation, known from X-ray, and some spectral features, e.g., to derive structure/spectral relationships to be employed subsequently. Finally, we will pay attention to a field where employment of solid-state CD spectroscopy is particularly significant, that is, the crystallization of achiral compounds as conglomerates, i.e., mechanical mixtures of homochiral crystals, where in each single crystal a preferential chiral conformation is consistently assumed.100 In these cases, solid-state CD spectroscopy lends itself as the tool of choice for a rapid screening of crystal optical activity.

The following sections are organized according to the methodology involved, in order of increasing complexity, and special attention will be paid to quantum-mechanics calculation approaches.

Empirical Correlations, Sector, and Helicity Rules

Empirical and semi-empirical correlations represent the oldest and simplest way of extracting information from CD spectra, but their application is now greatly downsized. The essence of empirical or semi-empirical (sector and helicity) rules20, 37–39 for interpreting CD spectra has been given in the Introduction section above (section “Assign Absolute Configurations”). What we want to stress here is that sector/helicity rules are especially suited to be applied to solid-state CD spectra, and, in turn, combination with X-ray structure determination offers a chance to check reliability of existing rules and establish new, more reliable ones. The reasoning for this statement lies in the fact that the conformational ambiguities, which unavoidably plague a safe application of empirical and semi-empirical rules,35, 39 are avoided in the solid state, where the molecular geometry is univocal and known. Therefore, the relationship between absolute structure and CD is safely established and lends itself to being rationalized and generalized through rules to be employed in further studies.

Unfortunately, not many examples of such kinds are found in the literature. An example of empirical correlation has been reported by Kamigata and coworkers about diphenyl dichalcogenides Ph[BOND]Y[BOND]Y[BOND]Ph, with Y = S, Se, and Te.74 These achiral compounds crystallized as optically-active conglomerates, and their single crystals exhibited solid-state CD spectra (KBr pellet) but were CD-silent after dissolution because of rapid racemization occurring in solution. Once the relationship between helicity (absolute C[BOND]Y[BOND]Y[BOND]C dihedral) and observed CD of the disulphide was inferred by X-ray, the authors correlated the helicity adopted in the single crystals of diselenide and ditelluride. Independent TDDFT calculations have corroborated the proposed correlation between disulfides and diselenides (see below, section “Conformational Studies by TDDFT and Ab Initio Calculations”).101

Gdaniec and Połonski have reported on the characterization of inclusion compounds formed by aromatic ketones (10, Scheme 3) and cholic acid (CA) as a chiral host.76 Five inclusion compounds could be crystallized and analyzed by X-ray and solid-state CD (KBr pellet). The CE around 330 nm due to nπ* transition of the carbonyl group is known to correlate with the intrinsic chirality of the nonplanar Ar[BOND]C[DOUBLE BOND]O moiety,102 a positive nπ* CE corresponding to a positive acute dihedral angle (P helicity) between the aromatic plane and the C[DOUBLE BOND]O bond. Absolute angles of twists observed in the X-ray structures of 10·CA complexes were all in keeping with the sign found in solid-state CD, according to the rule.76 Later, Zsila et al.103 have taken advantage of the above results to interpret the solid-state CD spectrum of HCl salt of tolperisone (11, Scheme 3), a muscle relaxant. Unfortunately, the X-ray structure of that compound was not available, thus the solid-state CD could not be used for an independent assessment of AC. We would like to remark that Połonski et al. had clearly recognized the potentiality the solid-state approach, in fact, they stated that “conformation in solution is by no means clear due to extreme flexibility […], and therefore, model systems with a better defined geometry would be desirable for this purpose [of testing the empirical rule]”.

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Scheme 3. Molecules whose solid-state CD spectra have been analyzed through helicity rules.

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Exciton Chirality and Related Methods

The exciton chirality CD (ECCD) method represents one of the most successful and popular approaches for the interpretation of CD spectra of bis- and multi-chromophoric organic compounds.35, 40, 41 It combines the immediacy of sector-like rules with the reliability of a nonempirical treatment. Theoretical basis, prerequisites, and scope of ECCD method have been summarized in the Introduction (section “Assign Absolute Configurations”). Here, we will present a few applications relative to solid-state CD spectra, a context where ECCD has been relatively much less employed with respect to the solution state. However again, consideration of a conformationally fixed and structurally well-characterized situation is not without value even for ECCD, given that unexpectedly assumed conformations may be the reason for an apparent sign reversal or diminished intensity of exciton couplets.104–107

