Petr Bour

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.

Simulations of oligopeptide vibrational CD: effects of isotopic labeling.

Simulated ir absorption and vibrational CD (VCD) spectra of four alanine‐based octapeptides, each having its main chain constrained to a different secondary structure conformation, were analyzed and compared with experimental results for several different peptides. The octapeptide simulations were based on transfer of property tensors from a series of ab initio calculations for a short L‐alanine based segment containing 3 peptide bonds with relative ϕ, ψ angles fixed to those appropriate for α‐helix, 310‐helix, ProII‐like helix, and β‐sheet‐like strand. The tripeptide force field (FF) and atomic polar tensors were obtained with density functional theory techniques at the BPW91/6‐31G** level and the atomic axial tensor at the mixed BPW91/6‐31G**/HF/6‐31G level. Allowing for frequency correction due to the FF limitations, the octapeptide results obtained are qualitatively consistent with experimental observations for ir and VCD spectra of polypeptides and oligopeptides in established conformations. In all cases, the correct VCD sign patterns for the amide I and II bands were predicted, but the intensities did have some variation from the experimental patterns. Predicted VCD changes upon deuteration of either the peptide or side‐chains as well as for 13C isotopic labeling of the amide CO at specific sites in the peptide chain were computed for analysis of experimental observations. A combination of theoretical modeling with experimental data for labeled compounds leads both to enhanced resolution of component transitions and added conformational applicability of the VCD spectra.

Interpretation of Raman and Raman Optical Activity Spectra of a Flexible Sugar Derivative, the Gluconic Acid Anion

Raman scattering and its polarized extension, Raman optical activity (ROA), are commonly used for monitoring of molecular conformational equilibria in solutions. This is complicated for saccharides due to extensive motions of the hydroxyl groups and other molecular parts. Standard interpretation procedures involving ab initio spectral simulations for a limited set of conformers are not adequate. In this study, a more general approach is proposed for the gluconic acid anion taken as a model compound, where quantum simulations of the spectra are directly coupled with molecular dynamics (MD) techniques. Such a multiscale approach reveals how the structural information is encoded in the broadened spectral lines. The spectra were simulated for solvent-solute clusters generated by MD. Conformational averaging was enabled by a limited library of conformers for which the spectral parameters could be calculated ab initio and moved on the MD geometries by Cartesian coordinate tensor transfer techniques. The B3LYP/CPCM/6-31+G** approximation was used as a default for computation of the source force fields and polarizability derivatives. The spectra thus obtained relatively faithfully reproduced most of the experimental features. The Amber and polarizable Amoeba MD force fields produced similar results; application of the latter, however, was limited by the long time necessary to achieve a converged conformational equilibrium. Both MD simulation and spectral averaging suggest that the hydroxyl groups as well as the backbone C-C bonds rotate relatively freely, with some restrictions in the vicinity of the carboxyl group. In spite of the averaging, spectral response of characteristic vibrational normal mode families, such as CH and OH bending, can clearly be identified in the spectra. The simulations thus confirm the experimental fact that flexible saccharides exhibit significant vibrational activity that reveals precious information about molecular structure and dynamics encoded in the Raman and ROA spectral shapes.

Vibrational Raman optical activity of 1-phenylethanol and 1-phenylethylamine: revisiting old friends.

The samples used for the first observations of vibrational Raman optical activity (ROA) in 1972, namely both enantiomers of 1-phenylethanol and 1-phenylethylamine, have been revisited using a modern commercial ROA instrument together with state-of-the-art ab initio calculations. The simulated ROA spectra reveal for the first time the vibrational origins of the first reported ROA signals, which comprised similar couplets in the alcohol and amine in the spectral range approximately 280-400 cm(-1). The results demonstrate how easy and routine ROA measurements have become, and how current ab initio quantum-chemical calculations are capable of simulating experimental ROA spectra quite closely provided sufficient averaging over accessible conformations is included. Assignment of absolute configuration is, inter alia, completely secure from results of this quality. Anharmonic corrections provided small improvements in the simulated Raman and ROA spectra. The importance of conformational averaging emphasized by this and previous related work provides the underlying theoretical background to ROA studies of dynamic aspects of chiral molecular and biomolecular structure and behavior.

On the influence of the water electrostatic field on the amide group vibrational frequencies.

For clusters of N-methylacetamide and water molecules the performance of the fixed-charged approximation was tested against continuum and explicit ab initio models. The dispersion of the vibrational frequencies when constant electrostatic potential was maintained at the solute atoms was compared to the distribution caused by geometry fluctuations.

Theoretical Modeling of Peptide α-Helical Circular Dichroism in Aqueous Solution

Reliable modeling of protein and peptide circular dichroism (CD) spectra in the far UV presents a challenge for current theoretical approaches. In this study, the time-dependent density functional theory (TDDFT), configuration interaction with single excitation (CIS), and transition dipole coupling (TDC) were used to assess the most important factors contributing to the CD spectra of the α-helical secondary structure. The dependence on the peptide chain length and also the role of the flexibility and solvent environment were investigated with a model oligopeptide Ac-(Ala)(N)-NH-Me, (N = 1, ..., 18). Both the TDDFT and TDC-like methods suggest that the CD curve typical for the α-helix arises gradually, but its basic characteristic is discernible already for peptides with 4-5 amino acid residues. The calculated dependence was in a qualitative agreement with experimental spectra of short α-helices stabilized by the histidine-metal binding. The TDDFT computations of the CD were found to be unusually sensitive to the basis set and solvent model. Explicit hydration and temperature fluctuations of the peptide geometry, simulated with the aid of molecular dynamics (MD), significantly influenced the CD and absorption spectral shapes. An extensive averaging over MD configurations is thus required to obtain a converged spectral profile in cluster simulations. On the other hand, both the TDDFT and TDC models indicate only a minor influence of the alanine side chains. The CIS and TDC calculations also point toward a relatively small effect of the helix-helix interaction on the CD spectral profiles. For a model system of two helices, the CIS method predicted larger changes in the spectra than TDC. This suggests other than interactions between peptide chains, such as mutual polarization, can have a minor, but measurable, effect on the CD spectrum.

