Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath

The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed.     

Vibrational spectroscopy of (SO4(2-)).(H2O)n clusters, n=1-5: harmonic and anharmonic calculations and experiment

The vibrational spectroscopy of (SO4(2-)).(H2O)n is studied by theoretical calculations for n=1-5, and the results are compared with experiments for n=3-5. The calculations use both ab initio MP2 and DFT/B3LYP potential energy surfaces. Both harmonic and anharmonic calculations are reported, the latter with the CC-VSCF method. The main findings are the following: (1) With one exception (H2O bending mode), the anharmonicity of the observed transitions, all in the experimental window of 540-1850 cm(-1), is negligible. The computed anharmonic coupling suggests that intramolecular vibrational redistribution does not play any role for the observed linewidths. (2) Comparison with experiment at the harmonic level of computed fundamental frequencies indicates that MP2 is significantly more accurate than DFT/B3LYP for these systems. (3) Strong anharmonic effects are, however, calculated for numerous transitions of these systems, which are outside the present observation window. These include fundamentals as well as combination modes. (4) Combination modes for the n=1 and n=2 clusters are computed. Several relatively strong combination transitions are predicted. These show strong anharmonic effects. (5) An interesting effect of the zero point energy (ZPE) on structure is found for (SO4(2-)).(H2O)(5): The global minimum of the potential energy corresponds to a C(s) structure, but with incorporation of ZPE the lowest energy structure is C2v, in accordance with experiment. (6) No stable structures were found for (OH-).(HSO4-).(H2O)n, for n相似文献   

Ab initio vibrational calculations for H2SO4 and H2SO4 x H2O: spectroscopy and the nature of the anharmonic couplings

Vibrational frequencies for fundamental, overtone, and combination excitations of sulfuric acid (H2SO4) and of sulfuric acid monohydrate cluster (H2SO4 x H2O) are computed directly from ab initio MP2/TZP potential surface points using the correlation-corrected vibrational self-consistent field (CC-VSCF) method, which includes anharmonic effects. The results are compared with experiment. The computed transitions show in nearly all cases good agreement with experimental data and consistent improvement over the harmonic approximation. The CC-VSCF improvements over the harmonic approximation are largest for the overtone and combination excitations and for the OH stretching fundamental. The agreement between the calculations and experiment also supports the validity of the MP2/TZP potential surfaces. Anharmonic coupling between different vibrational modes is found to significantly affect the vibrational frequencies. Analysis of the mean magnitude of the anharmonic coupling interactions between different pairs of normal modes is carried out. The results suggest possible mechanisms for the internal flow of vibrational energy in H2SO4 and H2SO4 x H2O.     

Vibrational spectroscopy of protonated imidazole and its complexes with water molecules: ab initio anharmonic calculations and experiments

The results of anharmonic frequency calculations on neutral imidazole (C3N2H4, Im), protonated imidazole (ImH+), and its complexes with water (ImH+)(H2O)n, are presented and compared to gas phase infrared photodissociation spectroscopy (IRPD) data. Anharmonic frequencies are obtained via ab initio vibrational self-consistent field (VSCF) calculations taking into account pairwise interactions between the normal modes. The key results are: (1) Prediction of anharmonic vibrational frequencies on an MP2 ab initio potential energy surface show excellent agreement with experiment and outstanding improvement over the harmonic frequencies. For example, the ab initio calculated anharmonic frequency for (ImH+)(H2O)N2 exhibits an overall average percentage error of 0.6% from experiment. (2) Anharmonic vibrational frequencies calculated on a semiempirical potential energy surface fitted to ab initio harmonic data represents spectroscopy well, particularly for water complexes. As an example, anharmonic frequencies for (ImH+)H2O and (ImH+)(H2O)2 show an overall average deviation of 1.02% and 1.05% from experiment, respectively. This agreement between theory and experiment also supports the validity and use of the pairwise approximation used in the calculations. (3) Anharmonic coupling due to hydration effects is found to significantly reduce the vibrational frequencies for the NH stretch modes. The frequency of the NH stretch is observed to increase with the removal of a water molecule or replacement of water with N2. This result also indicates the ability of the VSCF method to predict accurate frequencies in a matrix environment. The calculation provides insights into the nature of anharmonic effects in the potential surface. Analysis of percentage anharmoncity in neutral Im and ImH+ shows a higher percentage anharmonicity in the NH and CH stretch modes of neutral Im. Also, we observe that anharmonicity in the NH stretch modes of ImH+ have some contribution from coupling effects, while that of neutral Im has no contribution whatsoever from mode-mode coupling. It is concluded that the incorporation of anharmonic effects in the calculation brings theory and experiment into much closer agreement for these systems.     

