Alternative perturbation method for the molecular vibration–rotation problem

Abstract

ABSTRACT:This article introduces an alternative perturbation scheme to find approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. The method is implemented for the Watson Hamiltonian and applied to methane. The complete J ϭ 0 spectrum of this penta-atomic molecule of atmospheric interest is calculated up to 9200 cm Ϫ1 in a purely ab initio fashion. Then, the rotational spectra of the vibrational ground state is obtained up to J ϭ 18. The largest relative error is 2.10 Ϫ5 (for the highest J ϭ 18 level) after scaling of a single parameter. Without scaling the accuracy on the rotational levels is limited by that of the ab initio equilibrium bond distance. The convergence of our results is analyzed with respect to the different parameters involved in our approach. The important concept of vibrational mean-field configuration interaction is introduced.

Prediction of Accurate Anharmonic Experimental Vibrational Frequencies for Water Clusters, (H2O)n, n = 2−5

“…28,73,[78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93] An effective way to treat medium-sized molecules uses second-order perturbation theory (PT2), which has been shown to give good results. 37-39,94-96 The PT2 approach, while less expensive than a more rigorous converged variational calculation, is still computationally expensive.…”

From atoms to biomolecules: a fruitful perspective

“…Extensive calculations were also performed on methane [25][26][27][28][29], with the goal to predict the rotation-vibration spectrum which is of particular interest for evaluating methane abundance in planetary atmospheres. Our most recent results use an accurate potential energy surface calculated at the CCSD(T)/ACV5Z level of theory [119] and a dipole moment surface that we calculated at the IC-MRCI/ ACV5Z level.…”

“…The vibrational Schrödinger equation has been solved variationally, and perturbation theory was used to calculate the rotational spectrum of the ground vibrational state [29]. Note that the variational method developed for solving the vibrational problem, the vibrational mean field configuration interaction method (VMFCI) [26,27], is directly inspired from electronic ab initio SCF/CI theory. The rotational spectrum calculated in that way is in very good agreement with the one recently recorded at the SOLEIL synchrotron [14] and with the atmospheric HI-TRAN database [142].…”

An improved third order dipole moment surface for methane

“…Eigenstates converged to within the cm −1 accuracy (or better), up to, say, the tetradecad for a given PES have been obtained by means of various forms of configuration interactions (CI) [30][31][32][33][34] (earlier references can be found therein). We have used the vibrational mean field configuration interaction (VMFCI) method [35][36][37][38][39] to solve methane vibrational, stationary Schrödinger equation.…”

“…The VMFCI method has been combined with a generalized perturbation theory [28,35,44], to obtain effective rotational observable, from which accurate rotational spectra can be calculated [29,45].…”