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cif_rho.dic CIF dictionary

Version 1.0.1

Category view of data-item definitions

_ATOM_LOCAL_AXES_[RHO]
CIF 
This category allows the definition of local axes around each

atom in terms of vectors between neighbouring atoms.
High-resolution X-ray diffraction methods enable the
determination of the electron density distribution in crystal
lattices and molecules, which in turn allows for a
characterization of chemical interactions (Coppens, 1997;
Koritsanszky & Coppens, 2001). This is accomplished by the
construction of a mathematical model of the charge density
in a crystal and then by fitting the parameters of such a
model to the experimental pattern of diffracted X-rays. The
model on which this dictionary is based is the so-called
multipole formalism proposed by Hansen & Coppens (1978). In
this model, the electron density in a crystal is described
by a sum of aspherical "pseudoatoms" where the pseudoatom
density has the form defined in the _atom_rho_multipole_* items.
Each pseudoatom density consists of terms representing the
core density, the spherical part of the valence density and
the deviation of the valence density from sphericity. The
continuous electron density in the crystal is then modelled
as a sum of atom-centred charge distributions. Once the
experimental electron density has been established, the
"atoms in molecules" theory of Bader (1990) provides tools for
the interpretation of the density distribution in terms of its
topological properties.

Ref:  Bader, R. F. W. (1990). Atoms in molecules: a quantum
        theory. Oxford University Press.
      Coppens, P. (1997). X-ray charge densities and chemical
        bonding. Oxford University Press.
      Hansen, N. K. & Coppens, P.  (1978). Acta Cryst. A34,
        909-921.
      Koritsanszky, T. S. & Coppens, P. (2001). Chem. Rev. 101,
        1583-1621.

Example:
loop_
    _atom_local_axes_atom_label
    _atom_local_axes_atom0
    _atom_local_axes_ax1
    _atom_local_axes_atom1
    _atom_local_axes_atom2
    _atom_local_axes_ax2
        Ni2+(1)  DUM0      Z    Ni2+(1)  N(1)      X

    loop_
    _atom_site_label
    _atom_site_fract_x
    _atom_site_fract_y
    _atom_site_fract_z
    _atom_site_occupancy
        DUM0     0.80000     0.80000     0.80000    0.0

data_atom_local_axes_[rho]
   _name                       '_atom_local_axes_[rho]'
   _category                     category_overview
   _type                         null
    loop_ _example_detail
          _example
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
;   Example 1 - This example shows how the local axes can be defined
                around each atom in terms of vectors between neighbouring
                atoms.  If necessary, dummy atoms can be introduced into
                the atom_site list for this purpose.
;
;
    loop_
    _atom_local_axes_atom_label
    _atom_local_axes_atom0
    _atom_local_axes_ax1
    _atom_local_axes_atom1
    _atom_local_axes_atom2
    _atom_local_axes_ax2
        Ni2+(1)  DUM0      Z    Ni2+(1)  N(1)      X

    loop_
    _atom_site_label
    _atom_site_fract_x
    _atom_site_fract_y
    _atom_site_fract_z
    _atom_site_occupancy
        DUM0     0.80000     0.80000     0.80000    0.0
;
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     _definition
;              This category allows the definition of local axes around each
               atom in terms of vectors between neighbouring atoms.
               High-resolution X-ray diffraction methods enable the
               determination of the electron density distribution in crystal
               lattices and molecules, which in turn allows for a
               characterization of chemical interactions (Coppens, 1997;
               Koritsanszky & Coppens, 2001). This is accomplished by the
               construction of a mathematical model of the charge density
               in a crystal and then by fitting the parameters of such a
               model to the experimental pattern of diffracted X-rays. The
               model on which this dictionary is based is the so-called
               multipole formalism proposed by Hansen & Coppens (1978). In
               this model, the electron density in a crystal is described
               by a sum of aspherical "pseudoatoms" where the pseudoatom
               density has the form defined in the _atom_rho_multipole_* items.
               Each pseudoatom density consists of terms representing the
               core density, the spherical part of the valence density and
               the deviation of the valence density from sphericity. The
               continuous electron density in the crystal is then modelled
               as a sum of atom-centred charge distributions. Once the
               experimental electron density has been established, the
               "atoms in molecules" theory of Bader (1990) provides tools for
               the interpretation of the density distribution in terms of its
               topological properties.

               Ref:  Bader, R. F. W. (1990). Atoms in molecules: a quantum
                       theory. Oxford University Press.
                     Coppens, P. (1997). X-ray charge densities and chemical
                       bonding. Oxford University Press.
                     Hansen, N. K. & Coppens, P.  (1978). Acta Cryst. A34,
                       909-921.
                     Koritsanszky, T. S. & Coppens, P. (2001). Chem. Rev. 101,
                       1583-1621.
;
_atom_local_axes_atom_label
CIF 
This item is used to identify an atom for which a local axis

system is to be defined.  Its value must be identical to one
of the values given in the _atom_site_label list.

data_atom_local_axes_atom_label
    _name                      '_atom_local_axes_atom_label'
    _category                    atom_local_axes
    _type                        char
    _list                        yes
    _list_link_parent          '_atom_site_label'
    _list_mandatory              yes
    _definition
;              This item is used to identify an atom for which a local axis
               system is to be defined.  Its value must be identical to one
               of the values given in the _atom_site_label list.
;
_atom_local_axes_atom0
CIF 
Specifies 'atom0' in the definition of a local axis frame.

