Petr Bouř

Empirical modeling of the peptide amide I band IR intensity in water solution

An empirical correction to amide group vacuum force fields is proposed in order to account for the influence of the aqueous environment on the C=O stretching vibration (amide I). The dependence of the vibrational absorption spectral intensities on the geometry is studied with density functional theory methods at the BPW91/6-31G** level for N-methyl acetamide interacting with a variety of of water molecule clusters hydrogen bonded to it. These cluster results are then generalized to form an empirical correction for the force field and dipole intensity of the amide I (C=O stretch) mode. As an example of its extension, the method is applied to a larger (β-turn model) peptide molecule and its IR spectrum is simulated. The method provides realistic bandwidths for the amide I bands if the spectra are generated from the ab initio force field corrected by perturbation from an ensemble of solvent geometries obtained using molecular dynamic simulations.

Computational Analysis of Solvent Effects in NMR Spectroscopy.

Solvent modeling became a standard part of first principles computations of molecular properties. However, a universal solvent approach is particularly difficult for the nuclear magnetic resonance (NMR) shielding and spin-spin coupling constants that in part result from collective delocalized properties of the solute and the environment. In this work, bulk and specific solvent effects are discussed on experimental and theoretical model systems comprising solvated alanine zwitterion and chloroform molecules. Density functional theory computations performed on larger clusters indicate that standard dielectric continuum solvent models may not be sufficiently accurate. In some cases, more reasonable NMR parameters were obtained by approximation of the solvent with partial atomic charges. Combined cluster/continuum models yielded the most reasonable values of the spectroscopic parameters, provided that they are dynamically averaged. The roles of solvent polarizability, solvent shell structure, and bulk permeability were investigated. NMR shielding values caused by the macroscopic solvent magnetizability exhibited the slowest convergence with respect to the cluster size. For practical computations, however, inclusion of the first solvation sphere provided satisfactory corrections of the vacuum values. The simulations of chloroform chemical shifts and CH J-coupling constants were found to be very sensitive to the molecular dynamics model used to generate the cluster geometries. The results show that computationally efficient solvent modeling is possible and can reveal fine details of molecular structure, solvation, and dynamics.

Explicit versus implicit solvent modeling of Raman optical activity spectra.

Raman and Raman optical activity (ROA) spectra of molecules reflect not only molecular structure and conformation but also the dynamics and interactions with the solvent. For polar, biologically relevant molecules in aqueous environment, this often complicates the band assignment and interpretation of the spectra. In the present study, implicit dielectric and explicit solvent models are compared with respect to the influence of the choice of solvent model on the spectral shape. Lactamide and 2-aminopropanol were selected as model compounds, and the Raman and ROA spectra were measured for both enantiomers. Geometries of explicitly solvated clusters were derived from quantum-mechanical calculations, classical (MD), and Car-Parrinello (CPMD) molecular dynamics. The results indicate that although the dielectric model reasonably well reproduces the main spectral features, more faithful intensity profiles, including the inhomogeneous band broadening, are obtained from the explicit MD and CPMD clusters. Additionally, the CPMD clusters are capable of reproducing most spectral features better than the classical dynamics, provided the simulation time is long enough to allow for a complete sampling of the conformational space. The hydrogen-bonded water molecules of the first hydration shell significantly influence the spectral intensities, whereas the effect of loosely attached or distant solvent molecules is minor. In order to average the signal, however, a relatively large number of MD geometries need to be considered, as was also exemplified by simulations of the ROA spectrum of the achiral molecule glycine. An explicit solvent modeling of sizable systems thus requires extensive computations, which became possible only recently due to the development of efficient analytical computational techniques.

Partial optimization of molecular geometry in normal coordinates and use as a tool for simulation of vibrational spectra

A normal mode coordinate-based molecular optimization algorithm was implemented and its performance tested against other optimization techniques. In certain cases the method was found to be computationally simpler and numerically more stable than the optimization algorithms based on Cartesian or internal valence coordinates. The usual redundant/internal coordinate scheme provided fastest convergence for compact covalently bonded molecules, while the normal mode method was found to be more suitable for more weakly bonded molecular complexes. For constrained optimizations use of the normal coordinates allows one to naturally separate the lower-energy modes from those more typically studied with vibrational spectroscopy. Thus, it provides an appropriate tool for simulations of IR and Raman spectra of larger molecules and complex systems when specific conformations are desired.