It must be noticed that any system exhibiting exciton-coupled CD necessarily contains two or more strong chromophores which tend to interact, whenever allowed, not only intramolecularly but also intermolecularly. Therefore, solid-state CD spectra of such systems are likely to include solid-state intrinsic contributions,63, 64 from the couplings between distinct molecules packed in the crystals, which may be not easy to interpret. The importance of intermolecular exciton couplings in the solid state is emphasized by a recent report by Borovkov et al.108 about a bis-porphyrin compound forming chiral host-guest complexes, for which it was found that intermolecular couplings overcame intramolecular ones in determining the observed solid-state CD. The same phenomenon was observed by some of us for a (1-naphthyl)ethylidene ketal of α-L-rhamnopyranoside (12, Fig. 2), a synthetic compound whose X-ray structure was available.109 The solid-state CD spectrum of 12 (KBr pellet) was quite different and much more intense than that in acetonitrile solution and was dominated by a strong negative couplet centered around 228 nm, where 1Bb transition of the naphthalene (Np) chromophore occurs (Fig. 2). Accordingly, this was attributed to the exciton coupling between Np rings belonging to distinct molecules in the crystal. Proof of such interpretation was offered by CD calculations run with the DeVoe approach, a matrix-based method allowing for quantitative estimations of ECCD spectra of multichromophoric compounds.47, 110, 111 DeVoe-calculated CD on the single molecule of 12, using the X-ray geometry, consisted in a weak positive couplet with components at 225 and 195 nm, due to the coupling between Np and 1,4-dimethoxybenzene (DMB) chromophores. Then the calculation was run for a probe molecule of 12 surrounded by a cluster of Np and DMB groups belonging to the closest neighboring molecules found in the crystal and afforded a CD dominated by a strong Np/Np negative couplet as detected in the experimental solid-state CD (Fig. 2).109 This study represented the first example of a quantitative investigation of intermolecular exciton couplings in the solid state. (See also note added in proof).

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Figure 2. Solution and solid-state CD spectra of (1-naphthyl)ethylidene ketal of α-L-rhamnopyranoside (12), and DeVoe-calculated CD on the X-ray structure considering a probe molecule either isolated or surrounded by a cluster of nearby chromophores.

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The above findings are, however, far from being generally valid. In many other cases of solid-state ECCD spectra, the contribution from crystalline intermolecular couplings was negligible—or, at least, neglected, which allowed a straightforward stereochemical assignment. For example, palmarumycin M1 (9, Fig. 1b), a natural product extracted from Microsphaeropsis sp., an endophytic fungus of Larix decidua, contained a bicyclic 1,3-diol system, and its AC was established as (4S,4aS,5S,8R,8aS)-(9) by X-ray analysis of its 4-bromobenzoate (4-BrBz) diester (9a). This latter also showed solid-state and solution CD with a clear-cut positive couplet in the 210–275 nm region (Fig. 1b),84 due to the exciton coupling between ππ* 1La (or CT) transitions of the 4-BrBz chromophores, occurring at 245 nm and long-axis polarized in each aromatic ring.41 In the X-ray structure of 9a, aryl C1-C4 directions define a positive twist (dihedral angle ≈ +100°, Fig. 3), which corresponds to a positive chirality between 1La transition moments, reflected in the positive ECCD according to the exciton chirality rule41 for (4S,5S) absolute configuration. Thus, the CD spectrum of 9a is in keeping with the established AC of palmarumycin M1.

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Figure 3. Positive exciton chirality defined by 1La transition moments in the X-ray of palmarumycin M1 4,5-bis(4-bromobenzoate) (4S,4aS,5S,8R,8aS)-(9a).

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Other molecules for which solid-state ECCD spectra have been recently analyzed are sketched in Scheme 4. Szumna et al. have reported on chiral resorcin[4]arenes, bowl-shaped molecules, which assume a definite helicity supported by an intramolecular hydrogen bond network. The two compounds 14a–b (Scheme 4) were crystallized and characterized by X-ray and CD. Interestingly enough, 14a, with P helicity, showed similar solution and solid-state CD spectra consisting of a positive couplet in the aromatic 1Lb transition region around 300 nm.112, 113 On the contrary, 14b, with the same P helicity, showed a negative1Lb couplet in solution, and a monosignate solid-state CD. Rationalization of this apparent inconsistency required careful evaluation of polarization direction of 1Lb transition moments, with the help of TDDFT calculations on suitable molecular fragments. It turned out, almost surprisingly, that the two different R2 substituents in Scheme 4 effectively tilt 1Lb moment toward opposite directions with respect to the transverse aromatic axis (dashed line), thus giving rise to oppositely signed exciton couplings. The monosignate CD of 14b as KBr pellet was instead explained according to the diminished symmetry of the resorcinarene skeleton in the solid state with respect to the solution (C2 instead of C4).112

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Scheme 4. Molecules displaying exciton-coupled solid-state CD spectra.

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Komhoto et al.114, 115 have reported on a series of aromatic imides (15–16, Scheme 4) which crystallize in a S-shaped folded structure where effective intramolecular exciton couplings between the aromatic chromophores are possible. Consequently, they display exciton-coupled solid-state CD spectra, which were qualitatively analyzed and found in agreement to the observed interchromophoric helicity detected in the X-ray structures. The achiral imides 15a,b crystallized as conglomerates, and the preferential arrangement assumed by aromatic rings was deduced from comparison of their solid-state CD spectra with the chiral analogs15c,d. Compounds 16 display photochromic properties in solution, which were also monitored by CD spectroscopy, and reactive solution structures were inferred to be similar to solid-state onen by similarity of CD spectra in the two states.115 Other examples may be found in the literature where a solution structure was validated by ECCD analysis of its CD spectrum referred to the solid-state structure.116

When necessary, the interpretation and prediction of exciton-coupled CD spectra may be transferred on a quantitative ground by employing calculation approaches like the above-presented DeVoe's one. For example, the solid-state CD of (2-naphthyl)ethylidene ketal of α-L-rhamnopyranoside (13) could be reproduced by DeVoe calculations on the X-ray geometry.109 Interestingly enough, the experimental KCl-pellet CD showed no appreciable contribution from intermolecular couplings as found for the isomeric compound 12 discussed earlier, which was explained by the different packing of the molecules in the crystal.

