Rotation–vibration interactions in highly excited states of SO2and H2CO

Rotamers of Methanediol: Composite Ab Initio Predictions of Structures, Frequencies, and Rovibrational Constants

Geminal diols are known to be important intermediates in atmospheric ozonolysis and the aerosol cycle. Recently, the simplest member of this class, methanediol, was interrogated in the gas phase with infrared spectroscopy. To aid in future spectroscopic investigations of methanediol, including in the interstellar medium, we report fundamental frequencies and rovibrational constants for the two rotamers of this molecule using ab initio composite methods along with vibrational perturbation theory. Sensitivity of the predictions to the level of theory and the treatment of anharmonic resonances are carefully assessed. The OH stretching harmonic frequencies of both rotamers are particularly sensitive to the level of theory. The CH stretches of the C_s rotamer are sensitive to the treatment of anharmonic resonances with VPT2-based effective Hamiltonian models. Equilibrium bond distances and harmonic frequencies are converged conservatively to within 0.0005 Å and 3 cm^-1, respectively. The effect of tunneling on the rotational constants is investigated with a 2D variational calculation, based on a relaxed hydroxyl torsional potential energy surface. Tunneling is found to be negligible in the lower energy C₂ rotamer but should modify the rotational constants of the C_s rotamer on the order of MHz, giving rise to rotational line splittings of the same order. The rovibrational constants of the C_s rotamer are dominated by hydroxyl torsional effects, and here we see evidence for the breakdown of vibrational perturbation theory.

Exploring Expansions of the Potential and Dipole Surfaces Used for Vibrational Perturbation Theory

A scheme for evaluating expansions of the potential and dipole moment surfaces for vibrational perturbation theory is described. The approach is based on numerical differentiation of the Hessian in the coordinates of interest. It is shown that performing these calculations in internal coordinates generates expansions that are transferable among isotopologues of the molecule of interest. Additionally, re-expressing the expansion of the potential in terms of functions of the internal coordinates, for example, cosines of angles or exponential functions of the bond length displacements, provides expansions that can be used for higher-order perturbation theory calculations. The approach is explored and the results are discussed for water, HOD, ammonia, isomers of HNO₃, and halogenated methane.

Using collocation to study the vibrational dynamics of molecules

In this paper, I review collocation methods for solving the time-independent and the time-dependent Schroedinger equation. Unlike traditional variational methods, collocation methods do not require integrals and quadrature. Either collocation or quadrature is necessary if the potential does not have a special form. If the basis is a direct product of univariate bases and the quadrature grid is also a direct product, there exist variational methods that do not require quadrature approximations for potential energy matrix elements. These methods, however, do require storing, in computer memory, vectors with as many components as there are quadrature points. For this reason direct-product variational methods are poor for problems with more than five atoms. There are well established ideas for reducing the size of the basis in a variational calculation. Three such ideas are: 1) prune the direct product basis; 2) use basis functions that are products of multivariate functions; 3) optimise the basis functions (e.g. Multiconfiguration time-dependent Hartree). Reducing the basis size, however, is not enough to the make variational methods tractable because, for all three of these ideas, quadrature rears its ugly head. Collocation is an attractive alternative to variational methods.

Theoretical study of spectroscopic constants and anharmonic force field of formaldehyde

The equilibrium geometries of formaldehyde are optimized with B3LYP, B3PW91 and MP2 methods employing three basis sets 6-311++G(2d,2p), aug-cc-pVTZ and cc-pVTZ, respectively, which agree well with the corresponding experimental and previous theoretical data. The best optimized geometries are obtained at the theoretical level B3LYP/6-311++G(2d,2p) basis set. Basing on the calculated equilibrium geometries, the spectroscopic constants and anharmonic force field of H 2 CO are investigated. The results show that DFT method is superior to MP2 method at the calculation of spectroscopic constants and force constants of H 2 CO . The vibration–rotation interaction constants and fundamental vibrational wave numbers of H 2 CO are firstly theoretically calculated. The Coriolis coupling constants, cubic force constants and most of quartic force constants are firstly theoretically predicted.

Numerically constructed internal-coordinate Hamiltonian with Eckart embedding and its application for the inversion tunneling of ammonia

It is shown that the use of an Eckart-frame embedding with a kinetic energy operator expressed in curvilinear internal coordinates becomes feasible and straightforward to implement for arbitrary molecular compositions and internal coordinates if the operator is defined numerically over a (discrete variable representation) grid. The algorithm proposed utilizes the transformation method of Dymarsky and Kudin to maintain the rotational Eckart condition. In order to demonstrate the applicability and flexibility of our approach the non-rigid ammonia molecule is considered and the corresponding rotational-vibrational energy levels and wave functions are computed using kinetic energy operators with three different embeddings. Two of them fulfill the Eckart conditions corresponding to a trigonal pyramidal (C3v) and a trigonal planar (D3h) reference structure and the third one is a non-Eckart frame. The computed energy levels are, of course, identical, and the structure of the three different wave-function representations are analyzed in terms of the rigid rotor functions for a symmetric top. The possible advantages of one frame representation over another are discussed concerning the interpretation of the rovibrational states in terms of the traditional rigid rotor labels.