Determining the Absolute Configuration of Two Marine Compounds Using Vibrational Chiroptical Spectroscopy

Chiroptical techniques are increasingly employed for assigning the absolute configuration of chiral molecules through comparison of experimental spectra with theoretical predictions. For assignment of natural products, electronic chiroptical spectroscopies such as electronic circular dichroism (ECD) are routinely applied. However, the sensitivity of electronic spectral parameters to experimental conditions and the theoretical methods employed can lead to incorrect assignments. Vibrational chiroptical methods (vibrational circular dichroism, VCD, and Raman optical activity, ROA) provide more reliable assignments, although they, in particular ROA, have been little explored for assignments of natural products. In this study, the ECD, VCD, and ROA chiroptical spectroscopies are evaluated for the assignment of the absolute configuration of a highly flexible natural compound with two stereocenters and an asymmetrically substituted double bond, the marine antibiotic Synoxazolidinone A (SynOxA), recently isolated from the sub-Arctic ascidian Synoicum pulmonaria. Conformationally averaged nuclear magnetic resonance (NMR), ECD, Raman, ROA, infrared (IR) and VCD spectral parameters are computed for the eight possible stereoisomers of SynOxA and compared to experimental results. In contrast to previously reported results, the stereochemical assignment of SynOxA based on ECD spectral bands is found to be unreliable. On the other hand, ROA spectra allow for a reliable determination of the configuration at the double bond and the ring stereocenter. However, ROA is not able to resolve the chlorine-substituted stereogenic center on the guanidinium side chain of SynOxA. Application of the third chiroptical method, VCD, indicates unique spectral features for all eight SynOxA isomers in the theoretical spectra. Although the experimental VCD is weak and restricted by the limited amount of sample, it allows for a tentative assignment of the elusive chlorine-substituted stereocenter. VCD chiroptical analysis of a SynOxA derivative with three stereocenters, SynOxC, results in the same absolute configuration as for SynOxA. Despite the experimental challenges, the results convincingly prove that the assignment of absolute configuration based on vibrational chiroptical methods is more reliable than for ECD.

Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions

The difference spectroscopy of the Raman optical activity (ROA) provides extended information about molecular structure. However, interpretation of the spectra is based on complex and often inaccurate simulations. Previously, the authors attempted to make the calculations more robust by including the solvent and exploring the role of molecular flexibility for alanine and proline zwitterions. In the current study, they analyze the IR, Raman, and ROA spectra of these molecules with the emphasis on the force field modeling. Vibrational harmonic frequencies obtained with 25 ab initio methods are compared to experimental band positions. The role of anharmonic terms in the potential and intensity tensors is also systematically explored using the vibrational self-consistent field, vibrational configuration interaction (VCI), and degeneracy-corrected perturbation calculations. The harmonic approach appeared satisfactory for most of the lower-wavelength (200-1800 cm(-1)) vibrations. Modern generalized gradient approximation and hybrid density functionals, such as the common B3LYP method, provided a very good statistical agreement with the experiment. Although the inclusion of the anharmonic corrections still did not lead to complete agreement between the simulations and the experiment, occasional enhancements were achieved across the entire region of wave numbers. Not only the transitional frequencies of the C-H stretching modes were significantly improved but also Raman and ROA spectral profiles including N-H and C-H lower-frequency bending modes were more realistic after application of the VCI correction. A limited Boltzmann averaging for the lowest-frequency modes that could not be included directly in the anharmonic calculus provided a realistic inhomogeneous band broadening. The anharmonic parts of the intensity tensors (second dipole and polarizability derivatives) were found less important for the entire spectral profiles than the force field anharmonicities (third and fourth energy derivatives), except for a few weak combination bands which were dominated by the anharmonic tensor contributions.

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

On model examples, we compare the performance of the vibrational self‐consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi‐rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self‐consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing.

