Excitation energies in Be: A comparison of multiconfigurational linear response and full configuration interaction calculations

Abstract

Using a 〈9s9p5d〉 contracted GTO basis we have calculated low-lying excitation energies of singlet and triplet symmetry for the Be atom using Δfull CI, ΔCI(1s) with double occupancy in the 1s orbital, multiconfiguration linear response (MCLR), and ΔMCSCF approaches. The Δfull CI results agree very closely with the experimental excitation energies except for higher excitations where obvious basis set defects occur. The MCLR calculations shows that with an adequately chosen MCSCF reference state the MCLR calculation is capable of mimicking the Δfull CI results. The MCLR results are closer to the Δfull CI results than the ΔCI(1s). The ΔMCSCF excitation energies show that this approach can only be used with extreme care to determine excitation energies.

The Theory of Everything

“…We know this equation is correct because it has been solved accurately for small numbers of particles (isolated atoms and small molecules) and found to agree in minute detail with experiment (3)(4)(5). However, it cannot be solved accurately when the number of particles exceeds about 10.…”

“…But the schemes for approximating are not first-principles deductions but are rather art keyed to experiment, and thus tend to be the least reliable precisely when reliability is most needed, i.e., when experimental information is scarce, the physical behavior has no precedent, and the key questions have not yet been identified. There are many notorious failures of alleged ab initio computation methods, including the phase diagram of liquid 3 He and the entire phenomenonology of high-temperature superconductors (8)(9)(10). Predicting protein functionality or the behavior of the human brain from these equations is patently absurd.…”

“…The Higgs mechanism is nothing but superconductivity with a few technical modifications (31). Dirac fermions, spontaneous breaking of CP, and topological defects all occur in the low-energy spectrum of superfluid 3 He (32)(33)(34).…”

Excitation Energies from Time-Dependent Density-Functional Theory

“…[52,53]), a highly accurate ground-state exchange-correlation potential, obtained from quantum Monte-Carlo methods [54], is available for this system. With this potential, we calculated accurate Kohn-Sham orbitals and orbital energies of the beryllium atom.…”

Excited states of beryllium atom from explicitly correlated wave functions

“…They have been mainly carried out by using extensive Configuration Interaction type wave functions obtaining very accurate results [1]. Recently very precise values for the energy and related properties such as the electron affinity or mass shifts have been calculated by making use of the Quantum Monte Carlo method [2] and by using large expansions of exponentially correlated Gaussian functions [3].…”