Molecular structure in non-Born–Oppenheimer quantum mechanics

Extracting elements of molecular structure from the all-particle wave function

“…11,13,24 This problem was described in a numerical all-particle study of the H + 3 molecular ion by Cafiero and Adamowicz. 12 By calculating the expectation values of the proton-proton distance and the angle for the three protons it was not possible to decide whether the molecule has a linear or a triangular shape.…”

“…34 In the present work, small molecular systems are considered within non-relativistic all-particle quantum mechanics by means of a variational procedure joining the direction pioneered by Suzuki and Varga 26 and Adamowicz and coworkers. 12 After presenting the essential details of the numerical protocol, the evaluation of probability densities of structural parameters, related to n-particle densities, is discussed. The usefulness of these functions is presented through numerical examples and one-and two-dimensional motifs of the classical molecular structure are extracted from the groundstate all-particle wave functions of the three-particle H − , Ps − , and H + 2 , the four-particle Ps 2 and H 2 , and the five-particle H 2 D + molecular ion.…”

Non-Born–Oppenheimer variational calculations of HT+ bound states with zero angular momentum

“…[11][12][13][14][15][16][17][18][19] The approach is based on separating the operator describing the center of mass kinetic energy from the total Hamiltonian of the system and representing the remaining internal Hamiltonian in the reference frame centered at one of the particles ͑in most cases the heaviest particle͒. In the calculation we use the explicitly correlated n-particle Gaussian functions to expand the spatial part of the wave function.…”

Concepts in Computational Spectrometry: The Quantum and Chemistry

“…Such a systematic calculation on ethanol or comparable system is still beyond the capabilities of extant computational resources, but an almost rigorous calculation was performed on the trihydrogen cation, H þ 3 , in a nonrelativistic approximation [33]. As the simplest polyatomic species, this molecular ion comprises three protons as separate atomic nuclei and two associated electrons; after separation of variables pertaining to the origin of coordinates defined at one nucleus, a solution of Schrodingers equation, similar to above, yields energies of internal, or spectrally pertinent, states of this system.…”