Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller–Plesset perturbation theory

Abstract

We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We apply this method to and demonstrate its accuracy on two molecules: SiC, a quasilinear triatomic with significant bending anharmonicity, and CHNO, which contains a completely unhindered methyl rotor. In addition to these two examples, we discuss several key technical aspects of the method, including an efficient implementation of Eckart and quasi-Eckart frame embedding that does not rely on numerical finite differences.

The Molecular Structure of gauche‐1,3‐Butadiene: Experimental Establishment of Non‐planarity

“…The( Q) correction for the dihedral t is surprisingly large (almost 18 8), presumably because of the complex electron correlation associated with conjugation. Together with zero-point corrections from second-order vibrational Møller-Plesset theory [44] (VMP2) using FC-CCSD(T) calculations and the ANO1 basis set, [45,46] this structure accurately predicted the rotational constants for all isotopologues:the final calculations described here match all observed rotational constants to within 6MHz. All of the electronic structure calculations were carried out with CFOUR; [47] the VMP2 calculations were performed using NITROGEN.…”

The equilibrium structure of hydrogen peroxide

“…Semi-experimental equilibrium rotational constants (B se e ) were calculated by subtracting ab initio rotation-vibration parameters (B e − B 0 , frequently approximated in perturbation-theory-based methods as − 1 2 i α B i ) from the experimentally observed rotational constant values [11][12][13][14][15]. These rovibrational zero-point motion corrections were obtained with several treatments of the nuclear motion (second order vibrational perturbation theory (VPT2) [21], second-order vibrational Møller-Plesset theory (VMP2) [20], and variational) on potential energy surfaces (PES) using various levels of electronic structure theory [22,23]. Variational calculations on the "V+C+R+H" PES of Ref.…”

“…The VMP2 calculations represent the rovibrational Hamiltonian using several many-body expansions. For the calculations reported here, the expansion orders were (N V , N G1 , N G2 , N U , N V T , N Grv , N Grr ) = (5, 4, 4, 3, 3, 4, 4), including a dereferenced torsional coordinate [20]. Additionally, the virtual configuration space was constricted to a maximum of 8 quanta in both the dereferenced torsional mode and the sum of the excitations in the non-deferenced small amplitude modes.…”

“…The semi-experimental structure requires theoretical input from rovibrational calculations, for which we turn to numerically exact variational methods. These results also serve as a useful reference for assessing the performance of approximate rovibrational methods, in particular curvilinear coordinate vibrational second order Møller-Plesset perturbation theory (VMP2) [17][18][19] and a recently developed extension for J > 0 rovibrational calculations [20]. The use of a curvilinear coordinate description makes this method applicable to molecules exhibiting large amplitude nuclear motion.…”

The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges

“…As for the electronic structure case, dynamical correlation is efficiently recovered by vibrational perturbation theory, based either on harmonic wave functions 209,220 or on a vibrational SCF reference. 208,221 To increase the efficiency of vDMRG it is crucial to apply the variational correction only to the vibrational degrees of freedom displaying strong static correlation. The effect for the remaining modes may then be captured by perturbation theory.…”