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

[Gerald Knizia]

On Tue, 2014-06-17 at 09:35 -0400, Jayashree wrote: 
> Indeed, I think I have an issue with the factors. I have been using
> the EMSL basis library, which has different exponents from those in
> the MOLPRO basis library. Thanks for pointing this out! If I
> understand correctly, the library has the following columns for a
> given basis set:
> 
> 
>       Primitives
> Contractions...
> 13.007730
> 0.033495
> 0.000000
> 1.962079
> 0.234727
> 0.000000
> 0.444529
> 0.813751
> 0.000000
> 0.121949
> 0.000000
> 1.000000
> 
> 
> Is the 1st column exponent, 2nd the coefficient? What is the third
> column for?
> 
The third column is a second set of contraction coefficients. It
describes two contracted basis function shells made from the same
exponents: The first contraction involves all exponents except for the
last, the second one involves only the last.

> From your mail, I gather that MOLPRO library basis functions are NOT
> normalised-- is this correct? I believe the analogous ones in EMSL
> are. For example the same basis above in EMSL is 
> BASIS "ao basis" PRINT
> #BASIS SET: (4s) -> [2s]
> H    S
>      18.7311370              0.03349460       
>       2.8253937              0.23472695       
>       0.6401217              0.81375733       
> H    S
>       0.1612778              1.0000000        
> END

It's on the contrary. Molpro uses normalized functions, but EMSL will,
by default, not. The EMSL problem you are seeing is related to EMSL's
habit of having the button "optimize general contractions" checked by
default (it's on the main form). This uncontracts all contracted
functions as long as the linear span of the resulting basis sets is
equivalent. Consequently, unless you remove this check, the functions
you get from EMSL are not normalized and not compatible with the MO
coefficients Molpro uses. For Molpro's way of evaluating integrals, this
is not an optimization, so we do not do this---we use the sets as
published (fully normalized).

However, what I was referring to was something different. Namely, there
are factors of

pow(M_PI/(2*Alpha),.75) * sqrt(DoubleFact(2*l-1)/pow(4.*Alpha,l))

(see purple book, eq. 6.6.14), where DoubleFact(n) = n * (n-2) * (n-4)
* .. * 1, which have to be absorbed into the contraction coefficients in
order to convert from normalized primitive Gaussians to raw primitive
Gaussians. This is the normalization integral of an expression like

   Slm(r-A) exp(-Alpha (r-A)^2)

over space (R^3), (which is in this form, without pre-factors, normally
used in integral/basis function evaluation codes). But the library
coefficients refer to normalized primitives, i.e., to primitives which
include prefactors such that the given integral over space is unity. So
to convert the coefficients, the above factors have to be absorbed.

Best wishes,
Gerald