Anharmonic vibrational spectroscopy and investigation of intramolecular mode couplings in adenine

Vibrational frequencies for the nucleobase adenine are calculated by the vibrational self-consistent field (VSCF) and correlation corrected vibrational self-consistent field (CC-VSCF) methods using Hartree-Fock (HF), density functional theory (DFT) and second order Møller-Plesset (MP2) theories. A large number of potential energy surface (PES) points were computed in the anharmonic calculations corresponding to each method. The quartic force field (QFF) approximation was used to generate the full grid of points for the VSCF solver. We have implemented our new procedure for computing the mode-mode coupling integrals in the 2-mode coupling representations of the quartic force field (2MR-QFF) for prediction of coupling magnitudes. Calculations were performed using the 6-31G(d,p) basis set. Comparison of the calculated ab initio anharmonic spectra with Ar matrix experimental data of adenine reported in the literature reveals that, the CC-VSCF (DFT) wavenumbers show the best agreement. The experimental geometric parameters of adenine are compared with the theoretically optimized molecular structural parameters. These are found to be in good agreement. Vibrational assignments are based on the calculated potential energy distribution (PED) values.     

Efficient correlation-corrected vibrational self-consistent field computation of OH-stretch frequencies using a low-scaling algorithm

The authors present a new computational scheme to perform accurate and fast direct correlation-corrected vibrational self-consistent field (CC-VSCF) computations for a selected number of vibrational modes, which is aimed at predicting a few vibrations in large molecular systems. The method is based on a systematic selection of vibrational mode-mode coupling terms, leading to the direct ab initio construction of a sparse potential energy surface. The computational scaling of the CC-VSCF computation on the generated surface is then further reduced by using a screening procedure for the correlation-correction contributions. The proposed method is applied to the computation of the OH-stretch frequency of five aliphatic alcohols. The authors investigate the influence of different pseudopotential and all-electron basis sets on the quality of the correlated potential energy surfaces computed and on the OH-stretch frequencies calculated for each surface. With the help of these test systems, the authors show that their method offers a computational scaling that is two orders of magnitude lower than a standard CC-VSCF method and that it is of equal accuracy.     

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.     

Anharmonic vibrational spectra of hydroxylamine and its 15N, 18O, and deuterium substituted analogs

Vibrational self-consistent field (VSCF) and correlation-corrected vibrational self-consistent field (CC-VSCF) methods were used to compute the anharmonic frequencies of fundamentals, overtones, and combination transitions of natural abundance hydroxylamine, 15NH2OH, NH2(18)OH, ND2OD, ND2OH, and NH2OD isotopomers at second order M?ller-Plesset perturbation theory (MP2) in basis sets of triple-zeta quality. Frequencies of the fundamental transitions observed in the gas phase spectrum were reproduced by CC-VSCF treatment within 20 cm(-1) in TZV(d,p) and TZV(2d,2p) basis sets, and the change of basis set composition had only minor effect on the frequencies of the computed fundamentals. CC-VSCF computed wave numbers of overtone and combination transitions were typically within 1-40 cm(-1) of the gas phase band positions, except for those resulting from multiple excitations of v2, v3, and v7 fundamentals, because of a strong mutual coupling between these modes. Integral transition intensities calculated at MP2 level closely followed those of experimental spectrum, including intensity decrease in v1, 2v1, 3v1 progression, and 30-fold intensity increase of 2v8 in respect to that of v8 fundamental. The frequency of the OH torsional fundamental was found to be strongly dependent on the mode-mode interaction potential among v9 and v1, v7, v2, v4, v5 modes. Band shifts resulting from 15N, 18O and complete 2H substitutions were reproduced almost quantitatively by CC-VSCF computation in TZV(d,p) basis. Computed anharmonic isotope frequency shifts were different from those obtained in the harmonic approximation and no scaling procedure seemed capable of performing their interchange.     

Vibrational quasi-degenerate perturbation theory: applications to fermi resonance in CO2, H2CO, and C6H6

A quasi-degenerate perturbation method with vibrational self-consistent field (VSCF) reference wavefunction is developed. It simultaneously accounts for strong anharmonic mode-mode coupling among a few states (static correlation) by a configuration interaction theory and for weak coupling with a vast number of the other states (dynamic correlation) by a perturbation theory. A general formula is derived based on the van Vleck perturbation theory. An algorithm that selects a compact set of the most important VSCF configurations which contribute to the static correlation is proposed and a scheme to limit the number of configurations considered for dynamic correlation is also implemented. This method reproduces the vibrational frequencies of CO2 and H2CO that are subject to the strongest anharmonic mode-mode coupling within 10 cm(-1) of vibrational configuration interaction results in a computational expense reduced by a factor of one to two orders of magnitude. The method also reproduces the infrared absorption of C6H6 in the CH stretching (nu12) frequency region, in which combination tones nu13nu16 and nu2nu13nu18 appear on account of an intensity borrowing from nu12via the anharmonic coupling.     

Acceleration of Correlation-corrected Vibrational Self-consistent Field Calculation Times for Large Polyatomic Molecules

Acceleration of the correlation-corrected Vibrational self-consistent field (CC-VSCF) method for anharmonic calculations of vibrational states of polyatomic molecules is described. The acceleration assumes pairwise additive interactions between different normal modes, and employs orthogonality of the single-mode vibrational wavefunctions. This greatly reduces the effort in computing correlation effects between different vibrational modes, which is treated by second order perturbation theory in CC-VSCF. The acceleration can improve the scaling of the overall computational effort from N ⁶ to N ⁴, where N is the number of vibrational modes. Sample calculation times, using semi-empirical potential surfaces (PM3), are given for a series of glycine peptides. Large computational acceleration, and significant reduction of the scaling of the effort with system size, is found and discussed.     

