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ATOM_LOCAL_AXES
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.
_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.
Also known as: _atom_local_axes_atom0
_atom_local_axes.atom1
CIF
Specifies 'atom1' in the definition of a local axis frame. See definition atom_local_axes.atom0 for description.
Also known as: _atom_local_axes_atom1
_atom_local_axes.atom2
CIF
Specifies 'atom2' in the definition of a local axis frame. See definition atom_local_axes.atom0 for description.
Also known as: _atom_local_axes_atom2
_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.
Also known as: _atom_local_axes_atom_label
_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.
Also known as: _atom_local_axes_ax1
_atom_local_axes.ax2
CIF
Specifies 'ax2' in the definition of a local axis frame. See definition of atom_local_axes.ax1 for description.
Also known as: _atom_local_axes_ax2
ATOM_RHO_MULTIPOLE
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.
_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.
Also known as: _atom_rho_multipole_atom_label
_atom_rho_multipole.configuration
CIF
This item defines the electronic configuration of the atom given in atom_rho_multipole.atom_label as free text.
Also known as: _atom_rho_multipole_configuration
_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.
Also known as: _atom_rho_multipole_core_source
Example:
Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177-478.
_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.base, 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.
Also known as: _atom_rho_multipole_radial_function_type
_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.
Also known as: _atom_rho_multipole_scat_core
_atom_rho_multipole.scat_core_table
CIF
This table 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 table contains the st/l value as the key and the scattering factor as the value. E.g. {"0.00":"15.65","0.05":"15.32",.....etc }
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.
Also known as: _atom_rho_multipole_scat_core_table
_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.
Also known as: _atom_rho_multipole_scat_valence
_atom_rho_multipole.scat_valence_table
CIF
This table 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 table contains the st/l value as the key and the scattering factor as the value. E.g. {"0.00":"15.65","0.05":"15.32",.....etc }
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.
Also known as: _atom_rho_multipole_scat_valence_table
_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.
Also known as: _atom_rho_multipole_valence_source
Example:
Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177-478.
ATOM_RHO_MULTIPOLE_COEFF
CIF
Category defining multipole population coefficients P(l,m).
_atom_rho_multipole_coeff.list
CIF
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.base, 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.
Also known as: _atom_rho_multipole_coeff_list
_atom_rho_multipole_coeff.list_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.list.
_atom_rho_multipole_coeff.P00
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P00
_atom_rho_multipole_coeff.P00_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P00.
_atom_rho_multipole_coeff.P10
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P10
_atom_rho_multipole_coeff.P10_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P10.
_atom_rho_multipole_coeff.P11
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P11
_atom_rho_multipole_coeff.P11_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P11.
_atom_rho_multipole_coeff.P1_1
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P1_1_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P1_1.
_atom_rho_multipole_coeff.P20
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P20
_atom_rho_multipole_coeff.P20_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P20.
_atom_rho_multipole_coeff.P21
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P21
_atom_rho_multipole_coeff.P21_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P21.
_atom_rho_multipole_coeff.P22
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P22
_atom_rho_multipole_coeff.P22_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P22.
_atom_rho_multipole_coeff.P2_1
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P2_1_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P2_1.
_atom_rho_multipole_coeff.P2_2
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P2_2_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P2_2.
_atom_rho_multipole_coeff.P30
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P30
_atom_rho_multipole_coeff.P30_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P30.
_atom_rho_multipole_coeff.P31
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P31
_atom_rho_multipole_coeff.P31_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P31.
_atom_rho_multipole_coeff.P32
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P32
_atom_rho_multipole_coeff.P32_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P32.
_atom_rho_multipole_coeff.P33
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P33
_atom_rho_multipole_coeff.P33_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P33.
_atom_rho_multipole_coeff.P3_1
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P3_1_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P3_1.
_atom_rho_multipole_coeff.P3_2
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P3_2_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P3_2.
_atom_rho_multipole_coeff.P3_3
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P3_3_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P3_3.
_atom_rho_multipole_coeff.P40
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P40
_atom_rho_multipole_coeff.P40_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P40.
_atom_rho_multipole_coeff.P41
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P41
_atom_rho_multipole_coeff.P41_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P41.
_atom_rho_multipole_coeff.P42
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P42
_atom_rho_multipole_coeff.P42_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P42.
_atom_rho_multipole_coeff.P43
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P43
_atom_rho_multipole_coeff.P43_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P43.
_atom_rho_multipole_coeff.P44
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_P44
_atom_rho_multipole_coeff.P44_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P44.
_atom_rho_multipole_coeff.P4_1
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P4_1_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P4_1.
_atom_rho_multipole_coeff.P4_2
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P4_2_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P4_2.
_atom_rho_multipole_coeff.P4_3
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P4_3_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P4_3.
_atom_rho_multipole_coeff.P4_4
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
_atom_rho_multipole_coeff.P4_4_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.P4_4.
_atom_rho_multipole_coeff.Pc
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_Pc
_atom_rho_multipole_coeff.Pc_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.Pc.
