#\#CIF_2.0 # SPDX-License-Identifier: CC-BY-4.0 ###################################################################### # # # CIF Dictionary for the Multipole Model of # # aspherical atomic density distributions # # # # Converted from DDL1 to DDLm 20 June 2014 # # # ###################################################################### data_CIF_RHO _dictionary.title CIF_RHO _dictionary.class Instance _dictionary.version 2.0.3 _dictionary.date 2025-11-25 _dictionary.uri ;\ https://raw.githubusercontent.com/COMCIFS/Electron_Density_\ Dictionary/master/cif_rho.dic ; _dictionary.ddl_conformance 4.2.0 _dictionary.namespace CifCore _description.text ; The CIF_RHO dictionary records the definitions of data items specifying the Multipole Model of aspherical atomic density distributions used with in the Crystallographic Information Framework (CIF). ; save_CIF_RHO_HEAD _definition.id CIF_RHO_HEAD _definition.scope Category _definition.class Head _definition.update 2025-11-25 _description.text ; Groups all of the categories of definitions in the study of multipole modeling of aspherical atomic density distributions ; _name.category_id CIF_RHO _name.object_id CIF_RHO_HEAD _import.get [ {'dupl':Ignore 'file':cif_core.dic 'mode':Full 'save':CIF_CORE_HEAD} ] save_ save_ATOM_LOCAL_AXES _definition.id ATOM_LOCAL_AXES _definition.scope Category _definition.class Loop _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id CIF_RHO_HEAD _name.object_id ATOM_LOCAL_AXES _category_key.name '_atom_local_axes.atom_label' save_ save_atom_local_axes.atom0 _definition.id '_atom_local_axes.atom0' _alias.definition_id '_atom_local_axes_atom0' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_local_axes _name.object_id atom0 _name.linked_item_id '_atom_site.label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_local_axes.atom1 _definition.id '_atom_local_axes.atom1' _alias.definition_id '_atom_local_axes_atom1' _definition.update 2014-06-20 _description.text ; Specifies 'atom1' in the definition of a local axis frame. See definition of _atom_local_axes.atom0 for description. ; _name.category_id atom_local_axes _name.object_id atom1 _name.linked_item_id '_atom_site.label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_local_axes.atom2 _definition.id '_atom_local_axes.atom2' _alias.definition_id '_atom_local_axes_atom2' _definition.update 2014-06-20 _description.text ; Specifies 'atom2' in the definition of a local axis frame. See definition of _atom_local_axes.atom0 for description. ; _name.category_id atom_local_axes _name.object_id atom2 _name.linked_item_id '_atom_site.label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_local_axes.atom_label _definition.id '_atom_local_axes.atom_label' _alias.definition_id '_atom_local_axes_atom_label' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_local_axes _name.object_id atom_label _name.linked_item_id '_atom_site.label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_local_axes.ax1 _definition.id '_atom_local_axes.ax1' _alias.definition_id '_atom_local_axes_ax1' _definition.update 2024-03-30 _description.text ; 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. ; _name.category_id atom_local_axes _name.object_id ax1 _type.purpose State _type.source Assigned _type.container Single _type.contents Word loop_ _enumeration_set.state x X y Y z Z +x +X +y +Y +z +Z -x -X -y -Y -z -Z save_ save_atom_local_axes.ax2 _definition.id '_atom_local_axes.ax2' _alias.definition_id '_atom_local_axes_ax2' _definition.update 2024-03-30 _description.text ; Specifies 'ax2' in the definition of a local axis frame. See definition of _atom_local_axes.ax1 for description. ; _name.category_id atom_local_axes _name.object_id ax2 _type.purpose State _type.source Assigned _type.container Single _type.contents Word loop_ _enumeration_set.state x X y Y z Z +x +X +y +Y +z +Z -x -X -y -Y -z -Z save_ save_ATOM_RHO_MULTIPOLE _definition.id ATOM_RHO_MULTIPOLE _definition.scope Category _definition.class Loop _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id CIF_RHO_HEAD _name.object_id ATOM_RHO_MULTIPOLE _category_key.name '_atom_rho_multipole.atom_label' save_ save_atom_rho_multipole.atom_label _definition.id '_atom_rho_multipole.atom_label' _alias.definition_id '_atom_rho_multipole_atom_label' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id atom_label _name.linked_item_id '_atom_site.label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_rho_multipole.configuration _definition.id '_atom_rho_multipole.configuration' _alias.definition_id '_atom_rho_multipole_configuration' _definition.update 2014-06-20 _description.text ; This item defines the electronic configuration of the atom given in _atom_rho_multipole.atom_label as free text. ; _name.category_id atom_rho_multipole _name.object_id configuration _type.purpose