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.     

Transition rates between selected vibrational states in methyl halides; influence of anharmonicities

A semiclassical model of collision induced vibrational relaxation is discussed in terms of an effective collision mass for different values of vibrational energy release. Selected one, two and three quantum transitions of the methyl halides upon collision with rare gases are evaluated in the presence of resonant and nonresonant anharmonic couplings. It is found, that due to the anharmonic coupling the rates between CH stretching modes and the overtones of the CH bending modes become as large as the transfer rates between two CH stretching modes. This is in qualitative agreement with experiments. Without the anharmonic coupling they differ by two orders of magnitude.     

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.     

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.     

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.     

Anharmonic vibrational calculations modeling the raman spectra of intermediates in the photoactive yellow protein (PYP) photocycle

The role of anharmonic effects in the vibrational spectroscopy of the dark state and two major chromophore intermediates of the photoactive yellow protein (PYP) photocycle is examined via ab initio vibrational self-consistent field (VSCF) calculations and time-resolved resonance Raman spectroscopy. For the first time, anharmonicity is considered explicitly in calculating the vibrational spectra of an ensemble consisting of the PYP chromophore surrounded by model compounds used as mimics of the important active-site residues. Predictions of vibrational frequencies on an ab initio corrected semiempirical potential energy surface show remarkable agreement with experimental frequencies for all three states, thus shedding light on the potential along the reaction path. For example, calculated frequencies for vibrational modes of the red-shifted intermediate, PYPL, exhibit an overall average error of 0.82% from experiment. Upon analysis of anharmonicity patterns in the PYP modes we observe a decrease in anharmonicity in the C8-C9 stretching mode nu29 (trans-cis isomerization marker mode) with the onset of the cis configuration in PYPL. This can be attributed to the loss of the hydrogen-bonding character of the adjacent C9-O2 to the methylamine (Cys69 backbone). For several of the modes, the anharmonicity is mostly due to mode-mode coupling, while for others it is mostly intrinsic. This study shows the importance of the inclusion of anharmonicity in theoretical spectroscopic calculations, and the sensitivity of experiments to anharmonicity. The characterization of protein active-site residues by small molecular mimics provides an acceptable chemical structural representation for biomolecular spectroscopy calculations.     

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.     

New vibrational self-consistent field program for large molecules

A recently developed, general computer program that performs vibrational self-consistent field (VSCF) calculations for large molecules is described. The program, which we refer to as VSCF―95, requires as its only input a force field in mass-scaled normal coordinates. Currently, it is limited to a maximum of 200 normal modes, and the force field is limited to coupling terms involving a maximum of six normal modes, with a maximum order of six in any normal mode. As output the program returns VSCF energies for specified quantum states. We illustrate the code with two new applications. The first is to HCO, for which we use a full sixth-order force field. The second is to a model of the fullerene, C₆₀, for which we have calculated a 75,731-term force field, which includes all anharmonic terms up to fifth order, and all two-mode coupling terms up to fourth order. © 1996 by John Wiley & Sons, Inc.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

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   

Fast vibrational self-consistent field calculations through a reduced mode-mode coupling scheme

We present a new methodology to perform fast correlation-corrected vibrational self-consistent field (CC-VSCF) calculations using ab initio potential energy points calculated on the fly. Our method is based on the replacement of all-electron basis sets with a pseudo-potential basis for heavy atoms, and on an efficient reduction of the number of pair-coupling elements used in the CC-VSCF procedure. The method is applied to several test systems: H2O, NH3, and CH4, where it proves to be efficient, providing a speedup factor of 2 compared to a standard CC-VSCF calculation. We also apply our technique to the simulation of the vibrational spectrum of ethane and show that very accurate results can be obtained with a substantial speedup for this system.     

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo?ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.     

Vibrational spectroscopy for glycine adsorbed on silicon clusters: Harmonic and anharmonic calculations for models of the Si(1 0 0)-2 × 1 surface

The vibrational spectroscopy of a glycine molecule adsorbed on a silicon surface is studied computationally, using different clusters as models for the surface. Harmonic frequencies are computed using density functional theory (DFT) with the B3LYP functional. Anharmonic frequency calculations are carried out using vibrational self-consistent field (VSCF) algorithms on an improved PM3 potential energy surface. The results are compared with experiments on Glycine@Si(1 0 0)-2 × 1.

The main findings are: (1) Agreement of the computed frequencies with experiment improves with cluster size. (2) The anharmonic calculations are generally in better agreement with experiment than the harmonic ones. The improvements due to anharmonicity are most significant for hydrogenic stretching. (3) An important part of the anharmonic effects is due to anharmonic coupling between different normal modes of the system. (4) The anharmonic coupling between glycine vibrational modes is much larger than the anharmonic coupling between glycine and “phonon” (cluster) modes.

Implications of the results for surface vibrational spectroscopy are discussed.     

Numerical-analytic implementation of the higher-order canonical Van Vleck perturbation theory for the interpretation of medium-sized molecule vibrational spectra

Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the convergence of perturbation theory and solves a number of theoretical problems of VPT2, e.g., yields anharmonic constants y(ijk), z(ijkl), and allows the reliable evaluation of vibrational IR and Raman anharmonic intensities in the presence of resonances. Darling-Dennison and higher-order resonance coupling coefficients can be reliably evaluated as well. The method is illustrated on classic molecules: water and formaldehyde. A number of theoretical conclusions results, including the necessity of using sextic force field in the fourth order (CVPT4) and the nearly vanishing CVPT4 contributions for bending and wagging modes. The coefficients of perturbative Dunham-type Hamiltonians in high-orders of CVPT are found to conform to the rules of equality at different orders as earlier proven analytically for diatomic molecules. The method can serve as a good substitution of the more traditional VPT2.