• ## Crystallographic Information Framework Index

##### Electron density dictionary (rhoCIF) version 1.0.1

Names:

Definition:

```   These items are used when the radial dependence of the valence
electron  density, R(kappa'(l),l,r), of the atom specified in
_atom_rho_multipole_atom_label is expressed as a Slater-type
function [Hansen & Coppens (1978), equation (3)]:

R(kappa'(l),l,r) = [{zeta(l)}^{n(l)+3}^/{n(l)+2}!]
*(kappa'(l)*r)^n(l)^
*exp(-kappa'(l)*zeta(l)*r)

where:
kappa'(l)   = _atom_rho_multipole_kappa_prime[l]
zeta(l) = _atom_rho_multipole_slater_zeta[l]

R(kappa'(l),l,r) appears in the multipole formalism described by
Hansen & Coppens [1978, equation (2)] which gives the
electron density at position vector r with respect to an
atomic nucleus as:

rho(r) = Pc*rho_core(r) + Pv*kappa^3^*rho_valence(kappa*r)
+ sum{k'(l)^3^*R(kappa'(l),l,r)}
*sum{P(l,m)*d(l,m,theta,phi)}

where:
Pc     = _atom_rho_multipole_coeff_Pc
Pv     = _atom_rho_multipole_coeff_Pv
P(0,0) = _atom_rho_multipole_coeff_P00
Pc + Pv + P(0,0) = Z (the atomic number) for a neutral atom

kappa     = _atom_rho_multipole_kappa,
kappa'(l)  = _atom_rho_multipole_kappa_prime[l],
P(l,m) = _atom_rho_multipole_coeff_P[lm],

d(l,m,theta,phi) is the spherical harmonic of order l,m at the
position (theta, phi) with respect to spherical coordinates
centred on the atom.

The summations are performed over the index ranges
0 <= l <= lmax, -l <= m <= l respectively, where lmax is
the highest order of multipole applied.

The spherical coordinates are related to the local Cartesian
axes defined in category ATOM_LOCAL_AXES, z is the polar axis
from which the angle theta is measured, and the angle phi is
measured from the x axis in the xy plane with the y axis
having a value of phi = +90 degrees.

rho_core(r) and rho_valence(kappa*r) are the spherical core and
valence densities, respectively. They are obtained from
atomic orbital analytic wavefunctions such as those tabulated
by Clementi & Roetti (1974). They are also the Fourier
transforms of the X-ray scattering factors given in
_atom_rho_multipole_scat_core and
_atom_rho_multipole_scat_valence.

Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
Tables, 14, 177-478.
Hansen, N. K. & Coppens, P.  (1978).
Acta Cryst. A34, 909-921.

```

Appears in list containing _atom_rho_multipole_atom_label

Type: numb

Category: atom_rho_multipole