The definition employs three atom-site labels, 'atom0', 'atom1'
and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
'+/-X', '+/-Y' or '+/-Z'. For the atom defined by
'_atom_local_axes_atom_label', whose nuclear position is taken
as the origin, local axis 'ax1' is the vector from the origin to
atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
plane of 'ax1' and a vector
passing through the origin parallel to the vector atom1 -> atom2
(its positive direction making an acute angle with the vector
parallel to atom1 -> atom2), and a right-handed orthonormal
vector triplet is formed from the vector product of these two
vectors. In most cases, atom1 will be the same as the atom
specified by _atom_local_axes_atom_label. One or more 'dummy'
atoms (with arbitrary labels) may be used in the vector
definitions, specified with zero occupancy in the _atom_site_
description.  The values of *_atom0, *_atom1 and *_atom2 must
be identical to values given in the _atom_site_label list.

data_atom_local_axes_atom0
    _name                      '_atom_local_axes_atom0'
    _category                    atom_local_axes
    _type                        char
    _list                        yes
    _list_link_parent          '_atom_site_label'
    _list_reference            '_atom_local_axes_atom_label'

    _definition
;              Specifies 'atom0' in the definition of a local axis frame.
               The definition employs three atom-site labels, 'atom0', 'atom1'
               and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
               '+/-X', '+/-Y' or '+/-Z'. For the atom defined by
               '_atom_local_axes_atom_label', whose nuclear position is taken
               as the origin, local axis 'ax1' is the vector from the origin to
               atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
               plane of 'ax1' and a vector
               passing through the origin parallel to the vector atom1 -> atom2
               (its positive direction making an acute angle with the vector
               parallel to atom1 -> atom2), and a right-handed orthonormal
               vector triplet is formed from the vector product of these two
               vectors. In most cases, atom1 will be the same as the atom
               specified by _atom_local_axes_atom_label. One or more 'dummy'
               atoms (with arbitrary labels) may be used in the vector
               definitions, specified with zero occupancy in the _atom_site_
               description.  The values of *_atom0, *_atom1 and *_atom2 must
               be identical to values given in the _atom_site_label list.
;
_atom_local_axes_atom1
CIF 
Specifies 'atom1' in the definition of a local axis frame.

The definition employs three atom-site labels, 'atom0', 'atom1'
and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
'+/-X', '+/-Y' or '+/-Z'. For the atom defined by
'_atom_local_axes_atom_label', whose nuclear position is taken
as the origin, local axis 'ax1' is the vector from the origin to
atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
plane of 'ax1' and a vector
passing through the origin parallel to the vector
atom1 -> atom2 (its positive direction making an acute angle
with the vector parallel to atom1 -> atom2), and a right-handed
orthonormal vector triplet is formed from the vector product
of these two vectors. In most cases, atom1 will be the same
as the atom specified by _atom_local_axes_atom_label. One or
more 'dummy' atoms (with arbitrary labels) may be used in the
vector definitions, specified with zero occupancy in the
_atom_site_ description.  The values of *_atom0, *_atom1 and
*_atom2 must be identical to values given in the
_atom_site_label list.

data_atom_local_axes_atom1
    _name                      '_atom_local_axes_atom1'
    _category                    atom_local_axes
    _type                        char
    _list                        yes
    _list_link_parent          '_atom_site_label'
    _list_reference            '_atom_local_axes_atom_label'

    _definition
;              Specifies 'atom1' in the definition of a local axis frame.
               The definition employs three atom-site labels, 'atom0', 'atom1'
               and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
               '+/-X', '+/-Y' or '+/-Z'. For the atom defined by
               '_atom_local_axes_atom_label', whose nuclear position is taken
               as the origin, local axis 'ax1' is the vector from the origin to
               atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
               plane of 'ax1' and a vector
               passing through the origin parallel to the vector
               atom1 -> atom2 (its positive direction making an acute angle
               with the vector parallel to atom1 -> atom2), and a right-handed
               orthonormal vector triplet is formed from the vector product
               of these two vectors. In most cases, atom1 will be the same
               as the atom specified by _atom_local_axes_atom_label. One or
               more 'dummy' atoms (with arbitrary labels) may be used in the
               vector definitions, specified with zero occupancy in the
               _atom_site_ description.  The values of *_atom0, *_atom1 and
               *_atom2 must be identical to values given in the
               _atom_site_label list.
;
_atom_local_axes_atom2
CIF 
Specifies 'atom2' in the definition of a local axis frame.

