Field gradient integrals
Hi all,
I have recently had a little trouble with the implementation of field
gradient integrals over GTOs, i.e. <a|v(i,j)|b> where a and b are GTOs
centered at points A and B respectively and v(i,j) is a component of the
field gradient operator located at center C (= d/dxC d/dyC 1/rC for the x,y
component etc). I have used the McMurchie-Davidson algorithm as described
in the original article or by Helgaker and Taylor in their extensive
review. I noticed that if all centers coincide the results are correct.
However, if a and b are located somewhere else and the product a(r)b(r) has
a significant amplitude at point C, where the operator is located, the
results are incorrect. For example, two unnormalized 1s GTOs (exponent=1.0)
located at +1 bohr and the v(z,z) operator at the origin. In general in
these cases the algorithm returns <a|v(x,x)+v(y,y)+v(z,z)|b> <> 0
but it
must =0 for the correct integrals. Judging from tests with numerical
integration of the same integrals the algorithm appears to produce correct
integrals in the case that the amplitude of a*b at point C is very small. I
know from other integrals that the F[m] generation, E-coefficients,
R-coefficients etc. are all definitively correct and this makes me believe
that I have a conceptional problem with the singularity of the operator at
the origin and not just with the numerics.
I hope that this is a standard problem for anyone who has succesfully
implemented these integrals (and related ones like the one electron part of
the spin-orbit operator) and I would greatly appreciate if some experienced
persons could give me a hint about how to deal with it so I don't have to
reinvent the wheel.
Your help is much appreciated,
best regards,
Frank
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! Dr. Frank Neese !
! Fakultaet fuer Biologie !
! Universitaet Konstanz !
! D-78457 Konstanz !
! Germany !
! e-mail: Frank.Neese &$at$& uni-konstanz.de !
! Tel : 07531/883205 !
! FAX : 07531/882966 !
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