Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing.     

Ab initio spectrograms of the molecular vibrational spectrum

Theoretical spectrograms of the vibrational spectrum of 3,3-dimethylcyclopropene were constructed and juxtaposed with the experimental Raman and IR spectrograms. The theoretical spectrograms are represented as sets of vertical lines starting from the points corresponding to the values of the vibrational frequencies calculated from the scaled quantum-mechanical (QM) force field obtained at the HF/6-31G*//HF/6-31G* level. Two theoretical Raman spectrograms were constructed. In the first case, the heights of the vertical lines correspond to the QM values of the Raman scattering activities. In the second case they represent the relative differential Raman cross-sections calculated using the QM values of Raman scattering activities. The initial vibrational mode matrix remains virtually unchanged upon scaling of the QM force constant matrix because the dispersion of the scale factor values is low. Therefore, the heights of the theoretical lines for the IR spectrogram represent the QM intensities directly. The theoretical spectrogram based on the relative differential Raman cross-sections was shown to depict the experimental Raman spectrum more adequately. This makes it possible to use the results of the corresponding QM calculations more completely and obtain well-substantiated assignments of the vibrational frequencies.     

The performance of explicitly correlated methods for the computation of anharmonic vibrational frequencies

Anharmonic vibrational frequencies for closed-shell molecules computed with CCSD(T)-F12b/aug-cc-pVTZ differ from significantly more costly composite energy methods by a mean absolute error (MAE) of 7.5 cm⁻¹ per fundamental frequency. Comparison to a few available gas phase experimental modes, however, actually lowers the MAE to 6.0 cm⁻¹. Open-shell molecules have an MAE of nearly a factor of six greater. Hence, open-shell molecular anharmonic frequencies cannot be as well-described with only explicitly correlated coupled cluster theory as their closed-shell brethren. As a result, the use of quartic force fields and vibrational perturbation theory can be opened to molecules with six or more atoms, whereas previously such computations were limited to molecules of five or fewer atoms. This will certainly assist in studies of more chemically interesting species, especially for atmospheric and interstellar infrared spectroscopic characterization.     

Conformational properties of methyl vinyl sulfone: Ab initio geometry optimization and vibrational analysis

An ab initio conformational analysis of methyl vinyl sulfone (CH₂CHSO₂CH₃) has been carried out. Molecular geometry optimizations have been performed at the HF and MP2 levels of the theory. Relative energies of the stationary points have been determined by using different approaches, including electron correlation corrections up to the third order. The IR and Raman spectra of the liquid have been measured and a vibrational assignment is proposed. The height of the barrier to the methyl group internal rotation has been estimated. Theoretical calculations and vibrational spectra have shown that the predominant conformation of methyl vinyl sulfone has the C=C bond eclipsed with one of the S=O bonds. Similar eclipsed forms have been found in vinyl fluoro sulfone, vinyl chloro sulfone and divinyl sulfone by ab initio HF calculations.     

Ab initio vibrational analysis of hexafluoroethane C2F6

Quantum mechanical geometry optimizations and the calculation of vibrational frequencies of hexafluoroethane have been performed at the HF/6-31G*, MP2/6-31G*, CCSD/cc-pVDZ, and B3LYP/6-31G* levels. The force fields obtained were scaled. The necessity is stressed of carrying out the detailed analysis of the vibrational spectra of small reference molecules to determine sets of scale factors which are transferable to quantum mechanical force fields of large molecules for the purpose of predicting their vibrational spectra.     

The calculation of vibrational energy levels of polyatomic molecules including anharmonic effect using contact transformation perturbation method

Using contact transformation perturbation method based on the Taylor expansion of the potential energy function in terms of dimensionless normal coordinates up to sixth‐order, the vibrational energy levels in terms of force constants are derived. The contact transformation theory has been applied to simplify the calculation of perturbation effects. To calculate the second‐order vibrational energy correction, the third and fourth‐order terms of potential function have been placed in the first‐order perturbation Hamiltonian and the second‐order Hamiltonian contains hexatic ones. We present expressions which give relations between the fourth‐ and sixth‐order terms in dimensionless normal coordinates of the potential and the anharmonicity coefficients. For illustration, a set of vibrational energies levels of SO₂, and H₂O molecules including anharmonic effects has been calculated. © 2013 Wiley Periodicals, Inc.     