The definition employs three atom-site labels, 'atom0', 'atom1'
and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
'+/-X', '+/-Y' or '+/-Z'. For the atom defined by
'_atom_local_axes_atom_label', whose nuclear position is taken
as the origin, local axis 'ax1' is the vector from the origin to
atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
plane of 'ax1' and a vector
passing through the origin parallel to the vector atom1 -> atom2
(its positive direction making an acute angle with the vector
parallel to atom1 -> atom2), and a right-handed orthonormal
vector triplet is formed from the vector product of these
two vectors. In most cases, atom1 will be the same as the
atom specified by _atom_local_axes_atom_label. One or more
'dummy' atoms (with arbitrary labels) may be used in the
vector definitions, specified with zero occupancy in the
_atom_site_ description.  The values of *_atom0, *_atom1 and
*_atom2 must be identical to values given in the
_atom_site_label list.



data_atom_local_axes_atom2
    _name                      '_atom_local_axes_atom2'
    _category                    atom_local_axes
    _type                        char
    _list                        yes
    _list_link_parent          '_atom_site_label'
    _list_reference            '_atom_local_axes_atom_label'
    _definition
;              Specifies 'atom2' in the definition of a local axis frame.
               The definition employs three atom-site labels, 'atom0', 'atom1'
               and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
               '+/-X', '+/-Y' or '+/-Z'. For the atom defined by
               '_atom_local_axes_atom_label', whose nuclear position is taken
               as the origin, local axis 'ax1' is the vector from the origin to
               atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
               plane of 'ax1' and a vector
               passing through the origin parallel to the vector atom1 -> atom2
               (its positive direction making an acute angle with the vector
               parallel to atom1 -> atom2), and a right-handed orthonormal
               vector triplet is formed from the vector product of these
               two vectors. In most cases, atom1 will be the same as the
               atom specified by _atom_local_axes_atom_label. One or more
               'dummy' atoms (with arbitrary labels) may be used in the
               vector definitions, specified with zero occupancy in the
               _atom_site_ description.  The values of *_atom0, *_atom1 and
               *_atom2 must be identical to values given in the
               _atom_site_label list.

;









_atom_local_axes_ax1


CIF 

Specifies 'ax1' in the definition of a local axis frame.

The definition employs three atom-site labels, 'atom0', 'atom1'
and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
'+/-X', '+/-Y' or '+/-Z'. For the atom defined by
'_atom_local_axes_atom_label', whose nuclear position is taken
as the origin, local axis 'ax1' is the vector from the origin to
atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
plane of 'ax1' and a vector
passing through the origin parallel to the vector atom1 -> atom2
(its positive direction making an acute angle with the vector
parallel to atom1 -> atom2), and a right-handed orthonormal
vector triplet is formed from the vector product of these two
vectors. In most cases, atom1 will be the same as the atom
specified by _atom_local_axes_atom_label. One or more 'dummy'
atoms (with arbitrary labels) may be used in the vector
definitions, specified with zero occupancy in the _atom_site_
description.  The values of *_atom0, *_atom1 and *_atom2 must
be identical to values given in the _atom_site_label list.



data_atom_local_axes_ax1
    _name                      '_atom_local_axes_ax1'
    _category                    atom_local_axes
    _type                        char
    _list                        yes
    _list_reference            '_atom_local_axes_atom_label'
    loop_ _enumeration            x   X   y   Y   z   Z
                                 +x  +X  +y  +Y  +z  +Z
                                 -x  -X  -y  -Y  -z  -Z
    _definition
;              Specifies 'ax1' in the definition of a local axis frame.
               The definition employs three atom-site labels, 'atom0', 'atom1'
               and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
               '+/-X', '+/-Y' or '+/-Z'. For the atom defined by
               '_atom_local_axes_atom_label', whose nuclear position is taken
               as the origin, local axis 'ax1' is the vector from the origin to
               atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
               plane of 'ax1' and a vector
               passing through the origin parallel to the vector atom1 -> atom2
               (its positive direction making an acute angle with the vector
               parallel to atom1 -> atom2), and a right-handed orthonormal
               vector triplet is formed from the vector product of these two
               vectors. In most cases, atom1 will be the same as the atom
               specified by _atom_local_axes_atom_label. One or more 'dummy'
               atoms (with arbitrary labels) may be used in the vector
               definitions, specified with zero occupancy in the _atom_site_
               description.  The values of *_atom0, *_atom1 and *_atom2 must
               be identical to values given in the _atom_site_label list.
;









_atom_local_axes_ax2


CIF 

Specifies 'ax2' in the definition of a local axis frame.

The definition employs three atom-site labels, 'atom0', 'atom1'
and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
'+/-X', '+/-Y' or '+/-Z'. For the atom defined by
'_atom_local_axes_atom_label', whose nuclear position is taken
as the origin, local axis 'ax1' is the vector from the origin to
atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
plane of 'ax1' and a vector
passing through the origin parallel to the vector atom1 -> atom2
(its positive direction making an acute angle with the vector
parallel to atom1 -> atom2), and a right-handed orthonormal
vector triplet is formed from the vector product of these two
vectors. In most cases, atom1 will be the same as the atom
specified by _atom_local_axes_atom_label. One or more 'dummy'
atoms (with arbitrary labels) may be used in the vector
definitions, specified with zero occupancy in the _atom_site_
description.  The values of *_atom0, *_atom1 and *_atom2 must
be identical to values given in the _atom_site_label list.



