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(May 16, 2021)

This section discusses how to compute arbitrary electrostatic multipole moments
for an entire molecule, including both ground- and excited-state electron
densities. Occasionally, however, it is useful to decompose the electronic
part of the multipole moments into contributions from individual MOs. This
decomposition is especially useful for systems containing unpaired
electrons,
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J. Phys. Chem. A

(2008),
112,
pp. 6171.
Link
where the first-order moments $\u27e8x\u27e9$, $\u27e8y\u27e9$, and $\u27e8z\u27e9$ characterize the
centroid (mean position) of the half-filled MO, and the second-order moments
determine its radius of gyration, ${R}_{g}$, which characterizes the size of the
MO. Upon setting PRINT_RADII_GYRE = TRUE, Q-Chem will print out
centroids and radii of gyration for each occupied MO and for the overall
electron density of the Hartree-Fock or Kohn-Sham reference determinant.
If CIS or TDDFT excited states are requested, then this
keyword will also print out the centroids and radii of gyration for each
excited-state electron density.

Note: These keywords only apply to SCF, DFT, CIS, and TDDFT calculations. To compute these quantities for correlated wavefunctions, use keywords that specify properties calculations for the corresponding method, as described in Chapters 6 and 7. For example, to compute CCSD or EOM-CCSD multipole moments and other properties, use CC_REF_PROP = TRUE and CC_EOM_PROP = TRUE.

PRINT_RADII_GYRE

Controls printing of MO centroids and radii of gyration.

TYPE:

LOGICAL/INTEGER

DEFAULT:

FALSE

OPTIONS:

TRUE (or 1)
Print the centroid and radius of gyration for each occupied MO
and each density.
2
Print centroids and radii of gyration for the virtual MOs as well.
FALSE (or 0)
Do not calculate these quantities.

RECOMMENDATION:

None

Q-Chem can compute Cartesian multipole moments of the charge density to arbitrary order, both for the ground state and for excited states calculated using the CIS or TDDFT methods.

MULTIPOLE_ORDER

Determines highest order of multipole moments to print if wave function
analysis requested.

TYPE:

INTEGER

DEFAULT:

4

OPTIONS:

$n$
Calculate moments to $n$th order.

RECOMMENDATION:

Use the default unless higher multipoles are required.

CIS_MOMENTS

Controls calculation of excited-state (CIS or TDDFT) multipole moments

TYPE:

LOGICAL

DEFAULT:

FALSE

OPTIONS:

FALSE
Do not calculate excited-state moments.
TRUE
Calculate moments for each excited state.

RECOMMENDATION:

Set to TRUE if excited-state moments are desired. (This is a trivial
additional calculation.) The MULTIPOLE_ORDER controls how many
multipole moments are printed.