Expansion Formulae for Two-center Integer and Noninteger <Emphasis Type="Italic">n</Emphasis> STO Charge Densities and their Use in Evaluation of Multi-center Integrals

Using complete orthonormal sets of Ψ^α-exponential type orbitals (Ψ^α-ETOs, α =1, 0, −1, −2, ...) introduced by the author, the series expansion formulae are derived for the two-center integer and noninteger n STO (ISTO and NISTO) charge densities in terms of integer n STOs at a third center. The expansion coefficients occurring in these relations are presented through the two-center overlap integrals between STOs with integer and noninteger principal quantum numbers. The general formulae obtained for the STO charge densities are utilized for the evaluation of two-center Coulomb and hybrid integrals of NISTOs appearing in the Hartee–Fock–Roothaan approximation. The final results are expressed in terms of both the overlap integrals and the one-center basic integrals over integer n STOs. It should be noted that the result for the multi-center multielectron integrals with two-center noninteger n STO charge densities presented in this paper were not appeared in our past publications.     

Use of addition theorems in evaluation of multicenter nuclear-attraction and electron-repulsion integrals with integer and noninteger n Slater-type orbitals

Multicenter integrals appearing in the Hartree–Fock–Roothaan equations for molecules are calculated using different kinds of series expansion formulas obtained from the expansions of integer and noninteger n Slater-type orbitals, in terms of Ψ ^α -exponential-type orbitals (where α=1, 0, –1, –2,...) at a displaced center, that form complete orthonormal sets and are represented by linear combinations of integer n Slater-type orbitals. The convergence of these series is tested by calculating concrete cases. The accuracy of the results is quite high for quantum numbers, screening constants, and location of orbitals. Received: 13 February 2002 / Accepted: 11 March 2002 / Published online: 4 July 2002     

Use of auxiliary functions {Q_{ns}^q} and {G_{-ns}^q} in evaluation of multicenter integrals over integer and noninteger n-Slater type orbitals arising in Hartree–Fock–Roothaan equations for molecules

With the help of expansion relations for the two-center Slater type orbitals (STOs) charge densities established by the author from the use of complete orthonormal sets of Ψ ^α -exponential type orbitals (Ψ ^α -ETOs), where α = 1, 0, ? 1, ? 2, . . . , a large number of series expansion formulas for the multicenter integrals of integer and noninteger n-STOs (ISTOs and NISTOs) occurring in Hartree–Fock–Roothaan (HFR) equations for molecules is derived through the auxiliary functions ${Q_{ns}^q}$ and ${G_{-ns}^q}$ , and one- and two-center basic integrals of ISTOs. The analytical relations for basic integrals are presented. As an example of application, the calculations have been performed for the ground state of electronic configuration of ${{\it CH}_4((1a_1)^{2}(2a_1)^{2}(1t_{2x})^{2} (1t_{2y})^{2} (1t_{2z})^{2},{}^1A_1)}$ using combined HFR theory suggested by the author.     

Oxygen- versus carbon-coordination of the alpha-stabilized phosphorus ylide Ph<Subscript>3</Subscript>P=C(H)R in palladacycles bearing secondary amines

The ortho-metalated complex [Pd(x){κ ² (C,N)-[C₆H₄CH₂NRR′ (Y)}] (2a–4a and 2b–3b) was prepared by refluxing in benzene equimolecular amounts of Pd(OAc)₂ and secondary benzylamine [a, EtNHCH₂Ph; b, t-BuNHCH₂Ph followed by addition of excess NaCl. The reaction of the complexes [Pd(x){κ ² (C,N)-[C₆H₄CH₂NRR′ (Y)}] (2a–4a and 2b–3b) with a stoichiometric amount of Ph₃P=C(H)COC₆H₄-4-Z (Z = Br, Ph) (ZBPPY) (1:1 molar ratio), in THF at low temperature, gives the cationic derivatives [Pd(OC(Z-4-C₆H₄C=CHPPh₃){κ ² (C,N)-[C₆H₄CH₂NRR′(Y)}] (5a–9a, 4b–6b, and 4b′–6b′), in which the ylide ligand is O-coordinated to the Pd(II) center and trans to the ortho-metalated C(6)H(4) group, in an “end-on carbonyl”. Ortho-metallation, ylide O-coordination, and C-coordination in complexes (5a–9a, 4b–6b, and 4b′–6b′) were characterized by elemental analysis as well as various spectroscopic techniques.     

