On the equivalence of conformational and enantiomeric changes of atomic configuration for vibrational circular dichroism signs

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an "achiral" alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.     

Effects of complex formation on vibrational circular dichroism spectra

The determination of absolute configurations of chiral compounds using VCD is performed by comparing measured vibrational circular dichroism (VCD) spectra with calculated spectra. The process is based on two facts: the two enantiomers have rotational strengths of opposite sign, and the absolute configuration of the molecule used in the calculation is known. However, calculations on isolated molecules very often predict VCD intensities of very different magnitude or even different signs compared to the spectra measured in solution. Therefore, we have carefully analyzed what type of changes are induced by complexation of a solvent molecule to a solute. In the theoretical example of benzoyl-benzoic acid (in a particular chiral conformation) hydrogen bonded to the achiral NH3, we distinguish six cases, ranging from no or very small changes in the rotational strengths of solute modes (case A) to changes of sign of rotational strengths (case B), changes in magnitude (case C), nonzero rotational strengths for modes of the achiral solvent ("transfer of chirality", case D), large frequency shifts accompanied by giant enhancements of the IR and VCD intensities of modes involved in hydrogen bonding (case E), and emergence of new peaks (case F). In this work, all of these situations will be discussed and their origin will be elucidated. On the basis of our analysis, we advocate that codes for VCD rotational strength calculation should output for each mode i the angle xi(i) between the electric and magnetic transition dipole moments because only "robust modes" with xi far from 90 degrees should be used for the determination of the absolute configuration.     

Calculations of overtone NIR and NIR-VCD spectra in the local mode approximation: Camphor and Camphorquinone

We present a method to calculate near-infrared (NIR) and NIR-vibrational circular dichroism (NIR-VCD) spectra up to the second CH-stretching overtone region in the local mode approximation. Atomic polar tensors and atomic axial tensors are first evaluated by DFT methodology for all CH stretching coordinates with systematic positive and negative displacements off-equilibrium and therefrom anharmonic dipole moment functions are constructed by polynomial interpolations. No adjustable parameters are employed up to this point. Rotational and dipole strengths are finally calculated by evaluating transition moments of Morse-type wave-functions. The method is applied to the case of Camphor and Camphorquinone, for which relevant differences in the vibrational circular dichroism (VCD) data are observed, which are predicted by our approach. Further steps are still to be made for a more complete treatment: the ab initio evaluation of mechanical anharmonicity and the introduction of mechanical and electrical coupling between local modes.     

Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.Dedicated to Prof. Jan Linderberg     

A DFT conformational analysis and VCD study on methyl tetrahydrofuran-2-carboxylate

DFT calculations were performed on (S)-methyl tetrahydrofuran-2-carboxylate to facilitate the interpretation of IR and VCD spectra. The potential energy surface could not be described unambiguously using the 6-31G* basis set in combination with different density functionals including B1LYP, B3LYP, B3P86, B3PW91, B98, BHandH, BHandHLYP, MPW1PW91 and PBE1PBE. In contrast, a uniform conformational picture could be found using the cc-pVTZ basis set. Using this large basis set and the collection of nine functionals from above, the dipole and rotational strengths were calculated, and compared to experimental values which were extracted from the experimental IR and VCD spectra for (+)-(S)-methyl tetrahydrofuran-2-carboxylate. A detailed analysis on the agreement between experiment and simulated spectra was performed by assigning the experimental bands based on the harmonic fundamentals obtained for all functionals except BHandH, which performs badly over the whole line. Assessing the dipole strengths, all tested functionals perform equally well. For the rotational strengths, differences can be observed: B3LYP, B1LYP and B98 give the highest correlation with experiment, while PBE1PBE gives the lowest correlation. Comparable conclusions are obtained using a neighborhood similarity measure.     