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.

Relaxation of the CH stretch in liquid CHBr3: Solvent effects and decay rates using classical nonequilibrium simulations

This article addresses two questions regarding the decay of the CH stretch in liquid CHBr3. The first is whether the initial steps of the relaxation primarily involve energy redistribution within the excited molecule alone. Gas phase quantum mechanical and classical calculations are performed to examine the role of the solvent in this process. At the fundamental excitation level, it is found that CH stretch decay is, in fact, strongly solvent driven. The second question is on the applicability of a fully classical approach to the calculation of CH stretch condensed phase decay rates. To this end, nonequilibrium molecular dynamics simulations are performed. The results are compared with quantum mechanical rates computed previously. The two methods are found to be in fair agreement with each other. However, care must be exercised in the interpretation of the classical results.

Combination of perturbative and variational methods for calculating molecular spectra: Calculation of the υ=3–5 CH stretch overtone spectrum of CHF3

Highly excited states of the CHF3 molecule belonging to the third, fourth, and fifth Fermi polyad are calculated using a combination of the Van Vleck perturbation theory and a variational treatment. The perturbation theory preconditions the Hamiltonian matrix by transforming away all couplings except those between nearly degenerate states. This transformation is implemented so that eigenvalues can be found with significantly smaller matrices than that which would be needed in the original normal mode representation. Even with preconditioning, at the energies as high as 3-5 quanta in the CH stretch, it is not possible to directly diagonalize the Hamiltonian matrix due to the large basis sets required. Iterative methods, particularly the block-Davidson method, are explored for finding the eigenvalues. The methods are compared and the advantages discussed.

Including Anharmonicity in the Calculation of Rate Constants. 1. The HCN/HNC Isomerization Reaction

A method for calculating anharmonic vibrational energy levels in asymmetric top and linear systems that is based on second-order perturbation theory in curvilinear coordinates is extended to the bound generalized normal modes at nonstationary points along a reaction path. Explicit formulas for the anharmonicity coefficients, x(ij), and the constant term, E0, are presented, and the necessary modifications for resonance cases are considered. The method is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the HCN/HNC isomerization reaction. Although the results for this system are not very sensitive to the choice of coordinates, we find that the inclusion of anharmonicity leads to a substantial improvement in the vibrational energy levels. We also present detailed comparisons of rate constants computed with and without anharmonicity, with various approximations for incorporating tunneling along the reaction path, and with a more practical approach to calculating the vibrational partition functions needed for larger systems.

Combined perturbative-variational investigation of the vibrations of CHBr3 and CDBr3

A full dimensional vibrational treatment of CHBr(3) and CDBr(3) using Van Vleck perturbation theory followed by a variational calculation is presented. The calculation of a force field, and its adjustment for better match with experiment, is discussed. The computed eigenstates and spectral features are compared to experiment. Changes in intensities of the nu(1) and 2nu(4) bands upon simple alterations of the dipole moment expansion are described.

Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules

The use of energy selected bases (ESB) with iterative diagonalization of the Hamiltonian matrix is described for vibrations of tetra-atomic systems. The performance of the method is tested by computing vibrational states of HOOH below 10,000 cm(-1) (1296 A+ symmetry states) and H(2)CO below 13,500 cm(-1) (729 A(1) symmetry states). For iterative solutions, we tested both the implicitly restarted Lanczos method (IRLM) and the standard (nonreorthogonalizing) Lanczos approach. Comparison with other contracted basis approach as well as direct product grid representation shows superior performance of the ESB/IRLM approach. Of the two systems, H(2)CO is found to be more challenging than HOOH since it has much stronger couplings among vibrational modes, which leads to a drastically larger primitive basis set. For H(2)CO we also discuss some interesting behavior of the molecule in the high internal energy regime.

A perturbative calculation of the rovibrational energy levels of methane

The rovibrational energy levels of methane are determined from a quartic ab initio potential energy force field where the expansion coordinates are the Morse coordinates for the stretches and extension coordinates for the bends. Energies are calculated using canonical Van Vleck perturbation theory. Results are obtained for both rotation-vibration Hamiltonians expressed as functions of curvilinear and rectilinear normal coordinates. Second, fourth, and sixth order curvilinear results are compared with experimental results, and fourth order results for the rectilinear and curvilinear Hamiltonian are compared to each other. The calculated rovibrational levels are in good agreement with the experimental values for low J levels. The calculated rotational level splittings are in even better agreement with the experiment. In particular, the ground state tetrahedral splittings, which are as small as 10(-4) cm(-1), are well reproduced by our calculations at sixth order.