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.     

Extension of the experimental electron density analysis to metastable states: a case example of the spin crossover complex Fe(btr)2(NCS)2.H2O

An experimental electron density (ED) analysis of the spin crossover coordination complex Fe(btr)(2)(NCS)(2).H(2)O has been performed in the ground low-spin (LS) state and in the metastable thermally quenched high-spin (HS) state at 15 K by fitting a multipolar model to high-resolution X-ray diffraction measurements. The ED has been quantitatively analyzed using the quantum theory of atoms in molecules. This is the first time the ED distribution of a molecular metastable state has been experimentally investigated. The electron deformation densities and derived Fe 3d orbital populations are characteristic of LS (t(2g)(6) e(g)(0)) and HS (t(2g)(4) e(g)(2)) electron configurations and indicate significant sigma donation to the Fe d(x)2(-)(y)2 and d(z)2 atomic orbitals. The Fe-N(NCS) and Fe-N(btr) coordination interactions are characterized using the laplacian distribution of the ED, the molecular electrostatic potential, and the fragment charges obtained by integration over the topological atomic basins. A combination of electrostatic and covalent contributions to these interactions is pointed out. Interlayer interactions are evidenced by the presence of bond critical points in N...H hydrogen bonds involving the non-coordinated water molecule. Systematic differences in the atomic displacement parameters between the LS and HS states have been described and rationalized in terms of modifications of bond force constants.     

Bonding and (hyper)polarizability in the sodium dimer

We report a conventional ab initio and density functional theory study of the polarizability (alpha(alphabeta)/e(2)a(0) (2)E(h) (-1)) and hyperpolarizability (gamma(alphabetagammadelta)/e(4)a(0) (4)E(h) (-3)) of the sodium dimer. A large [18s14p9d2f1g] basis set is thought to yield near-Hartree-Fock values for both properties: alpha=272.28, Deltaalpha=127.22 and gamma=2157.6 x 10(3) at R(e)=3.078 87 A. Electron correlation has a remarkable effect on the Cartesian components of gamma(alphabetagammadelta). Our best value for the mean is gamma=1460.1 x 10(3). The (hyper)polarizability shows very strong bond-length dependence. The effect is drastically different for the longitudinal and transverse components of the hyperpolarizability. The following first derivatives were extracted from high-level coupled cluster calculations: (dalpha/dR)(e)=54.1, (dDeltaalpha/dR)(e)=88.1e(2)a(0)E(h) (-1), and (dgamma/dR)(e)=210 x 10(3)e(4)a(0) (3)E(h) (-3). We associate the (hyper)polarizability to bonding effects between the two sodium atoms by introducing the differential property per atom Q(diff)/2 identical with (Q[Na(2)(X (1)Sigma(g) (+))]/2-Q[Na((2)S)]). The differential (hyper)polarizability per atom is predicted to be strongly negative for the dimer at R(e), as [alpha(Na(2))/2-alpha(Na)]=-33.8 and [gamma(Na(2))/2-gamma(Na)]=-226.3 x 10(3). The properties calculated with the widely used B3LYP and B3PW91 density functional methods differ significantly. The B3PW91 results are in reasonable agreement with the conventional ab initio values. Last, we observe that low-level ab initio and density functional theory methods underestimate the dipole polarizability anisotropy. Experimental data on this important property are highly desirable.     

Structural anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations we investigate the structure of a system of particles interacting through a continuous core-softened interparticle potential. We found for the translational order parameter t a local maximum at a density rho(t-max) and a local minimum at rho(t-min)>rho(t-max). Between rho(t-max) and rho(t-min), the t parameter anomalously decreases upon increasing pressure. For the orientational order parameter Q(6) a maximum was observed at a density rho(t-max)相似文献   

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

On the charge distribution in ethanes and disilanes and correlations with equilibrium bond lengths; an ab initio study

