20 THE MCSCF PROGRAM MULTI

MULTI is a general MCSCF/CASSCF program written by

P. J. Knowles and H.-J. Werner (1984).

Bibliography:

H.-J. Werner and P. J. Knowles, J. Chem. Phys. 82, 5053 (1985).
P. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 115, 259 (1985).

All publications resulting from use of this program must acknowledge the above. See also:

H.-J. Werner and W. Meyer, J. Chem. Phys. 73, 2342 (1980).
H.-J. Werner and W. Meyer, J. Chem. Phys. 74, 5794 (1981).
H.-J. Werner, Adv. Chem. Phys. LXIX, 1 (1987).

This program allows one to perform CASSCF as well as general MCSCF calculations. For CASSCF calculations, one can optionally use Slater determinants or CSFs as a $N$-electron basis. In most cases, the use of Slater determinants is more efficient. General MCSCF calculations must use CSFs as a basis.

A quite sophisticated optimization method is used. The algorithm is second-order in the orbital and CI coefficient changes and is therefore quadratically convergent. Since important higher order terms in the independent orbital parameters are included, almost cubic convergence is often observed. For simple cases, convergence is usually achieved in 2-3 iterations. However, convergence problems can still occur in certain applications, and usually indicate that the active space is not adequately chosen. For instance, if two weakly occupied orbitals are of similar importance to the energy, but only one of them is included in the active set, the program might alternate between them. In such cases either reduction or enlargement of the active orbital space can solve the problem. In other cases difficulties can occur if two electronic states in the same symmetry are almost or exactly degenerate, since then the program can switch from one state to the other. This might happen near avoided crossings or near an asymptote. Problems of this sort can be avoided by optimizing the energy average of the particular states. It is also possible to force convergence to specific states by choosing a subset of configurations as primary space (PSPACE). The hamiltonian is constructed and diagonalized explicitly in this space; the coefficients of the remaining configurations are optimized iteratively using the P-space wavefunction as zeroth order approximation. For linear molecules, another possibility is to use the LQUANT option, which makes it possible to force convergence to states with definite $\Lambda$ quantum number, i.e., $\Sigma$, $\Pi$, $\Delta$, etc. states.