A study of the vibrations of fluoroform with a sixth order nine-dimensional potential: a combined perturbative-variational approach

Isotope effects on the resonance interactions and vibrational quantum dynamics of fluoroform 12,13CHF3

We report a comparison of the analysis of the low energy spectrum of ¹³CHF₃ and ¹²CHF₃ from the THz (FIR) range to the ν₁ fundamental at high resolution (δ[small nu, Greek, tilde] < 0.001 cm^-1 or otherwise Doppler limited) on the basis of FTIR spectra taken both with ordinary light sources and with the synchrotron radiation from the Swiss Light Source. Several vibrational levels are accurately determined including, in particular, the 2ν₄ CH-bending overtone and the ν₁ CH-stretching fundamental of ¹³CHF₃. Comparison of experimental results with those from accurate full dimensional vibrational calculations allows for a study of the time-dependent quantum dynamics of intramolecular vibrational redistribution (IVR) in the CH chromophore both on short time scales (fs) and longer time scales (ps) when coupling to the lower frequency modes becomes important and where the ¹²C/¹³C isotope effects are very large.

Assigning the low lying vibronic states of CH3O and CD3O

The assignment of lines in vibrational spectra in strongly mixing systems is considered. Several low lying vibrational states of the ground electronic X∼²E state of the CH₃O and CD₃O radicals are assigned. Jahn-Teller, spin-orbit, and Fermi couplings mix the normal mode states. The mixing complicates the assignment of the infrared spectra using a zero-order normal mode representation. Alternative zero-order representations, which include specific Jahn-Teller couplings, are explored. These representations allow for definitive assignments. In many instances it is possible to plot the wavefunctions on which the assignments are based. The plots, which are shown in the adiabatic representation, allow one to visualize the effects of various higher order couplings. The plots also enable one to visualize the conical seam and its effect on the wavefunctions. The first and the second order Jahn-Teller couplings in the rocking motion dominate the spectral features in CH₃O, while first order and modulated first order couplings dominate the spectral features in CD₃O. The methods described here are general and can be applied to other Jahn-Teller systems.

Simulation of Ã(2)A(1)←X̃(2)E laser excitation spectrum of CH3O and CD3O

A theoretical calculation of the laser-induced fluorescence excitation spectrum from X̃(2)E→Ã(2)A1 is carried out for CH3O and CD3O using a transition dipole moment surface expanded up to second order. The vibronic form of these operators is obtained using symmetry arguments. The Ã(2)A1 vibrational levels are calculated using Van Vleck perturbation theory, and the latter is used to adjust harmonic constants of the potential to match experimental fundamentals. The CH3O fit force field is tested on CD3O. For both molecules the transition energies are well reproduced, but there are systematic differences between experimental and theoretical intensities. The origins of these differences 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.

Variational Calculation of Specific, Highly Excited Vibrational States in DFCO: Comparison with Experimental Data

A stimulated emission pumping spectra of jet-cooled DFCO performed by Crane et al. (J. Mol. Spectrosc. 1997, 183, 273) has provided a great number of ro-vibrational lines up to 9000 cm(-1) of excitation energy. By combining a Jacobi-Wilson (JW) approach with a Davidson scheme, we calculate the lines provided by the experiment up to 9000 cm(-1) using an ab initio global potential energy surface (PES) developed by Kato et al. (J. Chem. Phys. 1997, 107, 6114). Comparisons between experimental and calculated data provide a critical test of the quality of the PES used. We show that the variational calculated energies can be efficiently corrected by taking into account the error observed for the A' fundamental transitions nu(i) (i = 1, ..., 5) and the first overtone 2nu(6). A detailed analysis of the eigenstates obtained by the calculation allows one to quantify the coupling between the different modes. Such an information is essential to understand and predict the energy flow through a DFCO molecule that is initially excited.

Comparison of Perturbative and Variational Treatments of Molecular Vibrations: Application to the Vibrational Spectrum of HFCO up to 8000 cm-1†

We calculated highly excited states of the HFCO molecule, comparing results from two methods. In the first method, Van Vleck perturbation theory is used to transform away all off-diagonal couplings except those between nearly degenerate states. This perturbative transformation leads to a matrix representation where eigenvalues are obtained with relatively small matrices. In the second method, variational eigenvalues are obtained by combining the Jacobi-Wilson approach with the block-Davidson scheme. The key ingredient here is a prediagonalized-perturbative scheme applied to a subspace of a curvilinear normal-mode basis set. Comparisons of the two methods provide a critical test of the less time-consuming perturbation theory. Two different coordinate sets are used to test the sensitivity of the results to coordinate choice. Perturbation theory also requires a polynomial fit to the potential. The implications of this restriction are investigated.

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.

Using simultaneous diagonalization and trace minimization to make an efficient and simple multidimensional basis for solving the vibrational Schrödinger equation

In this paper we improve the product simultaneous diagonalization (SD) basis method we previously proposed [J. Chem. Phys. 122, 134101 (2005)] and applied to solve the Schrodinger equation for the motion of nuclei on a potential surface. The improved method is tested using coupled complicated Hamiltonians with as many as 16 coordinates for which we can easily find numerically exact solutions. In a basis of sorted products of one-dimensional (1D) SD functions the Hamiltonian matrix is nearly diagonal. The localization of the 1D SD functions for coordinate qc depends on a parameter we denote alphac. In this paper we present a trace minimization scheme for choosing alphac to nearly block diagonalize the Hamiltonian matrix. Near-block diagonality makes it possible to truncate the matrix without degrading the accuracy of the lowest energy levels. We show that in the sorted product SD basis perturbation theory works extremely well. The trace minimization scheme is general and easy to implement.

Calculation of specific, highly excited vibrational states based on a Davidson scheme: Application to HFCO

We present the efficiency of a new modified Davidson scheme which yields selectively one high-energy vibrationally excited eigenstate or a series of eigenstates. The calculation of a highly vibrationally excited state psi located in a dense part of the spectrum requires a specific prediagonalization step before the Davidson scheme. It consists in building a small active space P containing the zero-order states which are coupled with the zero-order description of the eigenstate of interest. We propose a general way to define this active space P which plays a crucial role in the method. The efficiency of the method is illustrated by computing and analyzing the high-energy excited overtones of the out-of-plane mode [formula: see text] in HFCO. These overtone energies correspond to the 234th, 713th, and 1774th energy levels in our reference basis set which contains roughly 140,000 states. One of the main advantages of this Davidson scheme comes from the fact that the eigenstate and eigenvalue convergence can be assessed during the iterations by looking at the residual [formula: see text]. The maximum value epsilon allowed for this residual constitutes a very sensitive and efficient parameter which sets the accuracy of the eigenvalues and eigenstates, even when the studied states are highly excited and are localized in a dense part of the spectrum. The physical analysis of the eigenstates associated with the 5th, 7th, and 9th out-of-plane overtones in HFCO provides some interesting information on the energy localization in this mode and on the role played by the in-plane modes. Also, it provides some ideas on the numerical methods which should be developed in the future to tackle higher-energy excited states in polyatomics.