Semi-Empirical Quantum-Mechanics Methods

Semi-empirical implementations of molecular orbital theory represent efficient and computationally inexpensive tools for the prediction of molecular properties.16 They ignore core electrons and rely on various approximations like the neglect of differential overlap (NDO) to skip the explicit calculation of computationally demanding one- and two-electron integrals; these latter are either put to zero or suitably parameterized to atom-related values depending on quantities such as ionization potential and electron affinity. In the context of excited-state calculations, electron correlation is taken into account by means of a truncated configuration interaction (CI). When only singly excited states are included, a CI single (CIS) procedure is employed in connection with various semi-empirical models developed for spectroscopic purposes, such as CNDO/S (complete NDO) and ZINDO/S (Zerner's intermediate NDO).117 Both of them have been successfully employed for CD calculations, as demonstrated by recent reviews and articles.60, 61, 118–123 The main advantage of such techniques lies in the extreme quickness of calculations. The observed accuracy is usually good and may be even superior to more rigorous treatments; systematic wavelength shifts are common and must be taken into account.61 A major problem with CD calculations is the usually observed poor agreement between DL- and DV-computed rotational strengths. Because of the parametric essence of NDO methods, their efficiency depends case by case on the system investigated, and their consistency is somewhat limited. Both CNDO/S and ZINDO/S have been especially designed to treat aromatic and hetero-aromatic chromophores (including ligands for transition metals, for ZINDO). As a matter of fact, the large majority of literature reports on CD calculations with these two methods concerns aromatic and poly-aromatic compounds, especially biaryls.60, 61, 118–123

In the context relevant to the present review, the first application of CNDO/S to the AC determination of a natural product based on its solid-state CD was reported by some of us in 2005.124 Phomoxanthone A (17, Scheme 5), extracted from endophytic fungus Phomopsis sp., isolated from the stem of Costus sp., and endowed with antifungal and antibacterial activity, has a skeleton containing axial and central chirality elements. This combination often hampers the determination of the AC of chirality centers, because axial chirality is the major responsible for the observed optical activity.61, 123 Such a problem was circumvented by X-ray single-crystal analysis which afforded the desired relative configuration. Next, the solid-state CD spectrum (KBr pellet) was compared with that calculated with CNDO/S-CI using the X-ray structure as input; the very good agreement allowed determination of the axial chirality and AC assignment.124 It is interesting to notice that when AM1-optimized geometries were used as input, the calculated spectrum was found to be extremely sensitive to the inter-aryl dihedral angle θ (C4a–C4–C4′–C4a′) and changed its sign for a value of θ between 76° and 77°. At the same time, AM1 torsional energy scans predicted the existence of a flat low-energy valley for values of θ between 65° and 130°. Therefore, a small uncertainty in the estimation of the solution structure could in principle lead to the wrong AC assignment, if solution CD spectra would be considered. This example clearly demonstrated the great potentiality and usefulness of the solid-state CD calculation approach and opened the way to subsequent development based on the use of TDDFT calculations described in the next section.

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Scheme 5. Molecules whose absolute structure has been confirmed by semi-empirical calculations on solid-state X-ray geometry; the structure of cholic acid is shown in Scheme 3. Curved arrows denote chirality axes.

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In the field of characterization of conglomerates obtained from crystallization of achiral compounds, two reports from Połonski et al. described application of ZINDO/S-CI calculations for interpreting solid-state CD spectra of some aromatic compounds. In the first article,125 four N-aryl-N-nitrosamines (18a–d, Scheme 5) were considered; three of them gave crystalline inclusion compounds with cholic acid (CA), characterized by X-ray analysis and solid-state CD. In the complexes, the guests assumed a conformation with preferential helicity (M or P) of the nitrosamine moiety (negative and positive acute Ar[BOND]N[BOND]N[BOND]O dihedral, respectively), which was correlated with the sign of the lowest-energy CE around 400 nm in the solid-state CD spectra (KBr disc). A positive CE allied to nπ* transition corresponds to M helicity and vice versa. Actually, the CD of the inclusion compound of N-benzyl-N-phenyl derivative 18c consisted in a bisignate signal (positive couplet with crossover at 375 nm). Derivative 18d did not give an inclusion complex with cholic acid, but it was found to crystallize as a conglomerate. The solid-state CD spectrum of a crystal of 18d (KBr disc) was found similar to that of 18c·CA and allowed to establish the preferential helicity adopted as M, as well. This latter assignment, along with the CE sign/helicity relationship for all compounds, was substantiated by ZINDO/S-CI calculations using the X-ray geometries as input structures. They gave spectra in agreement with the expected trend, although considerably red-shifted with respect to the experimental ones.125 In the second article,126 a similar approach was followed for benzil (1,2-diphenyl-1,2-ethanedione, 19, Scheme 5), a compound known for long time to crystallize as a CD-active conglomerate. The preferential helicity adopted in the crystals (sign of O[BOND]C[BOND]C[BOND]O dihedral) was determined by comparison between solid-state CD spectra (KBr disc) of the two enantiomorphous crystals of 19 and of its inclusion compounds with cholic and deoxycholic acid, characterized by X-ray. Here, the twisted 1,2-dicarbonyl chromophore with M helicity generated a positive nπ* CE around 400 nm. Again, the assignment could be confirmed through ZINDO/S-CI calculations on X-ray geometries.126 The two examples above demonstrate the usefulness of quantum-mechanics predictions of CD spectra in the characterization of conglomerates formed by crystallization of organic compounds, potentially allowing for the determination of the molecular absolute conformation without the need for a chiral reference.

