Semiempirical optimizations in MOPAC
There seems to be some confusion about what Gaussian does during
semi-empirical optimizations. Here are some details:
1. Gaussian defaults to accuracy comparable to that produced by the
PRECISE keyword in MOPAC.
2. The step-size used in numerically differentiating the integrals as
part of the gradient calculation is small in Gaussian, because a
smaller step can be taken reliably if it is known in advance that
PRECISE is always turned on. This provides somewhat greater
accuracy in the derivatives. I think something like this (but
with different values for the step size) is done in MOPAC version
6 but not in earlier versions.
3. Only the energy and cartesian gradient are computed using code from
MOPAC; the rest of the optimization uses the standard Gaussian
routines in exactly the same manner as an ab initio optimization
would.
4. The cartesian forces are converted to internal coordinates using
different algorithms. I don't know the details of how MOPAC does
the conversion, but this appears to make a difference. Gaussian
uses analytic expressions and doesn't suffer from the sensitivity
to internal coordinate definition that MOPAC apparently does,
since MOPAC gives the warning message about small changes in
internal coordinates causing large displacements for cases where
Gaussian does not have difficulties.
5. Gaussian's default optimizer is not the same as either EF in
Gaussian or EF in MOPAC. It does use an RFO (Rational Function
Optimization) step for the quadratic portion of the step as in the
EF method, but it also does gradient-based linear corrections at
every step as suggested by Schlegel, and it uses an improved
version of Schlegel's update scheme for the Hessian. EF (Baker's
algorithm) is available as an option, but is usually inferior to
the default, since the default is a mixture of the best parts of
Baker's and Schlegel's methods.
Michael Frisch
Gaussian, Inc.
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