Vibrational anharmonic calculations in solution: performance of various DFT approaches

We report anharmonic spectra calculated for formaldehyde in acetonitrile solution using the quartic force field obtained for various DFT/solvent coupled models. A statistical study has been carried out for each mode by using several classes of DFT functionals and comparing them to the reference ab-initio CCSD(T)/cc-pVQZ calculations. Results lead to the recommended use of hybrid functionals associated with the 6-31+G** basis set and the Polarized Continuum model (PCM) to predict the expected shifts relative to the gas phase.     

Evidence of an isomeric pair in furan...HCl: Fourier transform infrared spectroscopy and ab initio calculations

For the first time the coexistence of a sigma- and a pi-complex in the C(4)H(4)O:HCl system has been observed, in the same supersonic expansion of a molecular jet seeded with argon (or helium) or in a flow-cooled cell at 240 K. This is an exception to the third of the Legon-Miller rules which claims the sigma-structure to be the only one to exist. On the grounds of energetic considerations and band contour simulations, two observed bands at 2787.7 and 2795.5 cm(-1) of the nu(s) HCl stretching frequency are assigned to the two complexes, recorded as Fourier transform infrared spectra with a resolution between 0.2 and 0.5 cm(-1). Complementary calculations show that the use of the standard second-order Moller-Plesset perturbation theory may be erroneous for such a complex, due of the overestimation of the dispersion contribution with respect to the electrostatic term. It is finally established that only a balanced version of the second-order Moller-Plesset perturbation method, spin-component scaled-MP2, or a higher level of theory like a coupled-cluster approach, can provide a reliable energetic analysis for this complex.     

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.     

Vibrational spectra of methyllithium and its aggregates: a new interpretation from ab initio anharmonic calculations

The complete quartic force field of methyllithium (CH₃Li) is computed at the B3LYP/cc-pVTZ level of theory. The vibrational energy levels calculated from a perturbational and a variational procedure are in agreement with the observed spectra except for the C–Li stretching and the symmetric methyl deformation modes for which a disagreement with the experimental assignment given by Andrews is apparent. This discrepancy between experiment and theory is so large that questions are raised either about a correct characterization of, or correct calculations for the monomeric species CH₃Li. Our theoretical study of methyllithium aggregates (CH₃Li)_n, with n = 2, 3, 4 and 6, gives a new interpretation of the experimental data.     

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.     

On the number of significant mode-mode anharmonic couplings in vibrational calculations: Correlation-corrected vibrational self-consistent field treatment of di-, tri-, and tetrapeptides

A computational study is made of the number of important anharmonic mode-mode couplings in the context of vibrational calculations for di-, tri-, and tetrapeptides. The method employed is the correlation-corrected vibrational self-consistent field (CC-VSCF) algorithm, which includes correlation effects between different vibrational modes. It is found that results of good accuracy can be obtained in calculations that include only N log N mode-mode coupling terms, where N is the number of modes. This simplification significantly accelerates CC-VSCF calculations for large molecules. A criterion based on the characteristics of the normal-mode displacements is employed to predict a priori unimportant coupling terms. The criterion is tested statistically using Spearman's rank correlation coefficient. The results are illustrated by calculations for several di-, tri-, and tetrapeptides using semiempirical PM3 potential surfaces. These results are analyzed and a statistical model for error estimation is given. The decrease in the number of included coupling from N(2) to N log N opens possibilities of anharmonic vibrational calculations for large peptides.     