New parallel software (P_Anhar) for anharmonic vibrational calculations: application to (CH(3)Li)(2)

We present the development of a new parallel computer code (P_Anhar_v1.0) to calculate the vibrational spectrum of medium size molecules using a variational algorithm. The method is applied to the determination of a complete quartic anharmonic force field (B3LYP/cc-pVTZ) for methyllithium, leading to a new interpretation of experimental data.     

Ab initio and DFT studies of the molecular structures and vibrational spectra of succinonitrile

The Molecular structure, conformational stability and vibrational frequencies of succinonitrile NCCH2CH2CN have been investigated with ab initio and density functional theory (DFT) methods implementing the standard 6-311++G* basis set. The potential energy surfaces (PES) have been explored at DFT-B3LYP, HF and MP2 levels of theory. In agreements with previous experimental results, the molecule was predicted to exist in equilibrium mixture of trans and gauche conforms with the trans form being slightly lower in energy. The vibrational frequencies and the corresponding vibrational assignments of succinonitrile in both C2h and C2 symmetry were examined theoretically and the calculated Infrared and Raman spectra of the molecule were plotted. Observed frequencies for normal modes were compared with those calculated from normal mode coordinate analysis carried out on the basis of ab initio and DFT force fields using the standard 6-311++G* basis set of the theoretical optimized geometry. Theoretical IR intensities and Raman activities are reported.     

Ab initio studies of solvent effect on molecular conformation and vibrational spectra of diacetamide

The conformational equilibria and vibrational spectra of diacetamide have been investigated by ab initio molecular orbital studies using the basis sets 6-31g(d,p) and 6-31++g(d,p) at Hartree-Fock and MP2 levels. The vibrational spectra of diacetamide have been satisfactorily interpreted taking into consideration the agreement between the calculated harmonic vibrational frequencies, infrared and Raman band intensities and shifts in deuterated molecules with those observed. The solvent effects were investigated by the self-consistent reaction field (SCRF) theory. The effect of solvent on the conformational equilibria and vibrational spectra is discussed. The calculated changes in the geometry and vibrational spectra on going from the gas phase to the solvent medium are in accord with the increasing weight of the dipolar resonance structure of the amide group in more polar solvents.     

Theoretical anharmonic Raman and infrared spectra with vibrational assignments for monofluoroaniline isomers

The ortho-meta-, and para-fluoro substituted anilines are prototype molecules for investigation of the interactions of both the amino group and the fluorine atom with the aromatic ring. The molecular structures, natural atomic charges and theoretical anharmonic Raman and infrared spectra of the three fluoroaniline isomers have been calculated by using the density functional B3LYP method with the extended 6-311++G(df,pd) basis set. The Raman and infrared spectra of 2FA, 3FA, and 4FA have been recorded. The detailed vibrational assignments of the experimental spectra have been made on the basis of the calculated potential energy distributions, PEDs. The effect of fluorine substituent on the aniline ring geometry and charge distribution, the nature of the characteristic “marker bands” and a quenching of intensities of some bands are discussed. It is shown that the frequencies of the NH₂ stretching vibrations depend on the degree of pyramidalization of the C-NH₂ group, in the isomers. In 2FA and 3FA, the NH₂ stretching frequencies are higher than those in 4FA. This corresponds to a more flattened structure of the amino group in 2FA and 3FA, in comparison to 4FA.     

