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International Journal of Quantum Chemistry

Ground states of atoms and molecules in strong magnetic fields

P. Schmelcher

Published Jan 1, 1998• 5 citations
Publisher

Abstract

The ground states of small atoms and molecules, namely those of the hydrogen, helium, and lithium atoms and the hydrogen molecular ion and hydrogen molecule, are studied in the presence of an external magnetic field. For the one-electron systems the ground state is of the same symmetry for arbitrary field strengths, and the corresponding binding energy shows a monotonic increase with increasing field strength. More interesting, the two- and three-electron systems show ground-state transitions which involve both transitions in the spin multiplicity and spatial quantum numbers. An outlook on the expected cascade of transitions in many electron atoms and molecules is provided. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 789–795, 1998

DOI
10.1002/(sici)1097-461x(1998)70:4/5<789::aid-qua25>3.0.co;2-w

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The Astrophysical Journal•Oct 1, 1977•36 citations
The ground states of small atoms and molecules, namely those of the hydrogen, helium, and lithium atoms and the hydrogen molecular ion and hydrogen molecule, are studied in the presence of an external magnetic field. For the one-electron systems the ground state is of the same symmetry for arbitrary field strengths, and the corresponding binding energy shows a monotonic increase with increasing field strength. More interesting, the two- and three-electron systems show ground-state transitions which involve both transitions in the spin multiplicity and spatial quantum numbers. An outlook on the expected cascade of transitions in many electron atoms and molecules is provided. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 789–795, 1998
Using a Hartree-Fock mesh method and a configuration-interaction approach based on a generalized Gaussian basis set, we investigate the behavior of the exchange and correlation energies of small atoms and molecules, namely, the helium and lithium atoms as well as the hydrogen molecule, in the presence of a magnetic field covering the regime B=0−−100a.u.B=0--100 \mathrm{a}.\mathrm{u}.B=0−−100a.u. In general, the importance of the exchange energy to the binding properties of atoms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions, and in particular due to the contributions of the tightly bound hydrogenic states which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.
The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.
The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the \ensuremath{\Sigma} manifold are studied for ungerade and gerade parity as well as singlet and triplet states covering a broad regime of field strengths from B=0B=0B=0 up to B=100a.u.B=100\mathrm{a}.\mathrm{u}.B=100a.u. A variety of interesting phenomena can be observed. For the ${}^{1}{\ensuremath{\Sigma}}_{g}$ state we found a monotonous decrease of the equilibrium distance and a simultaneous increase of the dissociation energy with growing magnetic-field strength. The ${}^{3}{\ensuremath{\Sigma}}_{g}$ state is shown to develop an additional minimum which has no counterpart in field-free space. The ${}^{1}{\ensuremath{\Sigma}}_{u}$ state shows a monotonous increase in the dissociation energy with a first increasing and then decreasing internuclear distance of the minimum. For this state the dissociation channel is ${\mathrm{H}}_{2}{\ensuremath{\rightarrow}\mathrm{H}}^{\mathrm{\ensuremath{-}}}{+\mathrm{H}}^{+}$ for magnetic field strengths $B\ensuremath{\gtrsim}20\mathrm{a}.\mathrm{u}.$ due to the existence of strongly bound ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ states in strong magnetic fields. The repulsive ${}^{3}{\ensuremath{\Sigma}}_{u}$ state possesses a very shallow van der Waals minimum for magnetic-field strengths smaller than 1.0 a.u. within the numerical accuracy of our calculations. The ${}^{1}{\ensuremath{\Sigma}}_{g}$ and ${}^{3}{\ensuremath{\Sigma}}_{u}$ states cross as a function of BBB and the ${}^{3}{\ensuremath{\Sigma}}_{u}$ state, which is an unbound state, becomes the ground state of the hydrogen molecule in magnetic fields $B\ensuremath{\gtrsim}0.2\mathrm{a}.\mathrm{u}.$ This is of particular interest for the existence of molecular hydrogen in the vicinity of white dwarfs. In superstrong fields the ground state is again a strongly bound state, the ${}^{3}{\ensuremath{\Pi}}_{u}$ state.
We use the combination of a two-dimensional Hartree-Fock and a diffusion quantum Monte Carlo method, both of which we recently presented in this journal [C. Schimeczek et al., Phys. Rev. A 88, 012509 (2013)], for a thorough investigation of the ground state configurations of all atoms and ions with Z=2Z=2Z=2--10 with the exception of hydrogen-like systems in strong magnetic fields. We obtain the most comprehensive data set of ground state configurations as a function of the magnetic field strength currently available and hence are able to analyze and compare the properties of systems with different core charges and electron numbers in detail.
The electronic structure of the ground state and some excited states of neutral atoms with the nuclear charge numbers 1< Z< 101<~Z<~101< Z< 10 and their singly positive ions are investigated by means of our two-dimensional mesh Hartree-Fock method for strong magnetic fields $0.5<~\ensuremath{\gamma}<~10000.$ For $\ensuremath{\gamma}=10000$ the ground-state configurations of all the atoms and ions considered are given by fully spin-polarized configurations of single-electron orbitals with magnetic quantum numbers ranging from m=0m=0m=0 to $m=\ensuremath{-}N+1,$ where N is the number of the electrons. Focusing on the fully spin-polarized situation, we provide critical values of the magnetic-field strength for which crossovers with respect to the spatial symmetries of the ground state take place. It is found that the neutral atoms and singly charged positive ions with 2< Z< 52<~Z<~52< Z< 5 have one fully spin-polarized ground-state configuration, whereas for 6< Z< 106<~Z<~106< Z< 10 one intermediate fully spin-polarized configuration with an orbital of 2p0{2p}_{0}2p0​ type occurs.
A simple and accurate variational method is formulated and applied to the ground and excited states of the hydrogen atom as well as the hydrogen molecule ion in a homogeneous magnetic field of arbitrary strength. For the ground state, the electronic wave function o is assumed to be a function of a single, appropriately chosen variable R which contains a variational parameter. The functional form of o, and the corresponding energy, are determined by solving a Schr6dinger- like equation, in which the variational parameter appears explicitly in the kinetic and potential energy terms. The variational parameter is optimized by minimizing the lowest eigenvalue of the equation. Excited states may also be obtained by a slight modification of the method, and explicit calculations are carried out for the m1 = - 1 first excited state of hydrogen and the ( )-state of H2 +. Numerical comparisons are made with some recent papers in the literature. Subject headings: atomic processes - magnetic fields - molecular processes - quantum mechanics