Structure and bonding in beta-HMX-characterization of a trans-annular N...N interaction

Chemical bonding in the beta-phase of the 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) crystal based on the experimental electron density obtained from X-ray diffraction data at 20 K, and solid state theoretical calculations, has been analyzed in terms of the quantum theory of atoms in molecules. Features of the intra- and intermolecular bond critical points and the oxygen atom lone-pair locations are discussed. An unusual N...N bonding interaction across the 8-membered ring has been discovered and characterized. Hydrogen bonding, O...O and O...C intermolecular interactions are reported. Atomic charges and features of the electrostatic potential are discussed.     

Experimental and theoretical electron density study of estrone

The electron density and the electrostatic potential (ESP) distributions of estrone have been determined using X-ray diffraction analysis and compared with theoretical calculations in the solid and gas phases. X-ray diffraction measurements are performed with a Rigaku Rapid rotating anode diffractometer at 20 K. The electron density in the estrone crystal has been described with the multipole model, which allowed extensive topological analysis and calculation of the ESP. From DFT calculations in the solid state a theoretical X-ray diffraction data set has been produced and treated in the same way as the experimental data. Two sets of single molecule DFT calculations were performed: (a) An electron density distribution was obtained via a single-point calculation with a large basis set at the experimental geometry and subsequently analyzed according to the quantum theory of atoms in molecules (AIM) to obtain the bond and most atomic properties, and (b) another electron density distribution was obtained with a smaller basis set, but at a geometry optimized using the same basis set for the analysis of atomic energies. An interesting locally stabilizing hydrogen-hydrogen bond path linking H(1) and H(11B) is found which represents the first characterization of such bonding in a steroid molecule. AIM delocalization indices were shown to be well correlated to the experimental electron density at the bond critical points through an exponential relationship. The aromaticity of ring A, chemical bonding, the O(1)...O(2) distance necessary for estrogenic activity, and the electrostatic potential features are also discussed.     

Bond Characterization of the 3-D Framework Structure of the Copper(Ⅱ) Isonicotinic Acid Complex Formed by Hydrogen Bonding

The crystal of qudra-aquabis(isonicotinato-N)copper(Ⅱ),Cu[(NC5H4COO)]2 . 4H2O was synthesized via hydrothermal method. Single crystal X-ray analysis at 100K (Siemens SmartCCD) and 25K (Nonius KappaCCD) are performed. The results reveal that the Cu atom is octahedrally coordinated by two Nitrogen atoms of pyridine rings in the axial positions and the four Oxygen atoms of the four water molecules in an equatorial orientation. The octahedral Cu(lI) center shows a large Jahn-Teller distortion with the distances of the Cu-N 2.0253(6)A, Cu-O(3)2.0124(6)~, Cu-O(4) 2.4304(7)A. By means of the hydrogen bonding connections, this compound is formed a 3D framework. In addition, the thermal displacement of each atom at 25K is about three-times smaller than that at 100K. Electron density distribution of this compound at 25K and 100K is also analyzed and compared in terms of multipole model. All topological properties based on X-ray diffraction result and theoretical calculation including the bond critical points (BCP), Laplacian of the electron density and electron density at the BCP will be presented.     

Exploring the lower limit in hydrogen bonds: analysis of weak C-H...O and C-H...pi interactions in substituted coumarins from charge density analysis

Experimental electron densities in coumarin, 1-thiocoumarin, and 3-acetylcoumarin have been analyzed based on the X-ray diffraction data at 90 K. These compounds pack in the crystal lattice with weak C-H...O and C-H...pi interactions, and variations in charge density properties and derived local energy densities have been investigated in the regions of intermolecular interactions. Theoretical charge density calculations on crystals using the B3LYP/6-31G* method show remarkable agreement with the derived properties and energy densities from the experiment. The intermolecular interactions follow an exponential dependence of electron density and energy densities at the bond critical points. The Laplacian follows a "Morse-like" dependence on the length of the interaction line. Based on the set of criteria defined using the theory of "atoms in molecules", it has become possible to distinguish between a hydrogen bond (C-H...O) and a van der Waals interaction (C-H...pi). This has resulted in the identification of a "region of overlap" in terms of electron densities, energy densities, and mutual penetration of the hydrogen and acceptor atoms with respect to the interaction length. This approach suggests a possible tool to distinguish between the two types of interactions.     

