Problems when calculation from simple

Now to the problem of calculating the transition densities. We need these quantities in order to be able to compute transition properties like the transition dipole moment. When we use a common orthonormal set of molecular orbitals for both the electronic states, the formalism developed in chapter 3 can be applied. For a one-electron operator A the transition matrix element is obtained from the simple formula ... 

There is very little problem in calculating an acceptable measure of solute size. Simple calculations of either molecular volume or area based on either Bondi s (Bondi, 1964) or McGowan s (Abraham, 1987) methods work almost as well as those derived from molecular mechanics and quantum chemistry (Leo, 1993). When volume in cubic Angstroms is used, V is normally scaled by 0.01 to produce a coefficient comparable to the others in the equation polarity/polarizability. 

There is no problem with varying time intervals with two-level simulation methods, but with a method like BDF, there is the problem that one needs multipoint time derivatives calculated from unequally spaced points in time. Feldberg and Goldstein [236] show how to do this and even show how to apply the Feldbergian correction of half a time interval in this case, that becomes necessary when using the simple start for BDF, described in Chap. 4 (see also the consistency proof for this procedure in Appendix B). 

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