Evaluation of two-center,two- and three-electron integrals involving correlation factors over Slater-type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

This article is concerned with the construction of the general algorithm for evaluating two-center, two- and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function r^k_ij derived in Part I of this series for k = ?1, 0, 1, 2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculations for different types of the two- and three-electron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.     

Energies of Resonances in Atoms and Ions with Three Electrons

The energies of resonances of ² Ssymmetry were calculated for atoms and ions with three electrons, H^2?, He^?, and Li, using the stabilization technique. The variational wave function was expanded over a large number (up to 2030) of normalized three-electron basis functions. The basis functions that made significant contributions to the energies were selected using a special procedure. Many high-energy resonances were found with energies of H^2? resonances ranging from 1 to 12 eV. The calculated energies of some He^? and Li resonances were compared with the experimental data and calculations of other authors. The selected basis set of three-electron wave functions was found to be efficient in calculations of high-energy resonances.     

Investigation of single MoFe3S4 cubane cluster: I. First successful synthesis by spontaneous self-assembly reaction and structure of (Et4N) [MoFe3S4(Et2NCSS)5]CH3CN

A single MoFe₃S₄ cubane-like cluster compound has been synthesized through spontaneous self-assembly of simple inorganic salts with organosulfur ligand for the first time. (Et₄N)-(MoFe₃S₄(Et₂NCSS)₅] CH₃CN(1) is quite stable in air. The crystal of 1 is monoclinic with space group P2/c, a=22.897 (3)Å, b= 12.399 (2)Å, c=20.928 (4)Å, β=97.15 (1)°, and Z=4. A full matrix least-squares refinement with 6725 unique reflections for all nonhydrogen atoms gives R=0.068. The anion of 1 is the first isolated single MoFe₃S₄ cubane cluster with core oxidation state [MoFe₃S₄]⁴⁺. The distance between the two 6-coordinate metal atoms (Mo, Fe) is 2.624 Å, which is the shortest M-M' bond observed for Mo-Fe-S clusters so far and the only one shorter than similar distances in FeMo-cofactor. The bond orders of this anion were calculated by EHMO method and the results coincide with the general rule. The structural feature and the unusual stability of 1 can be attributed to the bidentate chelating effect of Et₂NCSS-, which leads to high coordination of metal atoms and the various ligated types.     

Evaluation of two-center,two- and three-electron integrals involving correlation factors over Slater-type orbitals. I. Basic integrals

The modified and extended version of the Neumann expansion of the interrelectronic distance function r for u = ?1, 0, 1, 2, using the set of orthogonal polynomials normalized to unity, is presented. This expansion has been utilized to obtain analytical expressions for evaluating two-center two- and three-electron integrals in the Slater orbital basis occurring if variational correlated functions are used.     

γ‐Modification of poly[(N,N‐diethyl­dithio­carbamato)silver(I)]

In the title compound, catena‐poly[[tri­silver(I)‐tri‐μ₃‐N,N‐diethyl­dithio­carbamato‐3′κS:1κS′:2κS;1κS:2κS′:3κS;2κS:3κ²S,S′:1′κS′], [Ag₃(C₅H₁₀NS₂)₃]_n, the trigonally and tetra­hedrally coordinated Ag atoms are μ₃‐bridged by κ³‐ and κ⁴‐S₂CNEt₂ ligands to form a ribbon structure along the c axis. There is a twofold axis parallel to the b axis and passing through the tetra­hedrally coordinated Ag atom. The S₂CNEt₂ ligands coordinate the Ag atoms in η¹,η²‐ and η²,η²‐fashions, depending on the bridging S atoms. The distances between the trigonal Ag and S atoms are 2.4915 (11)–2.6205 (11) Å, while those between the tetra­hedral Ag and S atoms are 2.5457 (11) and 2.7145 (10) Å. The shortest Ag⋯Ag distance between trigonal Ag atoms is 2.8336 (7) Å, which indicates a weak Ag⋯Ag inter­action, whereas the shortest distance between trigonal and tetra­hedral Ag atoms is 3.463 (6) Å, which is considered as non‐bonding.     

