Vibrational many-body methods for molecules and extended systems

Vibrational many-body methods for molecules and extended systems have been developed that can account for the effects of anharmonicity in the potential energy surfaces (PESs) on energies and other observable properties. For molecules, we present a general scheme to calculate anharmonic vibrational frequencies and vibrationally-averaged structures along with applications to some key species in hydrocarbon combustion chemistry: HCO+, HCO, HNO, HOO, HOO–, CH3+, and CH3. We propose a hybrid, compact representation of PESs that combines the merits of two existing representations, which are a quartic force field (QFF) and numerical values on a rectilinear grid. We employed a combination of coupled-cluster singles and doubles (CCSD), CCSD with a second-order perturbation correction in the space of triples [CCSD(2)T] and in the space of triples and quadruples [CCSD(2)TQ], and a correlation-consistent basis set series to achieve the complete-correlation, complete-basis-set limits of the potential energy surfaces. The mean absolute deviation between the predicted and the observed frequencies is 11 cm –1.;For extended systems, we generalized the formulations of the vibrational self-consistent field (VSCF), vibrational Møller–Plesset perturbation (VMP), and vibrational coupled-cluster (VCC) methods on the basis of a QFF in normal coordinates. We have identified algebraically and eliminated several terms in the formalisms of VSCF that have nonphysical size dependence, leading to compact and strictly size-extensive equations. This size-extensive VSCF method (XVSCF) thus defined has no contributions from cubic force constants and alters only the transition energies of the underlying harmonic-oscillator reference from a subset of quartic force constants. The mean-field potential of XVSCF felt by each mode is shown to be effectively harmonic, making the XVSCF equations subject to a self-consistent analytical solution without a basis-set expansion and matrix diagonalization, which are necessary in VSCF. We implemented the XVSCF method for finite systems, and applied it to polyacenes up to tetracene as well as to a model system of a linear chain of masses interacting through a quartic force field. We showed that the results of XVSCF and VSCF approach each other as the size of the system is increased, implicating the inclusion of unnecessary, nonphysical terms in VSCF. We have also shown that apart from reducing the scaling of the VSCF calculation from quartic to quadratic, XVSCF is nearly three orders of magnitude faster than VSCF implemented with a reduced set of force constants. The second-order VMP and VCC methods based on the XVSCF reference are shown to account for anharmonic effects due to all cubic and quartic force constants in a size-extensive fashion.