Describe _type.source Recorded _type.container Single _type.contents Text save_ save_atom_rho_multipole.core_source _definition.id '_atom_rho_multipole.core_source' _alias.definition_id '_atom_rho_multipole_core_source' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id core_source _type.purpose Describe _type.source Recorded _type.container Single _type.contents Text _description_example.case ; Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177-478. ; save_ save_atom_rho_multipole.radial_function_type _definition.id '_atom_rho_multipole.radial_function_type' _alias.definition_id '_atom_rho_multipole_radial_function_type' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id radial_function_type _type.purpose Describe _type.source Recorded _type.container Single _type.contents Text save_ save_atom_rho_multipole.scat_core _definition.id '_atom_rho_multipole.scat_core' _alias.definition_id '_atom_rho_multipole_scat_core' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id scat_core _type.purpose Describe _type.source Recorded _type.container Single _type.contents Text save_ save_atom_rho_multipole.scat_core_table _definition.id '_atom_rho_multipole.scat_core_table' _alias.definition_id '_atom_rho_multipole_scat_core_table' _definition.update 2019-04-01 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id scat_core_table _type.purpose Number _type.source Assigned _type.container Array _type.dimension '[]' _type.contents Real _units.code none save_ save_atom_rho_multipole.scat_valence _definition.id '_atom_rho_multipole.scat_valence' _alias.definition_id '_atom_rho_multipole_scat_valence' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id scat_valence _type.purpose Describe _type.source Recorded _type.container Single _type.contents Text save_ save_atom_rho_multipole.scat_valence_table _definition.id '_atom_rho_multipole.scat_valence_table' _alias.definition_id '_atom_rho_multipole_scat_valence_table' _definition.update 2019-04-01 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id scat_valence_table _type.purpose Number _type.source Assigned _type.container Array _type.dimension '[]' _type.contents Real _units.code none save_ save_atom_rho_multipole.valence_source _definition.id '_atom_rho_multipole.valence_source' _alias.definition_id '_atom_rho_multipole_valence_source' _definition.update 2014-06-20 _description.text ; 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. ; _name.category_id atom_rho_multipole _name.object_id valence_source _type.purpose Describe _type.source Recorded _type.container Single _type.contents Text _description_example.case ; Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177-478. ; save_ save_ATOM_RHO_MULTIPOLE_COEFF _definition.id ATOM_RHO_MULTIPOLE_COEFF _definition.scope Category _definition.class Loop _definition.update 2024-04-02 _description.text ; Category defining multipole population coefficients P(l,m). ; _name.category_id ATOM_RHO_MULTIPOLE _name.object_id ATOM_RHO_MULTIPOLE_COEFF _category_key.name '_atom_rho_multipole_coeff.atom_label' save_ save_atom_rho_multipole_coeff.atom_label _definition.id '_atom_rho_multipole_coeff.atom_label' _definition.update 2024-04-02 _description.text ; An atom site label that serves as the ATOM_RHO_MULTIPOLE_COEFF category key. It should only be used when items from the ATOM_RHO_MULTIPOLE_COEFF and ATOM_RHO_MULTIPOLE categories are looped in separate lists. ; _name.category_id atom_rho_multipole_coeff _name.object_id atom_label _name.linked_item_id '_atom_rho_multipole.atom_label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_rho_multipole_coeff.list _definition.id '_atom_rho_multipole_coeff.list' _alias.definition_id '_atom_rho_multipole_coeff_list' _definition.update 2019-04-01 _description.text ; Specifies the multipole population coefficients P(l,m) for the atom identified in _atom_rho_multipole.atom_label. The list is ordered in increasing order of l, and then for each l in increasing order of m. 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. ; _name.category_id atom_rho_multipole_coeff _name.object_id list _type.purpose Measurand _type.source Derived _type.container List _type.dimension '[25]' _type.contents Real _units.code none _method.purpose Evaluation _method.expression ; With r as atom_rho_multipole_coeff atom_rho_multipole_coeff.list = [ r.P00, r.P10, r.P11, r.P1_1, r.P20, r.P21, r.P2_1, r.P22, r.P2_2, r.P30, r.P31, r.P3_1, r.P32, r.P3_2, r.P33, r.P3_3, r.P40, r.P41, r.P4_1, r.P42, r.P4_2, r.P43, r.P4_3, r.P44, r.P4_4] ; save_ save_atom_rho_multipole_coeff.list_su _definition.id '_atom_rho_multipole_coeff.list_su' _definition.update 2024-04-02 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.list. ; _name.category_id atom_rho_multipole_coeff _name.object_id list_su _name.linked_item_id '_atom_rho_multipole_coeff.list' _type.purpose SU _type.source Related _type.container List _type.dimension '[25]' _type.contents Real _units.code none save_ save_atom_rho_multipole_coeff.p00 _definition.id '_atom_rho_multipole_coeff.P00' _alias.definition_id '_atom_rho_multipole_coeff_P00' _name.category_id atom_rho_multipole_coeff _name.object_id P00 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p00_su _definition.id '_atom_rho_multipole_coeff.P00_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P00. ; _name.category_id atom_rho_multipole_coeff _name.object_id P00_su _name.linked_item_id '_atom_rho_multipole_coeff.P00' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p10 _definition.id '_atom_rho_multipole_coeff.P10' _alias.definition_id '_atom_rho_multipole_coeff_P10' _name.category_id atom_rho_multipole_coeff _name.object_id P10 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p10_su _definition.id '_atom_rho_multipole_coeff.P10_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P10. ; _name.category_id atom_rho_multipole_coeff _name.object_id P10_su _name.linked_item_id '_atom_rho_multipole_coeff.P10' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p11 _definition.id '_atom_rho_multipole_coeff.P11' _alias.definition_id '_atom_rho_multipole_coeff_P11' _name.category_id atom_rho_multipole_coeff _name.object_id P11 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p11_su _definition.id '_atom_rho_multipole_coeff.P11_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P11. ; _name.category_id atom_rho_multipole_coeff _name.object_id P11_su _name.linked_item_id '_atom_rho_multipole_coeff.P11' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p1_1 _definition.id '_atom_rho_multipole_coeff.P1_1' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P1_1' '_atom_rho_multipole_coeff_P1-1' _name.category_id atom_rho_multipole_coeff _name.object_id P1_1 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p1_1_su _definition.id '_atom_rho_multipole_coeff.P1_1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P1_1. ; _name.category_id atom_rho_multipole_coeff _name.object_id P1_1_su _name.linked_item_id '_atom_rho_multipole_coeff.P1_1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p20 _definition.id '_atom_rho_multipole_coeff.P20' _alias.definition_id '_atom_rho_multipole_coeff_P20' _name.category_id atom_rho_multipole_coeff _name.object_id P20 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p20_su _definition.id '_atom_rho_multipole_coeff.P20_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P20. ; _name.category_id atom_rho_multipole_coeff _name.object_id P20_su _name.linked_item_id '_atom_rho_multipole_coeff.P20' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p21 _definition.id '_atom_rho_multipole_coeff.P21' _alias.definition_id '_atom_rho_multipole_coeff_P21' _name.category_id atom_rho_multipole_coeff _name.object_id P21 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p21_su _definition.id '_atom_rho_multipole_coeff.P21_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P21. ; _name.category_id atom_rho_multipole_coeff _name.object_id P21_su _name.linked_item_id '_atom_rho_multipole_coeff.P21' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p22 _definition.id '_atom_rho_multipole_coeff.P22' _alias.definition_id '_atom_rho_multipole_coeff_P22' _name.category_id atom_rho_multipole_coeff _name.object_id P22 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p22_su _definition.id '_atom_rho_multipole_coeff.P22_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P22. ; _name.category_id atom_rho_multipole_coeff _name.object_id P22_su _name.linked_item_id '_atom_rho_multipole_coeff.P22' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p2_1 _definition.id '_atom_rho_multipole_coeff.P2_1' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P2_1' '_atom_rho_multipole_coeff_P2-1' _name.category_id atom_rho_multipole_coeff _name.object_id P2_1 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p2_1_su _definition.id '_atom_rho_multipole_coeff.P2_1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P2_1. ; _name.category_id atom_rho_multipole_coeff _name.object_id P2_1_su _name.linked_item_id '_atom_rho_multipole_coeff.P2_1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p2_2 _definition.id '_atom_rho_multipole_coeff.P2_2' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P2_2' '_atom_rho_multipole_coeff_P2-2' _name.category_id atom_rho_multipole_coeff _name.object_id P2_2 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p2_2_su _definition.id '_atom_rho_multipole_coeff.P2_2_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P2_2. ; _name.category_id atom_rho_multipole_coeff _name.object_id P2_2_su _name.linked_item_id '_atom_rho_multipole_coeff.P2_2' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p30 _definition.id '_atom_rho_multipole_coeff.P30' _alias.definition_id '_atom_rho_multipole_coeff_P30' _name.category_id atom_rho_multipole_coeff _name.object_id P30 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p30_su _definition.id '_atom_rho_multipole_coeff.P30_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P30. ; _name.category_id atom_rho_multipole_coeff _name.object_id P30_su _name.linked_item_id '_atom_rho_multipole_coeff.P30' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p31 _definition.id '_atom_rho_multipole_coeff.P31' _alias.definition_id '_atom_rho_multipole_coeff_P31' _name.category_id atom_rho_multipole_coeff _name.object_id P31 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p31_su _definition.id '_atom_rho_multipole_coeff.P31_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P31. ; _name.category_id atom_rho_multipole_coeff _name.object_id P31_su _name.linked_item_id '_atom_rho_multipole_coeff.P31' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p32 _definition.id '_atom_rho_multipole_coeff.P32' _alias.definition_id '_atom_rho_multipole_coeff_P32' _name.category_id atom_rho_multipole_coeff _name.object_id P32 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p32_su _definition.id '_atom_rho_multipole_coeff.P32_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P32. ; _name.category_id atom_rho_multipole_coeff _name.object_id P32_su _name.linked_item_id '_atom_rho_multipole_coeff.P32' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p33 _definition.id '_atom_rho_multipole_coeff.P33' _alias.definition_id '_atom_rho_multipole_coeff_P33' _name.category_id atom_rho_multipole_coeff _name.object_id P33 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p33_su _definition.id '_atom_rho_multipole_coeff.P33_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P33. ; _name.category_id atom_rho_multipole_coeff _name.object_id P33_su _name.linked_item_id '_atom_rho_multipole_coeff.P33' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p3_1 _definition.id '_atom_rho_multipole_coeff.P3_1' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P3_1' '_atom_rho_multipole_coeff_P3-1' _name.category_id atom_rho_multipole_coeff _name.object_id P3_1 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p3_1_su _definition.id '_atom_rho_multipole_coeff.P3_1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P3_1. ; _name.category_id atom_rho_multipole_coeff _name.object_id P3_1_su _name.linked_item_id '_atom_rho_multipole_coeff.P3_1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p3_2 _definition.id '_atom_rho_multipole_coeff.P3_2' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P3_2' '_atom_rho_multipole_coeff_P3-2' _name.category_id atom_rho_multipole_coeff _name.object_id P3_2 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p3_2_su _definition.id '_atom_rho_multipole_coeff.P3_2_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P3_2. ; _name.category_id atom_rho_multipole_coeff _name.object_id P3_2_su _name.linked_item_id '_atom_rho_multipole_coeff.P3_2' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p3_3 _definition.id '_atom_rho_multipole_coeff.P3_3' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P3_3' '_atom_rho_multipole_coeff_P3-3' _name.category_id atom_rho_multipole_coeff _name.object_id P3_3 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p3_3_su _definition.id '_atom_rho_multipole_coeff.P3_3_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P3_3. ; _name.category_id atom_rho_multipole_coeff _name.object_id P3_3_su _name.linked_item_id '_atom_rho_multipole_coeff.P3_3' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p40 _definition.id '_atom_rho_multipole_coeff.P40' _alias.definition_id '_atom_rho_multipole_coeff_P40' _name.category_id atom_rho_multipole_coeff _name.object_id P40 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p40_su _definition.id '_atom_rho_multipole_coeff.P40_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P40. ; _name.category_id atom_rho_multipole_coeff _name.object_id P40_su _name.linked_item_id '_atom_rho_multipole_coeff.P40' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p41 _definition.id '_atom_rho_multipole_coeff.P41' _alias.definition_id '_atom_rho_multipole_coeff_P41' _name.category_id atom_rho_multipole_coeff _name.object_id P41 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p41_su _definition.id '_atom_rho_multipole_coeff.P41_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P41. ; _name.category_id atom_rho_multipole_coeff _name.object_id P41_su _name.linked_item_id '_atom_rho_multipole_coeff.P41' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p42 _definition.id '_atom_rho_multipole_coeff.P42' _alias.definition_id '_atom_rho_multipole_coeff_P42' _name.category_id