H2+ion in a strong magnetic field: Lowest excited states

Abstract

As a continuation of our previous work (Phys. Rev. A68, 012504 (2003)) an accurate study of the lowest 1σ g and the low-lying excited 1σ u , 2σ g , 1π u,g , 1δ g,u electronic states of the molecular ion H + 2 is made. Since the parallel configuration where the molecular axis coincides with the magnetic field direction is optimal, this is the only configuration which is considered. The variational method is applied and the same trial function is used for different magnetic fields. The magnetic field ranges from 10 9 G to 4.414 × 10 13 G where non-relativistic considerations are justified. Particular attention is paid to the 1σ u state which was studied for an arbitrary inclination. For this state a one-parameter vector potential is used which is then variationally optimized.

H3+molecular ion in a magnetic field: Linear parallel configuration

“…⋆ the energy and equilibrium distance of H + 3 for these magnetic fields is for a case when a linear configuration is kept externally (see text), b [13], c our re-calculations based on the trial function from [13] (see text). Total energies for the H 2 molecule in 1 Σ g state as well as H + 2 and H 2+ 3 ions in 1σ g state in a magnetic field taken from [18], [19] and [20], respectively. Total energies for the ground state of the H atom and for the H − ion in a magnetic field from [21] and [22], respectively.…”

“…It depends on eleven variational parameters. A simple, obvious generalization of (4) is used to study in 1σ g state in a magnetic field taken from [18], [19] and [20], respectively. Total energies for the ground state of the H atom and for the H − ion in a magnetic field from [21] and [22], respectively.…”

EXOTIC MOLECULAR IONS (HeH)2+ AND ${\rm He}_2^{3+}$ IN A STRONG MAGNETIC FIELD: LOW-LYING STATES

“…The ground state trial function is the same as a function which was successfully used to explore the H + 2 molecular ion in a strong magnetic field for arbitrary inclination. 8,22 It has a form…”

“…We use the trial functions similar to those which were applied to study the excited states of H + 2 . 22 They have a form of (7) multiplied by a factor ρ |m| e imφ . It turns out that positive z-parity states 1π u , 1δ g exist (see Tables 5 and 6), while the states of the negative z-parity 1σ u , 1π g , 1δ u are repulsive.…”

The GW/BSE Method in Magnetic Fields

“…The description of excited states of molecules in strong magnetic fields poses a major challenge for quantum chemical methods. ( Delos et al, 1983 ; Turbiner and López Vieyra, 2004 ; Hampe and Stopkowicz, 2017 ; Stopkowicz, 2018 ; Hampe and Stopkowicz, 2019 ; Wibowo et al, 2021 ). On the one hand, it is well known that introducing magnetic fields also introduces a gauge-dependence when standard, real-valued Gaussian-type basis functions are used.…”