Synchrotron X-ray charge density study of coordination polymer Co3(C8H4O4)4(C4H12N)2(C5H11NO)3 at 16 K

The charge density (CD) of coordination polymer Co3(C8H4O4)4(C4H12N)2(C5H11NO)3 (1) has been determined from multipole modeling of structure factors obtained from single-crystal synchrotron X-ray diffraction measurements at 16 K. The crystal structure formally contains a negatively charged framework with cations and neutral molecules in the voids. However, the CD suggests that the framework is close to neutral, and therefore qualitative conclusions based on formal charge counting, e.g., about guest inclusion properties, will be incorrect. There are considerable differences in the charge distributions of the three unique benzenedicarboxylic acid linkers, which are widely used in coordination polymers. This suggests that the electrostatic properties of coordination polymer cavities, and thereby their inclusion properties, are highly tunable. The electron density topology shows that the tetrahedrally coordinated Co atom has an atomic volume which is 15% larger than that of the octahedrally coordinated Co atom. The crystal structure has both ferromagnetic and antiferromagnetic interactions, but no direct metal-metal bonding is evidenced in the CD. The magnetic ordering therefore takes place through superexchange in the oxygen bridges and the aromatic linkers. Bonding analysis of the experimental CD reveals that two oxygen atoms, O(1) and O(11), have significant covalent contributions to the metal-ligand bonding, whereas all other oxygen atoms have closed-shell interactions with the metals. This indicates that these two oxygen atoms are the key mediators of the magnetic ordering.     

Relativistic-consistent electron densities of the coinage metal clusters M2, M4, M4(2-), and M4Na2 (M = Cu, Ag, Au): a QTAIM study

We employ second-order M?ller-Plesset perturbation theory level in combination with recently developed pseudopotential-based correlation consistent basis sets to obtain accurate relativistic-consistent electron densities for small coinage metal clusters. Using calculated electron densities, we employ Bader's quantum theory of atoms in molecules (QTAIM) to gain insights into the nature of metal-metal bonding in the clusters M(2), M(4), M(4)(2-), and M(4)Na(2) (M = Cu, Ag, Au). For the simplest case of the metal dimer, M(2), we correlate the strength of the metal-metal bond with the value of the electron density at the bond critical point, the total energy density at the bond critical point, the sharing (delocalization) index, and the values of the two principle negative curvatures. We then consider changes to the metal-metal bonding and charge density distribution upon the addition of two metal atoms to form the metal tetramer, M(4), and then followed by the addition of an electron pair to form M(4)(2-) and finally followed by the addition of two alkali metal (sodium) ions to form M(4)Na(2). Using topological properties of the electron density, we present evidence for the existence of σ-aromaticity in Au(4)(2-). We also report the existence of two non-nuclear attractors in the molecular graph of Cu(4)(2-) and large negative charge accumulation in the nonbonded Cu basins of this cluster.     

Experimental and theoretical electron density distribution and magnetic properties of the butterfly-like complex [Fe(4)O(2)(O(2)CCMe(3))(8)(NC(5)H(4)Me)(2)].2CH(3)CN