data_atom_local_axes_ax2
    _name                      '_atom_local_axes_ax2'
    _category                    atom_local_axes
    _type                        char
    _list                        yes
    _list_reference            '_atom_local_axes_atom_label'
  loop_ _enumeration              x   X   y   Y   z   Z
                                 +x  +X  +y  +Y  +z  +Z
                                 -x  -X  -y  -Y  -z  -Z
    _definition
;              Specifies 'ax2' in the definition of a local axis frame.
               The definition employs three atom-site labels, 'atom0', 'atom1'
               and 'atom2', and two axis labels, 'ax1' and 'ax2', having values
               '+/-X', '+/-Y' or '+/-Z'. For the atom defined by
               '_atom_local_axes_atom_label', whose nuclear position is taken
               as the origin, local axis 'ax1' is the vector from the origin to
               atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
               plane of 'ax1' and a vector
               passing through the origin parallel to the vector atom1 -> atom2
               (its positive direction making an acute angle with the vector
               parallel to atom1 -> atom2), and a right-handed orthonormal
               vector triplet is formed from the vector product of these two
               vectors. In most cases, atom1 will be the same as the atom
               specified by _atom_local_axes_atom_label. One or more 'dummy'
               atoms (with arbitrary labels) may be used in the vector
               definitions, specified with zero occupancy in the _atom_site_
               description.  The values of *_atom0, *_atom1 and *_atom2 must
               be identical to values given in the _atom_site_label list.
;

###########################################
#                                         #
#   category ATOM_RHO_MULTIPOLE           #
#                                         #
###########################################












_ATOM_RHO_MULTIPOLE_[RHO]
CIF 

This category contains information about the multipole

coefficients used to describe the electron density.
High-resolution X-ray diffraction methods enable the
determination of the electron density distribution in
crystal lattices and molecules, which in turn allows for a
characterization of chemical interactions (Coppens, 1997;
Koritsanszky & Coppens, 2001). This is accomplished by
the construction of a mathematical model of the charge
density in a crystal and then by fitting the parameters of
such a model to the experimental pattern of diffracted
X-rays. The model on which this dictionary is based
is the so-called multipole formalism proposed by Hansen
& Coppens (1978). In this model, the electron density in
a crystal is described by a sum of aspherical "pseudoatoms"
where the pseudoatom density has the form defined in the
_atom_rho_multipole_* items. Each pseudoatom density
consists of terms representing the core density, the spherical
part of the valence density and the deviation of the valence
density from sphericity. The continuous electron density in the
crystal is then modelled as a sum of atom-centred charge
distributions. Once the experimental electron density has been
established, the "atoms in molecules" theory of Bader (1990)
provides tools for the interpretation of the density
distribution in terms of its topological properties.

Ref:  Bader, R. F. W. (1990). Atoms in molecules: a quantum
        theory. Oxford University Press.
      Coppens, P. (1997). X-ray charge densities and chemical
        bonding. Oxford University Press.
      Hansen, N. K. & Coppens, P.  (1978). Acta Cryst. A34,
        909-921.
      Koritsanszky, T. S. & Coppens, P. (2001). Chem. Rev. 101,
        1583-1621.

Example:


loop_
    _atom_rho_multipole_atom_label
    _atom_rho_multipole_coeff_Pv
    _atom_rho_multipole_coeff_P00
    _atom_rho_multipole_coeff_P11
    _atom_rho_multipole_coeff_P1-1
    _atom_rho_multipole_coeff_P10
    _atom_rho_multipole_coeff_P20
    _atom_rho_multipole_coeff_P21
    _atom_rho_multipole_coeff_P2-1
    _atom_rho_multipole_coeff_P22
    _atom_rho_multipole_coeff_P2-2
    _atom_rho_multipole_coeff_P30
    _atom_rho_multipole_coeff_P31
    _atom_rho_multipole_coeff_P3-1
    _atom_rho_multipole_coeff_P32
    _atom_rho_multipole_coeff_P3-2
    _atom_rho_multipole_coeff_P33
    _atom_rho_multipole_coeff_P3-3
    _atom_rho_multipole_coeff_P40
    _atom_rho_multipole_coeff_P41
    _atom_rho_multipole_coeff_P4-1
    _atom_rho_multipole_coeff_P42
    _atom_rho_multipole_coeff_P4-2
    _atom_rho_multipole_coeff_P43
    _atom_rho_multipole_coeff_P4-3
    _atom_rho_multipole_coeff_P44
    _atom_rho_multipole_coeff_P4-4
    _atom_rho_multipole_kappa
    _atom_rho_multipole_kappa_prime0
    _atom_rho_multipole_kappa_prime1
    _atom_rho_multipole_kappa_prime2
    _atom_rho_multipole_kappa_prime3
    _atom_rho_multipole_kappa_prime4
    Ni2+(1)  2.38(4)  0.32(4)  0.00  0.00 -0.02(1)
             0.00(2)  0.00     0.00  0.00  0.00
            -0.08(1)  0.00     0.00  0.00  0.00      0.06(1)  -0.04(1)
             0.05(1)  0.00     0.00  0.00  0.00     -0.20(1)   0.08(1)
             0.00     0.00
             1.04(1)  0.44(1)  0.44  1.15(4)   0.44  1.15



