Multi-electron systems in strong magnetic fields I: The 2D Landau–Hartree–Fock–Roothaan method

Abstract

We present a 2-dimensional Hartree–Fock–Roothaan code to calculate wave functions and energies of light to heavy atoms in strong external magnetic fields, as they occur in the vicinity of neutron stars. The code enhances the previously presented HFFERII method, resulting in a very high precision for the energies with typical deviations less than 1% compared to extremely precise fixed-phase diffusion quantum Monte Carlo calculations. Despite this high precision the code is highly optimized regarding speed and reliability, which allows calculating large amounts of states in short time, even with small-scale computing clusters. Program summaryProgram title: 2DLHFRCatalogue identifier: AETE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 121429No. of bytes in distributed program, including test data, etc.: 561163Distribution format: tar.gzProgramming language: Fortran 95.Computer: Cluster of 1-15 Fujitsu ESPRIMO P920.Operating system: Linux.Has the code been vectorized or parallelized?: Yes, parallelized using MPI. Tested on 2–60 processors.RAM: At least 1 GByte per coreClassification: 2.1.External routines: GFortran, LAPACK, BLAS, MPINature of problem:The modeling of highly magnetized atmospheres of neutron stars and magnetic white dwarfs is a difficult task and is further complicated by the lack of atomic data. The absorption features in the thermal emission spectra of neutron stars are still not fully understood, which leads to different interpretations and thus large uncertainties for the atmospheric parameters, such as the magnetic field strength, the gravitational redshift, or the predominant atomic composition. Therefore, a fast and reliable program to scan through the large parameter space is necessary.Solution method:The strong magnetic fields present on neutron stars favor a wave function expansion in terms of Landau channels. Contrary to previous attempts we use a full 2-dimensional basis and assign individual z-wave functions to each Landau channel. This allows for an accurate description of the single-particle orbitals. These are combined in a Slater determinant, resulting in Hartree–Fock–Roothaan equations, which are solved iteratively. As initial wave functions we rely on the solutions calculated by the HFFERII program and reuse the optimized B-spline basis sets and Landau coefficients to maximize the speed of the program presented here.Restrictions:Intense magnetic field strengths B/Z2≳5×104T are required to yield accurate results.Unusual features:2DLHFR is based upon the wave functions calculated with the HFFERII program package, presented in [C. Schimeczek, D. Engel, G. Wunner, Comp. Phys. Comm. 183 (2012) 1502]. In turn, the results of this program may be enhanced beyond the Hartree–Fock limit with quantum Monte Carlo methods, as is shown in the accompanying paper.Additional comments:The gfortran compiler is recommended for this program (http://gcc.gnu.org/onlinedocs/gfortran/).Running time:Seconds to minutes