TDDFT Calculations: The Solid-State CD/TDDFT Approach

Density functional theory (DFT) has been emerging in the last decades as the most widespread calculation method for the prediction of many different molecular properties, due to a very favourable compromise between accuracy and computational cost.16 In fact, for many problems, hybrid DFT functionals like the most popular B3LYP are capable of attaining degrees of accuracies similar to that of higher-level MO methods that include electron correlation (approaching full CI limit) at a considerably smaller cost. Time-dependent DFT (TDDFT) results from application of a perturbative approach to DFT. The linear response of a system to an oscillating field, expressed through a frequency-dependent polarizability, yields prediction of electronic excitations in terms of frequency and corresponding transition dipoles (electric and magnetic).127 In this case too, observed accuracies are very high at a limited computational effort,57 which makes now routine the prediction of absorption and electronic CD spectra of medium-sized molecules (≈30 nonhydrogen atoms).49, 52, 60 In fact, the last decade has seen an increasing number of publications concerning TDDFT CD calculations, only the most recent of which (not directly related to the solid state) are given in the bibliography.123, 128–152 Apart from the limitation put by the molecular size, the scope of TDDFT calculations is practically unlimited, still some pitfalls are known. Because of the nature of approach employed, TDDFT is intrinsically more accurate in the prediction of low-lying excited states.153 Moreover, deficiencies are observed in the description of poorly localized states such as charge-transfer, diffuse, and Rydberg states due to self-interaction errors and incorrect asymptotic behavior of exchange-correlation functionals (like B3LYP)154 employing adiabatic local density approximation. Daily efforts are put by researchers in developing new DFT functionals able to overcome such problems.155–157

In light of the positive features of TDDFT noticed above, it is not surprising that it is the method of choice also in the context of simulation of solid-state CD spectra of organic compounds. In particular, in the last 3 years, our groups have developed a so-called solid-state CD/TDDFT approach for the AC determination of natural products17, 18, 73, 84, 158–165 forming single crystals suitable for X-ray analysis, but devoid of heavy elements, which would be necessary for an unambiguous AC assignment based on X-ray resonant scattering. The method consists in the following steps: (1) isolation and structural identification of the natural compound; (2) growth of suitable crystals; (3) solid-state structure determination by X-ray single-crystal diffraction; (4) generation of an input geometry for CD calculations with initial arbitrary AC, after optimizing hydrogen atoms of the X-ray structure with DFT method (B3LYP/6-31G(d)166 level); (5) excited state calculations on the latter geometry with TDDFT, employing when necessary different functionals (e.g., B3LYP, PBE0,167 BH&HLYP,168, 169 BP86169, 170) and basis sets (TZVP,171 aug-TZVP,101 ADZP,172 aug-cc-pVDZ,173 etc.); (6) generation of a CD spectrum as sum of Gaussians by applying a Gaussian band shape of appropriate width to each calculated rotational strength; (7) measurement of CD spectrum of a microcrystalline solid sample as KCl pellet, and, for comparison, of CD spectra in solution of one or more solvents; (8) comparison between experimental solid-state CD spectrum and TDDFT-calculated one using the X-ray geometry. As noted in the Introduction (section “Prediction of Solid-State CD Spectra: Advantages and Limitations”), such a procedure is computationally very fast and free from the errors related to the conformational analysis. Moreover, since the experimental and the calculated CD refer to the same geometry, a good agreement is expected (and, as we shall see below, usually obtained) whenever a proper functional/basis set combination is chosen. As much time is saved in the generation of the input geometry, many combinations of functionals and basis sets may be tried in the TDDFT step. However, in almost all cases considered, we found that hybrid functionals B3LYP and BH&HLYP, and triple-ζ split-valence basis set TZVP (devoid of diffuse functions), led to a satisfying agreement. Usually, the most evident difference between B3LYP and BH&HLYP-calculated spectra is a systematic wavelength shift, due to the different fraction of “exact” HF exchange in the two functionals (B3LYP, 20%; BH&HLYP, 50%); the direction of such a shift depends on the nature of transitions involved. The main problem associated with the solid-state CD/TDDFT approach consists in the possible presence, in the solid-state CD spectra, of bands arising from intermolecular interactions in the crystals.63, 64 Such effects intrinsic to the solid state may be recognized by careful comparison between all available CD spectra (measured in various conditions and calculated) and thus taken into account. Thus far, we have applied the solid-state CD/TDDFT approach to thirteen different natural compounds, secondary metabolites of fungi, often endowed with biological activities such as antibiotic, antifungal, anti-inflammatory; their structures are reported in Scheme 6.17, 18, 73, 84, 158–165 For all compounds, we obtained a good agreement between experimental and calculated solid-state CD, which allowed us to assign the AC with great confidence, and, in almost all cases, this was the first reported AC assignment of the considered compound. As can be appreciated from Scheme 6, the compounds featured a great structural variability in terms of chromophores, presence of rings, flexibility, number and spatial relationship of chirality centers. This observation demonstrates the wide applicability of the method, still, further examples need to be studied to fully assess its scope. A few relevant cases among those reported are discussed in detail in the following.