Transfer of molecular property tensors in cartesian coordinates: A new algorithm for simulation of vibrational spectra

A direct transfer of Cartesian molecular force fields (FF) and electric property tensors is tested on model systems and compared to transfer in internal coordinates with an aim to improve simulation of vibrational spectra for larger molecules. This Cartesian transformation can be implemented easily and offers greater flexibility in practical computations. It can be also applied for transfer of anharmonic derivatives. The results for model calculations of the force field and vibrational frequencies for N-methylacetamide show that our method removes errors associated with numerical artifacts caused by nonlinearity of the otherwise required Cartesian to internal coordinate transformation. For determination of IR absorption and vibrational circular dichroism intensities, atomic polar and axial tensors were also transferred in the Cartesian representation. For the latter, which are dependent upon the magnetic dipole operator, a distributed origin gauge is used to avoid an origin dependence. Comparison of the results of transferring ab initio FF and intensity parameters from an amide dimer fragment onto a tripeptide with those from a conventionally determined tripeptide FF document some limitations of the transfer method and its possible applications in the vibrational spectroscopy. Finally, application to determination of the FF and spectra for helical heptapeptide are presented and compared to experimental results. © 1997 by John Wiley & Sons, Inc.     

Time-dependent density functional theory for calculating origin-independent optical rotation and rotatory strength tensors

An approach to calculate origin-independent electronic chiroptical property tensors using time-dependent density functional theory (TDDFT) and gauge-including atomic orbital (GIAO) basis sets is evaluated. Computations of origin-dependent optical rotation tensors and of rotatory strengths needed to simulate circular dichroism spectra are presented. The optical rotation tensor computations employ solutions of coupled perturbed Kohn-Sham equations for a dynamic electric field and a static magnetic field. Because the magnetic field is time independent, the GIAO treatment is somewhat simplified compared to a previously reported method, at some added computational cost if hybrid functionals are employed. GIAO rotatory strengths are also calculated, using transition density matrices from a standard TDDFT excitation energy module. A new implementation in the NWChem quantum chemistry package is employed for representative computations of origin-invariant chiroptical response tensors for methyloxirane, norbornenone, and the ketosteroid androstadienone. For the steroid molecule the vibrational structure of the CD spectrum is modeled explicitly by using calculated Franck-Condon factors. The agreement with experiment is favorable.     

Vibrational absorption and circular dichroism studies of trans-(3S,4S)-d6-cyclopentene in the gas phase

Vibrational absorption (IR) and circular dichroism (VCD) measurements of trans-(3S,4S)-d6-cyclopentene in the gas phase were performed in the C-H, C-D, and mid-infrared regions. In this study, we report the first VCD spectra recorded at high spectral resolution (up to 0.5 cm(-1)) with a very good signal-to-noise ratio (differential absorbance lower than 5 x 10(-6)). The quality of the experimental spectra allows us the observation of the vibration-rotation structure of the bands in both absorption and VCD spectra. Experimental spectra have been compared with the density functional theory (DFT) absorption and VCD spectra, calculated using B3LYP functional and cc-pVTZ basis set for the axial, equatorial, and planar conformers. Lorentzian and PQR band profiles have been used to convert the calculated dipolar and rotational strengths. In the mid-infrared (<2000 cm(-1)) region, predicted (population-weighted) spectra were in excellent agreement with experiment, allowing the determination of the absolute configuration of this molecule. Above 2000 cm(-1), a reasonable agreement was obtained even if anharmonicity was not considered and if Fermi resonance occurs in the C-D stretching region. Finally, a more precise analysis of the absorption spectrum has been achieved by taking into account anharmonicity of the C-H stretching and its coupling with the ring-puckering motion.     

Vibrational circular dichroism and absolute configuration of chiral sulfoxides: tert-butyl methyl sulfoxide

Mid-infrared vibrational unpolarised absorption and vibrational circular dichroism (VCD) spectra of CCl4 solutions of tert-butyl methyl sulfoxide (1) are reported. The spectra are compared to ab initio density functional theory (DFT) calculations carried out using two functionals, B3PW91 and B3LYP, and two basis sets, 6-31G* and TZ2P. The VCD spectra are calculated using Gauge-invariant atomic orbitals (GIAOs). The analysis of the VCD spectrum confirms the R(-)/S(+) absolute configuration of 1. The advantages and disadvantages of VCD spectroscopy in determining the absolute configurations of chiral sulfoxides are discussed.     

