Simulations of vibrational spectra from classical trajectories: calibration with ab initio force fields

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.     

Accurate theoretical IR and Raman spectrum of Al2O2 and Al2O3 molecules

The accurate harmonic vibration frequencies together with the infrared (IR) and Raman intensities of the most stable conformers of Al₂O₂ and Al₂O₃ molecules have been calculated by the density functional theory (DFT) method with B3LYP exchange–correlation potential and using a set of the augmented correlated consistent basis sets up to quintuple order. The anharmonic vibration frequencies of the non-linear Al₂O₂ molecule have also been calculated. The obtained equilibrium geometrical parameters, harmonic and anharmonic vibration frequencies along with the IR and Raman intensities good converge to their limits with increasing the size of the used basis set. A comparison of the calculated harmonic and anharmonic vibrational frequencies with the available experimental ones points out that the small differences between the calculated harmonic and experimental frequencies can be further substantially reduced when calculations of the anharmonic vibrational frequencies will be available for all types of molecular geometries.     

Intensity‐Carrying Modes in Raman and Raman Optical Activity Spectroscopy

We describe a quantum‐chemical approach for the determination of modes with maximum Raman and Raman optical activity (ROA) intensity by maximizing the intensities with respect to the Raman and Raman optical activity intensity, respectively, which is shown to lead to eigenvalue equations. The intensity‐carrying modes are in general hypothetical modes and do not directly correspond to a certain normal mode in the spectrum. However, they provide information about those molecular distortions leading to intense bands in the spectrum. Modes with maximum Raman intensity are presented for propane‐1,3‐dione, propane‐1,3‐dionate, and Λ‐tris(propane‐1,3‐dionato)cobalt(III). Moreover, the mode with highest ROA intensity is examined for this chiral cobalt complex and also for the (chiral) amino acid L ‐tryptophan. The Raman and ROA high‐intensity modes are an optimal starting guess for intensity‐tracking calculations, in which selectively normal modes with high Raman or ROA intensity are converged. We present the first Raman and ROA intensity‐tracking calculations. These reveal a high potential for large molecules, for which the selective calculation of normal modes with high intensity is desirable in view of the large computational effort required for the calculation of Raman and ROA polarizability property tensors.     

Demonstration of the ring conformation in polyproline by the Raman optical activity

Raman and Raman optical activity (ROA) spectra of poly-L-proline were recorded in a wide frequency range and analyzed with respect to the proline side chain conformation. The analysis was based on comparison to ab initio simulations of spectral band positions and intensities. The presence of two conformer states of the five-member ring was found, approximately equally populated in the polypeptide. Additionally, Raman and ROA spectral shapes indicated that the peptide adopts the polyproline II helical conformation, in both aqueous and TFE solutions. The helix, however, is perturbed by fluctuations, which affects the vibrational coupling among amino acid residues and broadens the ROA bands. Contributions of the side and main peptide chains to the polyproline ROA intensities have comparable magnitudes. Thus understanding of the origins of both signals is important for determination of the peptide structure by ROA.     

FT-IR and FT-Raman spectroscopic investigation, computed vibrational frequency analysis and IR intensity and Raman activity peak resemblance analysis on 2-nitroanisole using HF and DFT (B3LYP and B3PW91) calculations

Fourier-transform Raman and infrared spectra of 2-nitroanisole are recorded (4000-100 cm(-1)) and interpreted by comparison with respective theoretical spectra calculated using HF and DFT method. The geometrical parameters with C(S) symmetry, harmonic vibrational frequencies, infrared and Raman scattering intensities are determined using HF/6-311++G (d, p), B3LYP/6-311+G (d, p), B3LYP/6-311++G (d, p) and B3PW91/6-311++G (d, p) level of theories. A detailed vibrational spectral analysis has been carried out and assignments of the observed fundamental bands have been proposed on the basis of peak positions and relative intensities. The results of the calculations have been used to simulate IR and Raman spectra for the molecule that showed good agreement with the observed spectra. The SQM method, which implies multiple scaling of the DFT force fields has been shown superior to the uniform scaling approach. The vibrational frequencies and the infrared intensities of the C-H modes involved in back-donation and conjugation are also investigated.     

