Index

Electron density dictionary (rhoCIF) version 1.0.1

_atom_rho_multipole_radial_slater_

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]
     n(l)    = _atom_rho_multipole_radial_slater_n[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