Density functional theory study on vibrational circular dichroism as a tool for analysis of intermolecular systems: (1:1) cysteine-water complex conformations

This paper presents a discussion of the interaction energies for selected conformers of chiral l-cysteine and their (1:1) complexes with water at the B3LYP/aug-cc-pVDZ level. From among more than forty calculated 1:1 complexes three groups of complexes were singled out and examined by the B3LYP/aug-cc-pVDZ calculated vibrational circular dichroism (VCD) spectra. On the basis of analysis of the nu(OmicronEta) and nu(NuEta) and beta(OH2) and beta(NH2) ranges, the VCD spectra were found to be sensitive to conformational changes and water arrangement in cysteine complexes, and to be especially useful for discriminating between different chiral forms of intermolecular hydrogen-bonding complexes. In particular, we show that the VCD modes of an achiral water molecule after complex formation acquire significant rotational strengths whose signs change in line with the geometry of the complex. Moreover, for some water arrangements the VCD spectra can be sensitive to water-wagging conformers and, in temperatures low enough, the intensive nu(OmicronEtaWfree) and beta(H2O) VCD bands may be sufficiently separated to be splitted into pair of oppositely directed bands.     

固体酪氨酸^1^3C核磁屏蔽张量的实验与理论研究

应用最近发展的三回波二维慢速魔角旋转(Triple-Echo 2D MAT)实验方法测得了酪氨酸中各不等价碳的化学位移各向异性(CSA)张量主值。由从头计算获得的结果与实验值符合较好, 说明对于具有复杂结构的多原子体系, 对杂原子使用较小的基函数, 而对所关心的碳原子使用较大的基函数以提高计算精度, 这样可以达到既节省计算机空间与计算时间而不影响计算精度的目的。     

Even-tempered Slater-type orbitals revisited: from hydrogen to krypton

Even-tempered Slater-type orbital basis sets were developed in 1973, based on total atomic energy optimization. Here, we revisit ET STOs and propose new sets based on past experience and recent computational studies. From preliminary atomic and molecular tests, these sets are shown to be very well balanced and to perform, at lower cost, almost as well as a very large (close to complete) basis set.     

Determination of absolute configurations from vibrational circular dichroism: (+)-2-methylthiirane-3,3-d(2)

Experimental vibrational circular dichroism (VCD) spectra for the dextrorotatory enantiomer and theoretical VCD spectra obtained with localized molecular orbital theory using 6-31G* basis set for the (R) configuration of 2-methylthiirane-3,3-d(2) in the 700-1500 cm(-1) region are presented. The observed and predicted VCD signs are in very good agreement suggesting that the dextrorotatory enantiomer has the (R) configuration. This conclusion is also supported by the optical rotational data.     

Differentiation of beta-sheet-forming structures: ab initio-based simulations of IR absorption and vibrational CD for model peptide and protein beta-sheets.

Ab initio quantum mechanical computations of force fields (FF) and atomic polar and axial tensors (APT and AAT) were carried out for triamide strands Ac-A-A-NH-CH(3) clustered into single-, double-, and triple-strand beta-sheet-like conformations. Models with phi, psi, and omega angles constrained to values appropriate for planar antiparallel and parallel as well as coiled antiparallel (two-stranded) and twisted antiparallel and parallel sheets were computed. The FF, APT, and AAT values were transferred to corresponding larger oligopeptide beta-sheet structures of up to five strands of eight residues each, and their respective IR and vibrational circular dichroism (VCD) spectra were simulated. The antiparallel planar models in a multiple-stranded assembly give a unique IR amide I spectrum with a high-intensity, low-frequency component, but they have very weak negative amide I VCD, both reflecting experimental patterns seen in aggregated structures. Parallel and twisted beta-sheet structures do not develop a highly split amide I, their IR spectra all being similar. A twist in the antiparallel beta-sheet structure leads to a significant increase in VCD intensity, while the parallel structure was not as dramatically affected by the twist. The overall predicted VCD intensity is quite weak but predominantly negative (amide I) for all conformations. This intrinsically weak VCD can explain the high variation seen experimentally in beta-forming peptides and proteins. An even larger variation was predicted in the amide II VCD, which had added complications due to non-hydrogen-bonded residues on the edges of the model sheets.     

