Parameters TOLAI and RINCR

The key parameters TOLAI and RINCR control the interval size in the AIRY propagation.

Whenever R < RINCR, then no change is allowed in the interval size.

If, however, R > RINCR and TOLAI is .ge. 1, then the width of the next interval is set to be a constant multiple of the present interval size, namely

DRNOW(n+1) = DRNOW(n) * TOLAI

Thus, to ensure constant step sizes in the AIRY propagation, set TOLAI = 1. By setting TOLAI > 1, the interval sizes will be monotonically increasing, so that you will use larger step sizes at long range, where the potential presumably varies more slowly. Values of TOLAI in the range 1.1 - 1.3 are appropriate for in most calculations.

If, however, the control parameter TOLAI is set to be < 1, then, again only if R > RINCR, the interval sizes are adjusted using crude estimates of the error intoduced by the linear approximation to the W matrix (see M. H. Alexander, J. Chem. Phys. 81, 4510). These estimates are designated COFF and CDIAG. The width of the next interval is adjusted according to the following alogrithm:

DRNOW(n+1) = DRNOW(n) * (TOLAI/CMAX) ** (1/3)

where CMAX=max(COFF,CDIAG). If CMAX < TOLAI, then the interval width is increased, if CMAX > TOLAI, the interval width is decreased.

In this case (TOLAI < 1) decreasing the value of TOLAI should increase the accuracy of the integration, although there is no quantitive relation between the value of TOLAI and the desired accuracy in the S matrix.

The default value is TOLAI=1, which forces constant interval sizes in the AIRY propagation.

Regardless of the sign of TOLAI, no change in the interval width is made if R < RINCR
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