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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.

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.

Spectroscopy of magnetic circular dichroism (MCD) provides enhanced information on molecular structure and a more reliable assignment of spectral bands than absorption alone. Theoretical modeling can significantly enhance the information obtained from experimental spectra. In the present study, the time dependent density functional theory is employed to model the lowest-energy benzene transitions, in particular to investigate the role of the Rydberg states and vibrational interference in spectral intensities. The effect of solvent is explored on model benzene-methane clusters. For the lowest-energy excitation, the vibrational sub-structure of absorption and MCD spectra is modeled within the harmonic approximation, providing a very good agreement with the experiment. The simulations demonstrate that the Rydberg states have a much stronger effect on the MCD intensities than on the absorption, and a very diffuse basis set must be used to obtain reliable results. The modeling also indicates that the Rydberg-like states and associated transitions may persist in solutions. Continuum-like solvent models are thus not suitable for their modeling; solvent-solute clusters appear to be more appropriate, providing they are large enough.

Nuclear spin–spin coupling constants calculated using the sum-over-states (SOS) expansions were compared to experimental values and usual coupled-perturbed (CP) calculations. Rigid Kohn–Sham orbitals obtained from a hybrid density functional were used in the SOS model. Its accuracy for small molecules is comparable with the CP results, nevertheless calculated constants were uniformly underestimated. However, the SOS scheme is less limited by molecular size and can be applied for bigger systems than the CP method, as documented on the proton–proton coupling constants in α-pinene, β-pinene, and camphor molecules.

Vibrational motions of solid N-methylformamide (NMF) and its N-deuterated analogue are investigated using the inelastic neutron scattering (INS) technique at 15 K. The force field for obtaining the normal vibrational modes of the crystal is based on a quantum chemical calculation and a subsequent transfer of a harmonic force field of a smaller pentameric segment to a fragment of 11 NMF molecules. Two types of hydrogen bonds present in crystalline NMF are also modeled with dimers. The distinct bonding leads to a splitting of the N-hydrogen wagging mode in the spectrum. Although the hydrogen bonding has a profound effect on vibrational frequencies, the results indicate that an occurrence of a double-well potential for bonded hydrogen proposed previously is unlikely. Instead, a limited electronic conjugation along the hydrogen bonds in crystalline NMF is observed. Unlike in previous models, we simulate the relative INS intensity of each vibrational transition separately, which leads to a substantial improvem...

The similarity in shape makes separation and identification of fullerenes difficult. In this work, the magnetic circular dichroism (MCD) spectroscopy is presented as a useful tool for this purpose. Experimental C60 and C70 spectra were obtained and reproduced with the aid of density functional computations and the complex polarization propagator method. Theoretical spectra of other fullerenes revealed distinctive patterns extremely sensitive to molecular structure as well. Requiring tiny amounts of the sample, the MCD technique thus appears as a useful for detailed fullerene studies.

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.

An algorithm allowing simulating vibrational spectra from classical time-dependent trajectories was applied for infrared absorption, vibrational circular dichroism, Raman, and Raman optical activity of model harmonic systems. The implementation of the theory within the TINKER molecular dynamics (MD) program package was tested with ab initio harmonic force fields in order to determine the feasibility for more extended MD simulations. The results suggest that sufficiently accurate frequencies can be simulated with integration time steps shorter than about 0.5 fs. For a given integration time step, lower vibrational frequencies ( approximately 0-2000 cm(-1)) could be reproduced with a higher accuracy than higher-frequency vibrational modes (e.g., O-H and C-H stretching). In principle, the algorithm also provides correct intensities for ideal systems. In applied simulations, however, the intensity profiles are affected by an unrealistic energy distribution between normal modes and a slow energy relaxation. Additionally, the energy fluctuations may cause weakening of the intensities on average. For ab initio force fields, these obstacles could be overcome by an arbitrary normal mode energy correction. For general MD simulations, averaging of many shorter MD trajectories started with randomly distributed atomic velocities provided the best spectral shapes. alpha-pinene, D-gluconic acid, formaldehyde dimer, and the acetylprolineamide molecule were used in the tests.

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.

Previously proposed solvent correction to the amide I peptide vibration was extended so that it can be applied to a general solvated chromophore. The combined molecular and quantum mechanics (MMQM) method is based on a linear dependence of harmonic force field and intensity tensor components of the solute on solvent electrostatic field. For N-methylacetamide, realistic solvent frequency and intensity changes as well as inhomogeneous band widths were obtained for amide A, I, II , and III modes. A rather anomalous basis set size dependence was observed for the amide A and I vibrations, when bigger basis lead to narrowing of spectral bands and lesser molecular sensibility to the environment. For a model alpha-helical peptide, a W-shape of the vibrational circular dichroism signal observed in deuterated solvent for the amide I band was reproduced correctly, unlike with previous vacuum models.

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.

The surface-enhanced Raman optical activity theory [J. Chem. Phys.125, 124704 (2006)] is formulated in a matrix form, which makes the formalism simpler and allows to extend it for more complicated colloid and molecular systems.