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Scheme 6. Natural products whose AC has been assigned by means of the solid-state CD/TDDFT approach.

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Blennolide A (27) belongs to the family of ergochromes, a group of active mycotoxins. In particular, secalonic acid B, which represents the 2,2′-homodimer of 27, is a strong fungicide and algaecide. In the investigation of metabolites of fungus Blennoria sp., isolated from Carpobrotus edulis, the AC of 27 was established by application of the solid-state CD/TDDFT approach. The relative rigidity of the compound was witnessed by the great similarity between CD spectra recorded in CH2Cl2 solution and as KCl pellet (Fig. 4). This latter one could be well reproduced by TDB3LYP/TZVP calculations using as input structure the geometry with (5S,6S,10aR) configuration obtained by X-ray analysis of crystals.17 Other functionals tested (BH&HLYP, B2PLYP174) gave a CD spectrum coincident in shape and sign with the B3LYP-calculated one, apart from a 40 nm red-shift observed with BH&HLYP.

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Figure 4. Solution and solid-state CD spectra of blennolide A (5S,6S,10aR)-(27), and TDB3LYP/TZVP-calculated CD on the X-ray geometry. Vertical bars are dipole-length (DL) computed rotational strengths Rs; spectrum generated as sum of Gaussians with σ = 5800 cm−1 width, no wavelength correction (the same applies to all Figures 5–7 below).

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Macropodumine B (28a) is a unique zwitterionic natural compound containing a rare cyclopentadienyl anion and an iminio counter ion, belonging to the family of Daphniphyllum alkaloids, a group of fused-heterocyclic secondary fungal metabolites endowed with significant medicinal properties. Compound 28a had been isolated from D. macropodum, along with nine related metabolites including macropodumine C (28b, Fig. 5), and its solid-state structure determined by X-ray analysis.175 The AC of macropodumines B and C was established by comparison of their CD spectra with TDDFT-calculated ones, employing the solid-state geometry of 28a and DFT-calculated structures of 28b.158 In practice, the two compounds offered us the chance for a direct comparison between the methods relative to solid and solution states. For macropodumine B, the solid-state CD/TDDFT approach led to a calculated CD spectrum (TDB3LYP/TZVP) in very good agreement with the experimental solid-state one (KCl disc, Fig. 5a). Other functional/basis set combinations (using BH&HLYP functional and ADZP basis set, which includes diffuse functions) did not improve the observed agreement. After a moderate computational effort (<4 days calculation time), the AC could thus be established as (2R,5S,6S,18S)-28a. For macropodumine C, a MM-based conformational search followed by DFT geometry optimizations (B3LYP/6-31G(d)) revealed the presence of several minima due to the rotation of [BOND]CH2CH2OH and [BOND]COOCH3 substituents accompanied by fluctuations in the ring system. When used as input structures in TDB3LYP/TZVP calculations, the first 4 low-energy DFT minima (with Boltzmann populations >4% at 300 K) led to quite different CD spectra. Their weighted average was in agreement with the CD of 28b measured in CH3CN solution in the low-energy region, while some discrepancy was obtained at high energies (Fig. 5b). Overall, the AC could be established as (2S,4R,5S,6S,18R)-28b after a considerable computational effort (≈17 days). It is clear that for these two similar compounds the solid-state CD/TDDFT approach led to a safer AC establishment with a drastically smaller computational time (about 1:4.5 ratio).158 This observation cannot be generalized, although it must be observed that macropodumines 28a–b are relatively rigid, and for more flexible compounds, the advantage of employing the solid-state procedure may be greater.

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Figure 5. (a) Solid-state CD spectrum of macropodumine B (2R,5S,6S,18S)-(28a), and TDB3LYP/TZVP-calculated CD on the X-ray geometry. (b) Solution CD spectrum of macropodumine C (2S,4R,5S,6S,18R)-(28b), and Boltzmann-weighted (300 K) TDB3LYP/TZVP-calculated CD on DFT- optimized geometries. Vertical bars represent DL-computed Rs (values for absolute DFT minimum are shown for 28b), σ = 2500 cm−1.

