The role of d functions in ab initio calculations. II. The deformation densities of SO2, NO2, and their ions

Comparison of the optimized geometries and SCF energies for the series XO, XO₂, XO, XO, with X = S,N shows that d(S) functions cause larger bond shortening and energy drop than d functions centered on first-row atoms. This is further emphasized on comparing the separate effects of d(central atom) and d(O) functions for SO₂ and NO, which are similar only for the first-row molecule. The d(S) functions are also essential for proper prediction of the OSO angles. The deformation densities calculated for each series and the corresponding X–O shared populations, change as expected on adding electrons first into σ* then into π* molecular orbitals. In the regions around nuclei the deformation densities express the behavior of the atomic s and p valence orbitals or of their product inside their radial nodes. Introduction of d functions causes substantial polarization effects. For X = N these are mostly local except in the bonding regions where d(N) and d(O) functions are somewhat interchangeable. However, d(S) functions induce also unique changes in the deformation density near O. They cause π and π′ charge migration from O to S and a σ flow in the opposite direction. These effects are largest for the hypervalent species. The unique populations of the d(S) functions are much larger than those of d(N) and d(O) functions. The contribution of d(S) functions to bonding is related to the larger amplitude at small radii of the atomic 3d(S) orbital as compared with that of 3d(N). The difference in amplitudes is related to penetration effects. Diffuse p functions affect geometries and SCF energies of doubly, but not singly negative ions. However, they mostly describe the diffuse nonbonding clouds and do not affect bonding patterns.     

Ab initioMO calculations for the oxides,oxyacids, and oxyanions of S(IV) and S(VI)

Ab initio molecular orbital (MO ) calculations for two series of sulfur–oxygen compounds are reported: the S(IV ) system of SO₂, H₂SO₃, HSO, and SO, and the S(VI ) system of SO₃, H₂SO₄, HSO, and SO. Geometries about the sulfur atoms were optimized using the STO -3G* basis set; energies at these geometries were computed by the STO ?3G and 44-31G basis sets both with and without five Gaussian d orbitals on S. The sulfur–oxygen bond lengths and the angles about the central atoms agree fairly well with experiment. The stabilization energy associated with the addition of the d orbitals was found to be a constant amount per bond (ca. 54 and 28 kcal mole^?1 in the minimal and extended bases, respectively) in hypervalent compounds. The isomer HSO was predicted to be more stable than SO₂(OH)^?, but the reverse was true for HSO₂(OH) compared to SO(OH)₂. The deprotonation energies for the acids and the hydration energies for the oxides also were computed and discussed with reference to experimental data.     

The Physical Mechanism of the Chemical Bond

First the interplay of kinetic and potential energy via the uncertainty relation is described with the aid of a variational function for the ground state of the H atom. The H ion is used to illustrate the physical mechanism of the occurrence of the chemical bond. The formation of the chemical bond can be divided into three steps: 1. the quasi-classical (electrostatic) interaction of the unchanged electronic charges of the separate atoms; 2. the interference of the atomic orbitals, which (in the case of positive interference) leads to a displacement of charge into the bonding region and to a decrease in the kinetic energy; 3. deformation of the molecular orbitals to restore the correct balance of kinetic and potential energy. In simple models, it is often sufficient to consider just the second step. A two-electron bond is not fundamentally different from a one-electron bond. In larger molecules it is possible to distinguish between long-range and short-range interatomic contributions to the chemical bond. If the former are small, i. e. in molecules with non-polar bonds, a one-electron molecular orbital theory can be justified. Finally, the possibility of describing molecules by localized bonds is discussed.     

Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF?MO?LC(LCGO) Methode. V. Bindungsbeteiligung der Inneren Elektronen des C-Atoms

Using the results of ab initio calculations, by comparison of the “1s orbital energies” of the C atom in the compounds C₆H₆, C₅H, C₃H₆ (cyclopropane), C₂H₄ as well as at the C atom itself the bond electrons were found to have a significant influence on the inner electrons. The reason for this is pointed out and an explanation is given. The connection between the bonding and this “1s orbital energy” change as well as the importance of this result for quantum-chemical “models” is discussed.     

Vibrational Spectra,Force Constants and Bonding of the Tetrafluorochlorate(III) Anion,CIF, and of CIF5

The RAMAN spectrum of RbClF₄ is reported. The square-planar structure (D_4h symmetry) of ClF in RbClF₄ is confirmed. Force constants are calculated for ClF₄, indicating that the bonding in ClF₄ is best described by the semi?empirical molecular orbital model involving mainly two delocalized p electron?pairs of the chlorine atom for the formation of two semi?ionic 3 center?4 electron p–σ bonds. A very unusual occurrence of two bending modes at a frequency higher than that of one of the stretching modes has been observed in the vibrational spectra of ClF and a possible explanation is given. The approximately square-planar part of the ClF₅ molecule is compared with ClF. The assignment of the vibrational spectra and force constants reported by BEGUN et al. for ClF₅ are confirmed.     