data_atom_rho_multipole_[rho]
    _name                      '_atom_rho_multipole_[rho]'
    _category                    category_overview
    _type                        null
    loop_ _example_detail
          _example
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
; Example 1 - Multipole coefficients for the nickel ion in
              [Ni(H3L)][NO3][PF6], [H3L =
              N,N',N''-tris(2-hydroxy-3-methylbutyl)-1,4,7-triazacyclononane]
              [G.T. Smith et al. (1997). J. Am. Chem. Soc. 119, 5028-5034].
;
;
    loop_
    _atom_rho_multipole_atom_label
    _atom_rho_multipole_coeff_Pv
    _atom_rho_multipole_coeff_P00
    _atom_rho_multipole_coeff_P11
    _atom_rho_multipole_coeff_P1-1
    _atom_rho_multipole_coeff_P10
    _atom_rho_multipole_coeff_P20
    _atom_rho_multipole_coeff_P21
    _atom_rho_multipole_coeff_P2-1
    _atom_rho_multipole_coeff_P22
    _atom_rho_multipole_coeff_P2-2
    _atom_rho_multipole_coeff_P30
    _atom_rho_multipole_coeff_P31
    _atom_rho_multipole_coeff_P3-1
    _atom_rho_multipole_coeff_P32
    _atom_rho_multipole_coeff_P3-2
    _atom_rho_multipole_coeff_P33
    _atom_rho_multipole_coeff_P3-3
    _atom_rho_multipole_coeff_P40
    _atom_rho_multipole_coeff_P41
    _atom_rho_multipole_coeff_P4-1
    _atom_rho_multipole_coeff_P42
    _atom_rho_multipole_coeff_P4-2
    _atom_rho_multipole_coeff_P43
    _atom_rho_multipole_coeff_P4-3
    _atom_rho_multipole_coeff_P44
    _atom_rho_multipole_coeff_P4-4
    _atom_rho_multipole_kappa
    _atom_rho_multipole_kappa_prime0
    _atom_rho_multipole_kappa_prime1
    _atom_rho_multipole_kappa_prime2
    _atom_rho_multipole_kappa_prime3
    _atom_rho_multipole_kappa_prime4
    Ni2+(1)  2.38(4)  0.32(4)  0.00  0.00 -0.02(1)
             0.00(2)  0.00     0.00  0.00  0.00
            -0.08(1)  0.00     0.00  0.00  0.00      0.06(1)  -0.04(1)
             0.05(1)  0.00     0.00  0.00  0.00     -0.20(1)   0.08(1)
             0.00     0.00
             1.04(1)  0.44(1)  0.44  1.15(4)   0.44  1.15
;
    _definition
;              This category contains information about the multipole
               coefficients used to describe the electron density.
               High-resolution X-ray diffraction methods enable the
               determination of the electron density distribution in
               crystal lattices and molecules, which in turn allows for a
               characterization of chemical interactions (Coppens, 1997;
               Koritsanszky & Coppens, 2001). This is accomplished by
               the construction of a mathematical model of the charge
               density in a crystal and then by fitting the parameters of
               such a model to the experimental pattern of diffracted
               X-rays. The model on which this dictionary is based
               is the so-called multipole formalism proposed by Hansen
               & Coppens (1978). In this model, the electron density in
               a crystal is described by a sum of aspherical "pseudoatoms"
               where the pseudoatom density has the form defined in the
               _atom_rho_multipole_* items. Each pseudoatom density
               consists of terms representing the core density, the spherical
               part of the valence density and the deviation of the valence
               density from sphericity. The continuous electron density in the
               crystal is then modelled as a sum of atom-centred charge
               distributions. Once the experimental electron density has been
               established, the "atoms in molecules" theory of Bader (1990)
               provides tools for the interpretation of the density
               distribution in terms of its topological properties.


               Ref:  Bader, R. F. W. (1990). Atoms in molecules: a quantum
                       theory. Oxford University Press.
                     Coppens, P. (1997). X-ray charge densities and chemical
                       bonding. Oxford University Press.
                     Hansen, N. K. & Coppens, P.  (1978). Acta Cryst. A34,
                       909-921.
                     Koritsanszky, T. S. & Coppens, P. (2001). Chem. Rev. 101,
                       1583-1621.
;







_atom_rho_multipole_atom_label


CIF 

This item is used to identify the atom whose electron density is

described with an atom in the ATOM_SITE category. Its value
must be identical to one of the values in the _atom_site_label
list.



data_atom_rho_multipole_atom_label
    _name                      '_atom_rho_multipole_atom_label'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_link_parent          '_atom_site_label'
    _list_mandatory              yes
    _definition
;              This item is used to identify the atom whose electron density is
               described with an atom in the ATOM_SITE category. Its value
               must be identical to one of the values in the _atom_site_label
               list.
;









_atom_rho_multipole_coeff


CIF 

Data names:
_atom_rho_multipole_coeff_Pc
_atom_rho_multipole_coeff_Pv
_atom_rho_multipole_coeff_P00
_atom_rho_multipole_coeff_P10
_atom_rho_multipole_coeff_P11
_atom_rho_multipole_coeff_P1-1
_atom_rho_multipole_coeff_P20
_atom_rho_multipole_coeff_P21
_atom_rho_multipole_coeff_P2-1
_atom_rho_multipole_coeff_P22
_atom_rho_multipole_coeff_P2-2
_atom_rho_multipole_coeff_P30
_atom_rho_multipole_coeff_P31
_atom_rho_multipole_coeff_P3-1
_atom_rho_multipole_coeff_P32
_atom_rho_multipole_coeff_P3-2
_atom_rho_multipole_coeff_P33
_atom_rho_multipole_coeff_P3-3
_atom_rho_multipole_coeff_P40
_atom_rho_multipole_coeff_P41
_atom_rho_multipole_coeff_P4-1
_atom_rho_multipole_coeff_P42
_atom_rho_multipole_coeff_P4-2
_atom_rho_multipole_coeff_P43
_atom_rho_multipole_coeff_P4-3
_atom_rho_multipole_coeff_P44
_atom_rho_multipole_coeff_P4-4

Specifies the multipole population coefficients P(l,m) for

the atom identified in _atom_rho_multipole_atom_label.  The
multipoles are defined with respect to the local axes specified
in the ATOM_LOCAL_AXES category.  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*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],

  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.