Raman Optical Activity of Glucose and Sorbose in Extended Wavenumber Range

Raman optical activity (ROA) is pursued as a promising method for structural analyses of sugars in aqueous solutions. In the present study, experimental Raman and ROA spectra of glucose and sorbose obtained in an extended range (50–4000 cm⁻¹) are interpreted using molecular dynamics and density functional theory, with the emphasis on CH stretching modes. A reasonable theoretical basis for spectral interpretation was obtained already at the harmonic level. Anharmonic corrections led to minor shifts of band positions (up to 25 cm⁻¹) below 2000 cm⁻¹, while the CH stretching bands shifted more, by ∼180 cm⁻¹, and better reproduced the experiment. However, the anharmonicities could be included on a relatively low approximation level only, and they did not always improve the harmonic band shapes. The dependence on the structure and conformation shows that the CH stretching ROA spectral pattern is a sensitive marker useful in saccharide structure studies.     

Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.     

FTIR and FT Raman, molecular geometry, vibrational assignments, ab initio and density functional theory calculations for 1,5-methylnaphthalene

The FTIR and FT Raman vibrational spectra of 1,5-methylnaphthalene (1,5-MN) have been recorded using Brunker IFS 66 V Spectrometer in the range 3600-10 cm(-1) in the solid phase. A detailed vibrational spectral analysis has been carried out and assignments of the observed fundamental bands have been proposed on the basis of peak positions and relative intensities. The Optimized molecular geometry, harmonic frequencies, electronic polarizability, atomic charges, dipole moment, rotational constants and several thermodynamic parameters in the ground state were calculated using ab initio Hartree Fock (HF) and density functional B3LYP methods (DFT) with 6-311++ G(d) basis set. With the help of different scaling factors, the observed vibrational wavenumbers in FTIR and FT Raman spectra were analyzed and assigned to different normal modes of the molecule. Most of the modes have wavenumbers in the expected range. The results of the calculations were applied to simulated infrared and Raman spectra of the title compound which showed excellent agreement with the observed spectra.     

Vibrational spectroscopy of the G...C base pair: experiment, harmonic and anharmonic calculations, and the nature of the anharmonic couplings

The results of harmonic and anharmonic frequency calculations on a guanine-cytosine complex with an enolic structure (a tautomeric form with cytosine in the enol form and with a hydrogen at the 7-position on guanine) are presented and compared to gas-phase IR-UV double resonance spectral data. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces; the improved PM3 potential surfaces are obtained from standard PM3 theory by coordinate scaling such that the improved PM3 harmonic frequencies are the same as those computed at the RI-MP2/cc-pVDZ level. Comparison of the data with experimental results indicates that the average absolute percentage deviation for the methods is 2.6% for harmonic RI-MP2/cc-pVDZ (3.0% with the inclusion of a 0.956 scaling factor that compensates for anharmonicity), 2.5% for harmonic RI-MP2/TZVPP (2.9% with a 0.956 anharmonicity factor included), and 2.3% for adapted PM3 CC-VSCF; the empirical scaling factor for the ab initio harmonic calculations improves the stretching frequencies but decreases the accuracy of the other mode frequencies. The agreement with experiment supports the adequacy of the improved PM3 potentials for describing the anharmonic force field of the G...C base pair in the spectroscopically probed region. These results may be useful for the prediction of the pathways of vibrational energy flow upon excitation of this system. The anharmonic calculations indicate that anharmonicity along single mode coordinates can be significant for simple stretching modes. For several other cases, coupling between different vibrational modes provides the main contribution to anharmonicity. Examples of strongly anharmonically coupled modes are the symmetric stretch and group torsion of the hydrogen-bonded NH2 group on guanine, the OH stretch and torsion of the enol group on cytosine, and the NH stretch and NH out-of-plane bend of the non-hydrogen-bonded NH group on guanine.     

A combined theoretical and experimental study of the structure and vibrational absorption, vibrational circular dichroism, Raman and Raman optical activity spectra of the L-histidine zwitterion

A combined theoretical and experimental study of the vibrational absorption (VA)/IR, vibrational circular dichroism (VCD), Raman and Raman optical activity (ROA) spectra of l-histidine in aqueous solution has been undertaken to answer the questions (i) what are the species present and (ii) which conformers of the species are present under various experimental conditions. The VA spectra of l-histidine have been measured in aqueous solution and the spectral bands which can be used to identify both species (cation, zwitterion, anion) and conformer of the species have been identified and subsequently used to identify the species (zwitterion) and conformer (gauche minus minus, gauche minus plus for the side chain dihedral angles) present in solution at pH 7.6. The VCD spectral intensities have been used subsequently in combination with further theoretical studies to confirm the conclusions that have been arrived at by only analyzing the VA/IR spectra. Finally a comparison of measured Raman and ROA spectra of l-histidine with Raman and ROA spectral simulations for the conformers and species derived from the combined VA/IR and VCD experimental and theoretical work is presented as a validation of the conclusions arrived at from VA/IR and VCD spectroscopy. The combination of VA/IR and VCD with Raman and ROA is clearly superior and both sets of experiments should be performed.     