_atom_rho_multipole_coeff.Pv
CIF
Specifies a multipole population coefficients P(l,m) for the atom identified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_coeff_Pv
_atom_rho_multipole_coeff.Pv_su
CIF
Standard uncertainty of _atom_rho_multipole_coeff.Pv.
ATOM_RHO_MULTIPOLE_KAPPA
CIF
Category defining radial function expansion-contraction coefficients
_atom_rho_multipole_kappa.base
CIF
A radial function expansion-contraction coefficient (kappa = atom_rho_multipole_kappa.base and kappa'(l) = atom_rho_multipole_kappa.prime[l]) for the atom specified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_kappa
_atom_rho_multipole_kappa.base_su
CIF
Standard uncertainty of _atom_rho_multipole_kappa.base.
_atom_rho_multipole_kappa.list
CIF
Gives the radial function expansion-contraction coefficients (kappa = atom_rho_multipole_kappa.base 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.
Also known as: _atom_rho_multipole_kappa_list
_atom_rho_multipole_kappa.prime0
CIF
A radial function expansion-contraction coefficient (kappa = atom_rho_multipole_kappa.base and kappa'(l) = atom_rho_multipole_kappa.prime[l]) for the atom specified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_kappa_prime0
_atom_rho_multipole_kappa.prime0_su
CIF
Standard uncertainty of _atom_rho_multipole_kappa.prime0.
_atom_rho_multipole_kappa.prime1
CIF
A radial function expansion-contraction coefficient (kappa = atom_rho_multipole_kappa.base and kappa'(l) = atom_rho_multipole_kappa.prime[l]) for the atom specified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_kappa_prime1
_atom_rho_multipole_kappa.prime1_su
CIF
Standard uncertainty of _atom_rho_multipole_kappa.prime1.
_atom_rho_multipole_kappa.prime2
CIF
A radial function expansion-contraction coefficient (kappa = atom_rho_multipole_kappa.base and kappa'(l) = atom_rho_multipole_kappa.prime[l]) for the atom specified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_kappa_prime2
_atom_rho_multipole_kappa.prime2_su
CIF
Standard uncertainty of _atom_rho_multipole_kappa.prime2.
_atom_rho_multipole_kappa.prime3
CIF
A radial function expansion-contraction coefficient (kappa = atom_rho_multipole_kappa.base and kappa'(l) = atom_rho_multipole_kappa.prime[l]) for the atom specified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_kappa_prime3
_atom_rho_multipole_kappa.prime3_su
CIF
Standard uncertainty of _atom_rho_multipole_kappa.prime3.
_atom_rho_multipole_kappa.prime4
CIF
A radial function expansion-contraction coefficient (kappa = atom_rho_multipole_kappa.base and kappa'(l) = atom_rho_multipole_kappa.prime[l]) for the atom specified in atom_rho_multipole.atom_label.
Also known as: _atom_rho_multipole_kappa_prime4
_atom_rho_multipole_kappa.prime4_su
CIF
Standard uncertainty of _atom_rho_multipole_kappa.prime4.
ATOM_RHO_MULTIPOLE_RADIAL_SLATER
CIF
Category defining multipole population coefficients P(l,m).
_atom_rho_multipole_radial_slater.list
CIF
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)i = atom_rho_multipole_radial_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.base, 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.
Also known as: _atom_rho_multipole_radial_slater_list
_atom_rho_multipole_radial_slater.list_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.list.
_atom_rho_multipole_radial_slater.n0
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_n0
_atom_rho_multipole_radial_slater.n0_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.n0.
_atom_rho_multipole_radial_slater.n1
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_n1
_atom_rho_multipole_radial_slater.n1_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.n1.
_atom_rho_multipole_radial_slater.n2
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_n2
_atom_rho_multipole_radial_slater.n2_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.n2.
_atom_rho_multipole_radial_slater.n3
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_n3
_atom_rho_multipole_radial_slater.n3_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.n3.
_atom_rho_multipole_radial_slater.zeta0
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_zeta0
_atom_rho_multipole_radial_slater.zeta0_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.zeta0.
_atom_rho_multipole_radial_slater.zeta1
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_zeta1
_atom_rho_multipole_radial_slater.zeta1_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.zeta1.
_atom_rho_multipole_radial_slater.zeta2
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_zeta2
_atom_rho_multipole_radial_slater.zeta2_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.zeta2.
_atom_rho_multipole_radial_slater.zeta3
CIF
Items 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)]
Also known as: _atom_rho_multipole_radial_slater_zeta3
_atom_rho_multipole_radial_slater.zeta3_su
CIF
Standard uncertainty of _atom_rho_multipole_radial_slater.zeta3.
Revision history
Version 2.0.1 (2014-06-20) Initial conversion to DDLm (Syd Hall)
Version 2.0.2 (2019-04-03) Update import statements, improve DDLm conformance.
Version 2.0.3 (2022-10-17) Further improve DDLm conformance. Add missing su data names.