High angular momentum states of lithium atom, studied with symmetry-projected explicitly correlated Gaussian lobe functions

Relativistic two-electron atomic and molecular energies using LS coupling and double groups: Role of the triplet contributions to singlet states

The triplet contribution is computed to the 1 and 2 S0e1 states of the He atom, to the 1S0e1 state of the Li⁺ and Be²⁺ ions, and to the X¹Σ_g ⁺ ground state of the H₂ molecule by extensive use of double-group symmetry (equivalent to LS coupling for the atomic systems) during the course of the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) wave equation. The no-pair DCB energies are converged within sub-parts-per-billion relative precision, using an explicitly correlated Gaussian basis optimized to the non-relativistic energies. The α fine-structure constant dependence of the triplet sector contribution to the variational energy is α⁴E_h at leading order, in agreement with the formal perturbation theory result available from the literature.

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.

Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations

Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H 3 + = { p + , p + , p + , e - , e - } molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result obtained for this molecular ion with rotational-vibrational calculations carried out on a potential energy surface.

The order of three lowest-energy states of the six-electron harmonium at small force constant

The order of low-energy states of six-electron harmonium is uncertain in the case of strong correlation, which is not a desired situation for the model system being considered for future testing of approximate methods of quantum chemistry. The computational study of these states has been carried out at the frequency parameter ω = 0.01, using the variational method with the basis of symmetry-projected, explicitly correlated Gaussian (ECG) lobe functions. It has revealed that the six-electron harmonium at this confinement strength is an octahedral Wigner molecule, whose order of states is different than in the strong confinement regime and does not agree with the earlier predictions. The results obtained for ω = 0.5 and 10 are consistent with the findings based on the Hund's rules for the s(2)p(4) electron configuration. Substantial part of the computations has been carried out on the graphical processing units and the efficiency of these devices in calculation of the integrals over ECG functions has been compared with traditional processors.

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.

Excited S-symmetry states of positronic lithium and beryllium

The possibility of the existence of excited S-symmetry states of positronic lithium and beryllium, resulting from the positron attachment to high-spin P parent atomic states, is examined and confirmed with variational calculations in the basis of explicitly correlated Gaussian functions. The unexpectedly different order of the energies of the S and P states is explained by the formation of the positronium cluster structure and associated disappearance of the destabilizing centrifugal force. The annihilation properties of newly discovered states are discussed in the context of prospective experimental detection.