Summary: Gaussian98 Warning Message

["Fernando De La Vega" <fernando_dela_vega-0at0-hotmail.com>]

 Dear All,
 Last week I asked a question with regard to the warning received in
 Gaussian98 that reads:
"Warning!!: The  largest alpha MO coefficient is #########",
 where the #'s
 represent a given (usually large)  number.
I want to thank Douglas Fox (from Gaussian Tech Support), Antonio
 Marquez
 and Christoph van Wüllen for their response to my inquiry. Below I
 reproduced their answers.
 ----------------------------------------------------
 Douglas J. Fox:
Fernando, The warning is most relevant for post-HF calculations like
 Moller
 Plesset perturbation theory or coupled cluster, where the accuracy of
 the
 result is related to the accuracy of the MO integrals. When you have
 near
 linear dependencies in the basis set you will get large MO coefficients
 related to maintaining orthogonality. The side effect of large
 coefficients
 is loss of precision on any existing machine. Depending on the order
 that
 you add C1*I1+C2*I2-C3*I3+C4*I4 where C1 and C3 are large and of the
 same
 sign, if the integrals are all about the same size and C1*I1-C3*I3 is
 near
 zero the contribution from C2 or C4 can be lost if they are added
 before C3
 is subtracted. For HF and DFT calculations the code which checks this
 is run
 but seldom is it an issue, it is actually just after the SCF completes.
 For
 any post-HF method look to see that the correlation corrections are a
 moderate fraction of the total energy. It may not be an error but it is
 worth comparing with a slightly smaller basis or a different
 correlation
 method, CCSD is less sensitive than MP4, as a check.
 ---------------------------------------------------------------
 Antonio Marquez (marquez-0at0-us.es):
 Dear Fernando,
I guess that you mean that ####### is a LARGE number. This means that
 you
 have a nearly linearly dependent AO basis set. The closer you are to
 have a
 really linearly dependent basis set the biggest will be the number. For
 HF
 calculations this is not usually a problem as the large number(s)
 is(are) in
 one (or more) of the virtual MO that are just the orthogonal complement
 to
 your occupied MO. Problems may arise if these orbitals are used for a
 subsequent correlated ab initio calculation. During the 2e-integrals
 transformation to the MO basis the AO integrals will be mutiplied by
 the all
 the MO coefficients. If one or more of your coefficients if very high
 the
 numerical precision on your transformed MO integrals will be
 compromised and
 you have to be carefull with the result. The ways to circumvent this
 problem
 are either reduce the linear dependency in your AO basis set or use an
 algorithm to compute the 2e repulsion integrals that mantains a high
 degree
 of numerical accuracy.
 I hope this clarifies a little bit your doubts.
 ----------------------------------------------------------------
 Christoph van Wüllen (Christoph.vanWullen-0at0-TU-Berlin.De):
This means that you have a near-linear-dependency in your basis sets,
 e.g.
 if
 you have diffuse functions on two atoms which are quite close.
Since very similar wavefunctions can result from very different
 coefficients,
 numerical problems might arise in force constant or correlation
 calculations.
 If you are sure that there is no input error, proceed (with care).
 -----------------------------------------------------------
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