DFT vibrational calculations of rhodamine 6G adsorbed on silver: analysis of tip-enhanced Raman spectroscopy

The tip-enhanced near-field Raman (TERS) bands of Rhodamine 6G (R6G), that we reported earlier [Chem. Phys. Lett. 2001, 335, 369.], are assigned on the basis of density-functional theory (DFT) calculations at the 6-311++G(d,p) level. The Raman and infrared intensities as well as frequencies of the vibrational modes are used for band assignments. These vibrational modes, in combination with characterization of resonant electronic transitions using time-dependent DFT calculations, predict spectral changes in resonant Raman and surface-enhanced resonant Raman scatterings of R6G. Moreover, the TERS spectra of R6G are analyzed in detail, where interactions between the tip and R6G molecules and their enhancement mechanisms are discussed. Finally, we propose a novel Raman spectroscopy technique capable of detecting molecular vibrations at sub-nanometer scale.     

Vapor phase infrared spectroscopy and ab initio fundamental anharmonic frequencies of ammonia borane

The infrared absorption spectrum of ammonia borane vapor has been recorded between 3600 and 600 cm(-1). Of the eleven infrared active fundamental vibrational modes, seven modes of NH(3)(11)BH(3) and four modes of NH(3)(10)BH(3) were observed. The spectra were recorded with sufficient resolution to observe the rotational structure of the bands, which allowed for preliminary least-squares fitting of the band origins and rotational constants. First-principles electronic structure calculations were performed to obtain anharmonic band origins and their intensities. The band assignments are discussed in relation to other spectroscopic techniques that have been previously used to study this molecule. A semi-empirical estimate of the vapor pressure of ammonia borane at room temperature (22 °C) was made and found to be ~1 × 10(-4) Torr. The assignment of the measured modes was aided by the calculated anharmonic frequencies and their infrared intensities. The combination of the CCSD(T) harmonic frequencies with the B3LYP anharmonicities, obtained from second-order vibrational perturbation theory, was found to produce an overall best agreement with the measured band origins.     

Rapid anharmonic vibrational corrections derived from partial Hessian analysis

Vibrational analysis within a partial Hessian framework can successfully describe the vibrational properties of a variety of systems where the vibrational modes of interest are localized within a specific region of the system. We have developed a new approach to calculating anharmonic frequencies based on vibrational frequencies and normal modes obtained from a partial Hessian analysis using second-order vibrational perturbation theory and the transition optimized shifted Hermite method. This allows anharmonic frequencies for vibrational modes that are spatially localized to be determined at a significantly reduced computational cost. Several molecular systems are examined in order to demonstrate the effectiveness of this method including organic molecules adsorbed on the Si(100)-2×1 surface, model peptides in solution, and the C-H stretching region of polycyclic aromatic hydrocarbons. Overall, for a range of systems, anharmonic frequencies calculated using the partial Hessian approach are found to be in close agreement with the results obtained using full anharmonic calculations while providing a significant reduction in computational cost.     

Calculating molecular vibrational spectra beyond the harmonic approximation

We present a new approach for calculating anharmonic corrections to vibrational frequency calculations. The vibrational wavefunction is modelled using translated Hermite functions thus allowing anharmonic effects to be incorporated directly into the wavefunction whilst still retaining the simplicity of the Hermite basis. We combine this new method with an optimised finite-difference grid for computing the necessary third and fourth nuclear derivatives of the energy. We compare our combined approach to existing anharmonic models—vibrational self-consistent field theory (VSCF), vibrational perturbation theory (VPT), and vibrational configuration interaction theory (VCI)—and find that it is more cost effective than these alternatives. This makes our method well-suited to computing anharmonic corrections for frequencies in medium-sized molecules. Contribution of the Mark S. Gordon 65th Birthday Festschrift Issue.     

