Lowest order perturbative approximation to vibrational coupled cluster method in bosonic representation
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Ó Indian Academy of Sciences Sadhana (0123456789().,-volV)FT3](0123456 789().,-volV)
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Lowest order perturbative approximation to vibrational coupled cluster method in bosonic representation T DINESH and SUBRATA BANIK* School of Chemistry, University of Hyderabad, Hyderabad 500 046, Telangana, India E-mail: [email protected] MS received 27 April 2019; revised 30 July 2019; accepted 6 August 2019
Abstract. We propose a perturbative approximation to the vibrational coupled cluster method in bosonic representation to reduce the cost of calculating the cluster matrix elements by considering only the first order of S and r for the construction of the effective Hamiltonian er eS HeS er . With the systematic analysis of the results of two molecules, H2 O and 1,1-difluoroethylene, we find that the accuracy of the transition energies with such low order approximation is comparable to the fully converged VCCM. Keywords. Vibrational coupled cluster method; perturbation theory; effective Hamiltonian.
1. Introduction Development of efficient and accurate quantum mechanical method for the description of anharmonic vibrations in polyatomic molecules has been a key interest of many researchers. Within the Born-Oppenheimer approximation, the electronic Schro¨dinger equation generates the potential energy surface for the nuclear motion in the molecule. The Watson Hamiltonian describes the molecular vibrations in a simple and efficient way H¼
X P2 i
i
2
þ VðqÞ þ VW þ VC :
ð1Þ
Here, qi are the mass-weighted normal coordinates and Pi are the conjugate momenta. The terms VW and VC are the Watson’s mass-dependent term and Coriolis coupling term, respectively. The potential V(q) is usually approximated by the quartic polynomial of the Taylor series expansion VðqÞ ¼
X 1X 2 2 xi qi þ fijk qi qj qk 2 i ijk X þ fijkl qi qj qk ql : ijkl
ð2Þ
Here, xi is the harmonic frequency of ith vibrational mode, fijk and fijkl are the third and fourth derivatives of the electronic energy with respect to the mass-weighted normal coordinates at equilibrium geometry. The vibrational Hamiltonian with such quartic potential is a many-body Hamiltonian, and thus, the exact analytical solution of corresponding Schro¨dinger equation is not possible. Several approximate methods have been developed to solve the vibrational Schro¨dinger equation based on both variation principle and perturbation theory. The second order vibrational perturbation theory (VPT21–3) has been developed, where the Hamiltonian with only quadratic potential is taken as the zeroth order Hamiltonian and the cubic and quartic terms are treated as perturbations. Although, such approach has been used extensively by many authors with successful interpretations of infrared spectra of numerous molecules, the failure of the VPT2 is well-known when the one encounters vibrational resonances like Fermi resonance. The vibrational self-consistent field (VSCF) theory4–6 and its generalizations to multiconfigurational reference functions7 are developed and used extensivel
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