[molpro-user] Using numerical grid and weights in an external program

[Gerald Knizia]

On Wed, 2014-06-11 at 07:17 -0400, Jayashree wrote:

> I generated and saved a 3D grid in a molpro output file. The x,y,z
> coordinates and weights (w_k) are printed for each atom. [...]
> If I then sum the atomic contributions, I should get the total number
> of electrons. My question is:
> Is there a missing factor involved in this formula? 
> I tried a simple test of evaluating the atomic contribution to the
> electron ground state density where F stands for
> F(x,y,z) = sum(AO1,AO2) AO1(x,y,z)* AO2(x,y,z) Denmat(AO1,AO2)
> , and did not obtain the correct number of electrons.


I think this should work. The weights themselves represent the volume of
their respective integration points, and if you use them to sum the
number of electrons like this, you should get the total number of
electrons.

Are you sure that you have all normalization factors correctly applied
in the AOs themselves? A common problem when evaluating basis functions
is missing the factors between raw primitive Gaussians and normalized
primitive Gaussians (i.e., the factor converting between "library
format" of the contraction coefficients (which refer to primitive
functions normalized such that Int[r in R^3] mu^2(r) d^3r = 1) to what
you actually use in the code).

Beware also of the order of basis functions. Molpro's order of solid
harmonic functions is particularly creative.
-- 
Gerald Knizia