Application of combined Hartree–Fock–Roothaan theory to molecules with arbitrary number of closed and open shells

In this study, the applicability of the combined Hartree–Fock–Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH ₂ which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.     

Polymorphism for a novel phosphoramidate; NMR and X-ray crystallography

Abstract  

New phosphoramidates with formula 3-NC₅H₄C(O)NHP(O)XY (X=Y=Cl (1), X=Y=NH–C(CH₃)₃ (2a,2b), X=Y=N(C₄H₉)₂ (3), X=Cl, Y=N(C₂H₅)₂ (4) were synthesized and characterized by IR, ¹H-, ¹³C-, ³¹P-NMR spectroscopy and CHN elemental analysis. Surprisingly, the reaction of compound 2a with LaCl₃, 7H₂O in 3:1 M ratio leads to a polymorph of this compound (2b). NMR spectra indicate that ² J(PNH_amide) in 2b (7.0 Hz) is very much greater than in 2a (4.1 Hz), while δ(³¹P) values are identical for both of them. In IR spectra, υ(P=O) is weaker but υ(C=O) is stronger in 2a than in 2b. The structures of 2a, 2b were determined by X-ray crystallography. These compounds form centrosymmetric dimers via two intermolecular P=O……H–N hydrogen bonds. Strong intermolecular N–H…N, N–H…O and weak C–H…O hydrogen bonds lead to a three-dimensional polymeric cluster in the 2a while intermolecular strong N–H……N and weak C–H……O hydrogen bonds form a two-dimensional polymeric chain in 2b.     

The Electronic Structure and Bonding of the First p-Block Paddlewheel Complex,Bi<Subscript>2</Subscript>(trifluoroacetate)<Subscript>4</Subscript>, and Comparison to d-Block Transition Metal Paddlewheel Complexes: A Photoelectron and Density Functional Theory Study

The photoelectron spectrum and a density functional computational analysis of the first p-block paddlewheel complex, Bi₂(tfa)₄, where tfa = (O₂CCF₃)⁻, are reported. The photoelectron spectrum of Bi₂(tfa)₄ contains an ionization band between the region of metal-based ionizations and the region of overlapping ligand ionizations that is not seen in the photoelectron spectra of d-block paddlewheel complexes. This additional ionization arises from an a_1g symmetry combination of the tfa ligand orbitals that is directed for σ bonding with the metals, and the unusual energy of this ionization follows from the different interaction of this orbital with the valence s and p orbitals of Bi compared to the valence d orbitals of transition metals. There is significant mixing between the Bi–Bi σ bond and this a_1g M–L σ orbital. This observation led to a re-examination of the ionization differences between Mo₂(tfa)₄ and W₂(tfa)₄, where the metal–metal σ and π ionizations are overlapping for the Mo₂ molecule but a separate and sharp σ ionization is observed for the W₂ molecule. The coalescing of the σ and π bond ionizations of Mo₂(tfa)₄ is due to greater ligand orbital character in the Mo–Mo σ bond (∼7%) versus the W–W σ bond (∼1%). In tribute to F. Albert Cotton for sharing the beauty of symmetry and the joy and excitement in the exploration of metal–metal bonds.     

Gold(I)-Gold(III)-4,4′-bpy-phosphine complexes: Synthesis and multinuclear NMR study

Silver assisted de-bromination gives [Au₂(dppm/dppe/dppa) (OTf)₂], which on reaction with 4,4′-bpy and gold(I) phosphines in CH₂Cl₂ medium, by the self assembly technique, leads to [(PPh₃)Au(4,4′-bpy)Au(PPh₃)], (1a–1d,2), [{Au₂(dppm/dppe/dppa)}{(4,4-bpy)Au(PPh₃)}₂](NO₃)₄, (3), [{Au₄(dppm/dppe/dppa)₂(4,4-bpy)₂}](OTf)_4, (4), [{(PPh₃)Au^I(4,4′-bpy)}₂Au^III(C₆F₅/Mes)](NO₃)₃, (5) [dppm/dppe/dppa =diphenyl phosphino-methane(a), –ethane(b), ammine(c), C₆F₅/Mes pentafluorophenyl/mesitylene]. The maximum molecular peak of the corresponding molecule is observed in the ESI mass spectrum. Ir spectra of the complexes show –C=C–, –C=N–, as well as phosphine, mesitylene and pentafluorophenyl stretching. The ¹H-NMR spectra as well as ³¹P(¹H)-NMR suggest solution stereochemistry, proton movement and phosphorus proton interaction. Considering all the moities there are a lot of carbon atoms in the molecule reflected by the ¹³C(H)-NMR spectrum. In the ¹H–¹H COSY spectrum of the present complexes and contour peaks in the ¹H–¹³C-HMQC spectrum, assign the solution structure and stereoretentive transformation in each step.     