atom_rho_multipole_coeff _name.object_id P42 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p42_su _definition.id '_atom_rho_multipole_coeff.P42_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P42. ; _name.category_id atom_rho_multipole_coeff _name.object_id P42_su _name.linked_item_id '_atom_rho_multipole_coeff.P42' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p43 _definition.id '_atom_rho_multipole_coeff.P43' _alias.definition_id '_atom_rho_multipole_coeff_P43' _name.category_id atom_rho_multipole_coeff _name.object_id P43 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p43_su _definition.id '_atom_rho_multipole_coeff.P43_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P43. ; _name.category_id atom_rho_multipole_coeff _name.object_id P43_su _name.linked_item_id '_atom_rho_multipole_coeff.P43' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p44 _definition.id '_atom_rho_multipole_coeff.P44' _alias.definition_id '_atom_rho_multipole_coeff_P44' _name.category_id atom_rho_multipole_coeff _name.object_id P44 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p44_su _definition.id '_atom_rho_multipole_coeff.P44_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P44. ; _name.category_id atom_rho_multipole_coeff _name.object_id P44_su _name.linked_item_id '_atom_rho_multipole_coeff.P44' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p4_1 _definition.id '_atom_rho_multipole_coeff.P4_1' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P4_1' '_atom_rho_multipole_coeff_P4-1' _name.category_id atom_rho_multipole_coeff _name.object_id P4_1 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p4_1_su _definition.id '_atom_rho_multipole_coeff.P4_1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P4_1. ; _name.category_id atom_rho_multipole_coeff _name.object_id P4_1_su _name.linked_item_id '_atom_rho_multipole_coeff.P4_1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p4_2 _definition.id '_atom_rho_multipole_coeff.P4_2' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P4_2' '_atom_rho_multipole_coeff_P4-2' _name.category_id atom_rho_multipole_coeff _name.object_id P4_2 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p4_2_su _definition.id '_atom_rho_multipole_coeff.P4_2_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P4_2. ; _name.category_id atom_rho_multipole_coeff _name.object_id P4_2_su _name.linked_item_id '_atom_rho_multipole_coeff.P4_2' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p4_3 _definition.id '_atom_rho_multipole_coeff.P4_3' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P4_3' '_atom_rho_multipole_coeff_P4-3' _name.category_id atom_rho_multipole_coeff _name.object_id P4_3 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p4_3_su _definition.id '_atom_rho_multipole_coeff.P4_3_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P4_3. ; _name.category_id atom_rho_multipole_coeff _name.object_id P4_3_su _name.linked_item_id '_atom_rho_multipole_coeff.P4_3' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.p4_4 _definition.id '_atom_rho_multipole_coeff.P4_4' loop_ _alias.definition_id '_atom_rho_multipole_coeff_P4_4' '_atom_rho_multipole_coeff_P4-4' _name.category_id atom_rho_multipole_coeff _name.object_id P4_4 _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.p4_4_su _definition.id '_atom_rho_multipole_coeff.P4_4_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.P4_4. ; _name.category_id atom_rho_multipole_coeff _name.object_id P4_4_su _name.linked_item_id '_atom_rho_multipole_coeff.P4_4' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.pc _definition.id '_atom_rho_multipole_coeff.Pc' _alias.definition_id '_atom_rho_multipole_coeff_Pc' _name.category_id atom_rho_multipole_coeff _name.object_id Pc _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.pc_su _definition.id '_atom_rho_multipole_coeff.Pc_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.Pc. ; _name.category_id atom_rho_multipole_coeff _name.object_id Pc_su _name.linked_item_id '_atom_rho_multipole_coeff.Pc' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_coeff.pv _definition.id '_atom_rho_multipole_coeff.Pv' _alias.definition_id '_atom_rho_multipole_coeff_Pv' _name.category_id atom_rho_multipole_coeff _name.object_id Pv _import.get [{'file':templ_attr.cif 'save':rho_coeff}] save_ save_atom_rho_multipole_coeff.pv_su _definition.id '_atom_rho_multipole_coeff.Pv_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_coeff.Pv. ; _name.category_id atom_rho_multipole_coeff _name.object_id Pv_su _name.linked_item_id '_atom_rho_multipole_coeff.Pv' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_ATOM_RHO_MULTIPOLE_KAPPA _definition.id ATOM_RHO_MULTIPOLE_KAPPA _definition.scope Category _definition.class Loop _definition.update 2024-04-02 _description.text ; Category