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Manuscript Title: A compact program of the SCF-Xalpha scattered wave method: Version II.
Authors: S. Katsuki, M. Klobukowski, P. Palting
Program title: MSXALPHA/II
Catalogue identifier: ACXN_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 25(1982)39
Programming language: Fortran.
Computer: AMDAHL 470/V7.
Operating system: MTS.
RAM: 488K words
Word size: 8
Peripherals: disc.
Keywords: Quantum chemistry, Molecular physics, Structure, Symmetry, Muffin-tin approximation, Non-overlapping spheres, Xalpha approximation, Initial atomic orbitals, Ground state, Transition state.
Classification: 16.1.

Subprograms used:
Cat Id Title Reference
ACQI_v1_0 0001 ADAPT HFS FOR MSXALPHA CPC 25(1982)29

Nature of problem:
The contribution offered here is a modified version of the MSXalpha program presented earlier which has been extended to accommodate the handling of twenty-six symmetry point groups. Otherwise the program is the same in that it computes molecular orbitals and energy levels for the ground state and transition states using the muffin-tin and Xalpha approximations for the potential energy in the case of non-overlapping contingent spheres.

Solution method:
The starting atomic orbitals generate the potential in the muffin-tin and Xalpha approximations, once the physical space of the molecule is appropriately divided into regions of contiguous nonoverlapping spheres. The Runge-Kutta-Milne method is used to solve the radial Schrodinger equation in the spherical atomic regions and in the extramolecular region if the Waston sphere is present. Energy eigenvalues and eigenvectors are obtained by determining the zeros of the secular determinant with the aid of the Gaussian elimination procedure with complete pivoting. A special algorithm is used to distinguish zeros from poles. A perturbation technique is used to accelerate the search for and the determination of the zeros (energy eigenvalues). Normalization of the calculated eigenvectors is carried through according to the method of Ham and Segall. The newly determined molecular orbitals are now employed to construct the potential. Again eigenvalues and eigenvectors are determined. The process is repeated until self-consistency is achieved, i.e., until some predetermined criterion concerning the convergence of the eigenvalues is satisfied.

Only the spin-restricted case is handled. Moreover, the symmetry point groups which can be treated are: C2, C3, C4, C6, D2, D3, D4, D6, C2v, C3v, C4v, C6v, C2h, C3h, C4h, C6h, D2h, D3h, D4h, D6h, D2d, D3d, D4d, D6d, Td and Oh.

Unusual features:
The starting atomic orbitals may be either numerical Hartree-Fock orbitals or analytical Hartree-Fock orbitals in an STO or GTO basis. Let us define an atomic "species" as a set of symmetry equivalent atoms, i.e., by applying the operations of the symmetry group in question to any one member of the set, the other members of the species are generated. The present version of the program automatically generates all the members of a species, their coordinates and spherical harmonic basis functions, once these quantities are specified for one member of the species along with the specification of the symmetry group in question. Furthermore, the entire set of partner functions situated on the central atom which span the invariant subspace of a given irreducible representation is generated for a given maximum value of the quantum number l. Calculations may be done piece-wise and restarts may be made from a given iteration. Core orbitals may be frozen during a calculation. Initially valence levels are found by a brute-force scanning of an energy range with a determined mesh size. In order to reduce the computation time, in the next iterations only the narrow energy ranges around the perturbationally predicted eigenvalues are scanned. Although the program was not overlaid in the calculations reported here, the code was rewritten so as to facilitate an implementation of overlay features of an operating system. The input requirements were changed so as to match the output of the modified Hartree-Fock-Slater program. The HFS numerical AO's were used as the starting data in the calculations provided as the test cases. FORTRAN compatibility Since the program is written in IBM FORTRAN IV, the following features may render it incompatible with other FORTRAN compilers:
1) in subroutine INPOTL, arrays COEFF and DZT are four-dimensional;
2) apostrophes are used in FORMAT statements to define Hollerith strings in place of the standard field description nH;
3) array element expressions which involve another array element are used, e.g. NDG(IRG3(I));
4) IMPLICIT REAL*8 statement is used;
5) characters & and # are used in column 6 for continuation lines;
6) the ENTRY statement is used;
7) T format code is used.

Running time:
The compilation time (FORTRAN H compiler) was 50.1s on an Amdahl 470/V7. The CPU time of the initial calculation (the first test case) was 23.2s. It took 59.3 s of CPU time to complete the first three SCF iterations (the second test case).