The equilibrium electronic wave-functions for a series of fluoro- and chloro-ethanes and disilanes of general formula M₂H_6−nX_n, (M=C, Si; X=F, Cl), were analysed by the most commonly used methods for electron distribution, using the Mulliken and Löwdin populations, natural atomic orbital (NAO) populations and atoms in molecules (AIM) electron densities. Although the numerical values for local atomic charges vary greatly, all the methods correlate, but in markedly differing ways. The Mulliken charges seem the most selective in relation to systematic change of substituents in the current type of molecular structure. A number of examples occur where the AIM charges at C, Si centres are effectively identical in different molecules, where some differences might have been anticipated. These are often distinguished by Mulliken populations. The fluoroethanes exemplify this, since a plot of the AIM charges (for example on either the F or H centres) against the Mulliken charges for all members of the series, shows three nearly parallel lines, corresponding to those centres with 0, 1 or 2 fluorine atoms on the centre under study. The bond critical points at which the AIM charges are determined seem to be counter to intuition in some cases. This is a density rather than atomic orbital size issue however. The Mulliken and NAO charges seem more reasonable than those from the AIM method. There is an unexpected correlation of the local bond dipoles from the Mulliken analyses, with the calculated equilibrium bond lengths. These correlations lead to bond length values for the non-polarised bonds MX, which agree with data based on covalent radii for some bonds.     

Synchrotron X-ray charge-density study of coordination polymer [Mn(HCOO)2(H2O)2]infinity

Three high-quality single-crystal X-ray diffraction data sets have been measured under very different conditions on a structurally simple, but magnetically complex, coordination polymer, [Mn(HCOO)(2)(H(2)O)(2)](infinity) (1). The first data set is a conventional 100(2) K Mo(Kalpha) data set, the second is a very high resolution 100(2) K data set measured on a second-generation synchrotron source, while the third data set was measured with a tiny crystal on a high brilliance third-generation synchrotron source at 16(2) K. Furthermore, the magnetic susceptibility (chi) and the heat capacity (C(p)) have been measured from 2 to 300 K on pressed powder. The charge density of 1 was determined from multipole modeling of the experimental structure factors, and overall there is good agreement between the densities obtained separately from the three data sets. When considering the fine density features, the two 100 K data sets agree well with each other, but show small differences to the 16 K data set. Comparison with ab initio theory suggests that the 16 K APS data set provides the most accurate density. Topological analysis of the metal-ligand bonding, experimental 3d orbital populations on the Mn atoms, and Bader atomic charges indicate quite ionic, high-spin metal atoms. This picture is supported by the effective moment estimated from the magnetization measurements (5.840(2) mu(B)), but it is at variance with earlier spin density measurements from polarized neutron diffraction. The magnetic ordering originates from superexchange involving covalent interactions with the ligands, and non-ionic effects are observed in the static deformation density maps as well as in plots of the valence shell charge concentrations. Overall, the present study provides a benchmark charge density that can be used in comparison with future metal formate dihydrate charge densities.     

Mössbauer quadrupole splittings and electronic structure in heme proteins and model systems: a density functional theory investigation