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An example of a quite flexible compound was offered by tetrahydropyrenophorol (23, Scheme 6), a 16-membered dilactone extracted from Phoma sp., isolated from plant Fagonia cretica.73 X-ray analysis revealed a quasi-C2 symmetric solid-state structure with a rectangular shape. Use of solid-state CD/TDDFT approach led to (4S,7R,4′S,7′R)-23 AC assignment after very quick TDDFT calculations, because only the two quasi-degenerate nπ* transitions concur to the observed CD above 185 nm. If one should try to reproduce the solution CD spectra, full many input structures would need to be considered. In fact, a conformational analysis with MMFF and AM1 methods revealed the existence of at least 60 minima within 3 kcal/mol (AM1 energy). The extreme flexibility of compound 23 is demonstrated by the notable detail that the CD spectrum measured as KCl pellet is opposite to those measured in CH3CN and CH3OH solution (Fig. 6). Also interesting is that the sign of calculated nπ* band, for the X-ray geometry, was in agreement with a sector rule proposed by Snatzke for lactones.176 On systematic variation of relevant dihedral angles around the lactone moiety, we could verify and slightly modify the sector rule in the shape of nodal surfaces.73 Such kind of analyses, other examples of which may be found in the already cited literature,130, 135, 152, 162 are helpful in rejuvenating sector and helicity rules.

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Figure 6. Solution and solid-state CD spectra of tetrahydropyrenophorol (4S,7R,4′S,7′R)-(23), and TDB3LYP/TZVP-calculated CD on the X-ray geometry. Vertical bars are DL-computed Rs, σ = 6000 cm−1.

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A further possible situation where solid-state-based approaches may become especially significant concerns cases of compounds equilibrating in solution. For example, papyracillic acid A (24) exists in CDCl3 solution as a mixture of four tautomers (Scheme 7) with relative 4:2:1:1 ratio, relative to ring opening at the C-7 hemiacetal function and equilibration at C-4.84 Interpretation of CD spectra in solution would have required to consider all tautomers, each with its own conformational variability.128 On the contrary, in the solid-state CD/TDDFT scheme, only the single structure obtained by X-ray analysis of crystals needed to be taken into account and permitted assignment of AC as (4S,6S,7R)-24.84

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Scheme 7. Predicted tautomerism for papyracillic acid A (24).

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One of the most surprising and important observations we made in the course of our screening of the solid-state CD/TDDFT approach is that in the very large majority of cases, the presence of intermolecular interactions inside the crystals had negligible or small effects on the observed solid-state CD spectra. In principle, symmetry-allowed intermolecular exciton interactions may occur in chiral crystals, which should generate nonvanishing CD signals intrinsic to the solid state.63, 64 However, the very large majority of compounds depicted in Scheme 6 did not display any notable CD effect assignable to solid-state intermolecular exciton couplings, even in the presence of strong aromatic chromophores and when the intrinsic CD was modest.17, 18, 73, 84, 158–165 This conclusion was supported by the observed consistency between solid-state and solution spectra (taking into account conformational differences), and, above all, by the agreement obtained with calculated spectra. A possible exception is represented by hypothemycin (26), a well-known macrolide endowed with remarkable biological activity, which was extracted from fungus Phoma sp., isolated from Senecio kleinii.161 CD spectra of 26 recorded in solution and solid state were slightly different. However, MM-based conformational analysis, followed by DFT geometry optimizations, revealed a strong preference for a structure similar to the X-ray solid-state one. Interestingly enough, CD spectra calculated with TDDFT using either B3LYP or PBE0 functionals and TZVP basis set on the solid-state geometry were more similar to solution than to solid-state experimental CD (Fig. 7). We also noticed that the more discrepant regions (indicated by arrows in Fig. 7) coincided with ππ* transitions of the aromatic chromophore (a 2-hydroxy-4-methoxybenzoate). Therefore, we concluded that these regions are likely to be affected by intermolecular exciton interactions in the solid state. Even in this case, however, the overall effect on the CD spectra was such limited so not to hamper assignment of AC as (1R,2R,4S,5S,10S).161 A similar conclusion was reached for (1R,5R,6S,7S,10S,11S)-1β,10β-epoxydesacetoxymatricarin (25), a sesquiterpenoid isolated from Carthamus oxycantha, which also showed an extra band in the solid-state CD spectrum found neither in solution nor in the TDDFT-calculated one.159 However, the impact of crystalline intermolecular couplings on solid-state CD/TDDFT method has seemed very modest for all compounds analyzed thus far. A possible explanation lies in the fact that any single molecule in a crystal experiences couplings from dozens of surrounding molecules, and they may tend to cancel each other and sum to a negligible overall effect (see also note added in proof). This observation is again not universal, as exemplified by the situation for the (naphthyl)ethylidene ketal of a carbohydrate (12) discussed in a previous paragraph (section “Exciton Chirality and Related Methods”). A full rationalization of the observed behavior is desirable in light of a better understanding of chirogenesis phenomena occurring in the solid state.

