17.1 Charge and multipole embedding

Point Charge Embedding: The embedding of the quantum system in a electric potential of an (non-periodic) set of charges and multipole moments is driven by the data group $point_charges. In the simplest case it has the structure:

$point_charges  
   <x> <y> <z> <q>

where <x>, <y>, <z> are the coordinates and <q> the value of the point charge.

The point charge embedding is implemented in the dscf, ridft, grad, rdgrad, escf, ricc2, ccsdf12, and pnoccsd programs and can be used essentially with every method and for all properties including gradients with respect to nuclear coordinates. Exceptions are (auxiliary) basis set gradients, analytic second derivatives (aoforce (but they can be computed semi-numerical with Numforce.

For QM/MM applications it is also possible to compute the forces that the quantum system exerts on the point charges. For futher details about available options and the input see Sec. 20.2.7.

Point Mutipole Embedding: In addition to point charges one can also use point multipoles up to octupole moments. The input uses generalization of the point charge input:

$point_charges mxrank=3  
   <x> <y> <z> <q> <qx> <qy> <qz> <qxx> <qyy> <qzz> <qxy> <qxz> <qyz> ...

The value of keyword mxrank defines the maximum multipole rank (0=charge, 1=dipole, 2=quadrupole, 3=octupole) and the tensor components are given for each multipole site after the coordinates in canonical order. For the components of the octupole moment the canonical order is:

xxx yyy zzz xxy xxz xyy yyz xzz yzz xyz

The multipole embedding (beyond charges) is only implemented for (excitation) energies. Gradients are not (yet) available and symmetry can not be used.

Gaussian Smeared Charges: Instead of point charges one use Gaussian charge distributions of the form G(⃗r) = N exp(-α(⃗r-⃗r0)2). The input format is in this case:

$point_charges gaussians  
   <x> <y> <z> <q> <alpha>

The normalization factor N is determined internally such that the total (integrated) charge of the distribution is q = R3G(⃗r).

For Gaussian charge distributions gradients are available, but symmetry can not be used.