We report the results of a series of density functional theory (DFT) calculations aimed at predicting the (57)Fe M?ssbauer electric field gradient (EFG) tensors (quadrupole splittings and asymmetry parameters) and their orientations in S = 0, (1)/(2), 1, (3)/(2), 2, and (5)/(2) metalloproteins and/or model systems. Excellent results were found by using a Wachter's all electron basis set for iron, 6-311G for other heavy atoms, and 6-31G for hydrogen atoms, BPW91 and B3LYP exchange-correlation functionals, and spin-unrestricted methods for the paramagnetic systems. For the theory versus experiment correlation, we found R(2) = 0.975, slope = 0.99, intercept = -0.08 mm sec(-)(1), rmsd = 0.30 mm sec(-)(1) (N = 23 points) covering a DeltaE(Q) range of 5.63 mm s(-)(1) when using the BPW91 functional and R(2) = 0.978, slope = 1.12, intercept = -0.26 mm sec(-)(1), rmsd = 0.31 mm sec(-)(1) when using the B3LYP functional. DeltaE(Q) values in the following systems were successfully predicted: (1) ferric low-spin (S = (1)/(2)) systems, including one iron porphyrin with the usual (d(xy))(2)(d(xz)d(yz))(3) electronic configuration and two iron porphyrins with the more unusual (d(xz)d(yz))(4)(d(xy))(1) electronic configuration; (2) ferrous NO-heme model compounds (S = (1)/(2)); (3) ferrous intermediate spin (S = 1) tetraphenylporphinato iron(II); (4) a ferric intermediate spin (S = (3)/(2)) iron porphyrin; (5) ferrous high-spin (S = 2) deoxymyoglobin and deoxyhemoglobin; and (6) ferric high spin (S = (5)/(2)) metmyoglobin plus two five-coordinate and one six-coordinate iron porphyrins. In addition, seven diamagnetic (S = 0, d(6) and d(8)) systems studied previously were reinvestigated using the same functionals and basis set scheme as used for the paramagnetic systems. All computed asymmetry parameters were found to be in good agreement with the available experimental data as were the electric field gradient tensor orientations. In addition, we investigated the electronic structures of several systems, including the (d(xy))(2)(d(xz),d(yz))(3) and (d(xz),d(yz))(4)(d(xy))(1) [Fe(III)/porphyrinate](+) cations as well as the NO adduct of Fe(II)(octaethylporphinate), where interesting information on the spin density distributions can be readily obtained from the computed wave functions.     

Atomic properties of N(2)O(4) based on its experimental charge density

Nitrogen dioxide, being known to exist as a dimer N2O4 in the crystal with a very long N-N bond length of 1.76 A, was crystallized at low-temperature conditions on a diffractometer. High-resolution X-ray data (sin(theta/lambda) = 1.249 A-1) were recorded with a CCD area detector to allow the generation of an experimental charge density distribution. By making use of Bader's AIM theory, zero-flux surfaces were calculated, and we examined atomic volumes and atomic charges obtained from this experiment and various theoretical calculations. Four commonly used methods of computing atomic charges (Mulliken, AIM, NPA, and CHELP) were considered. The AIM charges are rather independent from the used basis set. Interestingly, the evaluated atomic volumes are very similar between experiment and theory, although in theory isolated molecules are considered. For the long N-N bond a bond order n of approximately 0.5 was derived from a comparison with appropriate model compounds.     

DFT calculations of 57Fe Mössbauer isomer shifts and quadrupole splittings for iron complexes in polar dielectric media: applications to methane monooxygenase and ribonucleotide reductase

To predict the isomer shifts of Fe complexes in different oxidation and spin states more accurately, we have performed linear regression between the measured isomer shifts (delta(exp)) and DFT (PW91 potential with all-electron triple-zeta plus polarization basis sets) calculated electron densities at Fe nuclei [rho(0)] for the Fe(2+,2.5+) and Fe(2.5+,3+,3.5+,4+) complexes separately. The geometries and electronic structures of all complexes in the training sets are optimized within the conductor like screening (COSMO) solvation model. Based on the linear correlation equation delta(exp) = alpha[rho(0) - 11884.0] + C, the best fitting for 17 Fe(2+,2.5+) complexes (totally 31 Fe sites) yields alpha = -0.405 +/- 0.042 and C = 0.735 +/- 0.047 mm s(-1). The correlation coefficient is r = -0.876 with a standard deviation of SD = 0.075 mm s(-1). In contrast, the linear fitting for 19 Fe(2.5+,3+,3.5+,4+) complexes (totally 30 Fe sites) yields alpha = -0.393 +/- 0.030 and C = 0.435 +/- 0.014 mm s(-1), with the correlation coefficient r = -0.929 and a standard deviation SD = 0.077 mm s(-1). We provide a physical rationale for separating the Fe(2+,2.5+) fit from the Fe(2.5+,3+,3.5+,4+) fit, which also is clearly justified on a statistical empirical basis. Quadrupole splittings have also been calculated for these systems. The correlation between the calculated (DeltaE(Q(cal))) and experimental (DeltaE(Q(exp))) quadrupole splittings based on |DeltaE(Q(exp))| = A |DeltaE(Q(cal))| + B yields slope A, which is almost the ideal value 1.0 (A = 1.002 +/- 0.030) and intercept B almost zero (B = 0.033 +/- 0.068 mm s(-1)). Further calculations on the reduced diferrous and oxidized diferric active sites of class-I ribonucleotide reductase (RNR) and the hydroxylase component of methane monooxygenase (MMOH), and on a mixed-valent [(tpb)Fe3+(mu-O)(mu-CH3CO2)Fe4+(Me3[9]aneN3)]2+ (S = 3/2) complex and its corresponding diferric state have been performed. Calculated results are in very good agreement with the experimental data.     