The structure and electron density distribution (EDD) of the carboxylate-bridge iron complex [Fe(III)(4)(micro(3)-O)(2)(O(2)CCMe(3))(8)(NC(5)H(4)Me)(2)].2CH(3)CN, 1, has been determined from synchrotron X-ray diffraction data (R(int) = 0.025) collected with the crystal cooled to 16(5) K. At this temperature complex 1 crystallized in the triclinic space group P with cell parameters a = 12.6926(7) A, b = 12.9134(8) A, c = 13.4732(8) A, alpha = 115.372(2) degrees, beta = 107.702(3) degrees, and gamma = 102.731(2) degrees. The theoretical EDD determined from a density functional theory (DFT) single point calculation of an entire molecule of 1 at the experimental geometry has been analyzed and compared to the experimental EDD. The latter is expressed in the framework of a multipolar model with parameters determined by least-squares refinement (R(w)(F(2)) = 0.024) based on the X-ray diffraction data. The central micro(3)-oxygen atom in 1 is significantly out of the plane spanned by the three Fe atoms coordinated to this oxygen. Comparison of measures for the bonding geometry around the iron atoms in 1 with the corresponding values for the iron atoms in relevant trinuclear complexes suggests that there are significant differences in the Fe-(micro(3)-O) bonds in the two cases. Analyses of both the experimental and theoretical EDDs reveal very significant differences between the two Fe-(micro(3)-O) bonds in 1, with one bond being much more directed and stronger than the other bond. A topological analysis of the EDDs using the atoms in molecules approach also reveals very distinct differences between the properties of the two Fe(III) atoms. A clear exponential relationship is found between the Laplacian of the experimental density at the bond critical points in the Fe-ligand bonds and their bond lengths. M?ssbauer spectroscopy of 1 shows two easily separable doublets corresponding to the two different iron sites. Magnetic susceptibility measurements between 4.2 and 300 K indicate antiferromagnetically coupled Fe(III) atoms constituting an S = 0 ground state.     

Charge density analysis of two polymorphs of antimony(III) oxide

High-resolution X-ray diffraction data have been collected on the cubic polymorph of antimony(III) oxide (senarmontite) to determine the charge distribution in the crystal. The results are in quantitative agreement with crystal Hartree-Fock calculations for this polymorph, and have been compared with theoretical calculations on the orthorhombic polymorph (valentinite). Information about the nature of bonding and relative bond strengths in the two polymorphs has been extracted in a straightforward manner via topological analysis of the electron density. All the close contacts in both polymorphs are found to be similar in nature based on the value of the Laplacian, the magnitude of the electron density and the local energy density at the bond critical points, and these characterise the observed interactions as substantially polar covalent, similar to molecular calculation results on Si-O and Ge-O. Electrostatic potential isosurfaces reveal the octopolar nature of this function for senarmontite, and shed light on the observed packing arrangement of Sb4O6 molecules in the crystal.     

Pointers toward the occurrence of C-F...F-C interaction: Experimental charge density analysis of 1-(4-fluorophenyl)-3,6,6-trimethyl-2-phenyl-1,5,6,7-tetrahydro-4H-indol-4-one and 1-(4-fluorophenyl)-6-methoxy-2-phenyl-1,2,3,4-tetrahydroisoquinoline

A charge density study of crystalline 1-(4-fluorophenyl)-3,6,6-trimethyl-2-phenyl-1,5,6,7-tetrahydro-4H-indol-4-one (A) and 1-(4-fluorophenyl)-6-methoxy-2-phenyl-1,2,3,4-tetrahydroisoquinoline (B) has been carried out using high-resolution X-ray diffraction data collected at 113(2) K. Weak intermolecular interactions of the type C-H...O, C-H...pi, and pi...pi hold the molecules together in the crystal lattice along with interactions of the type C-H...F and unusual C-F...F-C examined via charge density analysis. The topological features are evaluated in terms of Bader's theory of atoms in molecules through the first four criteria of Koch and Popelier. The C-F...F-C contact is observed to be across the center of symmetry in B and not in A, and further, this interaction appears to possess a certain correlation with the electron density properties at the critical point which suggests that such an interaction fits into the hierarchy of weak interactions.     