Calculation of Verdet constants with time-dependent density functional theory: implementation and results for small molecules

We report the implementation of a method by which to calculate Verdet constants for molecules. The method is based on gauge-including atomic orbitals (GIAOs) and density functional theory. Calculations based on this method afford magneto-optical rotations of the right magnitude for the molecules H2, N2, CO, HF, CH4, C2H2, H2O, and CS2. The results are in satisfactory agreement with experiment. We investigate the dependency of the results on the gauge origin if GIAOs are not chosen, the convergence of the results with the size of the basis set for AOs and GIAOs, and for H2O and CS2 a comparison of gas-phase and liquid phase values. For the small molecules studied here, large polarized basis sets with diffuse functions are required to obtain well converged results. The use of an asymptotically correct Kohn-Sham potential is advantageous.     

NMR spectra of free-base porphine, porphyrazine, phthalocyanine and naphthalocyanine as well as their metal complexes: density functional calculations

Nuclear magnetic shielding tensors of porphine have been calculated at density functional B3LYP and PBE level using the gauge independent atomic orbital (GIAO) method. The geometries used were optimized using the 6-31G(d) basis set and the NMR calculations were performed using 6-31G(d) and 6-311G(d,p) basis sets, respectively. The calculated NMR shielding tensors and chemical shifts of porphine are compared with previous calculations as well as experimental data and satisfying results are obtained. Further NMR calculations are extended to metal-free and metallo-porphyrazine, -phthalocyanine, and -naphthalocyanine for the first time and the results are compared with experimental data available. The chemical shifts of the atoms in these compounds are assigned according to the experimental data available.     

Analysis of vibrational circular dichroism spectra of (s)-(+)-2-butanol by rotational strengths expressed in local symmetry coordinates

The vibrational circular dichroism (VCD) spectra of (S)-(+)-2-butanol have been observed in dilute CS(2) solutions. Two strong VCD bands are assigned mainly to the OH bending modes with the aid of quantum chemical calculations. The calculated VCD spectra corresponding to these bands are shown to depend on the conformation of the OH group. To understand this feature, we have calculated the contribution of each local vibrational mode to the rotational strengths and concluded that the coupling of the group vibrations between the in-plane and out-of-plane modes about the locally assumed symmetry planes play a significant role in VCD. This finding has provided a new scope of VCD in relation to molecular vibrations.     

Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing CC analytic second-derivative code is described, focusing on the required modifications concerning integral evaluation and treatment of the unperturbed and perturbed two-particle density matrices. An extensive set of test calculations for LiH and BH (up to the full configuration-interaction limit), for a series of simple hydrides (HF, H(2)O, NH(3), and CH(4)) as well as the more challenging molecules CO, N(2), and O(3) [employing the CC singles and doubles (CCSD) and the CCSD approximation augmented by a perturbative treatment of triple excitations] demonstrates the importance of electron correlation for high-accuracy predictions of magnetizabilities and rotational g tensors.     

Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods

In this brief review, an overview about recent efforts to simulate the spectroscopic signatures of chiral molecules is given with focus on real time propagation approaches to solve the time-dependent Schrödinger equation. In particular the simulation of electric circular dichroism spectra and vibrational Raman optical activity is discussed. In comparison to linear absorption spectra, where only the response of the electric dipole moment is necessary, the response of the magnetic dipole moment and electric quadrupole moment is more intricate. Issues such as gauge origin dependence, basis set dependence, non-local potentials and the dipole approximation are addressed.