CamCASP/Programming/2

CamCASP => Programming => The DF-INTEGRAL module

Outline

This module consists of modules to calculate integrals needed for density-fitting, the density-fitting module, and modules to calculate integrals *using* primitive integrals in the auxiliary basis set and the density-fitting solution.

Through module df_int_operations and a lot of procedure overloading, a number of logical and computational operations are hidden from the higher-level energy subroutines. For example, to calculate the generalized OOOOAAAB-type 4-index Coulomb integral needed for the first-order exchange repulsion, subroutine calculate_e1exchS2 makes a call to open_gen_2eint('OOOO','AAAB',...) which does the following:

• DF: Performs the density-fitting for monomer A and dimer density-fitting. The integrals needed for the density-fitting will be automatically calculated.
• Integrals: The generalized integrals need various overlap, nuclear and 2-index Coulomb integrals. These will be identified and calculated.
• Assembly: All the components will be assembled into the required integrals.

These modules also need to decide on what needs re-calculation when molecules rotate. If the molecular basis alters, then everything needs to be re-calculated, but if all that happens is a rotation, then some molecular quantities need not be calculated again. In particular, the density-fitting solution remains invariant with respect to rotations. But rotations mix symmetry components of a shell. For example, (px,py,pz) would be mixed into (py,pz,-px) under a rotation by 90 degrees about the z-axis. This means that you cannot directly combine the density-fitting solution with primitive integrals calculated with the molecule in another orientation. In the next section we will describe what should be done.

Molecular rotations

First of all, as far as the dimer is concerned, a rotated molecule implies the dimer has changed. So *everything* needs to be recalculated. Let's look at monomer rotation only.

To see what's going on, consider the integral: <math>(aa'|bb')</math>. Using density-fitting (ignore integral robustness issues for now) we expand each pair of molecular orbitals as