  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.

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.



data_atom_rho_multipole_coeff_
    loop_ _name                '_atom_rho_multipole_coeff_Pc'
                               '_atom_rho_multipole_coeff_Pv'
                               '_atom_rho_multipole_coeff_P00'
                               '_atom_rho_multipole_coeff_P10'
                               '_atom_rho_multipole_coeff_P11'
                               '_atom_rho_multipole_coeff_P1-1'
                               '_atom_rho_multipole_coeff_P20'
                               '_atom_rho_multipole_coeff_P21'
                               '_atom_rho_multipole_coeff_P2-1'
                               '_atom_rho_multipole_coeff_P22'
                               '_atom_rho_multipole_coeff_P2-2'
                               '_atom_rho_multipole_coeff_P30'
                               '_atom_rho_multipole_coeff_P31'
                               '_atom_rho_multipole_coeff_P3-1'
                               '_atom_rho_multipole_coeff_P32'
                               '_atom_rho_multipole_coeff_P3-2'
                               '_atom_rho_multipole_coeff_P33'
                               '_atom_rho_multipole_coeff_P3-3'
                               '_atom_rho_multipole_coeff_P40'
                               '_atom_rho_multipole_coeff_P41'
                               '_atom_rho_multipole_coeff_P4-1'
                               '_atom_rho_multipole_coeff_P42'
                               '_atom_rho_multipole_coeff_P4-2'
                               '_atom_rho_multipole_coeff_P43'
                               '_atom_rho_multipole_coeff_P4-3'
                               '_atom_rho_multipole_coeff_P44'
                               '_atom_rho_multipole_coeff_P4-4'
    _category                    atom_rho_multipole
    _type                        numb
    _type_conditions             esd
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _definition
;              Specifies the multipole population coefficients P(l,m) for
               the atom identified in _atom_rho_multipole_atom_label.  The
               multipoles are defined with respect to the local axes specified
               in the ATOM_LOCAL_AXES category.  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*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],

                 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.

                 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.

               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.
;









_atom_rho_multipole_configuration


CIF 

This item defines the electronic configuration of the atom

given in _atom_rho_multipole_atom_label as free text.



data_atom_rho_multipole_configuration
    _name                      '_atom_rho_multipole_configuration'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _definition
;              This item defines the electronic configuration of the atom
               given in _atom_rho_multipole_atom_label as free text.
;









_atom_rho_multipole_core_source


CIF 

This item gives the source of the orbital exponents and

expansion coefficients used to obtain the spherical core
density of the atom defined in _atom_rho_multipole_atom_label.
Alternatively, the core density may be obtained as described
in the _atom_rho_multipole_scat_core item.

Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
        Tables, 14, 177-478.

Example:


Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables,
    14, 177-478.



data_atom_rho_multipole_core_source
    _name                      '_atom_rho_multipole_core_source'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _example
;   Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables,
    14, 177-478.
;
    _definition
;              This item gives the source of the orbital exponents and
               expansion coefficients used to obtain the spherical core
               density of the atom defined in _atom_rho_multipole_atom_label.
               Alternatively, the core density may be obtained as described
               in the _atom_rho_multipole_scat_core item.

               Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
                       Tables, 14, 177-478.
;









_atom_rho_multipole_kappa


CIF 

Data names:
_atom_rho_multipole_kappa
_atom_rho_multipole_kappa_prime0
_atom_rho_multipole_kappa_prime1
_atom_rho_multipole_kappa_prime2
_atom_rho_multipole_kappa_prime3
_atom_rho_multipole_kappa_prime4

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.



data_atom_rho_multipole_kappa_
    loop_  _name               '_atom_rho_multipole_kappa'
                               '_atom_rho_multipole_kappa_prime0'
                               '_atom_rho_multipole_kappa_prime1'
                               '_atom_rho_multipole_kappa_prime2'
                               '_atom_rho_multipole_kappa_prime3'
                               '_atom_rho_multipole_kappa_prime4'
    _category                    atom_rho_multipole
    _type                        numb
    _type_conditions             esd
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _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.
;









_atom_rho_multipole_radial_function_type


CIF 

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.



data_atom_rho_multipole_radial_function_type
    _name                      '_atom_rho_multipole_radial_function_type'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _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.

