Anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second-order perturbative approach

The paper reports main results of a comprehensive study of the vibrational spectrum of ketene computed using second-order perturbation theory treatment based on quartic, cubic and semidiagonal quartic force constants. Two different models--a homogeneous model using the same density functionals and basis functions for the harmonic calculations and anharmonic corrections, and a hybrid model in which the two parts of the calculation are conducted using different density functionals and basis sets--have been employed in the present calculations. Different DFT and CCSD methods and DZ and TZ extended basis sets involving diffuse and polarization functions have been used to calculate optimized and vibrationally averaged geometrical parameters, the harmonic and anharmonic vibrational frequencies and the spectroscopic constants such as anharmonicity constants, rotational constants, rotation-vibration coupling constants, Nielsen's centrifugal distortion constants and Coriolis coupling constants. Homogeneous model is found to be superior to the hybrid model in several respects. Difficulties in the hybrid model may arise due to one of the following reasons: (a) the basic requirement that the geometry optimization and frequency calculations must be done at the same level of theory to have valid frequencies is not met in the hybrid model; (b) the molecular structure gets reoptimized at the low level for anharmonic corrections; (c) in addition, the perturbation could also diverge for the above reasons, particularly for the very low, very anharmonic terms where the harmonic approximation is not close enough to make the perturbation work.     

Vibrational anharmonicity and harmonic force fields for dichloromethane from quantum-chemical calculations

Anharmonic and related constants have been calculated for CH2Cl2, CD2Cl2, and CHDCl2 by using the program Gaussian03 and B3LYP and MP2 models. Bases used were 6-311++G** and cc-pVTZ. The size of grid used in the B3LYP/6-311++G** model had a noticeable effect on resulting data. Features of the MP2/6-311++G** calculations suggested a deleterious effect of the absence of f functions in this basis set. The need for the replacement of second-order terms in the perturbation theory formulas for the vibrational anharmonic constants x ij in the presence of Fermi resonance was explored, and minor resonances were found associated with the cubic constants varphi 122 and varphi 299 (d 0 isotopomer), phi122 and phi849 (d2), and phi278 (d1). Computed xij values for nuCH and nuCD motions agree quite well with earlier experimental data. Observed anharmonic frequencies, nu obsd, were corrected to "observed" harmonic frequencies, omega obsd, by using computed differences Delta = omegaQC-nuQC. These differences Delta are larger for the antisymmetric nuasCH2 mode than for symmetric nusCH2 motion. This fact made it necessary to use differing scale factors for the two kinds of CH stretching force constants in a subsequent scaling of the harmonic force field to nuobsd. Force field scaling was also carried out by refining to omega obsd. In both approaches, the B3LYP models required differing scale factors for symmetric and antisymmetric CCl stretching force constants, indicating a failure to compute an accurate C-Cl stretch-stretch interaction force constant. The MP2/cc-pVTZ force field was preferred. Both scaled and unscaled harmonic force fields were used to calculate centrifugal distortion constants (CDCs) and contributions to the vibrational dependence of the rotational constants (alphas). Variations in the CDCs can, in part, be explained by the magnitudes of the frequencies used in the scaling process.     

Anharmonic Force Fields and Perturbation Theory in the Interpretation of Vibrational Spectra of Polyatomic Molecules

The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotational-vibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.     

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.     

Ab initio Study of Anharmonic Force Field and Spectroscopic Constants for Germanium Dichloride

Ab initio study of the equilibrium structure, spectroscopy constants, and anharmonic force field for several isotopomers of germanium dichloride (⁷⁰GeCl₂, ⁷²GeCl₂, and ⁷⁶GeCl₂) have been carried out at the MP2 and CCSD(T) levels of theory using cc-pVTZ basis set. The calculated geometries, rotational constants, vibration-rotation interaction constants, harmonic frequencies, anharmonic constants, quartic and sextic centrifugal distortion constants, cubic and quartic force constants are compared with experimental data. For small mass differences of the Ge isotopes, the isotopic effects for germanium dichloride are much weaker. The agreements are satisfactory for these two methods, but the deviations of CCSD(T) results are slightly larger than that of MP2, because of CCSD(T)'s inadequate treatment of electron correlation in hypervalent Cl atom.     