Ab initio prediction of the vibrational spectra of the hydrogen‐bonded complexes between CO and HONO2

The vibrational characteristics (vibrational frequencies and infrared intensities) for free and complexed CO and HONO₂ have been predicted using ab initio calculations at SCF and MP2 levels with different basis sets and B3LYP/6?31G(d,p) calculations. The ab initio calculations show that the complexation between HONO₂ and CO leads to two stable structures: CO … HONO₂ (1A) and OC … HONO₂ (1B). The changes in the vibrational characteristics from free monomers to complexes have been estimated. It was established that the most sensitive to the complexation is the stretching O? H vibration. In agreement with the experiment, its vibrational frequency in the complexes is shifted to lower frequency (Δν = ?123 cm^?1). The magnitude of the wave number shift is indicative of relatively strong hydrogen‐bonded interaction. The ab initio calculations at different levels predict an increase of the infrared intensity of the stretching O? H vibration for structure 1A more than five times and for structure 1B more than nine times. The most consistent agreement between the computed values of the frequency shifts for structure 1B and those experimentally observed suggests that this structure is preferred. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

FC(O)NCS 分子振动光谱的理论研究

采用DFT(B3LYP)方法,以6-3G*为基组对FC(O)NCS的顺式和反式两种构型的几何结构,振动谐性力场和红外光谱进行了研究。B3LYP/6-31G*计算水平和大多数有机分子的一套固定标度因子进行标度。根据标度后的理论力场进行简正坐标分析得到的势能分布(PED)和红外光谱强度值对FC(O)NCS分子的顺式和反式两种构型的振动基频进行了理论归属。     

Ab initio prediction of vibrational spectra: A database approach

Efforts to develop a database of quadratic force fields for organic molecules are described. The database is based on systematic ab initio calculations, scaled to reproduce the experimentally observed frequencies. The choice of the theoretical method, the basis sets, geometries, internal coordinates and the scaling procedure are discussed. A key point in the procedure is the automatic generation of the internal valence coordinates. This is also very advantageous for geometry optimization. The database should permit the prediction of vibrational frequencies for most organic molecules to 10–20 cm⁻¹, together with semiquantitative intensities. The accuracy is sufficient to identify unknown compounds from a list of reasonable candidates.     

Structure and vibrational spectra of mononitroalkanes

Structures and force fields for several mononitroalkane molecules were determined by ab initio quantum-chemical methods. The data obtained were used for calculation of the frequencies and modes of normal vibrations. Potentialities of different methods (RHF, MP2, and B3LYP) and basis sets for estimation of the structures and spectra were studied.     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

First-principles calculation of geometry and anharmonic vibrational spectra of thioformamide and thioformamide-d2

The equilibrium geometry of thioformamide HCSNH2 has been determined at the MP2 and CCSD(T) electron correlation levels under C(s) symmetry constraints using triple-zeta basis sets up to cc-pVTZ. All optimized planar structures are true minima on the potential-energy surface and are characterized by the C-N bond length within 1.353-1.343 A, C-S distances of 1.656-1.628 A, and NCS angle between 125.7 degrees and 125.9 degrees . The wave number of the NH2 out-of-plane wagging mode computed in the harmonic approximation shows stronger dependence on the basis set rather than the electron correlation level and varies from 85.9 cm(-1) at CCSD(T)cc-pVDZ level to 335 cm(-1) at MP2/aug-cc-pVTZ level. Anharmonic vibrational spectra of HCSNH2 and HCSND2 have been determined directly from the potential-energy surfaces computed at MP2 level in triple-zeta valence (TZV)(2df,2p) and TZV+(2df,2p) basis sets using vibrational self-consistent-field (VSCF) and correlation-corrected VSCF (CC-VSCF) methods. CC-VSCF wave numbers of fundamental, first overtone, and most intense combination transitions are reported for thioformamide and those of fundamentals for thioformamide-d2. The NH2 wagging (nu12) mode is strongly anharmonic and its fundamentals have been computed at 406.9 cm(-1) [TZV(2df,2p)] and 399.5 cm(-1) [TZV+(2df,2p)], which is remarkably close to the experimental energy of 393 cm(-1). Anharmonically computed fundamentals of this mode in thioformamide-d2, 299.7 cm(-1) [TZV(2df,2p)] and 299.6 cm(-1) [TZV+(2df,2p)], are only approximately 7 cm(-1) higher than the transition energy (293 cm(-1)) observed in the gas phase spectrum of HCSND2. The first overtone of the NH2 wagging mode of thioformamide (nu12 (02)) has been calculated by CC-VSCF procedure at 830.8 cm(-1) [TZV(2df,2p)] and 880.0 cm(-1) [TZV+(2df,2p)], which implies "negative" (nu12 (02)>2*nu12 (01)) anharmonicity of this mode.     