defining radial function expansion-contraction coefficients ; _name.category_id ATOM_RHO_MULTIPOLE _name.object_id ATOM_RHO_MULTIPOLE_KAPPA _category_key.name '_atom_rho_multipole_kappa.atom_label' save_ save_atom_rho_multipole_kappa.atom_label _definition.id '_atom_rho_multipole_kappa.atom_label' _definition.update 2024-04-02 _description.text ; An atom site label that serves as the ATOM_RHO_MULTIPOLE_KAPPA category key. It should only be used when items from the ATOM_RHO_MULTIPOLE_KAPPA and ATOM_RHO_MULTIPOLE categories are looped in separate lists. ; _name.category_id atom_rho_multipole_kappa _name.object_id atom_label _name.linked_item_id '_atom_rho_multipole.atom_label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_rho_multipole_kappa.base _definition.id '_atom_rho_multipole_kappa.base' _alias.definition_id '_atom_rho_multipole_kappa' _name.category_id atom_rho_multipole_kappa _name.object_id base _import.get [{'file':templ_attr.cif 'save':rho_kappa}] save_ save_atom_rho_multipole_kappa.base_su _definition.id '_atom_rho_multipole_kappa.base_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.base. ; _name.category_id atom_rho_multipole_kappa _name.object_id base_su _name.linked_item_id '_atom_rho_multipole_kappa.base' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_kappa.list _definition.id '_atom_rho_multipole_kappa.list' _alias.definition_id '_atom_rho_multipole_kappa_list' _definition.update 2019-04-01 _description.text ; 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. ; _name.category_id atom_rho_multipole_kappa _name.object_id list _type.purpose Measurand _type.source Derived _type.container List _type.dimension '[6]' _type.contents Real _units.code none _method.purpose Evaluation _method.expression ; With k as atom_rho_multipole_kappa atom_rho_multipole_kappa.list = [ k.base, k.prime0, k.prime1, k.prime2, k.prime3, k.prime4] ; save_ save_atom_rho_multipole_kappa.list_su _definition.id '_atom_rho_multipole_kappa.list_su' _definition.update 2024-04-02 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.list. ; _name.category_id atom_rho_multipole_kappa _name.object_id list_su _name.linked_item_id '_atom_rho_multipole_kappa.list' _type.purpose SU _type.source Related _type.container List _type.dimension '[6]' _type.contents Real _units.code none save_ save_atom_rho_multipole_kappa.prime0 _definition.id '_atom_rho_multipole_kappa.prime0' _alias.definition_id '_atom_rho_multipole_kappa_prime0' _name.category_id atom_rho_multipole_kappa _name.object_id prime0 _import.get [{'file':templ_attr.cif 'save':rho_kappa}] save_ save_atom_rho_multipole_kappa.prime0_su _definition.id '_atom_rho_multipole_kappa.prime0_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.prime0. ; _name.category_id atom_rho_multipole_kappa _name.object_id prime0_su _name.linked_item_id '_atom_rho_multipole_kappa.prime0' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_kappa.prime1 _definition.id '_atom_rho_multipole_kappa.prime1' _alias.definition_id '_atom_rho_multipole_kappa_prime1' _name.category_id atom_rho_multipole_kappa _name.object_id prime1 _import.get [{'file':templ_attr.cif 'save':rho_kappa}] save_ save_atom_rho_multipole_kappa.prime1_su _definition.id '_atom_rho_multipole_kappa.prime1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.prime1. ; _name.category_id atom_rho_multipole_kappa _name.object_id prime1_su _name.linked_item_id '_atom_rho_multipole_kappa.prime1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_kappa.prime2 _definition.id '_atom_rho_multipole_kappa.prime2' _alias.definition_id '_atom_rho_multipole_kappa_prime2' _name.category_id atom_rho_multipole_kappa _name.object_id prime2 _import.get [{'file':templ_attr.cif 'save':rho_kappa}] save_ save_atom_rho_multipole_kappa.prime2_su _definition.id '_atom_rho_multipole_kappa.prime2_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.prime2. ; _name.category_id atom_rho_multipole_kappa _name.object_id prime2_su _name.linked_item_id '_atom_rho_multipole_kappa.prime2' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_kappa.prime3 _definition.id '_atom_rho_multipole_kappa.prime3' _alias.definition_id '_atom_rho_multipole_kappa_prime3' _name.category_id atom_rho_multipole_kappa _name.object_id prime3 _import.get [{'file':templ_attr.cif 'save':rho_kappa}] save_ save_atom_rho_multipole_kappa.prime3_su _definition.id '_atom_rho_multipole_kappa.prime3_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.prime3. ; _name.category_id atom_rho_multipole_kappa _name.object_id prime3_su _name.linked_item_id '_atom_rho_multipole_kappa.prime3' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_kappa.prime4 _definition.id '_atom_rho_multipole_kappa.prime4' _alias.definition_id '_atom_rho_multipole_kappa_prime4' _name.category_id atom_rho_multipole_kappa _name.object_id