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10.2 Wave Function Analysis

10.2.9 Atomic dipoles and quadrupoles

(May 7, 2024)

It can sometimes be desirable to go beyond atomic partial charges to calculate atomic dipoles and quadrupoles. This is useful in particular for certain types of force fields, which use these terms to more accurately model charge anisotropy. QChem provides the ability to calculate atomic dipoles and quadrupoles, using a method inspired by the formulations of Ref. 1194 Sokalski W. A., Poirier R. A.
Chem. Phys. Lett.
(1983), 98, pp. 86.
. We simply evaluate atomic contributions to the multipole moment by assigning contributions from each atom’s basis functions. However, we avert any basis set dependence and delocalization errors by using intrinsic atomic orbitals, 660 Knizia G.
J. Chem. Theory Comput.
(2013), 9, pp. 4834.
which have been shown to have excellent convergence with basis set. 37 Aldossary A., Head-Gordon M.
J. Chem. Phys.
(2022), 157, pp. 094102.
The atomic quadrupoles available from this method are the traceless quadrupoles, which are the more commonly used type in force field contexts.

We calculate atomic dipoles and (traceless) quadrupoles using the following equations:

μAu=αonAβ2PαβIAOχα|uA-u^|χβ (10.25)
QAuv=αonAβ2PαβIAOχα|32(uA-u^)(vA-v^)-12||rA-r^||2δuv|χβ (10.26)

Here A is the atom index, r is the vector (x,y,z), and u=x,y, or z. δ is the Kronecker delta function, χ represents an intrinsic atomic orbital, α and β are the IAO indices, P is the one-particle density matrix, and the IAO superscript on the density matrix indicates that this is the density matrix in the IAO basis. Additionally, the inclusion of uA, vA, and rA (the coordinates of atom A) ensures that the multipoles are origin-invariant.

The calculation of atomic dipoles and quadrupoles is controlled with the following $rem variable:


       Enables atomic multipole calculation
       FALSE Do not calculate IAO atomic multipoles TRUE Calculate IAO atomic multipoles

Example 10.5  Input for calculating atomic dipoles and quadrupoles via the IAO/IBO procedure.

0 1
F         0.0000000000    0.0000000000    0.2314949765
H         0.0000000000    0.0000000000    1.1541050235

jobtyp sp
method hf
basis aug-cc-pvtz
do_ibo true
do_atomic_multipoles true

min_basis autosad
ibo_mem 1000