Interpretation of the vibrational spectra of nitramines on the basis ofab initio calculations

It is shown that, unlike conventional methods of vibrational spectroscopy, the use ofab initia harmonic force fields, IR and Raman intensities, and depolarizations makes possible a rigorous interpretation of the experimental spectra of the simplest aliphatic nitramines (CH₃)₂NNO₂, CH₃NHNO₂, H₂NNO₂, and their isotopomers. The scale factors, which were introduced for each compound to remove the systematic errors of the SCF MO LCAO calculation by fitting the parameters to the observed frequencies, were mutually adjusted during the solution of the inverse vibrational problem. The set of transferable scale factors established in this work can be used directly to analyze spectra of larger molecules. Some common patterns of the force fields and vibrational spectra of nitramines are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya No. 12, pp. 2106–2117, December, 1994.The authors are grateful to the Russian Foundation for Basic Research (Project No. 93-03-4410) and to the Robert A. Welch Foundation for financial support of the parts of this work performed at the Department of Chemistry of Moscow State University and at the University of Texas at Austin, USA. The authors also acknowledge the support by the Scientific Technical Program Universities of Russia.     

DNA oligonucleotide-cis-platin binding: Ab initio interpretation of the vibrational spectra

The cis-platin binding to the d(CCTGGTCC)*d(GGACCAGG) model DNA octamer was monitored with infrared absorption (IR) and vibrational circular dichroism (VCD) spectroscopies. The spectra were modeled with the aid of density functional computations and a Cartesian coordinate-based transfer of molecular property tensors from smaller DNA fragments. Because of the fragmentation, the tensors could be calculated with a higher precision. Environmental effects, such as the presence of the solvent or the cis-platin ligand, could be included in the modeling. The solvent was modeled by an explicit inclusion of hydrogen-bound water molecules, positions of which were estimated from a molecular dynamics simulation, or by the polarized continuum COSMO model. The B3LYP and BPW91 functionals used for the calculations of the spectral parameters were combined with the relativistic LANL2DZ platinum pseudo-potentials. The simulations reproduced the main IR and VCD DNA spectral features and explained most of the changes observed experimentally upon metal binding. The results confirmed that the influence of the ligand on DNA vibrational properties is quite complex; it originates in the geometry deformation and normal mode coupling pattern changes of the platinated octamer, as well as in local perturbations of the electronic structure and force field of the GC base pairs to which the platinum is bound. Many of the local effects could be accounted for by a point charge used in place of the metal in the GC complex.     

Ab initio calculation of the vibrational and electronic spectra of trans- and cis-azobenzene

We report accurate geometries and harmonic force fields for trans- and cis-azobenzene determined by second-order M?ller-Plesset perturbation theory. For the trans isomer, the planar structure with C(2h) symmetry, found in a recent gas electron diffraction experiment, is verified. The calculated vibrational spectra are compared with experimental data and density functional calculations. Important vibrational frequencies are localized and discussed. For both isomers, we report UV spectra calculated using the second-order approximate coupled-cluster singles-and-doubles model CC2 with accurate basis sets. Vertical excitation energies and oscillator strengths have been determined for the lowest singlet n(pi)* and (pi)(pi)* transitions. The results are compared with the available experimental data and second-order polarization propagator (SOPPA) and density functional (DFT) calculations. For both isomers, the CC2 results for the excitation energies into the S(1) and S(2) states agree within 0.1 eV with experimental gas-phase measurements.