Experimental and theoretical charge density distribution in a host-guest system: synthetic terephthaloyl receptor complexed to adipic acid

The experimental charge density distributions in a host-guest complex have been determined. The host, 1,4-bis[[(6-methylpyrid-2-yl)amino]carbonyl]benzene (1) and guest, adipic acid (2). The molecular geometries of 1 and 2 are controlled by the presence in the complex of intermolecular hydrogen bonding interactions and the presence in the host 1 of intramolecular hydrogen bonding motifs. This system therefore serves as an excellent model for studying noncovalent interactions and their effects on structure and electron density, and the transferability of electron distribution properties between closely related molecules. For the complex, high resolution X-ray diffraction data created the basis for a charge density refinement using a pseudoatomic multipolar expansion (Hansen-Coppens formalism) against extensive low-temperature (T = 100 K) single-crystal X-ray diffraction data and compared with a selection of theoretical DFT calculations on the same complex. The molecules crystallize in the noncentrosymmetric space group P2(1)2(1)2(1) with two independent molecules in the asymmetric unit. A topological analysis of the resulting density distribution using the atoms in molecules methodology is presented along with multipole populations, showing that the host and guest structures are relatively unaltered by the geometry changes on complexation. Three separate refinement protocols were adopted to determine the effects of the inclusion of calculated hydrogen atom anisotropic displacement parameters on hydrogen bond strengths. For the isotropic model, the total hydrogen bond energy differs from the DFT calculated value by ca. 70 kJ mol(-1), whereas the inclusion of higher multipole expansion levels on anisotropic hydrogen atoms this difference is reduced to ca. 20 kJ mol(-l), highlighting the usefulness of this protocol when describing H-bond energetics.     

Critical Points in a Crystal and Procrystal

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, –1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.     

Bond characterization on a Cr-Cr quintuple bond: a combined experimental and theoretical study

A combined experimental and theoretical charge density study on a quintuply bonded dichromium complex, Cr(2)(dipp)(2) (dipp = (Ar)NC(H)N(Ar) and Ar = 2,6-i-Pr(2)-C(6)H(3)), is performed. Two dipp ligands are bridged between two Cr ions; each Cr atom is coordinated to two N atoms of the ligands in a linear fashion. The Cr atom is in a low oxidation state, Cr(I), and in low coordination number condition, which stabilizes a metal-metal multiple bond, in this case, a quintuple bond. Indeed, it gives an ultrashort Cr-Cr bond distance of 1.7492(1) ? in the complex. The bond characterization of such a quintuple bond is undertaken both experimentally by high-resolution single-crystal X-ray diffraction and theoretically by density functional calculation (DFT). Electron densities are depicted via deformation density and Laplacian distributions. Bond characterizations of the complex are presented in terms of topological properties, Fermi hole function, source function (SF), and natural bonding orbital (NBO) analysis. The electron density at the Cr-Cr bond critical point (BCP) is 1.70 e/?(3), quite a high value for metal-metal bonding and mainly contributed from the metal ion itself. The quintuple bond is confirmed with one σ, two π, and two δ interactions by NBO analysis and Fermi hole function. The molecular orbitals (MOs) illustrate that five bonding orbitals are predominantly contributed from the 3d orbitals of the Cr(I) ion. The effective bond order from NBO analysis is 4.60. The detail comparison between experiment and theory will be given. Additionally, three closely related complexes are calculated for systematic comparison.     

Electron density distribution of an oxamato bridged Mn(II)-Cu(II) bimetallic chain and correlation to magnetic properties

The electron density distribution of the ferrimagnetic MnCu(pba)(H2O)3.2H2O chain compound, where pba stands for 1,3-propylenebis(oxamato), has been derived from high resolution X-ray diffraction measurements at 114 K using a multipolar model. The analysis of the chemical bonding has been carried out through the "Atoms in Molecules" formalism and thoroughly interpreted with regards to the strong intrachain and weak interchain magnetic couplings. The topological properties of the electron density on the oxamato bridge indicate large electron delocalization and conjugation effects, in addition to high charge transfer from both metals to the bridge. The resulting positive charges on Mn (+1.45 e) and Cu (+1.56 e) induce charge polarization of the bridge, leading to a shift of electron density from the central C atoms to the metal coordinating O and N atoms. The Mn-bridge interactions are mainly closed-shell interactions with low electron density at the corresponding bond critical points, whereas the Cu-bridge interactions exhibit significant covalent character. The Cu-N bonds are moreover stronger than the Cu-O bonds. The 3d Cu and Mn orbital populations are consistent with pyramidal and regular octahedral environments, respectively, in agreement with the loss of degeneracy due to ligand field effects. Interchain interaction pathways are evidenced by the existence of four bond critical points in hydrogen bond regions. Finally, these intrachain and interchain bonding features are correlated to the results of experimental and theoretical spin density distributions, as well as magnetic measurements.     

