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CHAPTER 13. PROPERTIES AND ANALYSIS, AND GRAPHICS
Electrostatic moments:
for the above modules.
up to quadrupole moments are calculated by default
Relativistic corrections: $mvd leads to calculation of relativistic corrections for
the SCF total density in case of dscf and ridft, for the SCF+MP2 density in
case of rimp2 and mpgrad and for that of the calculated excited state in case of
egrad.P
Quantities calculated are expectation values < p2 >, < p4 > and the Darwin
term ( 1/ZA ∗ ρ(RA )). Note, that at least the Darwin term requires an accurate
description of the cusp in the wave function, thus the use of basis sets with uncontracted steep basis functions is recommended. Moreover note, that when using of
ECPs these quantities are not too reasonable (a respective warning is written to the
output).
Population analyses: Population analyses are driven by the keyword $pop.
Without any extension Mulliken population analyses (MPA) are carried out for all
densities present in the respective program, e.g. total (and spin) densities leading to
Mulliken charges (and unpaired electrons) per atom in RHF(UHF)-type calculations
in dscf or ridft, SCF+MP2 densities in rimp2 or mpgrad, excited state densities
in egrad. Suboptions (see Section 15.2.17) also allow for calculation of Mulliken
contributions of selectable atoms to selectable MOs including provision of data for
graphical output (simulated density of states).
With $pop nbo a Natural Population Analysis (NPA) [127] is done. Currently only
the resulting charges are calculated.
With $pop paboon a population analyses based on occupation numbers [128] is performed yielding ”shared electron numbers (SENs)” and multicenter contributions.
For this method always the total density is used, i.e. the sum of alpha and beta
densities in case of UHF, the SCF+MP2-density in case of MP2 and the GHF total
density for (two-component-)GHF. Note that the results of such an analysis may depend on the choice of the number of modified atomic orbitals (”MAOs”). By default,
numbers of MAOs which are reasonable in most cases are taken (see Section 15.2.17).
Nevertheless it is warmly recommended to carefully read the information concerning
MAOs given in the output before looking at the numbers for atomic charges and
shared electron numbers. For different ways of selecting MAOs see Section 15.2.17.
Generation of localized MOs: $localize enables calculation of localized molecular orbitals. Per default a Boys localization including all occupied MOs is carried
out (i.e. the squared distance of charge centers of different LMOs is maximized). As
output one gets localized MOs (written to files lmos or lalp /lbet in UHF cases),
informations about dominant contributions of canonical MOs to LMOs and about
location of LMOs (from Mulliken PA) are written to standard output.
Fit of charges due to the electrostatic potential: $esp_fit fits point charges
at the positions of nuclei to electrostatic potential arising from electric charge dis-