prime4 _import.get [{'file':templ_attr.cif 'save':rho_kappa}] save_ save_atom_rho_multipole_kappa.prime4_su _definition.id '_atom_rho_multipole_kappa.prime4_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_kappa.prime4. ; _name.category_id atom_rho_multipole_kappa _name.object_id prime4_su _name.linked_item_id '_atom_rho_multipole_kappa.prime4' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_ATOM_RHO_MULTIPOLE_RADIAL_SLATER _definition.id ATOM_RHO_MULTIPOLE_RADIAL_SLATER _definition.scope Category _definition.class Loop _definition.update 2024-04-02 _description.text ; Category containing the terms of a Slater-type function representation of the radial dependence of the electron density, R(kappa'(l),l,r), according to the formalism of Hansen & Coppens (1978), equation (3). Ref: Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909-921. ; _name.category_id ATOM_RHO_MULTIPOLE _name.object_id ATOM_RHO_MULTIPOLE_RADIAL_SLATER _category_key.name '_atom_rho_multipole_radial_slater.atom_label' save_ save_atom_rho_multipole_radial_slater.atom_label _definition.id '_atom_rho_multipole_radial_slater.atom_label' _definition.update 2024-04-02 _description.text ; An atom site label that serves as the ATOM_RHO_MULTIPOLE_RADIAL_SLATER category key. It should only be used when items from the ATOM_RHO_MULTIPOLE_RADIAL_SLATER and ATOM_RHO_MULTIPOLE categories are looped in separate lists. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id atom_label _name.linked_item_id '_atom_rho_multipole.atom_label' _type.purpose Link _type.source Related _type.container Single _type.contents Word save_ save_atom_rho_multipole_radial_slater.n0 _definition.id '_atom_rho_multipole_radial_slater.n0' _alias.definition_id '_atom_rho_multipole_radial_slater_n0' _name.category_id atom_rho_multipole_radial_slater _name.object_id n0 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.n0_su _definition.id '_atom_rho_multipole_radial_slater.n0_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.n0. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id n0_su _name.linked_item_id '_atom_rho_multipole_radial_slater.n0' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.n1 _definition.id '_atom_rho_multipole_radial_slater.n1' _alias.definition_id '_atom_rho_multipole_radial_slater_n1' _name.category_id atom_rho_multipole_radial_slater _name.object_id n1 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.n1_su _definition.id '_atom_rho_multipole_radial_slater.n1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.n1. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id n1_su _name.linked_item_id '_atom_rho_multipole_radial_slater.n1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.n2 _definition.id '_atom_rho_multipole_radial_slater.n2' _alias.definition_id '_atom_rho_multipole_radial_slater_n2' _name.category_id atom_rho_multipole_radial_slater _name.object_id n2 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.n2_su _definition.id '_atom_rho_multipole_radial_slater.n2_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.n2. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id n2_su _name.linked_item_id '_atom_rho_multipole_radial_slater.n2' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.n3 _definition.id '_atom_rho_multipole_radial_slater.n3' _alias.definition_id '_atom_rho_multipole_radial_slater_n3' _name.category_id atom_rho_multipole_radial_slater _name.object_id n3 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.n3_su _definition.id '_atom_rho_multipole_radial_slater.n3_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.n3. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id n3_su _name.linked_item_id '_atom_rho_multipole_radial_slater.n3' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.n_list _definition.id '_atom_rho_multipole_radial_slater.n_list' _alias.definition_id '_atom_rho_multipole_radial_slater_n_list' _definition.update 2024-04-23 _description.text ; 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. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id n_list _type.purpose Measurand _type.source Derived _type.container List _type.dimension '[4]' _type.contents Real _units.code none _method.purpose Evaluation _method.expression ; With s as atom_rho_multipole_radial_slater atom_rho_multipole_radial_slater.n_list = [ s.n0, s.n1, s.n2, s.n3 ] ; save_ save_atom_rho_multipole_radial_slater.n_list_su _definition.id '_atom_rho_multipole_radial_slater.n_list_su' _definition.update 2024-04-23 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.n_list. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id n_list_su _name.linked_item_id '_atom_rho_multipole_radial_slater.n_list' _type.purpose SU _type.source Related _type.container List _type.dimension '[4]' _type.contents Real _units.code none save_ save_atom_rho_multipole_radial_slater.zeta0 _definition.id '_atom_rho_multipole_radial_slater.zeta0' _alias.definition_id '_atom_rho_multipole_radial_slater_zeta0' _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta0 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.zeta0_su _definition.id '_atom_rho_multipole_radial_slater.zeta0_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.zeta0. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta0_su _name.linked_item_id '_atom_rho_multipole_radial_slater.zeta0' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.zeta1 _definition.id '_atom_rho_multipole_radial_slater.zeta1' _alias.definition_id '_atom_rho_multipole_radial_slater_zeta1' _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta1 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.zeta1_su _definition.id '_atom_rho_multipole_radial_slater.zeta1_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.zeta1. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta1_su _name.linked_item_id '_atom_rho_multipole_radial_slater.zeta1' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.zeta2 _definition.id '_atom_rho_multipole_radial_slater.zeta2' _alias.definition_id '_atom_rho_multipole_radial_slater_zeta2' _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta2 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.zeta2_su _definition.id '_atom_rho_multipole_radial_slater.zeta2_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.zeta2. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta2_su _name.linked_item_id '_atom_rho_multipole_radial_slater.zeta2' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.zeta3 _definition.id '_atom_rho_multipole_radial_slater.zeta3' _alias.definition_id '_atom_rho_multipole_radial_slater_zeta3' _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta3 _import.get [{'file':templ_attr.cif 'save':rho_slater}] save_ save_atom_rho_multipole_radial_slater.zeta3_su _definition.id '_atom_rho_multipole_radial_slater.zeta3_su' _definition.update 2022-10-17 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.zeta3. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta3_su _name.linked_item_id '_atom_rho_multipole_radial_slater.zeta3' _units.code none _import.get [{'file':templ_attr.cif 'save':general_su}] save_ save_atom_rho_multipole_radial_slater.zeta_list _definition.id '_atom_rho_multipole_radial_slater.zeta_list' _alias.definition_id '_atom_rho_multipole_radial_slater_zeta_list' _definition.update 2024-04-23 _description.text ; 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. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta_list _type.purpose Measurand _type.source Derived _type.container List _type.dimension '[4]' _type.contents Real _units.code none _method.purpose Evaluation _method.expression ; With s as atom_rho_multipole_radial_slater atom_rho_multipole_radial_slater.zeta_list = [ s.zeta0, s.zeta1, s.zeta2, s.zeta3] ; save_ save_atom_rho_multipole_radial_slater.zeta_list_su _definition.id '_atom_rho_multipole_radial_slater.zeta_list_su' _definition.update 2024-04-23 _description.text ; Standard uncertainty of _atom_rho_multipole_radial_slater.zeta_list. ; _name.category_id atom_rho_multipole_radial_slater _name.object_id zeta_list_su _name.linked_item_id '_atom_rho_multipole_radial_slater.zeta_list' _type.purpose SU _type.source Related _type.container List _type.dimension '[4]' _type.contents Real _units.code none save_ loop_ _dictionary_audit.version _dictionary_audit.date _dictionary_audit.revision 2.0.1 2014-06-20 ; Initial conversion to DDLm (Syd Hall) ; 2.0.2 2019-04-03 ; Update import statements, improve DDLm conformance. ; 2.0.3 2025-11-25 ; Further improve DDLm conformance. Add missing su data names. Changed _dictionary.namespace from CifRho to CifCore (bm). Declared the ATOM_RHO_MULTIPOLE_COEFF, ATOM_RHO_MULTIPOLE_KAPPA and ATOM_RHO_MULTIPOLE_RADIAL_SLATER categories as looped. Added the _atom_rho_multipole_coeff.atom_label, _atom_rho_multipole_kappa.atom_label and _atom_rho_multipole_radial_slater.atom_label data items. (AV) Changed the source of the _atom_rho_multipole_coeff.list_su and _atom_rho_multipole_radial_slater.list_su data items to 'Related'. Changed the content type of _atom_local_axes.ax* data items to 'Word'. Changed definition of _atom_rho_multipole_coeff.list to specify ordering by l then m in the definition, and to exclude Pc, Pv, on advice of J. Hester. Added _atom_rho_multipole_kappa.list_su. Changed _atom_rho_multipole_radial_slater.list to _atom_rho_multipole_radial_slater.n_list and _atom_rho_multipole_radial_slater.zeta_list to clarify ordering within separate lists. (bm) Updated the CIF_CORE dictionary import statement with the new Head category name. (av) Changed name of Head category in accordance with convention. (bm) ;