Structure of the Alanine Hydration Shell as Probed by NMR Chemical Shifts and Indirect Spin-Spin Coupling

The structure of the alanine hydration shell was modeled by Carr-Parinello molecular dynamics (CPMD) to explain subtle differences in NMR chemical shifts and indirect spin-spin coupling constants of the neutral (zwitterionic), cationic, and anionic forms of this amino acid. In comparison with classical molecular dynamics (MD), the quantum mechanical CPMD approach revealed a more structured solvent and significant differences in the radial and angular distributions of the water molecules around the solute. In particular, the solvent was predicted to be organized around the uncharged COOH and NH(2) residues to a similar degree as that for the charged ones. This was not the case with MD. For snapshot CPMD configurations, the NMR parameters were computed by density functional theory (DFT) and averaged. Obtained values were significantly closer to experimental parameters known for (15)N and (13)C isotopically labeled alanine than those calculated by the conventional implicit dielectric solvent model. The NMR results also quantitatively reflect a superiority of the CPMD over the MD explicit solvent treatment. A further improvement of the computed spin-spin coupling constants could be achieved by taking into account vibrational averaging beyond the harmonic approximation. Differently positioned water molecules in the clusters cause an unexpectedly large scattering of the NMR parameters. About 10-15 dynamics snapshots were required for a satisfactory convergence of the shifts and couplings. The NMR chemical shift was found to be much more sensitive to the molecular hydration than the coupling. The results thus indicate a large potential of the NMR spectroscopy and quantum simulations to probe not only the structure of molecules but also their interactions with the environment.

Comparison of Quantitative Conformer Analyses by Nuclear Magnetic Resonance and Raman Optical Activity Spectra for Model Dipeptides

Interpretation of the Raman optical activity (ROA) of peptides is difficult because of molecular flexibility and interaction with the solvent. Typically, simulations and experiments are compared in terms of a qualitative agreement between the spectra. However, on a series of the Pro-Gly, Gly-Pro, Pro-Ala, and Ala-Pro dipeptides more precise conformer ratios could be obtained with the aid of the density functional computations and numerical decomposition of the spectral shapes. All observed transitions were assigned, and the computed transition frequencies were scaled accordingly. Then the populations predicted by the optical spectroscopy agreed within a few percent with an analysis of the spin-spin coupling constants based on the Karplus equations, which was confirmed also by a comparison of calculated and experimental NMR couplings. The results are supported by molecular dynamics simulations and related to the previous conformational studies of similar molecules.

Relative importance of first and second derivatives of nuclear magnetic resonance chemical shifts and spin-spin coupling constants for vibrational averaging

Relative importance of anharmonic corrections to molecular vibrational energies, nuclear magnetic resonance (NMR) chemical shifts, and J-coupling constants was assessed for a model set of methane derivatives, differently charged alanine forms, and sugar models. Molecular quartic force fields and NMR parameter derivatives were obtained quantum mechanically by a numerical differentiation. In most cases the harmonic vibrational function combined with the property second derivatives provided the largest correction of the equilibrium values, while anharmonic corrections (third and fourth energy derivatives) were found less important. The most computationally expensive off-diagonal quartic energy derivatives involving four different coordinates provided a negligible contribution. The vibrational corrections of NMR shifts were small and yielded a convincing improvement only for very accurate wave function calculations. For the indirect spin-spin coupling constants the averaging significantly improved already the equilibrium values obtained at the density functional theory level. Both first and complete second shielding derivatives were found important for the shift corrections, while for the J-coupling constants the vibrational parts were dominated by the diagonal second derivatives. The vibrational corrections were also applied to some isotopic effects, where the corrected values reasonably well reproduced the experiment, but only if a full second-order expansion of the NMR parameters was included. Contributions of individual vibrational modes for the averaging are discussed. Similar behavior was found for the methane derivatives, and for the larger and polar molecules. The vibrational averaging thus facilitates interpretation of previous experimental results and suggests that it can make future molecular structural studies more reliable. Because of the lengthy numerical differentiation required to compute the NMR parameter derivatives their analytical implementation in future quantum chemistry packages is desirable.