Isolation and X-ray structure analysis of citreohybridonol from marine-derived Penicillium atrovenetum

The anti-neuroinflammatory meroterpenoid citreohybridonol was isolated for the first time from a sponge-derived fungus Penicillium atrovenetum. In this study, in addition to isolation and structure featuring, its unambiguous absolute configuration was determined exclusively by single crystal X-ray diffraction. The C-17-keto tautomer was clearly observed in X-ray analysis. The substance crystallises in the monoclinic space group P2₁ with a = 10.7496(5) Å, b = 14.3286(7) Å, c = 17.4909(8) Å, β = 103.235(2)°, V = 2622.5(2) Å³, Z = 2, D_calcd = 1.280 g/cm³. The chirality of the asymmetric carbon atoms was as follows: C3 (S), C5 (R), C6 (S), C8 (S), C9 (R), C10 (R), C13 (R), C14 (R).     

Analytical Hartree–Fock wave functions for the atoms Cs to Lr

 Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet. Received: 6 December 1999 / Accepted: 29 February 2000 / Published online: 12 May 2000     

原子配分参数、配分连接性指数及其应用

结构决定性质，性质反映结构，这是化学、生物学等学科的一条基本规律。因此，分子的微观结构与性质之间存在着密切关系。物质的理化性质、生物活性等数据的获取，迄今主要来自于实验。如能建立结构与性能之间的数量关系用以估算与预测分子的性质，这无疑是一项十分有意义的工作。拓扑指数法以其计算简单、准确性高、应用范围广而在上述领域中发挥重要作用犤１～４犦。拓扑指数是对分子结构进行的定量描述，使分子之间的结构差异定量化。自Wiener提出第一个拓扑指数（W）犤５犦以来，迄今已有２００余种拓扑指数问世。其中一部分能够有效地…     

Description of correlated densities for few‐electron atoms by simple functional forms

Simple analytical functional forms for the electron density of two‐ and three‐electron atoms which reproduce fairly the correlated (exact) values are presented. The procedure is based on the fitting of an auxiliary f(r) function which has adequate properties for this purpose and can be extended to more complex atoms. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 443–454, 1999     

Jahn-Teller distortion,ferromagnetic coupling,and electron delocalization in a high-spin Fe–Fe bonded dimer

Fe₂(N,N’-diphenylformamidinate)₄, 1, first synthesized in 1994, is one of very few non-organometallic compounds with Fe–Fe distances, (2.46 Å) suggestive of an Fe–Fe bond. The electronic structure of 1 has been unclear because of its distorted D₂ geometry, as well as its reported S = 4 ground state. Computational investigations using DFT methods have shown that the D₂ geometry is the result of a Jahn-Teller distortion away from D₄ symmetry, in which the ground state would be orbitally degenerate. Broken symmetry methods have shown that ferromagnetic coupling between the two high-spin Fe(II) ions in 1 is a consequence of spin delocalization caused by a three-electron σ bond and a weaker three-electron δ bond between the Fe atoms. The relationship between ferromagnetic coupling and an Fe–Fe bond is established from results using hybrid functionals having variable amounts of Hartree-Fock exchange, which is found, surprisingly, to mitigate Fe–Fe bonding.     

Solid‐State 17O NMR Spectroscopy of Paramagnetic Coordination Compounds

High‐quality solid‐state ¹⁷O (I=5/2) NMR spectra can be successfully obtained for paramagnetic coordination compounds in which oxygen atoms are directly bonded to the paramagnetic metal centers. For complexes containing V^III (S=1), Cu^II (S=1/2), and Mn^III (S=2) metal centers, the ¹⁷O isotropic paramagnetic shifts were found to span a range of more than 10 000 ppm. In several cases, high‐resolution ¹⁷O NMR spectra were recorded under very fast magic‐angle spinning (MAS) conditions at 21.1 T. Quantum‐chemical computations using density functional theory (DFT) qualitatively reproduced the experimental ¹⁷O hyperfine shift tensors.     

