Quartic Potential Energy Surface Research Articles

Фундаментальный анализ сингулярных и резонансных явлений в колебательных полиадах молекулы дифторсилилена

The singular structure of the lower vibrational states of the difluorosilylene molecule (up to four quanta of total excitation) was studied by expanding the energies of each state in the series of high-order Rayleigh-Schrödinger perturbation theory and analyzing their implicit multivalued properties using the fourth degree Padé-Hermite approximants. The quartic potential energy surface in dimensionless normal coordinates was calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of the values of multivalued approximants reproduces the variational solution with high accuracy, while other values, starting from the fourth polyad, in many cases coincide with the energies of other states of the polyad. The Fermi and Darling-Dennison resonances are analyzed on the basis of the coincidence of the singular complex branch points of the approximants for interacting states inside or near a circle of unit radius on the complex plane. It was found that a pair of states can have several coinciding branch points of solutions, including those inside the unit circle. It is concluded that this approach is an effective method for determining the polyad structure of vibrational states. The calculation parameters are selected, which are necessary for the reproducibility of key results. The calculations were carried out using a software package in the Fortran language using a package of arithmetic calculations with a long mantissa of real numbers (200 digits).

Disentangling the IR spectra of 2,3,3,3-tetrafluoropropene using an ab initio description of vibrational polyads by means of canonical Van Vleck perturbation theory

The vibrational spectra of 2,3,3,3-tetrafluoropropene (2333TFP) are studied in the infrared experimentally and theoretically by the canonical second-order Van Vleck operator perturbation theory (CVPT2) and full quartic potential energy surface (PES). 2333TFP belongs to hydrofluoroolefins (HFOs) considered among the most promising alternatives to the hydrofluorocarbons presently in use in refrigeration. The medium resolution infrared spectra of gaseous 2333TFP were recorded in the range 9500–30 cm−1. The integrated IR intensities for all bands falling between 6300–400 cm−1 were accurately determined. Theoretical descriptions of up to four-quanta anharmonic vibrational states of 2333TFP are performed using the state-of-the-art numerical-analytic implementation of CVPT2. High quality harmonic frequencies, obtained at different coupled-cluster levels of theory up to the CCSD(T*)-F12c/VTZ-F12 model were combined with the full quartic MP2/cc-pVTZ anharmonic force field to form the hybrid PES. All Fermi and Darling-Dennison resonances were detected using a universal criterion and treated with the variational CVPT2/VCI stage by using two-, three-, and four-quanta harmonic oscillator basis sets. General recommendations for choosing such basis sets in future studies are formulated. In addition to all fundamentals and their resonance satellites, the vibrational analysis led to the assignment of virtually all observed first/second overtone and binary/ternary combination bands. Computed dipole moment first derivatives in the principal axis system yielded reliable predictions of band shapes for fundamental transitions in good agreement with observed counterparts. Computed anharmonic IR intensities showed an excellent agreement with observed data in the measured ranges. The fundamental spectroscopic effect of excited resonances is observed experimentally and explained theoretically as a universal mechanism of formation of vibrational polyads. The efficiency of the CVPT2/VCI approach employed is clearly demonstrated and can be considered as a benchmark for modeling vibrational states and interpretation of vibrational spectra of semi-rigid molecules.

Wigner Distribution by Adiabatic Switching in Normal Mode or Cartesian Coordinates and Molecular Applications.

We recently presented a simple, classical trajectory-based method for generating the Wigner phase space density using classical trajectories evolving under an adiabatically switched potential. The adiabatically switched Wigner (ASW) distribution is an approximation to the exact Wigner function, which was found to be highly accurate on model systems. In this paper we discuss the implementation of the ASW procedure to polyatomic molecules both in normal mode coordinates and in Cartesian coordinates. We present its application to a six-degree-of-freedom model based on an ab initio quartic potential energy surface developed for formaldehyde in the normal mode representation and for butyne in Cartesian coordinates using the CHARMM force field. Comparisons of equilibrium properties against accurate quantum mechanical results indicate that the ASW is reliable and highly accurate over a wide temperature range in both the coordinate systems. Further, the ASW density is invariant under classical evolution, thus it is ideally suited to quasiclassical trajectory simulations. We also describe a very simple ASW-based procedure for obtaining complex-valued quasiclassical time correlation functions and vibrational spectra.