Ab initio study of spectroscopic constants and anharmonic force field of 74GeCl2

The equilibrium structure, spectroscopy constants, and anharmonic force field of germanium dichloride have been calculated at MP2, B3LYP, and CCSD(T) levels of theory employing two basis sets, cc-pVDZ and cc-pVTZ, respectively. The computed geometries, rotational constants, and vibration-rotation interaction constants, and quartic centrifugal distortion constants are compared with the available experimental data. The harmonic frequencies, anharmonic constants, and cubic and quartic force constants are predicted. The calculated results show that the MP2 results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from B3LYP. The CCSD(T) method is also an advisable choice to study anharmonic force field of molecules.     

Force fields and assignments of the vibrational spectra of acridine and phenazine—an ab initio study

A complete set of force constants and their corresponding scale factors in non-redundant local coordinates were obtained by fitting the in-plane ab initio Hartree–Fock (HF) vibrational frequencies computed using 4-21G and 6-31G^** basis sets to the experimental ones. Using these force constants the potential energy distribution (PED) of the normal modes was obtained and based on the PED the earlier empirical assignments were either confirmed or reassigned for all the in-plane fundamentals. The force constants of acridine and phenazine are compared to those of anthracene to study the similarities and differences. Probable assignment is proposed for the out-of-plane fundamentals of acridine based on Durig's simple scaling of the local force constants.     

Calculation of the anharmonic effect on the main reactions referring to ethylbenzene combustion mechanism

About 11 reactions related to ethylbenzene are studied in this paper using transition state theory. The YL method proposed by Yao and Lin is utilized to calculate the anharmonic and the harmonic rate constants in these reaction processes in the temperature range of 300–4,000 K, energy diagram and the temperature dependence of the rate coefficients are also presented. The calculations indicate that the harmonic rate constants are larger than the anharmonic rate constants in most cases. Especially, there is a temperature junction between the high and low relationship between the anharmonic and harmonic rate constants in several reactions. Furthermore, the calculated values are in good agreement with other theoretical ones within the allowable error. Finally, the kinetic parameters and the thermodynamic parameters are calculated. To sum up, it can be concluded that the anharmonic effect in these reactions is very significant and cannot be ignored.     

Scaled quantum chemical force fields for 1,1-difluorocyclopropane and the influence of vibrational anharmonicity

Potential functions and harmonic (omega(i)) and anharmonic (nu(i)) fundamental frequencies have been calculated for 1,1-difluorocyclopropane (DFCP) and its d4 and d2 isotopomers using the program Gaussian 03. B3LYP and MP2 models were employed, each with the bases 6-311++G** and cc-pVTZ. Anharmonicity corrections Delta(i) = omega(i) - nu(i) are listed and shown to be different for symmetric and antisymmetric CH stretching modes in situations where Fermi resonance appears to be absent. The same effect is missing in C2H4, for which similar calculations were made. The quadratic force fields for DFCP have been scaled in symmetry coordinate space with 15 scale factors both to observed frequencies nu(obsd)and also to omega (obsd), where omega(obsd) = nu(obsd) + Delta. With nu(obsd) especially, different scale factors are needed for the symmetric and antisymmetric CH stretching force constants due to their differing anharmonicities. The source of the latter in the quartic and cubic force field is explored. MP2 calculations of valence interaction force constants involving the stretching of bonds on a common carbon atom are preferred to those from a B3LYP model. In either model, scaling to omega(obsd) rather than to nu(obsd) does not remove the necessity of varying scale factors for differing types of motion in the same group. Theoretical values of the five quartic centrifugal distortion constants are listed for the normal species and compared with new experimental data. The predictions are sufficiently good to be useful in fitting pure rotational transitions. A weakness is identified in the current Gaussian 03 code for the calculation of vibration-rotation quantities, and limitations are noted in the manner in which Fermi resonance is handled.     