Indium-containing heterofullerenes and their η5-π-complexes

The molecular and electronic structure of hypothetical metallofullerenes In₅C₅₅ (1a) and In₁₀C₆₀ (2a) were simulated by the MNDO/PM3 method. Formally, heterofullerene1a is obtained from the C₆₀ cluster by replacement of the carbon atoms at α-positions relative to one of the pentagons by In atoms, and cluster2a is obtained from the C₇₀ cluster by replacement of the carbon atoms framing the polar pentagons of this fullerene by In atoms. Along with clusters1a and2a, their η⁵-π-complexes ln(η⁵-1a (1b) and ln₂(2η⁵-2a) (2b) with one (1b) and two (2b) exohedral In atoms coordinated to the pentagons (pent ^*) isolated by In atoms were also studied. The energies of the In—pent ^* bonds in1b and2b are approximately equal to 104 kcal mol⁻¹. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 880–883, May, 1998.     

Perspective on “An extended Hückel theory. I. Hydrocarbons”

 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH⁺ ₃ and N⁺ ₂ using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two ²A₁ states, very similar and showing great mixing of the (2a _l ⁻¹) and (3a _l ⁻²5a _l ¹) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH₃. The possible contribution of a ²Π _g (3σ _g ⁻²1π _g ¹) state to the A shake-up peak of N₂ at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH₃ and 37 eV for N₂. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Gold(I)-diphenylphosphinomethane–arylazoimidazole: synthesis and multinuclear NMR investigation

Reaction of [Au₂(dppm)Cl₂] with AgOTf in CH₂Cl₂ medium followed ligand addition and leads to [Au₂(dppm)(RaaiR′)](OTf) [RaaiR′ = p-R–C₆H₄–N = N–C₃H₂–NN–1–R′, (1–3), abbreviated as N,N′-chelator, where N(imidazole) and N(azo) represent N and N′, respectively; R = H (a), Me (b), Cl (c) and R′ = Me (1), CH₂CH₃ (2), CH₂Ph (3), OSO₂CF₃ is the triflate anion, and dppm is the diphenylphosphinomethane-ring]. The ¹H-n.m.r. spectral measurements suggest methylene, –CH₂–, in RaaiEt gives a complex AB type multiplet while in RaaiCH₂Ph it shows AB type quartets with coupling constant of avg. 6 Hz. Considering all the moities there are a lot of different carbon atoms in the molecule which gives a lot of different peaks in the ¹³C-n.m.r spectrum. In the ¹H–¹H-COSY spectrum of the present complexes and contour peaks in the ¹H–¹³C-HMQC spectrum in the present complexes, assign the solution structure and stereoretentive transformation in each step.     

Theoretical study of ionization potentials in monosubstituted benzenes

Monosubstituted benzenes, in which the substituents participate in the π-electron system, are studied following a classification in two classes according to the π-electronic structure of the substituent. For this type of molecule, a relation is established between the nature of the substituent and, on the one hand, the energies of the two highest occupied molecular orbitals and, on the other hand, their respective differences. The two orbitals referred to above have π-character and belong to the a₂ and b₁ species if a C_2v point group is assumed. Simple symmetry arguments lead to the conclusion that the a₂ orbitals have, essentially, an intraring character, whereas the π-orbitals of the substituents do give an important contribution to the b₁ orbitals. Therefore, an a₂ electron must have a larger interaction with the benzene ring and a smaller kinetic energy, whereas a b₁ electron must have a larger interaction with the substituent and a larger kinetic energy. It is also expected that the changes in the π-electronic structure of the substituent must much more influence the variations on the b₁ energies and on the components of orbital energies associated with the substituent than the variations on the a₂ energies and on the intraring components of the orbital energies. A modified version of the MOPAC program was prepared to perform the decomposition of the orbital energies in their kinetic and potential energy components and these in their monocentric and bicentric terms. MNDO calculations on nine monosubstituted benzenes, using the modified MOPAC program, give good confirmation of the symmetry predictions and prove the consistency of the classification of the substituents that is introduced. © 1993 John Wiley & Sons, Inc.     

