Electron density dictionary (rhoCIF) version 1.0.1

_atom_rho_multipole_kappa_

Definition:

   Gives the radial function expansion-contraction coefficients
   (kappa = _atom_rho_multipole_kappa and
   kappa'(l) = _atom_rho_multipole_kappa_prime[l])
   for the atom specified in _atom_rho_multipole_atom_label.

   The coefficients refer to 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{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
     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 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.

     R(kappa'(l),l,r) is defined in the _atom_rho_multipole_radial_*
     items.

     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.

     The order, l, of kappa' refers to the order of the multipole
     function, 0 <= l <= 4.  The values of kappa' are normally
     constrained to be equal.

   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