For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.

The assignment of vibrational states is an integral part of quantum chemical calculations, which supports the analysis of experimental infrared spectra. In variational calculations, usually, it is the leading coefficient of the configuration interaction vector, which provides the state identity. However, this concept will possibly fail in case of special coordinate systems, such as, for example, localized normal coordinates, or within calculations for overtones of non-Abelian molecules, when a real valued configuration basis has been employed. A combination of both renders a proper assignment fairly tedious. We present a route to overcome this problem by using a highly efficient calculation of multidimensional overlap integrals based on the Smolyak quadrature. Beside this, a general protocol for the symmetry assignment of vibrational states will be discussed, which completes a general assignment. Extensive benchmark calculations are provided for the fundamental modes and overtones of chloromethane, CH3Cl, in canonical and localized normal coordinates based on accurate potential energy surfaces obtained from explicitly correlated coupled-cluster theory. In addition, the linear CNNC molecule has been studied, for which hardly any reference data do exist.

Finite basis vibrational configuration interaction theory (VCI) is a highly accurate method for the variational calculation of state energies and related properties, but suffers from fast growing computational costs in dependence of the size of the correlation space. In this series of papers, concepts and techniques will be presented, which diminish the computational demands and thus broaden the applicability of this method to larger molecules or more complex situations. This first part focuses on a highly efficient implementation of the vibrational angular momentum (VAM) terms as occurring in the Watson Hamiltonian and the prediagonalization of initial subspaces within an iterative configuration selective VCI implementation. Working equations and benchmark calculations are provided, the latter demonstrating the increased performance of the new algorithm.

Vibrational configuration interaction calculations (VCI) have been performed to study the impact of the nature of the underlying coordinate systems, i.e., canonical vs localized normal coordinates, on accurate vibrational structure calculations for non-Abelian molecules. Once the correlation space is represented by real-valued primitive Hartree products, the assignment of vibrational states beyond the fundamentals is usually a tedious task and is further complicated by the use of non-symmetry-adapted coordinates. Our recently presented approach based on sparse grid integration of overlap integrals of the VCI wave function with the corresponding harmonic oscillator wave function has been used to determine and assign all fundamentals and vibrational overtones of allene and its deuterated isotopologue. Excellent agreement with available experimental results is observed in all cases.

Bose-Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit PT -symmetric states. As proposed by Kreibich et al [Phys. Rev. A 87, 051601(R) (2013)], in the mean-field limit the dynamical behaviour of this system, especially that of the PT -symmetric states, can be simulated by embedding it into a Hermitian four-well system with time-dependent parameters. In this paper we go beyond the mean-field approximation and investigate manybody effects in this system, which are in lowest order described by the single-particle density matrix. The conditions for PT symmetry in the single-particle density matrix cannot be completely fulfilled by using pure initial states. Here we show that it is mathematically possible to achieve exact PT symmetry in the four-well many-body system in the sense of the dynamical behaviour of the single-particle density matrix. In contrast to previous work, for this purpose, we use mixed initial states fulfilling certain constraints and use them to calculate the dynamics.