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Applications
In this section we present results of calculations of the potential energy
surface(PES) for simple systems. The PES is invariant with respect to a
translation and/or rotation of the nuclear configuration. Hence, the number
independent variables needed to characterize the PES is reduced by 5 and 6 for
a linear and a non-linear system, respectively.
The magnesium dimer
In this particular case, the PES reduces to a function of only one variable,
the internuclear distance R.
A few technical details:
The one-electron basis set adopted in this work is an uncontracted
(23s16p9d7f3g2h) set of Gaussian type functions (GTFs). The calculation is
perform by the EXGEM program. The basic approximation, i.e. the root function,
is a restricted Hartree-Fock (RHF) wavefunction. For the subsystem, i.e. the
isolated atoms, we use canonical orbitals. The orbitals for the dimer are
localized by a least-squares procedure which minimize the "distortion" of the
subsystems in supersystem. The full configuration interaction (FCI)
corrections are calculated in an orbital subspace comprising the 60 virtual
orbitals derived from intra- and interpair natural orbitals (NOs).
The potential energy curve, U(r), is displayed in Fig.1
The
Mg 
belongs to a class of molecules which has been, and still is a challenge to
computational quantum molecular mechanics. The calculated binding energy is 21
% larger than the currently accepted experimental value ( J.Mol.Spectr.
65,46(1977)). Due to the reliability of the extended geminal models for weak
intermolecular interactions, demonstrated in a large number of calculations(
Røeggen I, Extended geminal models. In: Surján P R (Ed) Topics in
Current Chemistry, Vol 203. Springer, Berlin, p 89 ), experimentalist should
reconsider their determination of the binding energy of
Mg .
The potential energy surface of the
(H )
dimer.
Within the rigid rotor approximation ( frozen bond lengths ), the PES is a
function of three angles (
) and the intersystem distance R. The definition of these coordinates should
be from Fig.2.
In Fig.3 we display a region of the PES characterized by R = 6.5 au and
 .
The two minima at (
) = ( 90,0,0 ) and (
) = ( 0,90,0) ( T structures ), are separated by a saddle point at (
) = ( 44.94, 44.94, 0 ).
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