The effect of oxidation on the stability of G:C base pair: a MP2 study

The base-pairing energies of eleven oxidized G:C base pairs were characterized by Møller–Plesset perturbation theory. The analysis was focused on the base pairs consisting of guanine and one of the following cytosine derivatives: G:C1 (5-hydroxycytosine); G:C2 (5-hydroxyuracil); G:C3 (5,6-dihydroxy-cytosine); G:C4 (5,6-dihydroxy-uracil); G:C5 (cytosine glycol);G:C6 (isodialuric acid); G:C7 (uracil glycol), and the base pairs between cytosine and one of the following guanine derivatives: G8:C (8-oxo-guanine); G9:C (6-enol-8-keto-guanine); G10:C (xantho-sine); and G11:C (8-hydroxy-guanine). Full geometry optimizations have been performed for the studied complexes by MP2 method. The interaction energies were corrected for the basis-set superposition error (BSSE), using the full Boys-Bernardi counterpoise correction scheme. The results obtained show that the interaction energies of the base pairs decrease in the following order: G8:C > G:C5 ~ G:C1 > G:C3 ~ G:C ~ G11:C > G:C2 > G:C4 > G:C7 > G:C6 > G10:C > G9:C.     

Vibrational characterization of L-leucine phosphonate analogues: FT-IR, FT-Raman, and SERS spectroscopy studies and DFT calculations

This study reports the Raman (FT-Raman) and absorption infrared (FT-IR) spectra, based on calculated wavenumbers and normal modes of vibrations, of the following compounds: L-Leu-D-NH-CH(Me)-PO(3)H(2) (LI), L-Leu-NH-C(Me)(2)-PO(3)H(2) (LII), L-Leu-D-NH-CH(Et)-PO(3)H(2) (LIII), L-Leu-L-NH-CH(Et)-PO(3)H(2) (LIV), L-Leu-L-NH-CH(EtOH)-PO(3)H(2) (LV), L-Leu-NH-C(Me)(Et)-PO(3)H(2) (LVI), L-Leu-L-NH-CH(PrA)-PO(3)H(2) (LVII), L-Leu-L-NH-CH(c-Pr)-PO(3)H(2) (LVIII), L-Leu-L-NH-CH(t-Bu)-PO(3)H(2) (LIX), L-Leu-L-NH-CH(BuA)-PO(3)H(2) (LX), L-Leu-L-NH-CH(c-Bu)-PO(3)H(2) (LXI), and L-Leu-L-NH-C(Adm)-PO(3)H(2) (LXII). The equilibrium geometries and vibrational wavenumbers were calculated using density functional theory (DFT) at the B3LYP, 6-311++G** level using Gaussian 03, Raint, GaussSum 0.8, and Gar2ped software. We briefly compare and analyze the experimental and calculated vibrational wavenumbers in the range 4000-400 cm(-1). In addition, the Raman wavenumbers are compared to those from the surface-enhanced Raman scattering (SERS) spectra for the phosphono analogues of l-leucine (l-Leu) adsorbed on a colloidal silver surface in an aqueous solution. The geometries of these molecules etched on the silver surface were deduced from observed changes in both the intensity and broadness of Raman bands in the spectra of the bound versus free species. For example, LVI appears to adsorb onto the colloidal silver particles mainly through the amine group and amide bond, which assists in the adsorption process, whereas LII shows strongly enhanced SERS bands due to the rocking, twisting, and stretching vibrations of the N(amid)C(sg)(Me)(2)P fragment, suggesting that this peptide's interaction with the silver surface occurs mainly via this fragment. On the other hand, the most dominant SERS bands of LIII and LIV due to the P═O bond stretches reflect P═O···Ag complex formation.     

Nucleic acid base pair dynamics: the impact of sequence and structure using free-energy calculations

Molecular dynamics free-energy calculations of base pair opening within double helical DNA and RNA are used to explain why A-tracts (oligo-adenine repeats) greatly increase the lifetimes of AT base pairs, whereas the structural and the chemical changes involved in passing from B-DNA to A-RNA have comparatively small effects.     

The formate anion: the harmonic and anharmonic force fields

Harmonic and anharmonic symmetry force constant matrices have been obtained for six isotopically substituted species of the formate anion. The valence force fields derived from the above matrices were used to recalculate the vibrational frequencies. These force fields are compared with others previously reported and obtained via other methods.     