Ab initio calculations of anharmonic vibrational spectroscopy for hydrogen fluoride (HF)n (n = 3, 4) and mixed hydrogen fluoride/water (HF)n(H2O)n (n = 1, 2, 4) clusters

Anharmonic vibrational frequencies and intensities are computed for hydrogen fluoride clusters (HF)n, with n = 3, 4 and mixed clusters of hydrogen fluoride with water (HF)n(H2O)n where n = 1, 2. For the (HF)4(H2O)4 complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Potential energy surfaces for these systems are obtained at the MP2/TZP level of electronic structure theory. Vibrational states are calculated from the potential surface points using the correlation-corrected vibrational self-consistent field method. The method accounts for the anharmonicities and couplings between all vibrational modes and provides fairly accurate anharmonic vibrational spectra that can be directly compared with experimental results without a need for empirical scaling. For (HF)n, good agreement is found with experimental data. This agreement shows that the M?ller-Plesset (MP2) potential surfaces for these systems are reasonably reliable. The accuracy is best for the stiff intramolecular modes, which indicates the validity of MP2 in describing coupling between intramolecular and intermolecular degrees of freedom. For (HF)n(H2O)n experimental results are unavailable. The computed intramolecular frequencies show a strong dependence on cluster size. Intensity features are predicted for future experiments.     

BSSE‐corrected geometry and harmonic and anharmonic vibrational frequencies of formamide–water and formamide–formamide dimers

The basis set superposition error (BSSE) influence in the geometry structure, interaction energies, and intermolecular harmonic and anharmonic vibrational frequencies of cyclic formamide–formamide and formamide–water dimers have been studied using different basis sets (6‐31G, 6‐31G**, 6‐31++G**, D95V, D95V**, and D95V++**). The a posteriori “counterpoise” (CP) correction scheme has been compared with the a priori “chemical Hamiltonian approach” (CHA) both at the Hartree–Fock (HF) and second‐order Møller–Plesset many‐body perturbation (MP2) levels of theory. The effect of BSSE on geometrical parameters, interaction energies, and intermolecular harmonic vibrational frequencies are discussed and compared with the existing experimental data. As expected, the BSSE‐free CP and CHA interaction energies usually show less deep minima than those obtained from the uncorrected methods at both the HF and MP2 levels. Focusing on the correlated level, the amount of BSSE in the intermolecular interaction energies is much larger than that at the HF level, and this effect is also conserved in the values of the force constants and harmonic vibrational frequencies. All these results clearly indicate the importance of the proper BSSE‐free correlation treatment with the well‐defined basis functions. At the same time, the results show a good agreement between the a priori CHA and a posteriori CP correction scheme; this agreement is remarkable in the case of large and well‐balanced basis sets. The anharmonic frequency correction values also show an important BSSE dependence, especially for hydrogen bond stretching and for low frequencies belonging to the intermolecular normal modes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the Calculation of the Anharmonic Effect of Unimolecular Reactions of HOCO

HOCO is the intermediate of the reaction H + CO₂ → HO + CO. In this study, all the geometries in the collision reaction H + CO₂ were optimized at MP2/6‐311++G** level with Gaussian 03 program and a potential energy surface which shows that three unimolecular reactions were in the process of HOCO → HO + CO. For the three reactions, YL method proposed by L. Yao and S. H. Lin is applied to calculate the anharmonic and harmonic total number of states, the density of states and rate constants. The anharmonic values for rate constants calculated in this study are much lower than harmonic values, which indicate that anharmonic effects are significant and can not be neglected. After convert the experimental lifetime of HOCO into rate constants, the values are close to the calculations in our research, which shows that YL method used in our study is suitable for studying the rate constants of unimolecular reaction.     

Tensor formalism in anharmonic calculations

Internal displacements, related by a non linear transformation to an underlying system of cartesian coordinates, are considered for anharmonic calculations. A new tensor notation is proposed for anharmonic force constants, in terms of Christoffel symbols explicitly tabulated for stretching and bending.     

