Explicitly correlated Gaussian calculations of the 2P(o) Rydberg spectrum of the lithium atom

Using Koopmans' theorem for constructing basis sets: approaching high Rydberg excited states of lithium with a compact Gaussian basis

For accurate ab initio description of Rydberg excited states, this study suggests generating appropriate diffuse basis functions by cheap variational optimization of virtual orbitals of the corresponding ion core. By following this approach, dozens of converged correlated lithium Rydberg states, namely, all the states up to 24 ²S, 25 ²P, 14 ²D, 16 ²F and 16 ²G, not yet achieved via other ab initio approaches, could be obtained at the EOM-CCSD level of theory with compact and mostly state-selective contracted Gaussian basis sets. Despite its small size and Gaussian character, the optimized basis leads to highly accurate excitation energies that differ merely in the order of meV from the reference state-of-the-art explicitly correlated Gaussian method and even surpass Full-CI results on the Slater basis by an order of magnitude.

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.

Solving the Schrödinger equation with the free-complement chemical-formula theory: Variational study of the ground and excited states of Be and Li atoms

The chemical formula theory (CFT) proposed in Paper I of this series [H. Nakatsuji et al., J. Chem. Phys. 149, 114105 (2018)] is a simple variational electronic structure theory for atoms and molecules. The CFT constructs simple, conceptually useful wave functions for the ground and excited states, simultaneously, from the ground and excited states of the constituent atoms, reflecting the spirits of the chemical formulas. The CFT wave functions are also designed to be used as the initial wave functions of the free complement (FC) theory, that is, the exact theory producing the exact wave functions of the Schrödinger accuracy. This combined theory is referred to as the FC-CFT. We aim to construct an exact wave function theory that is useful not only quantitatively but also conceptually. This paper shows the atomic applications of the CFT and the FC-CFT. For simplicity, we choose the small atoms, Be and Li, and perform variational calculations to essentially exact levels. For these elements, a simple Hylleraas CI type formulation is known to be potentially highly accurate: we realize it with the CFT and the FC-CFT. Even from the CFT levels, the excitation energies to the Rydberg excited states were calculated satisfactorily. Then, with increasing the order of the FC theory in the FC-CFT, all the absolute energies and the excitation energies of the Be and Li atoms were improved uniformly and reached rapidly to the essentially exact levels in order 3 or 4 with moderately small calculational labors.

Testing Quantum Electrodynamics in the Lowest Singlet State of Neutral Beryllium-9

We report spectroscopic results on the 2s2p^{1}P_{1} state in neutral atomic beryllium-9. The absolute frequency for the center of gravity is determined to be 42 565.4501(13)  cm^{-1}, a factor of 130 more precise than the previous experimental measurement. The result is in agreement with and a factor of 8 more precise than the current best theoretical estimate of 42 565.441(11)  cm^{-1}, which was calculated including the effects of quantum electrodynamics. Because of the large natural linewidth of the transition, the hyperfine constants were not able to be extracted to high precision.

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

Method of construction of wave functions approximating eigenfunctions of the [Formula: see text] operator is proposed for high angular momentum states of few-electron atoms. Basis functions are explicitly correlated Gaussian lobes, projected onto irreducible representations of finite point groups. Variational calculations have been carried out for the lowest states of lithium atom, with quantum number L in the range from 1 to 8. Nonrelativistic energies accurate to several dozens of nanohartree have been obtained. For 2(2)P, 3(2)D, and 4(2)F states they agree well with the reference results. Transition frequencies have been computed and compared with available experimental data.

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.