Molecular structure, harmonic and anharmonic frequency calculations of 2,4-dichloropyrimidine and 4,6-dichloropyrimidine by HF and density functional methods

Quantum chemical calculations of energies, geometrical structural parameters, harmonic and anharmonic frequencies of 2,4-DCP and 4,6-DCP were carried out by HF and density functional theory methods with 6-311++G(d,p) as basis set. The assignment of each normal mode has been made using the observed and calculated frequencies, their IR and Raman intensities. A detailed interpretation of the FT-IR and FT-Raman spectra of 2,4-DCP and 4,6-DCP was reported on the basis of the calculated potential energy distribution (PED). A comparison of theoretically calculated vibrational frequencies at B3LYP/6-311++G(d,p) with FT-IR and FT-Raman experimental data shows good agreement between them. Natural atomic charges of 2,4-DCP and 4,6-DCP were calculated and compared with pyrimidine molecule.     

Vibrational spectroscopy and DFT calculations of 1,3-dibromo-2,4,6-trimethylbenzene: Anharmonicity,coupling and methyl group tunneling

The Raman, IR and INS spectra of 1,3-dibromo-2,4,6-trimethylbenzene (DBMH) were recorded in the 80–3200 cm⁻¹ range. The molecular conformation and vibrational spectra of DBMH were computed at the MPW1PW91/LANL2DZ level. Except for the methyl 2 environment, the agreement between the DFT calculations and the neutron diffraction structure is almost perfect (deviations < 0.01 Å for bond lengths, <0.2° for angles). The frequencies of the internal modes of vibration were calculated with the harmonic and anharmonic approximations; the later method yields results that are in remarkable agreement with the spectroscopic data, resulting in a confident assignment of the vibrational bands. Thus, no scaling is necessary. The coupling, in phase or anti-phase, of the motions of symmetrical CBr and CMe bonds is highlighted. Our DFT calculations suggest that the torsion of methyl groups 4 and 6 is hindered in deep wells, whereas methyl group 2 is a quasi-free rotor. The failure of the calculations to determine the frequencies of the methyl torsional modes is explained as follows: DFT does not consider the methyl spins and assumes localization of the protons, whereas the methyl groups must be treated as quantum rotors.     

Vibrational and electronic spectra of benzophenone in different phase states: Ab initio calculations and experiment

An ab initio method has been used to perform quantum mechanical calculations of the formation energy of different conformers of benzophenone: planar molecule, twisted molecule, planar molecule dimer, twisted molecule dimer; electronic and vibrational spectra of these conformers were also obtained. An assessment of the medium (solvent) influence on the optimal geometry, dipole moment and stability of different forms of benzophenone was performed in the self-consistent reaction field approximation. It is shown that the twisted conformer is more stable than the planar one (the difference of free energies is 32 kJ/mol for free molecules) and it becomes even more stable with the increase in solvent polarity. The calculated electronic and vibrational spectra agree well with the experimental data and properly reflect the complication of the vibrational spectrum when passing from the gaseous phase to the condensed state of benzophenone. The difference between spectral properties of the two dimer forms allows their identification from the spectra and qualitative explanation of the observed peculiarities of phosphorescence of the amorphous phase of benzophenone by the stabilization of different conformers.     

Vibrational corrections of dipolar couplings: methylfluoride and 1,1-difluoroethene

Previously calculated vibrational corrections for methylfluoride are discussed and harmonic corrections are applied to 1,1-difluoroethane. For both molecules, vibrational motions do not account for inconsistencies between the measured anisotropic couplings and the geometry.     

Site-selective luminescence spectroscopy of impurity centres in solids: Model calculations and experiment

A theoretical model is presented which describes quantitatively the elimination of the inhomogeneous broadening in luminescence spectra of inpurity centres on site-selective laser excitation. The model explains our experimental data showing a remarkable dependence of the excitation selectivity on the excitation frequency: there is a gradual disappearance of the selectivity upon increasing the excitation frequency within the 0-0 transition band of various impurity porphyrins in amorphous matrices.