Photoelektronen-Spektren und Moleküleigenschaften. 133 [1, 2]. Trifluormethyldisulfan und Derivate F3CSSX (X  CF3, F,Cl, Br)

Photoelectron Spectra and Molecular Properties. 133. Trifluoromethyldisulfane and Derivates F₃CSSX (X?CF₃, F, Cl, Br) The He(I) photoelectron spectra of trifluoromethyldisulfane F₃CSSH and its derivatives F₃CSSX (X?CF₃, F, Cl, Br) are assigned by Koopmans correlations, IE = ?ε, with MNDO eigenvalues and by radical cation state comparison. Of special interest are the n/n splittings, which amount to 1.15 eV F₃C? SS? F or 0.87 eV in F₃? SS? Cl, and the dependance of which on the dihedral angle ω(XS? SX), on the SS bond length and on the acceptor effect of the F₃C substituents is discussed.     

Quantum chemistry study on B14, B,and B14H

The structure of B₁₄, B, and B₁₄H in octahedral symmetry has been investigated by ab initio calculations at the STO-3G and 4–31G levels. The relationship of molecular orbitals among them has been analyzed and it can be found that the number of valence bonding orbitals of high borane obeys the Wade rule. The similarities and difference between boron clusters and carbon clusters are also discussed. © 1994 John Wiley & Sons, Inc.     

Hartree Fock instabilities of sulfur-nitrogen ring systems: S2N2

The Hartree-Fock instablities of S₂N₂ are reported and compared with those of S₃N and S₄N. These unsaturated sulfur nitrogen planar rings are π electron rich and although the symmetry adapted HF solutions are singlet stable at the experimental bond lengths they become unstable with only a very modest increase in bond length. The broken symmetry solutions for S₂N₃, S₃N, and S₄N are of planar C_2v type with one of the nitrogens stripped of its π electrons, producing a π hole.     

Application of the Equivalent Bond Orbital Model to the C2s-Ionization Energies of Saturated Hydrocarbons

It is shown that the ab initio STO-3G treatment applied to simple saturated linear, branched and cyclic hydrocarbons, assuming standard geometries, yields orbital energies ? for their canonical orbital φ_j which correlate perfectly with the observed C_2s ionization energies I, if Koopmans' approximation is accepted. Applying the Foster-Boys localization procedure to these canonical orbitals φ_j leads to localized orbitals λμ and their corresponding Hartree-Fock matrix F_λ = (F_λ,μv). An examination of the matrix elements F_λ,μv, i.e. of the self-energies A_μ = F_λ,μμ of the localized CC- and CH-orbitals λ_μ and of the cross terms F_{λ, μv} (μ ≠ v) between them, leads to the conclusion that a satisfactory approximation should be obtained by setting A_μ = A for all μ, F_λ,μv = B if λ_μ and λ_v are vicinal and neglecting all other cross terms. The resulting model is nothing but the well-known equivalent bond orbital model of Lennard-Jones & Hall, which however can now be calibrated using the known C_2s-ionization energies of hydrocarbons. Due to the discrete structure and the wider range (∽ 8 eV) of the C_2s band systems in the photoelectron spectra of these molecules this leads to a more satisfactory parametrization than using the narrower and badly resolved C_2p band system. Comparison of calculated band positions using the calibrated model with observed C_2s-band ionization energies for a series of hydrocarbons reveals that the simple equivalent bond orbital model is better than one might have expected.     

Kristallstruktur und schwingungsspektrometrische Daten von cis-Na2[Pd(SO3)2en] · 4 H2O

Crystal Structure and Data from Vibrational Spectra of cis-Na₂[Pd(SO₃)₂en] · 4 H₂O The compound cis-Na₂[Pd(SO₃)₂en] · 4 H₂O (en = 1,2-diaminoethane) crystallizes in the orthorhombic space group Pnma with a = 623.7(2), = 1070.9(10), c = 1989.5(30) pm and Z = 4. In the [Pd(SO₃)₂en]^2? anions the trans-influence of the sulfite ligands manifests itself in long Pd? N bonds with short Pd? S distances. A set of Na⁺ ions is present in face-sharing octahedra Na(OH₂)₆⁺, forming rods [Na(OH₂)_6/2]⁺ parallel to [100]. A second set of Na⁺ ions is surrounded by two H₂O molecules and four O atoms from SO₃ ligands of two anions to form likewise octahedra with face-sharing, yielding rods [Na(OH₂)_2/2{(OSO₂)₂Pd en}_2/2]^? parallel to [100]. Comparatively low v(Pd? N)-frequencies reveal the trans-influence of the sulfite ligands also in the vibrational spectra.     