Anharmonic midinfrared vibrational spectra of benzoic acid monomer and dimer

Anharmonic vibrational calculations for the benzoic acid monomer and dimer in the mid-IR regime (500-1800 cm(-1)) are reported. Harmonic frequencies and intensities are obtained at the DFT/B3LYP level of theory employing D95(d,p) and cc-pVTZ basis sets. Anharmonic corrections obtained from standard perturbation theory lead to redshifts of 1%-3%. In almost all cases, the resulting frequencies deviate by less than 1% from previous measurements [Bakker et al., J. Chem. Phys. 119, 11180 (2003)]. Calculated intensities are in qualitative agreement with the absorption experiment, with the cc-pVTZ values being superior to the D95(d,p) ones for a few modes of the dimer. The antisymmetric out-of-plane bending mode of the dimer, which is strongly blueshifted with respect to the monomer frequency, represents a remarkable exception: The harmonic frequencies obtained for the two basis sets differ notably from each other, and the anharmonically corrected frequencies deviate from the experimental value by 8% [D95(d,p)] or 3% (cc-pVTZ). Nonperturbative calculations in reduced dimensionality reveal that the relatively small total anharmonic shift (few tens of cm(-1)) comprises of partly much larger contributions (few hundreds of cm(-1)) which are mostly canceling each other. Many of the individual anharmonic couplings are beyond the validity of second-order perturbation theory based on cubic and semidiagonal quartic force constants only. This emphasizes the need for high-dimensional, nonperturbative anharmonic calculations at high quantum-chemical level when accurate frequencies of H-atom vibrations in double hydrogen bonds are sought for.     

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.     

On Feasibility of “Spectroscopic” Calculations of XH Bond Dissociation Energies for Polyatomic Molecules from Fundamental Vibration Frequencies Using the Anharmonic Molecular Model

This paper discusses the applicability of the variational technique using a minimal Morse-harmonic basis set to calculations of the fundamental spectrum and the potential function parameters for polyatomic molecules. The potential function is assumed to be the sum of the Morse function for XH bonds and the harmonic function for the skeletal and deformation vibrations. The initial approximation for the potential function is found by ab initio calculations and refined by solving the inverse mechanical problem (selecting the scaling indices). The thus selected harmonic part of the potential function gives equally good agreement between the experimental and calculated transition frequencies in both harmonic and anharmonic approximations. The anharmonic (Morse) term of the potential function (bond dissociation energy) is selected by solving the inverse mechanical problem until the best agreement between the experimental and calculated CH bond stretching frequencies has been achieved. Problem solving ends with the construction of a transmission curve in the IR spectrum. Variations of the dipole moment of the molecule induced by vibrations are found by ab initio calculations.     

Experimental infrared spectra of matrix isolated complexes of HCl with 4-substituted pyridines. Evaluation of anharmonicity and matrix effects using data from ab initio calculations

Infrared spectra have been measured for HCl complexes with 4-cyanopyridine, 4-chloropyridine, pyridine and 4-methylpyridine isolated in argon and nitrogen matrices at about 12 K. The experimental spectra are dramatically different from computed MP2/6-31+G(d,p) harmonic spectra, a consequence of the anharmonicity of the potential energy surface in the hydrogen-bonding region. Comparisons of computed and experimental data suggest that the experimental spectra correspond to complexes with HCl distances that are much longer than the computed equilibrium distances. These longer distances, R_cor(HCl), are related to the average HCl distance in the ground vibrational state of the proton-stretching mode. The value of R_cor(HCl) determines values of three effective anharmonic force constants for the HCl stretch, the NH stretch and the coupling between them for each complex. The simulated anharmonic spectra obtained when these anharmonic force constants are used in place of the corresponding harmonic constants show spectral patterns with respect to both frequencies and intensities that are very similar to those observed in the experimental spectra obtained in Ar and N₂ matrices. 1D anharmonic potential curves related to the experimental spectra are presented. They provide insight into anharmonicity of the hydrogen-bonded proton stretch for these systems, and into the sensitivity of the potential energy surface to the environment.     

Finite-field method calculations. III. Dipole moment gradients,polarisability gradients and field-induced shifts in bond lengths,vibrational levels,

In this paper, the finite-field method is applied in calculating polarisabilities and, by extension, polarisability gradients. The method is also used to examine the shifts in a number of properties induced by electric fields of given strength. Model calculations at the SCF and Cl levels are reported for LiH. Estimates of the Raman scattering intensity and depolarisation ratio, obtained from the calculated polarisability gradient components, are presented. The dipole moment gradient, which is related to the infrared absorption intensity, is also reported. The properties for which field-dependent shifts are given comprise bond length, vibrational levels, spectroscopic constants, harmonic force constant, first anharmonic constant and dipole moment gradient.     

A note on the AB initio calculation of intermolecular potentials: the HF dimer

Large scale SCF and CEPA PNO calculations have been performed for the HF dimer. The geometry has been optimized at the SCF level. Stabilization energies and harmonic force constants have been computed and compared with previous results.     

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.