Synthesis and Crystal Structure of Two iso-closo 11-Vertex p-Bromobenzoate Ruthenoborane Clusters： [（PPh3）（p-BrC6H4CO2）2RUB10H8 and [（PPh3）2Ru（p-BrC6H4CO2）-（PPh3）RuB10H9]

The title clusters [（PPh3）（p-BrC6H4CO2）2RuB10H8] （1） and [（PPh3）2Ru（PPh3）（p-BrC6H4CO2）RuB10H9] （2） have been prepared and characterized by elemental analysis, FT-IR, ^1H, ^13C NMR spectra and single-crystal X-ray diffraction analysis. The clusters crystallize in monoclinic system, space group C2/c, with a =2.569（4） nm, b= 1.546（2） nm, c= 1.927（3） nm ,8=95.11（2）°, Z=8, V=7.622（21） nm^3, Dc=1.533 Mg/m^3, F（000）=3472, S= 1.009, R= 0.0418, wR=0.0775 and triclinic system, space group P-l, with a=1.3142（3） nm, b= 1.3761（3） nm, c=1.8503（4） nm, a =90.445（4）°,β=105.950（4）°, γ108.980（4）°, Z=2, V=3.0251（12） nm^3, Dc = 1.434 Mg/m^3, F（000）= 1316, S=1.007, R=0.0464, wR=0.1175, respectively for 1 and 2. In the structures, both of the dusters are based on a closo-type C2v 1： 2 ： 4 ： 2 ： 2 RUB10 stack with the metal occupying the unique six-connected apical position. In cluster 1, the metal center has three exo-polyhedral ligands： one triphenylphosphine and two dative oxygen atoms of p-bromobenzoates. The other oxygen atoms of two p-bromobenzoate are additionally bonded to B（2） and B（3） atoms respectively, resulting in two exo-cyclic five-membered Ru-O-C-O-B rings and engendering a symmetrical conformation. The cluster 2 is a bimetallic species in which the second ruthenium is bound to the {RUB10} center via one Ru-Ru bond and two {RuHμB} bridges resulting in one closo distorted exo-polyhedral Ru（1）-Ru（2）-B（3）-B（6） tetrahedron.     

A dinuclear molybdenum cluster containing i-mnt ligand: synthesis and crystal structure of [Mo_2S_4(i-mnt)_2] (Et_4N)_2

A dinuclear molybdenum(V) cluster compound (Et4N)2[Mo2S4(i-mnt)2] (i-mnt=l,l-dicyanoethylene-2,2-dithiol, (S2C=C(CN)2]2-) has been prepared by the ligand substitution reaction of Mo2S4(iso-pr2dtp)2 (iso-pr2dtp=S2P(OC3H7)2-) with K2(i-mnt) in the presence of Bt4NI. This cluster was characterized by inrrared spectrum, UV-Vis spectrum and single crystal structure analy-sis. The cluster anion [Mo2S4(i-mnt)2]2- possesses C, symmetry with a crystallographic mirror plane through two bridging S atoms. By the S....S supramolecular interactions between two adjacent cluster anions the [Mo2S4(i-mnt)2]2- anions are linked to form infinite chains along the b axis. Crystal data: monoclinic, space group C2/m, a=1.8748(6), b=1.5360(4), c=1.4322(5) nm, ,β=112.02(2)°, V=3.823(4) nm3, Z=4, Dc=1.50 g/cm3. The final R=0.038 and .RW=0.053 for 3015 observed unique reflections.     

A novel asymmetrical phosphine tetracobalt complex ofo-Mercaptophenol: Synthesis,structure, and properties of Co4mp4(Hmp)(PBu 3 n )3 (H2mp=o-Mercaptophenol)

Complex Co₄mp₄(Hmp)(PBu ₃ ⁿ )₃ (1) (H₂mp=o-Mercaptophenol) was obtained from the reaction of CoCl₂ and H₂mp in the presence of PBu ⁿ ₃ and NaOMe with restricted oxidation. X-ray crystallographic data: triclinic, space group ,a=15.657(5) Å,b=20.469(8) Å,c=12.383(3) Å,=93.59(3)°, =112.45(2)°, =93.65(3)°,V=3648.7 ų,Z=2,D _c =1.33 g/cm³;R=0.065. The molecule consists of four cobalt atoms unsymmetrically bridged by S or S and O atoms from four of the five mp ligands. The fifth mp is terminally chelated to Co(4) which is in a distorted trigonal bipyramidal geometry, while Co(1)-Co(3) are square pyramidal. Atom Co(2) is bonded to Co(1) and Co(3) (average distance 2.632 Å) with strong interactions while Co(4) is only loosely connected to Co(1) (3.402 Å) and Co(3) (2.956 Å) through oxygen bridges and a hydrogen bond. The different coordination environments O₂S₂P, S₄P, and O₄S of the cobalt atoms make the molecule highly asymmetrical. XPS fitting data confirm the difference of the Co atoms. FABMS data indicate the possible fragmentation routes. The complex is paramagnetic with _eff=5.2 _B.     