;









_atom_rho_multipole_radial_slater


CIF 

Data names:
_atom_rho_multipole_radial_slater_n0
_atom_rho_multipole_radial_slater_zeta0
_atom_rho_multipole_radial_slater_n1
_atom_rho_multipole_radial_slater_zeta1
_atom_rho_multipole_radial_slater_n2
_atom_rho_multipole_radial_slater_zeta2
_atom_rho_multipole_radial_slater_n3
_atom_rho_multipole_radial_slater_zeta3
_atom_rho_multipole_radial_slater_n4
_atom_rho_multipole_radial_slater_zeta4

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.



data_atom_rho_multipole_radial_slater_
    loop_ _name                '_atom_rho_multipole_radial_slater_n0'
                               '_atom_rho_multipole_radial_slater_zeta0'
                               '_atom_rho_multipole_radial_slater_n1'
                               '_atom_rho_multipole_radial_slater_zeta1'
                               '_atom_rho_multipole_radial_slater_n2'
                               '_atom_rho_multipole_radial_slater_zeta2'
                               '_atom_rho_multipole_radial_slater_n3'
                               '_atom_rho_multipole_radial_slater_zeta3'
                               '_atom_rho_multipole_radial_slater_n4'
                               '_atom_rho_multipole_radial_slater_zeta4'
    _category                    atom_rho_multipole
    _type                        numb
    _type_conditions             esd
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _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.
;









_atom_rho_multipole_scat_core


CIF 

This item gives the scattering factor for the core electrons

of the atom  specified in _atom_rho_multipole_atom_label as a
function of sin(theta)/lambda. The text should contain only a
table of two columns, the first giving the value of
sin(theta)/lambda, the second giving the X-ray scattering factor
at this point in reciprocal space.

The atomic core scattering factors are used in least-squares
fitting of the items in _atom_rho_multipole_coeff_* and
_atom_rho_multipole_kappa_* to experimental X-ray structure
factors [see for example Coppens (1997)]. This item enables
them to be supplied in the form of a numerical table. Normally
they originate from atomic orbital analytic wavefunctions
such as those tabulated by Clementi & Roetti (1974).

Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
        Tables, 14, 177-478.
      Coppens, P. (1997). X-ray charge densities and
        chemical bonding. Oxford University Press.



data_atom_rho_multipole_scat_core
    _name                      '_atom_rho_multipole_scat_core'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _definition
;              This item gives the scattering factor for the core electrons
               of the atom  specified in _atom_rho_multipole_atom_label as a
               function of sin(theta)/lambda. The text should contain only a
               table of two columns, the first giving the value of
               sin(theta)/lambda, the second giving the X-ray scattering factor
               at this point in reciprocal space.

               The atomic core scattering factors are used in least-squares
               fitting of the items in _atom_rho_multipole_coeff_* and
               _atom_rho_multipole_kappa_* to experimental X-ray structure
               factors [see for example Coppens (1997)]. This item enables
               them to be supplied in the form of a numerical table. Normally
               they originate from atomic orbital analytic wavefunctions
               such as those tabulated by Clementi & Roetti (1974).

               Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
                       Tables, 14, 177-478.
                     Coppens, P. (1997). X-ray charge densities and
                       chemical bonding. Oxford University Press.
;









_atom_rho_multipole_scat_valence


CIF 

This item gives the scattering factor for the valence electrons

of the atom specified in _atom_rho_multipole_atom_label as a
function of sin(theta)/lambda. The text should contain only a
table of two columns, the first giving the value of
sin(theta)/lambda, the second giving the X-ray scattering factor
at this point in reciprocal space.

The atomic valence scattering factors are used in least-squares
fitting of the items in _atom_rho_multipole_coeff_* and
_atom_rho_multipole_kappa_* to experimental X-ray structure
factors [see for example Coppens (1997)]. This item enables
them to be supplied in the form of a numerical table. Normally
they originate from atomic orbital analytic wavefunctions
such as those tabulated by Clementi & Roetti (1974).

Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
        Tables, 14, 177-478.
      Coppens, P. (1997). X-ray charge densities and
        chemical bonding. Oxford University Press.



data_atom_rho_multipole_scat_valence
    _name                      '_atom_rho_multipole_scat_valence'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _definition
;              This item gives the scattering factor for the valence electrons
               of the atom specified in _atom_rho_multipole_atom_label as a
               function of sin(theta)/lambda. The text should contain only a
               table of two columns, the first giving the value of
               sin(theta)/lambda, the second giving the X-ray scattering factor
               at this point in reciprocal space.

               The atomic valence scattering factors are used in least-squares
               fitting of the items in _atom_rho_multipole_coeff_* and
               _atom_rho_multipole_kappa_* to experimental X-ray structure
               factors [see for example Coppens (1997)]. This item enables
               them to be supplied in the form of a numerical table. Normally
               they originate from atomic orbital analytic wavefunctions
               such as those tabulated by Clementi & Roetti (1974).

               Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
                       Tables, 14, 177-478.
                     Coppens, P. (1997). X-ray charge densities and
                       chemical bonding. Oxford University Press.
;









_atom_rho_multipole_valence_source


CIF 

This item gives the source of the orbital exponents and

expansion coefficients used to obtain the spherical valence
density of the atom defined in _atom_rho_multipole_atom_label.
Alternatively the valence density may be obtained as described
in the _atom_rho_multipole_scat_valence item.

Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
        Tables, 14, 177-478.