A novel series of nickel(II)-dppe-arylazoimidazole complexes. Synthesis and spectroscopic characterization

Reaction of [Ni(dppe)Cl₂/Br₂] with AgOTf in CH₂Cl₂ medium following ligand addition leads to [Ni(dppe)(OSO₂CF₃)₂] and then [Ni(dppe)(RaaiR)](OSO₂CF₃)₂ [RaaiR′ = p–R–C₆H₄–N=N–C₃H₂–NN-1–R′,(1–3), abbreviated as N,N′-chelator, where N(imidazole) and N(azo) represent N and N′, respectively; R = H (a), Me (b), Cl (c) and R′ = Me (1), CH₂CH₃ (2), CH₂Ph (3), OSO₂CF₃ is the triflate anion]. ³¹P{¹H}-NMR confirm that stable bis-chelated square planar Ni(II) azoimine–dppe complex formation with one sharp peaks. The ¹H NMR spectral measurements suggest azoimine link is present with lot of phenyl protons in the aromatic region. Considering all the moities there are a lot of different carbon atoms in the molecule which gives many different peaks in the ¹³C(¹H)-NMR spectrum. In the ¹H-¹H COSY spectrum in the present complexes and contour peaks in the ¹H-¹³C-HMQC spectrum in the present complexes, assign the solution structure and stereoretentive conformation in each complexes.     

The strength of the σ-, π- and δ-bonds in Re2Cl 8 2−

The geometry of Re₂Cl₈²⁻ has been optimized for the eclipsed (D _4h ) equilibrium conformation and for the staggered (D _4d ) conformation at BP86/TZ2P. The nature of the Re–Re bond which has a formal bond order four has been studied with an energy decomposition analysis (EDA). The EDA investigation indicates that the contribution of the b ₂ (δ _xy ) orbitals to the Re–Re bond in the ground state is negligibly small. The vertical excitation of one and two electrons from the bonding δ orbital into the antibonding δ* orbitals yielding the singly and doubly excited states and gives a destabilization of 17.5 and 36.1 kcal/mol, respectively, which is nearly the same as the total excitation energies. The preference for the D _4h geometry with eclipsing Re–Cl bonds is explained in terms of hyperconjugation rather than δ bonding. This is supported by the calculation of the triply bonded Re₂Cl₈ which also has an eclipsed energy minimum structure. The calculations also suggest that the Re–Re triple bond in Re₂Cl₈ is stronger than the Re–Re quadruple bond in Re₂Cl₈²⁻. A negligible contribution of the δ orbital to the metal–metal bond strength is also calculated for Os₂Cl₈ which is isoelectronic with Re₂Cl₈²⁻. Contribution of the Mark S. Gordon 65th Birthday Festschrift Issue. Theoretical Studies of Inorganic Compounds. 38. Part 37 (2006) Bessac F, Frenking G, Inorg Chem 45:6956.     

Expansion formulae for two-center charge densities of integer and noninteger n generalized exponential type orbitals with hyperbolic cosine and their use in evaluation of multicenter multielectron integrals

The expansion formulae are derived for the two-center charge densities of integer and noninteger n generalized exponential type orbitals with hyperbolic cosine (GETOHC) in terms of corresponding charge densities of generalized exponential type orbitals (GETO) presented in our previous paper. The general formulae obtained for the GETOHC charge densities are utilized for the evaluation of multicenter multielectron integrals appearing in the Hartree–Fock–Roothaan (HFR) and explicitly correlated theories when the GETOHC are employed as basis functions.     

Molecular and crystal structure of methyl-4-anti-hydroxyimino-1-dioxolano-13-isopropyl-10a,7-dimethylpentacyclo×[10b.8.5.04b,10b.06a,10a.01a,4a]icos-14-ene-7-carboxylate

Synthesis is performed and the molecular structure is analyzed of methyl-4-anti-hydroxyimino-1-dioxolano-13-isopropyl-10a,7-dimethylpentacyclo[10b.8.5.0^4b,10b.0^6a,10a.0^1a,4a]icos-14-ene-7-carboxylate IIa. Compound IIa C₂₇H₄₀O₄ crystallizes in monoclinic symmetry with cell parameters: a = 13.785(13) ?, b = 7.302(7) ?, c = 13.817(13) ?, β = 94.799(19)°, space group P2(1), Z = 2, d = 1.164 g/cm³. Original Russian Text Copyright ? 2009 by I. E. Smirnova, E. V. Tret’yakova, O. B. Kazakova, and Z. A. Starikova __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 2, pp. 393–395, March–April, 2009.     

