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(6) |
The approximate wave function
of the state labeled
is:
![]() |
(7) |
![]() |
(8) |
The traditional mchf program has been extended to
accomplish a simultaneous optimization of energy expressions derived from
several different terms or even several eigenvalues of the same term.
Additionally, the energy energy functional is represented as a
weighted average of energy functionals for expansions of wave functions
for different LS terms or parity. This approach facilitates the
Breit-Pauli calculations for complex atomic systems, while previously
somewhat arbitrary methods have been applied (cross-wise optimization,
).
mchf was modified for systematic, large-scale methods using
dynamic memory allocation and sparse matrix methods. All orbitals
in a wave function expansion are assumed to be orthonormal.
Configuration states are restricted to at most eight (8)
subshells in addition to the closed shells common to all configuration
states. The maximum size is limited by the available memory and disk
space. The wave function expansions are obtained from orbital sets
of increasing size, allowing for the monitoring of convergence.
The Davidson algorithm [#!dvdson!#] is applied for finding the
needed eigenvalues and eigenvectors. In this version of the code,
non-orthogonality is not supported. In the present atsp2K_MCHF package, it is not foreseen that optimization would be
over different parities, only over different terms of the same parity,
and we refer to this as "simultaneous optimization".
Suppose represents and energy functional for term
and eigenvalue
, assuming orbitals and also wave functions are
normalized. Then optimization was performed on the functional