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

# _atom_rho_multipole_radial_function_type

**Name:**

`'_atom_rho_multipole_radial_function_type'`

**Definition:**

Specifies the function R(kappa'(l),l,r) used for the radial dependence of the valence electron density in the multipole formalism described by Hansen & Coppens [1978, equation (2)] which gives the electron density at position vector r with respect to the nucleus of the atom specified in _atom_rho_multipole_atom_label as: rho(r) = Pc*rho_core(r) + Pv*k^3^*rho_valence(kappa*r) + sum{kappa'(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. This item need not be given if a Slater function is used. The parameters of the Slater function should be given using the _atom_rho_multipole_radial_slater_* items. 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:** char

**Category:** atom_rho_multipole