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Figure 7. Solution and solid-state CD spectra of hypothemycin (1R,2R,4S,5S,10S)-(26), and TDB3LYP/TZVP-calculated CD on the X-ray geometry; σ = 3000 cm−1. Arrows indicate solid-state CEs not predicted by calculations.

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Apart from the continuous investigation run by our groups discussed so far, other applications of a procedure similar to the solid-state CD/TDDFT approach can be found in the literature, concerning synthetic compounds. It must be stressed that the latter approach seems especially suitable for natural products for two reasons. First, they frequently have rather complicated structures, containing several chirality centers, which may be difficult to elucidate by NMR; this observation justifies the efforts toward obtaining crystals amenable to X-ray analysis. Second, they are often available in very small amounts, which prevent further derivatization to introduce chromophores suitable for other CD options or chemical fragments with known configuration and/or containing heavy atoms for X-ray analysis. Nonetheless, it is clear that solid-state CD calculation approaches can be profitably employed for synthetic compounds too, as demonstrated by the two following examples. Azumaya and co-workers177 have reported in 2006 on the synthesis of 12 achiral N-aryl aromatic sulphonamides and on the isolation of four of them (31a–d, Scheme 8) in enantiopure crystalline form upon spontaneous resolution. For each compound 31a–d, the two enantiomorphous forms were characterized by solid-state CD spectra as KBr pellets. For 31a–c, in addition, X-ray analysis led to the assignment of the absolute structure. The major chirality element in these compounds is represented by the N[BOND]S chiral axis, around which the two aryl rings are arranged synclinal to each other with a positive or negative Ar[BOND]N[BOND]S[BOND]Ar′ dihedral angle (+syn and –syn conformation, respectively). When the solid-state geometries were employed as input structures for TDB3LYP/6-31G(d) calculations, the trends observed in experimental solid-state CD spectra could be reproduced and the absolute structure found by X-ray confirmed.177

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Scheme 8. Molecules whose absolute structure has been confirmed by TDDFT calculations on solid-state X-ray geometry. Curved arrow denotes chirality axis.

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Within their systematic investigation of cis-1,2-dihydroxy-3,5-cyclohexadienes (32a–j) obtained by enzymatic oxidation of p-disubstituted benzenes,178 Gawronski and coworkers studied, in particular, the 3-cyano-6-fluoro derivative 32j whose solid-state structure was available.179 The ACs of cis-dihydrodiols 32a–j had been established by chemical correlations or other methods, but an independent assignment was sought in CD spectra interpreted by means of TDDFT calculations. Solution CD spectra of compounds 32a–i were consistent in three different solvents (water, acetonitrile, cyclohexane). CD calculations were run on four conformers, found by DFT geometry optimizations at B3LYP/6-311++G(d,p) level. One couple of conformers had P diene helicity and another couple M helicity, and the conformation of OH groups was found dictated by intramolecular O[BOND]H···O and O[BOND]H···π hydrogen bonds (Fig. 8, top). The large basis set is justified by the fact that relative populations had to be estimated with great accuracy, because conformers with opposite helicity led to oppositely signed ππ* CEs, and thus the Boltzmann-weighted CD depended strongly on the conformer population. CD calculations with TDDFT, using mPW1PW91 functional180 and the very large 6-311++G(2d,2p) basis set, led to expected confirmation of AC assignment for all compounds 32a–i, based on the good agreement with solution CD spectra, especially in cyclohexane.178 In the case of 32j, however, the diagnostic ππ* band at 284 nm was almost CD silent in cyclohexane and opposite to the expected one (based on the known AC) in the other two solvents (Fig. 8). Then, a solid-state approach was employed, by measuring the solid-state CD spectrum as KBr pellet and running CD TDDFT calculations on the X-ray geometry. In this way, the AC (1R,2R)-32j was determined and reconciled with the chemical correlation. The authors observe that such a “solid-state confrontation method […] appears to be generally applicable, [however] its limitation is a possible contribution of the CD signals intrinsic to the solid state”.178 We would like to stress that in their case too the computational time-saving with respect to the solution method must have been considerable due to the large basis sets employed, partially compensated by the small molecular size.

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Figure 8. Top: Diastereomeric M- and P-helicity conformations of diols 32. Bottom: Solution CD spectra of diol (1R,2R)-(32j), Boltzmann-weighted (300 K) TD-mPW1PW91/6-311++G(2d,2p)-calculated CD on DFT-optimized geometries, and CEs measured on a solid-state sample (KBr pellet). Adapted from Ref.178, Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

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Conformational Studies by TDDFT and Ab Initio Calculations

As already mentioned, solid-state CD spectra lend themselves as a source of comprehensive information of the molecular structure in the solid state beyond the assignment of absolute configuration. Normally, however, the knowledge of solid-state conformation adopted in crystalline samples is gained through X-ray analysis. Measurement of solid-state CD spectra and their interpretation through semi-empirical or nonempirical means may be then used to correlate the known conformation with the observed spectrum and thus to validate the interpretative approach. Two examples from the literature will clarify what just stated.

