Charge asymmetry in rovibrationally excited HD+ determined using explicitly correlated all-particle Gaussian functions

Deformed explicitly correlated Gaussians

Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli-Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light-matter coupled systems in cavity QED.

Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.

A comparison of two types of explicitly correlated Gaussian functions for non-Born-Oppenheimer molecular calculations using a model potential

A new functional form of the explicitly correlated Gaussian-type functions (later called Gaussians or ECGs) for performing non-Born-Oppenheimer (BO) calculations of molecular systems with an arbitrary number of nuclei is presented. In these functions, the exponential part explicitly depends on all interparticle distances and the preexponential part depends only on the distances between the nuclei. The new Gaussians are called sin/cos-Gaussians and their preexponential part is a product of sin and/or cos factors. The effectiveness of the new Gaussians in describing non-BO pure vibrational states is investigated by comparing them with r(m)-Gaussians containing preexponential multipliers in the form of non-negative powers of internuclear distances (the internuclear distance in the diatomic case). The testing is performed for a diatomic system with the nuclei interacting through a Morse potential. It shows that the new sin/cos-Gaussian basis set is capable of providing equally accurate results as obtained with the r(m)-Gaussians. However, especially for lower vibrational states, more sin/cos-Gaussians are needed to reach a similar accuracy level as obtained with the r(m)-Gaussians. Implementation of the sin/cos-Gaussians in non-BO calculations of diatomic and, in particular, of triatomic systems, which will follow, will provide further assessment of the efficiency of the new functions.

Charge asymmetry in the rovibrationally excited HD molecule

The recently developed method for performing all-particle non-Born-Oppenheimer variational calculations on diatomic molecular systems excited to the first excited rotational state and simultaneously vibrationally excited is employed to study the charge asymmetry and the level lifetimes of the HD molecule. The method uses all-particle explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians are optimized with the aid of the analytical energy gradient determined with respect to these parameters.