11. Why don't the semi-empirical methods usually allow elements beyond Xenon?

HyperChem uses Slater orbitals and calculates integrals and their gradients analytically. Thus for each increase in principal quantum number we have to program new code for the integrals and their analytic gradients. With high quantum numbers the gradient code becomes very complex and invloves many more types of integrals (i.e. combinations of quantum numbers). So far nobody in the world has derived analytical gradient equations for Slater orbital integrals involving a principal quantum number of six.

MOPAC does not use analytic gradients of Slater orbitals, but uses either Slater orbitals with derivatives evaluated by finite difference or analytic derivatives of Gaussian orbitals (where linear combinations of Gaussians are used to approximate a Slater orbital).

Once one has taken the trouble to derive and code the integral and integral derivative expressions, as we have for HyperChem, the code is faster and/or more accurate than finite difference or using combinations of Gaussian orbitals to represent Slater orbitals.

HyperChem represents the state of the art for Slater orbitals with analytic gradients. To go further in the periodic table using the same philosphy involves considerable effort and a large increase in executable file size. Adding the ability to use Gaussian orbitals would also involve considerable effort and increase in file size. Using finite difference gradients with Slater orbitals would involve less programming effort than the alternatives, but would decrease program execution speed.

A recent addition to HyperChem allows for PM3 calculations for elements 80 thru 83 /Hg, Tl, Pb and Bi/; also MNDO parameters are included for Hg /Z=80/ and Pb /Z=82/.

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