Topological analysis and charge density studies of an alpha-diimine macrocyclic complex of cobalt(II)--a combined experimental and theoretical study

A combined experimental and theoretical study of the paramagnetic [Co(II)(C12H20N8)(H2O)2] x 2 ClO4 complex was made on the basis of the electron density distribution and topological analysis. Accurate single-crystal diffraction data were measured on a suitable crystal with Mo(K alpha) radiation at 125 K. The CoII ion is coordinated in a square bipyramidal fashion with four imino nitrogen atoms at the equatorial plane and two water molecules at the axial positions. The hydrogen-bonding interaction at 125 K between the coordinated water molecule and the ClO(4)(-) ion makes the space group different from that at 298 K. Parallel MO calculations were made at UHF and DFT/UB3LYP. The agreement between experiment and theory is reasonably good. The chemical bonding characterization is presented in terms of the topological properties associated with bond critical points and the natural bond orbital (NBO) analysis as well. The Co-N(imino) and Co-O(water) bonds are dative bonds, where the lone-pair electrons of N or O serve as a -donor; however, a certain covalent character is identified in the Co-N(imino) bond. A delocalized C-N, N-N pi-bond model is proposed. The d-orbital energies of Co in this complex are such that E(d(xz)) is approximately equal to E(d(yz)) is approximately equal to E(dx(2-y2)) < E(d(z2)) < E(d(xy)); notice that d(xy) and d(z2) are d(sigma) orbitals in this case. The Co(II) ion is in a low-spin d7 state with the singly occupied d(z2) orbital. The asphericity in electron density at Co and Cl nuclei is nicely demonstrated by the Laplacian of electron density. The envelope plot of the isovalue Laplacian surface around the nucleus gives the exact shape of such asphericity. The isovalue Laplacian surfaces of these two nuclei show significantly different VSCC character in both experimental and theoretical results.     

Synthesis, physical properties, multitemperature crystal structure, and 20 K synchrotron X-ray charge density of a magnetic metal organic framework structure, Mn3(C8O4H4)3(C5H11ON)2

A new magnetic metal organic framework material has been synthesized, Mn3(C8O4H4)3(C5H11ON)2, 1. Magnetic susceptibility measurements from 2 to 400 K reveal anti-ferromagnetic ordering at approximately 4 K and a total magnetic moment of 6.0 micro(B). The magnetic phase transition is confirmed by heat capacity data (2-300 K). The crystal structure is studied by conventional single-crystal X-ray diffraction data at 300, 275, 250, 225, 200, 175, 150, 125, and 100 K, and synchrotron data at 20 K. There is a phase transition between 100 and 20 K due to ordering of the diethylformamide molecules. The X-ray charge density is determined based on multipole modeling of a second 20 K single-crystal synchrotron radiation data set. The electron distributions around the two unique Mn centers are different, and both have substantial anisotropy. Orbital population analysis reveals large electron donation (1.7 e) to each Mn atom and the maximum possible number of unpaired electrons is 3.2 for both Mn sites. Thus, there is a considerable orbital component to the magnetic moment. Bader topological analysis shows an absence of Mn-Mn bonding, and the magnetic ordering is via super-exchange through the oxygen bridges. Formal electron counting suggests Mn2+ sites, but this is not supported by the Bader atomic charges, Mn1 = +0.11 e, Mn2 = +0.17 e. The topological measures show the dominant metal-ligand interactions to be electrostatic, and a simple exponential correlation is derived between Mn-O bond lengths and the values of nabla2rho at the bond critical points.     