Raman and photoacoustic infrared spectra of fluorene derivatives: Experiment and calculations

Raman and photoacoustic (PA) infrared spectra of fluorene and four derivatives (2,3-benzofluorene, 2-methylfluorene, 2-ethylfluorene and 1,8-dimethylfluorene) were recorded and analyzed in this investigation. Mid- and far-infrared PA spectra were examined from about 2000 to 100 cm⁻¹. The Raman spectra spanned the same wavenumber range. Observed bands in both PA and Raman spectra were compared with DFT (harmonic) and variational (anharmonic) calculations, and with published spectra. The DFT calculations provided single-molecule frequencies, whereas the variational method yielded results for both monomeric and dimeric species. Many previously unknown bands, including numerous features due to combination and overtone transitions, were identified and assigned in this work.     

Raman spectra of long chain hydrocarbons: anharmonic calculations, experiment and implications for imaging of biomembranes

First-principles anharmonic vibrational calculations are carried out for the Raman spectrum of the C-H stretching bands in dodecane, and for the C-D bands in the deuterated molecule. The calculations use the Vibrational Self-Consistent Field (VSCF) algorithm. The results are compared with liquid-state experiments, after smoothing the isolated-molecule sharp-line computed spectra. Very good agreement between the computed and experimental results is found for the two systems. The combined theoretical and experimental results provide insights into the spectrum, elucidating the roles of symmetric and asymmetric CH(3) and CH(2) hydrogenic stretches. This is expected to be very useful for the interpretation of spectra of long-chain hydrocarbons. The results show that anharmonic effects on the spectrum are large. On the other hand, vibrational degeneracy effects seem to be rather modest at the resolution of the experiments. The degeneracy effects may have more pronounced manifestations in higher-resolution experiments. The results show that first-principles anharmonic vibrational calculations for hydrocarbons are feasible, in good agreement with experiment, opening the way for applications to many similar systems. The results may be useful for the analysis of CARS imaging of lipids, for which dodecane is a representative molecule. It is suggested that first-principles vibrational calculations may be useful also for CARS imaging of other systems.     

Vibrational spectroscopy of triacetone triperoxide (TATP): anharmonic fundamentals, overtones and combination bands

The vibrational spectrum of triacetone triperoxide (TATP) is studied by the correlation-corrected vibrational self-consistent field (CC-VSCF) method which incorporates anharmonic effects. Fundamental, overtone, and combination band frequencies are obtained by using a potential based on the PM3 method and yielding the same harmonic frequencies as DFT/cc-pVDZ calculations. Fundamentals and overtones are also studied with anharmonic single-mode (without coupling) DFT/cc-pVDZ calculations. Average deviations from experiment are similar for all methods: 2.1-2.5%. Groups of degenerate vibrations form regions of numerous combination bands with low intensity: the 5600-5800 cm(-1) region contains ca. 70 overtones and combinations of CH stretches. Anharmonic interactions are analyzed.     

Raman under nitrogen. The high-resolution Raman spectroscopy of crystalline uranocene, thorocene, and ferrocene

The utility of recording Raman spectroscopy under liquid nitrogen, a technique we call Raman under nitrogen (RUN), is demonstrated for ferrocene, uranocene, and thorocene. Using RUN, low-temperature (liquid nitrogen cooled) Raman spectra for these compounds exhibit higher resolution than previous studies, and new vibrational features are reported. The first Raman spectra of crystalline uranocene at 77 K are reported using excitation from argon (5145 A) and krypton (6764 A) ion lasers. The spectra obtained showed bands corresponding to vibrational transitions at 212, 236, 259, 379, 753, 897, 1500, and 3042 cm(-1), assigned to ring-metal-ring stretching, ring-metal tilting, out-of-plane CCC bending, in-plane CCC bending, ring-breathing, C-H bending, CC stretching and CH stretching, respectively. The assigned vibrational bands are compared to those of uranocene in THF, (COT)2-, and thorocene. All vibrational frequencies of the ligands, except the 259 cm(-1) out-of-plane CCC bending mode, were found to increase upon coordination. A broad, polarizable band centered about approximately 460 cm(-1) was also observed. The 460 cm(-1) band is greatly enhanced relative to the vibrational Raman transitions with excitations from the krypton ion laser, which is indicative of an electronic resonance Raman process as has been shown previously. The electronic resonance Raman band is observed to split into three distinct bands at 450, 461, and 474 cm(-1) with 6764 A excitation. Relativistic density functional theory is used to provide theoretical interpretations of the measured spectra.