Isotope shifts of the three lowest S1 states of the B+ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections

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.

Lowest ^{2}S Electronic Excitations of the Boron Atom

A theoretical ab initio approach for calculating bound states of small atoms is developed and implemented. The approach is based on finite-nuclear-mass [non-Born-Oppenheimer (non-BO)] nonrelativistic variational calculations performed with all-particle explicitly correlated Gaussian functions and includes the leading relativistic and quantum electrodynamics energy corrections determined using the non-BO wave functions. The approach is applied to determine the total and transition energies for the lowest four ^{2}S electronic excitations of the boron atom. The transition energies agree with the available experimental values within 0.2-0.3  cm^{-1}. Previously, such accuracy was achieved for three- and four-electron systems.

Prediction of (1)P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the seven lowest 1s(2)2s np ((1)P), n = 2...8, states of the beryllium atom. The calculations explicitly include the effect of finite mass of (9)Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12,500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s(2)2s np ((1)P) →1s(2)2s(2) ((1)S) transition is about 12 cm(-1). The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm(-1).

Assessment of the accuracy the experimental energies of the 1P(o) 1s(2)2s6p and 1s(2)2s7p states of 9Be based on variational calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the six lowest states of the (1)P(o) 1s(2)2snp state series of the (9)Be atom. The wave functions of the states are expanded in terms of all-particle, explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations. The exponential parameters of the Gaussians are variationally optimized using the analytical energy gradient determined with respect to those parameters. Besides providing reference non-relativistic energies for the considered states, the calculations also allow to assess the accuracy of the experimental energies of the (1)P(o) 1s(2)2s6p and 1s(2)2s7p states and suggest their refinement.