Three-membered ring or open chain molecule - (F3C)F2SiONMe2 a model for the alpha-effect in silicon chemistry

(F3C)F2SiONMe2 was prepared from LiONMe2 and F3CSiF3. It was characterized by gas IR and multinuclear solution NMR spectroscopy and by mass spectrometry. Its structure was elucidated by single crystal X-ray crystallography and by gas electron diffraction. (It exists as a conformer mixture.) Important findings were extremely acute SiON angles [solid 74.1(1) degrees , gas anti 84.4(32) degrees and gauche 87.8(20) degrees] and short Si...N distances [solid 1.904(2) A]. The bending potential of the SiON unit was calculated at the MP2/6-311++G(3df,2dp) level of theory and appears very flat and highly asymmetric. The calculated atomic charges (NPA) are counterintuitive to the expected behavior for a classical Si-N dative bond, as upon formation of the Si...N bond electron density is transferred mainly from oxygen to nitrogen, while the silicon charge is almost unaffected. Despite the molecular topology of a three-membered ring, the topology of the electron density shows neither a bond critical point between Si and N atoms nor a ring critical point, but the electron density and Laplacian values are related to other hypercoordinate Si compounds. The electronic properties of (F3C)F2SiONMe2 were compared to those of the adduct (F3C)F2(MeO)Si-NMe3, whose properties and structure were also calculated. The charge distribution and Laplacian values along the Si-N vectors in both molecules are similar but not equivalent. (F3C)F2SiONMe2 contains thus a nonclassical Si...N bond, and its properties can be regarded as a new model for the explanation of the old postulate of an alpha-effect in silicon chemistry, explaining the behavior of compounds with geminal Si and N atoms.     

Experimental electron density analysis of Mn2(CO)10: metal-metal and metal-ligand bond characterization

The experimental electron density rho(r) of Mn2(CO)10 was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules (QTAM) was applied to rho(r) and its Laplacian [symbol: see text] 2 rho(r). The QTAM analysis of rho(r) showed the presence of a bond critical point (rc); its associated bond path connects the two Mn atoms, but no cross interaction line was found between one manganese and the equatorial carbonyls of the other. The distribution of [symbol: see text] 2 rho(r) indicated "closed-shell" interactions for the metallic Mn-Mn bond and the dative Mn-CO bonds. The values of the topological parameters of the density at rc, rho(rc), [symbol: see text] 2 rho(rc), G(rc) (kinetic energy density), and V(rc) (potential energy density), characterize the bonds and are intermediate to those corresponding to typical ionic and covalent bonds.     

Molecular model with quantum mechanical bonding information

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.     

Experimental and theoretical charge density distribution of the colossal magnetoresistive transition metal sulfide FeCr2S4

The total charge density distribution rho(r) of the colossal magnetoresistive transition metal sulfide FeCr(2)S(4) was evaluated through a multipole formalism from a set of structure factors obtained both experimentally, by means of single crystal high-quality x-ray diffraction data collected at T=23 K, and theoretically, with an extended-basis unrestricted Hartree-Fock periodic calculation on the experimental geometry. A full topological analysis, followed by the calculation of local energy density values and net atomic charges, was performed using the quantum theory of atoms in molecules. The experimental and theoretical results were compared. Good agreement was found for the topological properties of the system, as well as for the atomic net charges and the nature of the chemical bonds. An analysis of the electron density rho(r), its Laplacian nabla(2)[rho(r)], and the total energy density H(r) at the bond critical points was employed to classify all the interactions that resulted as predominantly closed shell (ionic) in nature. The topological indicators of the bonded interactions for Fe are distinct from those for Cr. The Fe-S bond distances were found to be 0.145 A shorter than the ideal values computed on the basis of Shannon's crystal radii, much shorter than the Cr-S distances with respect to their ideal Shannon lengths. Concomitantly, rho(r) and |H(r)| at the bond critical points are greater for Fe-S interactions, indicating that the local concentration of charge density in the internuclear region is larger for the tetrahedrally coordinated iron than for the octahedrally coordinated chromium. The isosurface in the real space for nabla(2)[rho(r)]=0 was plotted for both iron and chromium, pointing out the local zones of valence shell charge concentration and relating them to the partial d-orbital occupancy of the two transition metal atoms.