Laplacian field of the effectively unpaired electron density: determination of many-body effects on electron distributions

This work carries out the study of the Laplacian field function of the electron density L(r) = -nabla2rho(r) splitted in two contributions rho(r) = rho(p)(r) + rho(u)(r), which correspond to the effectively paired and effectively unpaired electron densities, respectively. The visualization of the concentration and depletion of these fields and their spatial localization show no contribution of the effectively unpaired electrons to the conventional bonding among two centers, but the field -nabla2rho(u)(r) provides an interesting structure. We also study the reliability of the information contained in the partitioning of this electron density field function for describing nonclassical bondings as the three-center two-electron ones.     

On the basis‐set dependence of local and integrated electron density properties: Application of a new computer program for quantum‐chemical density analysis

A new computer program for post‐processing analysis of quantum‐chemical electron densities is described. The code can work with Slater‐ and Gaussian‐type basis functions of arbitrary angular momentum. It has been applied to explore the basis‐set dependence of the electron density and its Laplacian in terms of local and integrated topological properties. Our analysis, including Gaussian/Slater basis sets up to sextuple/quadruple‐zeta order, shows that these properties considerably depend on the choice of type and number of primitives utilized in the wavefunction expansion. Basis sets with high angular momentum (l = 5 or l = 6) are necessary to achieve convergence for local properties of the density and the Laplacian. In agreement with previous studies, atomic charges defined within Bader's Quantum Theory of Atoms in Molecules appear to be much more basis‐set dependent than the Hirshfeld's stockholder charges. The former ones converge only at the quadruple‐zeta/higher level with Gaussian/Slater functions. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Building molecular charge distributions from fragments: Application to HIV-1 protease inhibitors

Interaction energies are a function of the molecular charge distribution. In previous work, we found that the set of atomic partial charges giving the best agreement with experimental vacuum dipole moments were from density functional theory calculations using an extended basis set. Extension of such computations to larger molecules requires an atomic partial charge calculation beyond present computational resources. A solution to this problem is the calculation of atomic partial charges for segments of the molecule and reassociation of such fragments to yield partial charges for the entire molecule. Various partitions and reassociation methods for five molecules relevant to HIV-1 protease inhibitors are examined. A useful method of reassociation is introduced in which atomic partial charges for a large molecule are computed by fitting to the combined electrostatic potential calculated from the fragment partial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. © 1997 by John Wiley & Sons, Inc.     

Understanding the electronic structure, reactivity, and hydrogen bonding for a 1,2-diphosphonium dication

The experimental charge density for hexamethyldiphosphonium ditriflate has been determined from low-temperature high-resolution X-ray diffraction data. These results have been compared with theoretically calculated values for the isolated gas-phase compound. Analysis of the topological and atomic basin properties has provided insight into the exact nature of the P-P bond in both the crystalline and the gas-phase structures. The rho(b)(r) and nabla2rho(b)(r) values highlight the covalent nature of the P-P bond, while the atomic charges indicate a localization of the positive charges on the two phosphorus atoms. This seems to indicate that a covalent bond is formed despite a strong electrostatic repulsion between these two heteroatoms. The topological properties and electrostatic potentials have also been shown to provide significant insight into the chemical reactivity of the title compound. A topological analysis of P2Me4, P2Me5(+), and P2Me6(+2) species has provided information about the progression of the P-P bond in the synthesis of the title compound. An investigation of the different hydrogen-bonding networks present in the crystalline and gas-phase structures, along with their affect on the electronic structure of the title compound has also been investigated. This has all led to significant new insight into the electronic structure, reactivity, and weak hydrogen bonding in prototypical 1,2-diphosphonium dications.     

Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis

We present the Voronoi Deformation Density (VDD) method for computing atomic charges. The VDD method does not explicitly use the basis functions but calculates the amount of electronic density that flows to or from a certain atom due to bond formation by spatial integration of the deformation density over the atomic Voronoi cell. We compare our method to the well-known Mulliken, Hirshfeld, Bader, and Weinhold [Natural Population Analysis (NPA)] charges for a variety of biological, organic, and inorganic molecules. The Mulliken charges are (again) shown to be useless due to heavy basis set dependency, and the Bader charges (and often also the NPA charges) are not realistic, yielding too extreme values that suggest much ionic character even in the case of covalent bonds. The Hirshfeld and VDD charges, which prove to be numerically very similar, are to be recommended because they yield chemically meaningful charges. We stress the need to use spatial integration over an atomic domain to get rid of basis set dependency, and the need to integrate the deformation density in order to obtain a realistic picture of the charge rearrangement upon bonding. An asset of the VDD charges is the transparency of the approach owing to the simple geometric partitioning of space. The deformation density based charges prove to conform to chemical experience.     

价电子平均能级连接性指数及其应用

定义价电子平均能级（δi）为：δi=(ni-1)(ni+ΣEij)0.5/(1+mi)。由δi建构分子连接性指数（mQ）,其中,0Q=Σ(δi)-0.5、1Q=Σ(δiδj)-0.5。0Q与无机物总键能ΔE、0Q2与过渡元素卤化物的ΔfHmθ、1Q0.5与碱金属卤化物晶格能U、0Q及1Q与无机氢化物pKa的相关系数分别为0.9734、0.9769、0.9906、0.9945,均优于文献方法。mQ是一种结构选择性、性质相关性俱佳的拓扑指数。     

Standard absolute entropy, S degrees 298 values from volume or density. 1. Inorganic materials

Standard absolute entropies of many inorganic materials are unknown; this precludes a full understanding of their thermodynamic stabilities. It is shown here that formula unit volume, V(m)(), can be employed for the general estimation of standard entropy, S degrees 298 values for inorganic materials of varying stoichiometry (including minerals), through a simple linear correlation between entropy and molar volume. V(m)() can be obtained from a number of possible sources, or alternatively density, rho, may be used as the source of data. The approach can also be extended to estimate entropies for hypothesized materials. The regression lines pass close to the origin, with the following formulas: For inorganic ionic salts, S degrees 298 /J K(-)(1) mol(-)(1) = 1360 (V(m)()/nm(3) formula unit(-)(1)) + 15 or = 2.258 [M/(rho/g cm(-)(3))] + 15. For ionic hydrates, S degrees 298 /J K(-)(1) mol(-)(1) = 1579 (V(m)()/nm(3) formula unit(-)(1)) + 6 or = 2.621 [M/(rho/g cm(-)(3))] + 6. For minerals, S degrees 298 /J K(-)(1) mol(-)(1) = 1262 (V(m)()/nm(3) formula unit(-)(1)) + 13 or = 2.095 [M/(rho/g cm(-)(3))] + 13. Coupled with our published procedures, which relate volume to other thermodynamic properties via lattice energy, the correlation reported here complements our development of a predictive approach to thermodynamics and ultimately permits the estimation of Gibbs energy data. Our procedures are simple, robust, and reliable and can be used by specialists and nonspecialists alike.     

Theoretical electron density distributions for Fe- and Cu-sulfide earth materials: a connection between bond length, bond critical point properties, local energy densities, and bonded interactions

Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, rho(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, rho(rc), the Laplacian, triangle down2rho(rc), the local kinetic energy, G(rc), and the oxidation state of Fe increase as the local potential energy density, V(rc), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of rho(rc) and triangle down2rho(rc) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of rho(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediate in character with the low-spin Fe-S interactions having greater shared character than the high-spin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu+Fe3+S2. The bond length is shorter and the rho(rc) value is larger for the FeS4 tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS6 octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe3S4 slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S8 rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.