Circular dichroism enhancement in large DNA aggregates simulated by a generalized oscillator model.

An increased circular dichroism (CD) signal of large molecular aggregates formed upon DNA condensation was observed a long time ago, and is often referred to as ψ‐CD. The effort to understand this phenomenon is further motivated by the latest DNA packing studies and advances in macromolecular chemistry. In the present work, the transition dipole coupling model describing interactions of molecules with light has been extended to handle systems of arbitrary size. The analytical formulae obtained retain the simplicity and computational speed of the standard approach. The origin of the ψ‐effect was investigated on several model systems. The results suggest that the CD enhancement is primarily caused by delocalized phonon‐like excitations in nucleic acid strands. The size of the system exhibiting the effect thus does not need to be comparable with or greater than the wavelength of the absorbed light. Small structural irregularities still allow for the enhancement while a larger disorder breaks it. The modeling is consistent with previous experimental electronic and vibrational CD studies, and makes it possible to correlate the enhancement with the geometry of the nucleic acid systems.

Ab initio modeling of the electronic circular dichroism induced in porphyrin chromophores.

The optical activity in porphyrins can easily be induced by a chiral environment, but it is difficult to determine the underlying mechanisms purely on an experimental basis. Therefore, in this study, magnitudes of the perturbational, dipolar, and direct covalent contributions to the electronic circular dichroism (CD) are evaluated with the aid of quantum chemical computations. Electronic properties of model porphyrin chromophores are analyzed. Time-dependent density functional theory (TD DFT), particularly with the hybrid B3LYP functional, appeared suitable for estimation of the electronic excitation energies and spectral intensities. The transition dipole coupling (TDC) between chirally stacked porphyrins was determined as the most important mechanism contributing to their optical activity. This is in agreement with previous experimental observations, where chiral matrices often induce the stacking and large CD signals. About a 10 times smaller signal could be achieved by a chiral orientation of the phenyl or similar residues covalently attached to the porphyrin core. Also, this prediction is in agreement with known experiments. Perturbation models realized by a chirally arranged porphyrin and a point charge, or by a porphyrin and the methane molecule, provided the smallest CD signals. The electrically neutral methane induced similar CD magnitudes as those of the charge, but spectral shapes were different. For a complex of porphyrin and the alanine cation, a significant influence of the solvent on the resultant CD spectral shape was observed, while for the charge and methane perturbations, a negligible solvent effect was found. Detailed dependence of the induced optical activity on variations of geometrical parameters is discussed. The simulations of the induced porphyrin activity can thus bring important information about the structure and intermolecular interactions in chiral complexes.

Molecular dynamics with restrictions derived from optical spectra

The information about molecular structure coded in the optical spectra must often be deciphered by complicated computational procedures. A combination of spectral modeling with the molecular dynamic simulations makes the process simpler, by implicit accounting for the inhomogeneous band broadening and Boltzmann averaging of many conformations. Ideally, geometries of studied systems can be deduced by a direct confrontation of such modeling with the experiment. In this work, the comparison is enhanced by restrictions to molecular dynamics propagations based on the Raman and Raman optical activity spectra. The methodology is introduced and tested on model systems comprising idealized H2O2, H2O3 molecules, and the alanine zwitterion. An additional gradient term based on the spectral overlap smoothed by Fourier transformation is constructed and added to the molecular energy during the molecular dynamics run. For systems with one prevalent conformation the method did allow to enrich the Boltzmann ensemble by a spectroscopically favored structure. For systems with multiconformational equilibria families preferential conformations can be selected. An alternative algorithm based on the comparison of the averaged spectra with the reference enabling iterative updates of the conformer probabilities provided even more distinct distributions in shorter times. It also accounts for multiconformer equilibria and provided realistic spectra and conformer distribution for the alanine.

Vibrational and electronic optical activity of the chiral disulphide group: Implications for disulphide bridge conformation

Using dihydrogendisulphide (H(2)S(2)), dimethyl- ((CH(3))(2)S(2)), and diethyldisulphide ((CH(3)CH(2))(2)S(2))as model molecules, theoretical ECD, VCD, and ROA spectra of nonplanar disulphides were calculated by DFT methods. Most of the calculated electronic and vibrational chiroptical features suffer an equivocal relation between calculatedsigns of ECD, VCD, or ROA and the sense of disulphide nonplanarity as noted earlier for low-lying ECD bands. This is a consequence of local C(2) symmetry of a disulphide group causing most electronic and vibrational transitions to occur as pairs falling to alternative A, B symmetry species, which become degenerate and switch their succession (and consequently the observed chiroptical sign pattern) at the energetically most favorable perpendicular conformation. According to present calculations, the key to resolving this ambiguity may involve the S-S stretching vibrational mode at approximately 500 cm(-1). The relation of signs of the relevant VCD and ROA features to sense of disulphide chirality seems simpler and less ambiguous. The right-handed arrangement of the S-S group (0 < chi(S-S) < 180 degrees) results in mostly negative VCD signals. Although relation to ROA still suffers some ambiguity, it gets clearer along the series H(2)S(2)-(CH(3))(2)S(2)-(CH(3)CH(2))(2)S(2). ROA is also attractive for the analysis of disulphide-containing peptides and proteins, because applying it to aqueous solutions is not problematic.