Calculation of the 4S?4P0 spectrum of lithiumlike ions by the Hylleraas method

The energies of the five lowest ⁴S and ⁴P⁰ states for three-electron ions for 3?Z?10 have been calculated by the Hylleraas method. The largest basis set used contained 97 terms with odd as well as even powers of r_ij. The change of scale r′ = Zr was applied to the Hamiltonian so that the same basis sets could be used for all the three-electron ions leading to great savings in computing time.     

Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I. Three-electron integrals

A method to evaluate the nonrelativistic electron-repulsion, nuclear attraction and kinetic energy three-electron integrals over Slater orbitals appearing in Hylleraas-CI (Hy-CI) electron structure calculations on atoms is shown. It consists on the direct integration over the interelectronic coordinate r _ij and the sucessive integration over the coordinates of one of the electrons. All the integrals are expressed as linear combinations of basic two-electron integrals. These last are solved in terms of auxiliary two-electron integrals which are easy to compute and have high accuracy. The use of auxiliary three-electron ones is avoided, with great saving of storage memory. Therefore this method can be used for Hy-CI calculations on atoms with number of electrons N ≥ 5. It has been possible to calculate the kinetic energy also in terms of basic two-electron integrals by using the Hamiltonian in Hylleraas coordinates, for this purpose some mathematical aspects like derivatives of the spherical harmonics with respect to the polar angles and recursion relations are treated and some new relations are given.     

Ab initio configuration interaction study on electronically excited 4-dimethylamino-4′-cyanostilbene

Ab initio configuration interaction calculations have been performed to examine the electronic structures of both trans-4-dimethylamino-4′-cyanostilbene (DCS) and four types of perpendicularly twisted DCSs, trans-DCS is predominantly excited into the S₁ state out of low-lying excited states. The S₁ state is an intramolecular charge-transfer (ICT) state in which the dipole moment is about twice as large as that in S₀. The excited DCS at the 4-dimethylanilino twisted conformation, which becomes S₁ in polar solvents, has a very much larger dipole moment than that in S₁ to trans-DCS. This means that the geometrical structure of the twisted ICT (TICT) is the 4-dimethylanilino twisted form, not the dimethylamino twisted one which is well know from the TICT structure of 4-dimethylaminobenzonitrile. Received: 16 December 1998 / Accepted: 19 March 1999 / Published online: 9 September 1999     

Na3Fe2S4, ein Thioferrat mit gemischt valenter sk∞/1[FeS2]-Kette

Na₃Fe₂S₄ has been prepared from Na₂S, S and Fe. It crystallizes in space group Pnma,a=6.6333 (5) Å,b=10.675 (1) Å,c=10.677 (2) Å,Z=4. The crystal structure, as determined from single crystal four-circle diffractometer data (R=2.8%), consists of sk/1[FeS₂]-chains formed by slightly distorted edge sharing [FeS₄]-tetrahedra, the iron atoms having a formal valency of +2.5. The sodium ions are approximately octahedrally coordinated. Exposed to air, Na₃Fe₂S₄ readily takes up water to form a hydrate by a pertially topochemical reaction.

     

A Supermolecule Assembled by Sodium Cation,Crown Ether and α‐Dawson Heteropolyanion

The supermolecular based on sodium molybdate(VI) and sulfate, dibenzo‐18‐crown‐6 was synthesized in acetonitrile and characterized by elemental analysis, IR, ¹H NMR, single crystal X‐ray diffraction, indicating that it contains [S₂Mo₁₈O₆₂]⁴⁺ and [Na(DB18C6)(H₂O)]⁺, where each sodium ion is deviated from the plane defined by the oxygen atoms in the corresponding crown ether. The compound crystallizes in the monoclinic space group C2/c with a=3.29332(10) nm, b=1.90917(6) nm, c=2.63132(7) nm, β=121.6630(10)°, V=14081.8(7) nm³, Z=8, T=293(2) K, and R₁ (wR₂)=0.0177 (0.1525). The compound exhibits a novel organic‐inorganic structure, in which the crown ether‐sodium complexes are coordinated to the terminal oxygen atoms of Mo₁₈O₅₄ and the oxygen atoms of water molecule.