Vibrational spectroscopy of tolane; Coriolis coupling between Raman-active modes of g symmetry

ABSTRACTVibrational spectroscopy of tolane (diphenylacetylene), which has 66 normal modes, has been advanced. Anharmonic wavenumber predictions were made with the quartic potential energy surface obtained with B3LYP/cc-pVTZ model and the second-order perturbation theory (VPT2). Infrared (IR) intensity and Raman activities were computed at the harmonic level. The IR spectrum of the crystal and Raman spectra of the liquid and the crystal tolane were newly recorded. The lingering problem of an excess of polarised Raman bands at wavenumbers appropriate for fundamentals, other than ag modes, has now been attributed to Coriolis coupling within modes of g symmetry species. Consequently, D2h point symmetry group has been confirmed for a planar tolane molecule. Assignments for almost all fundamentals of tolane are now secure. The assignment for ν32 remains questionable. Remaining unassigned fundamentals are: ν34 and ν35, which, as au symmetry species, are IR- and Raman-inactive transitions, and ν59(b2u), which is predicted to have a very low wavenumber.

Performance of different density functionals for the calculation of vibrational frequencies with vibrational coupled cluster method in bosonic representation

An accurate description of anharmonic vibrational frequencies of polyatomic molecules is a challenging task. It requires an ab initio method to solve the vibrational Schrodinger equation along with extensive electronic structure calculations to generate the quartic potential energy surface (PES) in mass-weighted normal coordinates. The computation of such quartic PES is very expensive. Even for a medium-size molecule, highly accurate ab initio methods like CCSD, CCSD(T) become formidable. The DFT stands as valuable alternative in this case. In this work, we investigate the performances of several commonly used density functionals, namely, B3LYP, BLYP, B3LYPD, M06, M062x, PBE1PBE, B3P86, LC- $$\omega $$ PBE, X3LYP, B3PW91, and B97D for the evaluation of anharmonic vibrational frequencies of semi-rigid molecules. The quality of the results is assessed by the comparison with experimental values. To this end, we used a set of 19 molecules of various sizes (4–9 atoms). The vibrational coupled cluster method (VCCM) in bosonic representation is used to solve the vibrational structure problem. The hybrid functionals B3P86, B3LYP, B3PW91, PBE1PBE, and X3LYP found to give more accurate result of the fundamental frequencies than the other functionals. Our results show that the error in the BLYP and B97D calculation is due to the inadequate description of the harmonic force field. For the LC- $$\omega $$ PBE, M06, and M062x, the anharmonic force constants leads to the error. It is found that the comparative performances of the DFT functionals with VCCM are consistent with the second-order vibrational perturbation theory.

On the choice electronic structure method to calculate the quartic potential energy surface for the vibrational calculation of polyatomic molecules

A systematic study is made on the effects of electronic structure calculations on anharmonic spectra of polyatomic molecules. Our study is focused on the choice of electronic structure method and basis set to calculate the quartic potential energy surface (PES). We used two correlated methods Moller–Plesset perturbation theory and density functional theory with B3LYP functional and two different types of basis sets, aug-cc-pVTZ and 6-311G(2d,2p) to calculate the PES and linear DMS. For the vibrational description, we used the vibrational self-consistent field theory and the vibrational coupled cluster theory in bosonic representation.

Theoretical study on the vibrational structure of S0 thiophosgene from the origin to dissociation

In this work, using our vibrational variational calculation method and a recently derived refined quartic potential energy surface for S0 thiophosgene, we have carried out large scale vibrational calculations to analyze the vibrational structure of this electronic state in the whole range of vibrational excitation energies down from the origin and up to the dissociation limit (at ↼20,000cm↙1). In the lower excited vibrational range we have achieved satisfactory coincidence of calculated to experimentally measured frequencies, while at the higher vibrational excitations our main objective has been to estimate what part of the available vibrational level density is effectively involved into the vibrational mixing and IVR. The results from our calculations have been compared to the available experimentally obtained dataset (obtained from synchrotron IR, SEP and LIF spectra) as well as to conclusions from the analyses by other authors using local coupling models.

Anharmonic Vibrational Analysis of the Infrared and Raman Gas-Phase Spectra of s-trans- and s-gauche-1,3-Butadiene.