Veciana and coworkers181 have synthesized and crystallized a chiral phenyl α-nitronyl nitroxide radical (33, Scheme 9) and characterized its solid-state structure by X-ray analysis and CD. This latter was interpreted by means of CIS/3-21G(d) calculations. The CIS method consists in the orthogonalization of single-excited states obtained by standard SCF procedure.16 The CD spectrum of 33 shows two bands at 470 and 340 nm, assigned to nπ* and ππ* transitions of the nitronyl nitroxide moiety (ONCNO), respectively. CIS calculations on 33 and on appropriately modified geometries demonstrated that the sign of the two bands is dictated by two distinct conformational parameters, that is, the helicity of the 5-membered ring and the twist angle between the planes of phenyl and ONCNO moiety.181 In a second article, such a piece of information was employed to interpret solid-state CD spectra of a series of crystalline α-nitronyl nitroxide radicals.182

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Scheme 9. Molecules whose solid-state conformation was investigated by CIS and TDDFT calculations. Curved arrows denote chirality axes.

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Recently, some of us have reported the CD spectra in solution and solid state of a series of diglycosyl disulfides and diselenides.101 Intrinsically chiral disulfides have diagnostic CD spectra whose sign in the nσ* region between 220 and 300 is known to correlate with the disulfide helicity (C[BOND]S[BOND]S[BOND]C dihedral angle φ) according to a quadrant rule.101 The applicability of the same rule to diselenides was investigated by means of TDDFT calculations, employing ad hoc models consisting in dimethyl diselenide (CH3[BOND]Se[BOND]Se[BOND]CH3) and compound 34b (Scheme 9). This represented a truncated analog of peracetylated diglucosyl diselenide (Ac4GlcSeSeGlcAc4, 34a) whose X-ray structure was available. This simplification permitted saving of computational time without affecting the calculated red-shifted transitions of the diselenide chromophore. TDB3LYP/TZVP calculations on CH3[BOND]Se[BOND]Se[BOND]CH3, with variable C[BOND]Se[BOND]Se[BOND]C dihedral angles, confirmed that the sign of the lowest energy nσ* transition of the diselenide chromophore is related to the C[BOND]Se[BOND]Se[BOND]C dihedral angle φ following a quadrant-like dependence. That is, the first calculated CE is positive for 0 < φ < 90° and negative for 90° < φ < 180°; obviously, the sign reverts for the opposite helicity (negative values of φ). TDB3LYP/TZVP calculation on a geometry of 34b obtained from the X-ray structure of 34a reproduced well the long-wavelength region of the solid-state CD spectrum of 34a. In particular, the negative CE observed at 315 nm was in keeping with the value of φ = –82° found in the solid-state structure of 34a.

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED

Nowadays, direct calculation of chiroptical spectra of moderately complex molecules is possible with high-level calculation approaches combining robustness and practicability. To demonstrate how fast technological and computational development proceeds, it is sufficient to notice that in an authoritative review about theoretical approaches to ECD published in 2000, the authors observed that TDDFT “method has not been used for optical activity calculations”.183 Less than 10 years later, TDDFT has become the most popular tool in the field. Although ab initio or TDDFT prediction of the CD spectrum of a biopolymer is still not routine, excited-state calculations of small and medium-sized organic molecules are perfectly treatable even on a common desktop computer.

What still poses a limit to CD (and other properties) calculations is conformational flexibility. No matter how fast and reliable the conformational sampling may be, taking into account dozens of conformations populated at the operating temperature, for a moderately flexible organic compound, will always represent a formidable task for any high-level calculation. In this respect, the possibilities offered by solid-state methods are certainly worth attention, not only for the characterization of solid-state-specific optical activity but also for the stereochemical investigation of synthetic and natural products. Quantum-mechanics calculations of solid-state CD spectra appear a very efficient tool for the absolute configurational assignment of organic compounds, with limitations discussed above to be kept in mind. At the present time, the method still looks not fully exploited in the literature, but further applications are expected in the future. In fact, it is common to find situations where chiral compounds with complex structure have been characterized by X-ray crystal analysis, but their configuration has been assigned by TDDFT calculations on DFT-optimized structures with the aim to reproduce solution CD spectra, requiring consideration of several minima and/or inclusion of time-consuming solvent models.129, 139

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED

We gratefully acknowledge all our coworkers whose names are given in the references.

NOTE ADDED IN PROOF

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED

Bringmann, Kuroda and co-workers have recently reported184 on CNDO/S and ZINDO/S calculations on molecular clusters of dioncophylline A as found in crystals, to predict the contribution of neighboring effects (intermolecular couplings) to the solid-state CD spectrum. They concluded that these effects, although present, are negligible, because of mutual cancellation of various coupling terms. Considering the single, isolated molecule as input for TDDFT or DFT/MRCI calculations is thus sufficient to reproduce the solid-state CD of dioncophylline A.

LITERATURE CITED

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXAMPLES OF APPLICATION
  5. CONCLUSIONS
  6. Acknowledgements
  7. NOTE ADDED IN PROOF
  8. LITERATURE CITED
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