We conceived alternative ways for estimating the 10Dq, exploiting
the facilities of the ADF code, which can work with fractional
populations, controllable by input keywords. In the frame of DFT,
the fractional orbital populations are conceptually allowed [40],
with the meaning of an averaging performed on assemblies of Slater
Determinants with integer occupation numbers in a selected
set of ‘‘active orbitals’’. Aside of the regular calculations having
the occupations of frontier orbitals determined by the usual tn
2gemg
LF scheme (HS or LS after case, depending on the normal occurrence
of the given species) we performed iterative processes with
orbital occupations smeared equally over each orbital assimilated
to the LF sequence. Thus, for each LF-type MO we imposed a
(n + m)/5 occupation, working in restricted spin frame, or in other
words, we used a pseudo-spherical t3ðnþmÞ=5
2g e2ðnþmÞ=5
g configuration
of the molecular system. The averaged configuration has the same
formal meaning as the barycenter of spherically perturbed but yet
fivefold degenerated d orbitals (see Scheme 1). Then, one may conventionally
equate the gap between the DFT computations in regular
tn
2gemg
and smeared t3ðnþmÞ=5
2g e2ðnþmÞ=5
g occupation schemes with
the LFSE energy, obtaining a corresponding estimation of the split
parameter, by the formula
We conceived alternative ways for estimating the 10Dq, exploiting
the facilities of the ADF code, which can work with fractional
populations, controllable by input keywords. In the frame of DFT,
the fractional orbital populations are conceptually allowed [40],
with the meaning of an averaging performed on assemblies of Slater
Determinants with integer occupation numbers in a selected
set of ‘‘active orbitals’’. Aside of the regular calculations having
the occupations of frontier orbitals determined by the usual tn
2gemg
LF scheme (HS or LS after case, depending on the normal occurrence
of the given species) we performed iterative processes with
orbital occupations smeared equally over each orbital assimilated
to the LF sequence. Thus, for each LF-type MO we imposed a
(n + m)/5 occupation, working in restricted spin frame, or in other
words, we used a pseudo-spherical t3ðnþmÞ=5
2g e2ðnþmÞ=5
g configuration
of the molecular system. The averaged configuration has the same
formal meaning as the barycenter of spherically perturbed but yet
fivefold degenerated d orbitals (see Scheme 1). Then, one may conventionally
equate the gap between the DFT computations in regular
tn
2gemg
and smeared t3ðnþmÞ=5
2g e2ðnþmÞ=5
g occupation schemes with
the LFSE energy, obtaining a corresponding estimation of the split
parameter, by the formula
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