A quantum-mechanical (hybrid MP2/cc-pVTZ and CCSD(T)/cc-pVTZ) full quartic potential energy surface (PES) in rectilinear normal coordinates and the second-order operator canonical Van Vleck perturbation theory (CVPT2) are employed to predict the anharmonic vibrational spectra of s-trans- and s-gauche-butadiene (BDE). These predictions are used to interpret their infrared and Raman scattering spectra. New high-temperature Raman spectra in the gas phase are presented in support of assignments for the gauche conformer. The CVPT2 solution is based on a PES and electro-optical properties (EOP; dipole moment and polarizability) expanded in Taylor series. Higher terms than those routinely available from Gaussian09 software were calculated by numerical differentiation of quadratic force fields and EOP using the MP2/cc-pVTZ model. The integer coefficients of the polyad quantum numbers were derived for both conformers of BDE. Replacement of harmonic frequencies by their counterparts from the CCSD(T)/cc-pVTZ model significantly improved the agreement with experimental data for s-trans-BDE (root-mean-square deviation ≈ 5.5 cm(-1)). The accuracy in predicting the rather well-studied spectrum of fundamentals of s-trans-BDE assures good predictions of the spectrum of s-gauche-BDE. A nearly complete assignment of fundamentals was obtained for the gauche conformer. Many nonfundamental transitions of the BDE conformers were interpreted as well. The predictions of multiple Fermi resonances in the complex CH-stretching region correlate well with experiment. It is shown that solving a vibrational anharmonic problem through a numerical-analytic implementation of CVPT2 is a straightforward and computationally advantageous approach for medium-size molecules in comparison with the standard second-order vibrational perturbation theory (VPT2) based on analytic expressions.

Ab Initio Anharmonic Analysis of Vibrational Spectra of Uracil Using the Numerical-Analytic Implementation of Operator Van Vleck Perturbation Theory.

The numerical-analytic implementation of the operator version of the canonical Van Vleck second-order vibrational perturbation theory (CVPT2) is employed for a purely ab initio prediction and interpretation of the infrared (IR) and Raman anharmonic spectra of a medium-size molecule of the diketo tautomer of uracil (2,4(1H,3H)-pyrimidinedione), which has high biological importance as one of the four RNA nucleobases. A nonempirical, semidiagonal quartic potential energy surface (PES) expressed in normal coordinates was evaluated at the MP2/cc-pVTZ level of theory. The quality of the PES was improved by replacing the harmonic frequencies with the "best" estimated CCSD(T)-based values taken from the literature. The theoretical method is enhanced by an accurate treatment of multiple Fermi and Darling-Dennison resonances with evaluation of the corresponding resonance constants W and K (CVPT2+WK method). A prediction of the anharmonic frequencies as well as IR and Raman intensities was used for a detailed interpretation of the experimental spectra of uracil. Very good agreement between predicted and observed vibrational frequencies has been achieved (RMSD ∼4.5 cm(-1)). The model employed gave a theoretically robust treatment of the multiple resonances in the 1680-1790 cm(-1) region. Our new analysis gives the most reliable reassignments of IR and Raman spectra of uracil available to date.

A refined quartic potential energy surface and large scale vibrational calculations for S0 thiophosgene

In this work we present a full 6D quartic potential energy surface (PES) for S0 thiophosgene in curvilinear symmetrized bond-angle coordinates. The PES was refined starting from an ab initio field derived from acc-pVTZ basis set with CCSD(T) corrections for electron correlation. In the present calculations we used our variational method that was recently tested on formaldehyde and some of its isotopomers, along with additional improvements. The lower experimentally known vibrational levels for 35Cl2CS were reproduced quite well in the calculations, which can be regarded as a test for the feasibility of the obtained quartic PES.

Vibrational energy levels for CH 4 from an ab initio potential

Many areas of astronomy and astrophysics require an accurate high temperature spectrum of methane (CH 4). The goal of the present research is to determine an accurate ab initio potential energy surface (PES) for CH 4. As a first step towards this goal, we have determined a PES including up to octic terms. We compare our results with experiment and to a PES based on a quartic expansion. Our octic PES gives good agreement with experiment for all levels, while the quartic PES only for the lower levels.

Evidence of Fermi resonance in core-ionized methane

A full quartic potential energy surface is determined for core-ionized methane and used to investigate coupling between vibrational modes. A strong Fermi resonance is found between the first excited state of the symmetric stretching mode ν1′ and a doubly excited bending mode, whereas the corresponding interaction is less pronounced for v1′=2. In terms of the carbon 1s photoelectron spectrum of methane, the net effect of the mode coupling is to reduce the apparent contribution from anharmonicity to peak positions. The contribution from anharmonicity to the intensity of each peak is dominated by cubic and quartic terms in the symmetric stretching coordinate, and remains significant. This resolves a paradox pointed out in a recent experimental work [Carroll et al., Phys. Rev. A 59, 3386 (1999)].