Kinetics of the heterobimetallic complexes formation in the reactions between chromium(III) macrocyclic species and [Fe(CN)<Subscript>6</Subscript>]<Superscript>4−</Superscript> ions

Formation of a singly bridged heterobimetallic Cr^III–NC–Fe^II anation product of the cis − [Cr(cycb)(H₂O)₂]³⁺ and trans − [Cr(cyca)(H₂O)₂]³⁺ complexes, where cyca and cycb are meso- and rac-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane respectively, by [Fe(CN)₆]⁴⁻ ions is accompanied by an intensive absorbance increase within 390–470 nm due to an intermetal electron transition. A bell-shape of the pseudo-first order rate constants/pH profile observed for the reactions which have been studied under a large excess of the iron(II) complex is in accordance with the highest reactivity of the chromium(III) complexes in their monohydroxomonoaqua forms. The reaction mechanism has been discussed based on the determined rate law.     

Aminoxyl Radicals from N-Phenyl-1-(2-oxo-1-azacycloalkyl)-methanesulfonamides

The synthesis and reaction with two oxidation agents is described for N-phenyl-1-(2-oxo-1-azacycloalkyl)methanesulfonamides. Their oxidation was carried out using RO_2^·R{\rm O}_{2^\bullet} radicals and 3-chloroperbenzoic acid. In both cases, the EPR spectra of corresponding aminoxyl radicals were recorded. Their simulation confirmed that the –SO₂– group in the neighbourhood of the – NO^·{{\rm NO}^\bullet} – fragment does not prevent the interaction of the unpaired electron with the methylene protons and the nitrogen atom of the heterocyclic ring.     

Cooperative N–H···N,N–H···O,and O–H···N bonded molecular dimers of two new 3,5-diaryl-1<Emphasis Type="Italic">H</Emphasis>-pyrazoles

Two new 3,5-diaryl-1H-pyrazoles: 3(5)-(4-tert-butylphenyl)-5(3)-(naphthalene-2-yl)-1H-pyrazole (1) and 5-(4-(benzyloxy)phenyl)-3-(furan-2-yl)-1H-pyrazole (2) were synthesized and characterized. Two strong ions peaks [2M]⁺ and [2M + Na]⁺ observed in the ESI–MS spectra are attributed to the dimerization process in solution formed by intermolecular N–H···N hydrogen bonds. The crystal structures have been determined by X-ray crystal structure analysis. Compound 1 exists as a pair of tautomers 1a and 1b, and its dimer [R ₂²(6) motif] is formed by the tautomers 1a and 1b. Compound 2 only exists as a 2a tautomer, and interesting intermolecular N–H···O and O–H···N hydrogen bonds link two pyrazoles and two methanol molecules, leading to the formation of an R ₄⁴(10) dimer motif.     

Synthesis and structure of some group VII 1,2-diacyl cyclopentadiene complexes and their pyridazine derivatives

A series of 1,2-diacyl cyclopentadienyl tricarbonyl manganese and rhenium complexes, [M(CO)₃{η⁵-1,2-C₅H₃(CO-(R)₂}] (3a–c and 4a–b), were isolated utilizing a straightforward, 3-step route. The synthetic pathway began with a 1,2-diacyl cyclopentadiene (fulvene), followed by the formation of its corresponding thallium salt and transmetallation with the appropriate pentacarbonyl metal bromide. X-ray crystallographic analysis and high-accuracy mass spectrometry confirmed the structures of the both the 4-methoxyphenyl and 4-chlorophenyl diacyl rhenium complexes, [Re(CO)₃{η⁵-1,2-C₅H₃(CO-(4-OCH₃)C₆H₄)₂}] (4a) and [Re(CO)₃{η⁵-1,2-C₅H₃(CO-(4-Cl)C₆H₄)₂}] (4b). Diacyl complexes 3a–c and 4a–b were then ring-closed with hydrazine hydrate to form their corresponding pyridazine complexes, [M(CO)₃{η⁵-1,2-C₅H₃(1,4-(R)₂N₂C₂}] (5a–c and 6a–b), in good yields (60–83%). The pyridazyl ligands were found to be relatively labile, and recrystallization of the target complexes 5a–c and 6a–b afforded only the free pyridazine ligands.