Example:


Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables,
   14, 177-478.



data_atom_rho_multipole_valence_source
    _name                      '_atom_rho_multipole_valence_source'
    _category                    atom_rho_multipole
    _type                        char
    _list                        yes
    _list_reference            '_atom_rho_multipole_atom_label'
    _example
;  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables,
   14, 177-478.
;
    _definition
;              This item gives the source of the orbital exponents and
               expansion coefficients used to obtain the spherical valence
               density of the atom defined in _atom_rho_multipole_atom_label.
               Alternatively the valence density may be obtained as described
               in the _atom_rho_multipole_scat_valence item.

               Ref:  Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data
                       Tables, 14, 177-478.
;

# ------ EOF ------ EOF ------ EOF -------- EOF -------- EOF ------- EOF











_ATOM_SITE_[RHO]
CIF 

Data items in the ATOM_SITE category record details about

the atom sites in a crystal structure, such as the positional
coordinates, atomic displacement parameters, magnetic moments
and directions.



data_atom_site_[rho]
    _name                      '_atom_site_[rho]'
    _category                    category_overview
    _type                        null
      _definition
;              Data items in the ATOM_SITE category record details about
               the atom sites in a crystal structure, such as the positional
               coordinates, atomic displacement parameters, magnetic moments
               and directions.
;







_atom_site_label


CIF 

The _atom_site_label is a unique identifier for a particular

site in the crystal, and is fully defined in the core CIF
dictionary. The child data names itemized here are in
addition to those in the core dictionary.



data_atom_site_label_rho
   _name                       '_atom_site_label'
   _category                     atom_site
   loop_
        _list_link_child       '_atom_local_axes_atom0'
                               '_atom_local_axes_atom1'
                               '_atom_local_axes_atom2'
                               '_atom_local_axes_atom_label'
                               '_atom_rho_multipole_atom_label'
# added from the entry in the core dictionary to make a self-contained
# unit (BM 2003-06-12)
    _type                        char
    _list                        yes
    _list_mandatory              yes
    _definition
;              The _atom_site_label is a unique identifier for a particular
               site in the crystal, and is fully defined in the core CIF
               dictionary. The child data names itemized here are in
               addition to those in the core dictionary.
;

########################################################
#                                                      #
#  Category ATOM_LOCAL_AXES                            #
#                                                      #
########################################################













Revision history






1999-07-07   Created as rhoCIF dictionary by P.R. Mallinson.




2000-10-13   Simplified CIF structure into two loops,
corresponding to newly-defined categories atom_rho
and atom_local. Introduced reference to multipole
formalism, more rigorous definition of local axis
systems, and rationalised definition of dummy atoms.
Clarified example of use of dummy atom.




2000-10-16   Additions and changes made by I.D.Brown to bring the
dictionary into better conformance with the other CIF
dictionaries.  Category definitions added.  Category
names changed to atom_local_axes and atom_rho_multipole.
Items ordered alphabetically.




2000-10-18   Removed ambiguities in description of _ATOM_LOCAL_AXES.
Individual items in this category defined separately.
Definition of core population Pc added. Substituted
new example, with literature reference.




2000-10-20   Version 0.5.  I.D.Brown.  Corrected datanames and some
spelling. added the equation for the electron density
to the definition.




2000-10-23   Further clarification of _ATOM_LOCAL_AXES definition.




2002-03-04   Version 0.61. I.D.Brown. Addition of parent links and
enumeration lists.




2002-10-18   Version 0.62. I.D.Brown. Further additions to the
atom_rho_multipole category based on input from
Paul Mallinson. Tightening up of definitions.
_atom_local_axes_label changed to
_atom_local_axes_atom_label to conform to CIF style.




2002-10-31   Version 0.63. P.R. Mallinson and I.D. Brown. Amended
descriptions of rho_core(r) and rho_valence(kr) in
definitions which refer to them.




2002-11-20   Version 0.64. P.R. Mallinson and I.D. Brown. Changed
names _atom_rho_multipole_scat_*_source to
_atom_rho_multipole_*_source.




2003-06-04   Version 0.65. P.R. Mallinson. Changed kappa',
kappa" nomenclature to kappa, kappa'.




2003-06-14   Version 0.66. B. McMahon. Fixed a few typos; added a
_definition for _atom_site_label explaining its extension
to the core definition; added _definition to the category
overviews; tidied up layout and other stylistic edits.




2003-07-02   Version 0.67. P.R. Mallinson. Expanded category overview
definitions and _atom_rho_multipole_*_source definitions.
Specified summation ranges in expressions used in
_atom_rho_multipole_* definitions.




2003-07-11   Version 0.68. B. McMahon. Implemented Paul's fix for index
ranges -l <= m <= l, and moved the example in the *_source
items as suggested by IDB.




2003-08-19   Version 0.69. I.D.Brown.  Made minor corrections suggested
during final COMCIFS approval which was received on this date.




2003-08-19   Release version 1.0. IUCr.




2005-01-20 NJ Ashcroft: minor corrections to hyphenation, spelling and
punctuation.




2005-06-14 NJ Ashcroft: category overview added for ATOM_SITE
category.











 


 











     

     



  
  

  							
    
  
    
 
      
      

  
						
  




International Tables for Crystallography


Volume G: Definition and exchange of crystallographic data


First online edition (2006)


Edited by S. R. Hall and B. McMahon



An essential guide and reference to CIF for programmers, data managers handling crystal-structure information and practising crystallographers.