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Manuscript Title: BNDPKG: a package of programs for the calculation of electronic energy bands by the LCGO method.
Authors: C.S. Wang, J. Callaway
Program title: BNDPKG
Catalogue identifier: ACXZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 14(1978)327
Programming language: Fortran.
Computer: IBM 360/65.
Operating system: OS/360.
RAM: 238K words
Word size: 8
Peripherals: disc.
Keywords: Solid state physics, Crystal, Band structure, Block function, Self-consistent, Density of state, Lcgo method.
Classification: 7.3.

Nature of problem:
This program calculates self-consistent energy levels, wave functions and the density of states for cubic crystals with one atom per unit cell (simple cubic, body centered, or face centered) by expansion in a set of independent Gaussian orbitals.

Solution method:
(i) A starting potential is constructed from overlapping atomic charge densities. Fourier coefficients of this potential are determined.
(ii) Hamiltonian, overlap, and generalized overlap integrals are computed using a basis of independent Gaussian orbitals. The integrals are performed analytically. The basis set is tested for approximate linear dependence.
(iii) The Hamiltonian and overlap matrices are diagonalized to obtain energy levels and wave functions for the starting potential.
(iv) Wave functions from step (iii) are used to construct the change in the charge density and in the potentials. The starting potential is modified, and the process is repeated until convergence is obtained.
(v) After convergence of the self-consistent procedure, final corrections are made to the potential. The Hamiltonian integrals are recalculated. Final energy bands and the density of states are determined.

The program is specifically limited to simple, body centered, and face centered cubic crystals. Ferromagnetic (but not anti-ferromagnetic) order is allowed. Practical considerations limit the application of the program to atoms of large atomic number. Although integrals can be calculated for s, p, d, and f orbitals, the number of Gaussian functions required to give a good description of atomic wave functions in heavy atoms increases. We have made band calculations for atoms as heavy as nickel; the heaviest atom for which analytic self-consistent field wave functions required in the construction of the starting charge density are available at present is zinc. The dimensions of variables are appropriate for the test case of this program (for which data is also given), which is band structure of body centered cubic lithium. Dimensions will have to be altered for other cases. Comments concerning dimensioning of variables will be found elsewhere in the text.

Unusual features:
The program is written in IBM 360 extended FORTRAN. Non-standard features include:
(1) Arrays with more than three dimensions.
(2) Apostrophes to define hollerith strings in Format and Data statements.
(3) Data set in type statements.
(4) Array element expressions involving more than one variable.
(5) READ statements including end-of-data jump, e.g. READ(1,END=210)
(6) IMPLICIT statements.

Running time:
Execution time depends primarily on the number of Gaussian orbitals included in the basic set, and the number of iterations required to achieve self-consistency. Approxiamtely twice as much time will be required if ferromagnetic order is considered. The test case for which data is included in the package, the band structure of lithium, requires a total of 89 min on an IBM 360/65.