Format for Microstates

After the geometry data plus any symmetry data are read in, data defining each microstate is read in, using format 20I1, one microstate per line. The microstate data is preceded by the word ``MICROS'' on a line by itself. There is at present no mechanism for using MICROS with a reaction path.

For a system with n M.O.'s in the C.I. (use OPEN=(n1,n) or C.I.=n to do this), the populations of the n alpha M.O.'s are defined, followed by the n beta M.O.'s. Allowed occupancies are zero and one. For n=6 the closed-shell ground state would be defined as 111000111000, meaning one electron in each of the first three alpha M.O.'s, and one electron in each of the first three beta M.O.'s.

Users are warned that they are responsible for completing any spin manifolds. Thus while the state 111100110000 is a triplet state with component of spin = 1, the state 111000110100, while having a component of spin = 0 is neither a singlet nor a triplet. In order to complete the spin manifold the microstate 110100111000 must also be included.

If a manifold of spin states is not complete, then the eigenstates of the spin operator will not be quantized. When and only when 100 or fewer microstates are supplied, can spin quantization be conserved.

There are two other limitations on possible microstates. First, the number of electrons in every microstate should be the same. If they differ, a warning message will be printed, and the calculation continued (but the results will almost certainly be nonsense). Second, the component of spin for every microstate must be the same, except for teaching purposes. Two microstates of different components of spin will have a zero matrix element connecting them. No warning will be given as this is a reasonable operation in a teaching situation. For example, if all states arising from two electrons in two levels are to be calculated, say for teaching Russel-Saunders coupling, then the following microstates would be used:

         Microstate       No. of alpha, beta electrons  Ms  State

           1100                    2     0              1   Triplet
           1010                    1     1              0   Singlet
           1001                    1     1              0   Mixed
           0110                    1     1              0   Mixed
           0101                    1     1              0   Singlet
           0011                    0     2             -1   Triplet

Constraints on the space manifold are just as rigorous, but much easier to satisfy. If the energy levels are degenerate, then all components of a manifold of degenerate M.O.'s should be either included or excluded. If only some, but not all, components are used, the required degeneracy of the states will be missing.

As an example, for the tetrahedral methane cation, if the user supplies the microstates corresponding to a component of spin = 3/2, neglecting Jahn-Teller distortion, the minimum number of states that can be supplied is $90 = (6!/(1!5!))(6!/(4!2!))$.

While the total number of electrons should be the same for all microstates, this number does not need to be the same as the number of electrons supplied to the C.I.; thus in the example above, a cationic state could be 110000111000.

The format is defined as 20I1 so that spaces can be used for empty M.O.'s.