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Manuscript Title: A general program for computing angular integrals of the non- relativistic Hamiltonian with non-orthogonal orbitals.
Authors: A. Hibbert, C.F. Fischer
Program title: MCHF_NONH
Catalogue identifier: ABZW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 64(1991)417
Programming language: Fortran.
Computer: VAX 11/780.
Operating system: VMS, Sun UNIX.
RAM: 122K words
Word size: 32
Peripherals: disc.
Keywords: Atomic physics, structure, Configuration Interaction, racah, Coefficients of, Fractional parentage, recoupling coefficients, Slater integrals, Complex atoms, function wave, Bound states, Ls coupling.
Classification: 2.1.

Subprograms used:
Cat Id Title Reference
ABZU_v1_0 MCHF_LIBRARIES CPC 64(1991)399

Nature of problem:
In configuration interaction calculations as well as variational calculations such as MCHF, the wave function is expanded in terms of a number of configuration state functions. To determine the coefficients in the expansion or the radial functions, as in MCHF, the interaction matrix needs to be expressed in terms of sums of radial integrals. In the presence of non-orthogonal orbitals, the integrals are L- integrals and Slater integrals, possibly multiplied by overlap integrals. The program calculates the coefficients of these integrals and produces a file INT.LST appropriate for input to the MCHF88 program or MCHF_CI.

Solution method:
The coefficients of the integrals and their overlap factors are obtained from integration over all spin and angular coordinates. Integration over the radial coordinates is expressed either as unity, zero, or as expressions for radial integrals. A scheme for calculating the coefficients was described by Fano [1], which formed the basis of the earlier WEIGHTS program [2] for orthonormal orbitals. The present program is based on an extension of this procedure to non-orthogonal orbitals [3].

Restrictions:
Any number of s-, p-, or d- electrons are allowed in a shell, but no more than two electrons in a shell with l>= 3. If l>=4, the LS term for the shell is restricted to those allowed for l=4. Only the shells outside a set of closed shells common to all configurations need be specified. A maximum of 5 (five) shells (in addition to the common closed shells) is allowed. This restriction may be removed by changing dimension statements and some format statements.

Running time:
The time required for the test runs is 0.4 and 1.3 seconds, respectively, on a SUN 3/160 with a floating point board.

References:
[1] U. Fano, Phys. Rev. 140(1965)A67.
[2] A. Hibbert, Computer Phys. Commun. (1970)359; 2(1971)180; 6(1973)59.
[3] A. Hibbert, C. Froese Fischer, M.R. Godefroid, Computer Phys. Commun. 51(1988)285.