Structure and stability of Be6, Be,and Be clusters

The structure and stability of Be₆, Be, and Be clusters have been investigated at the B3LYP, B3PW91, and second‐order Møller–Plesset (MP2) levels of theory, along with the 6‐311G* basis set for neutral and cationic clusters and the 6‐311+G* basis set for anion clusters. CCSD(T)/6‐311+G* has also been used to calculate some neutral structure to find the most stable structure. Twelve Be₆, six Be, and eight Be isomers are identified. The distortion octahedron structure, pentagonal pyramids structure, and trapezoidal bipyramid structure are found to be the most stable structure on the neutral, cationic, and anionic surface, respectively. They are in agreement with the results reported previously. Natural bond orbital (NBO) analysis, molecular orbital (MO) pictures, and the nucleus independent chemical shift (NICS) values suggest aromatic of the neutral and cationic clusters and antiaromatic of the anionic cluster. The multi‐center σ bonds and delocalized π bonds play important role in the bonding of the beryllium clusters. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Dicyanmethanido- und Cyanamido-oxoanionen. Untersuchungen zum sauerstoffanalogen Charakter der C(CN)2- und NCN-Gruppen

The equivalence of the C(CN)₂- and the NCN-groups with oxygen in the series of homologous ions C(CN), N(CN), OCN^? and NOC(CN), NO causes us to postulate a more general value of this relation. Arguments for the formulation of a pseudochalkogen series C(CN)₂? NCN? O are discussed. Synthesis, structure and reactivity of some dicyanmethanido- and cyanamido-oxoanions RCOY^?, CO₂Y^2?, COY, NOY^?, NO₂Y^?, PO₃Y^3?, PO₂Y and SO₂Y^2? are described. (Y ? C(CN)₂, NCN.) The preparation of some triorganoleadacyles is reported.     

Dipole,quadrupole, octupole,and dipole–octupole polarizabilities at real and imaginary frequencies for H,HE, and H2 and the dispersion-energy coefficients for interactions between them

We have calculated certain dynamic polarizabilities (for both real and imaginary frequencies) for H, He, and H₂ and the dispersion-energy coefficients for long-range interactions between them. We have done so in a sum-over-states formalism with explicitly electron-correlated wave functions to describe the states. To be precise, we have determined the dipole (α₁), quadrupole (α₂), and octupole (α₃) polarizabilities of H and He for real frequencies (ω) in a range between zero and the first electronic-transition frequency and for imaginary frequencies (iω) on a 32-point Gauss-Legendre grid running from zero to ?ω = 20 E_h, and for H₂, we have found the dipole (α), quadrupole (C), and dipole–octupole (E) polarizability tensors for the same real and imaginary frequencies. The dispersion-energy coefficients, obtained by combining the sum-over-states for-malism for the polarizabilities with analytic integration over ω, gave values of C₆, C₈, and C₁₀ for the atom–atom systems; C, C, C, C, and C for the atom–diatom systems; and C₆, C and C for the H₂? H₂ system. Nearly all the results are considered to be more reliable than those hitherto published and some have been obtained for the first time, e.g., C(iω), E(ω), and E(iω) for H₂ and C, C, and C for the H? H₂ system. © 1993 John Wiley & Sons, Inc.     

Metal–metal bond energies in Mo2, Mo2Cl,and Mo2(O2CH)4

Previous attempts to determine the strengths of multiple metal-metal bonds are reviewed. Estimates of 73 and 97 kcal/mole for the Mo? Mo bond energies in Mo₂Cl and Mo₂(O₂CH)₄, respectively, are obtained by combining the known experimental bond energy in Mo₂ (96.5 ± 5 kcal/mole) with the results of SCF-Xα-SW calculations on Mo₂, Mo₂Cl, and Mo₂(O₂CH)₄. Possible errors in the estimates are discussed. It is noted that the quadruple bonds in the complexes are predicted stronger per component than the sextuple bond in the diatomic.     

Reaction mechanism of cysteine proteases model compound HSH with diketone inhibitor PhCOCOCH3−nXn, (X = F,Cl, n = 0, 1, 2)

Caspases are a family of cysteine proteases, which play a crucial role in apoptosis and inflammation. The reaction mechanisms involving the cysteine proteases model compound HSH with diketone (PhCOCOCH_3‐nX_n, (X = F, Cl, n = 0, 1, 2) substrate have been studied using B3LYP/6‐311+G* level of density functional theory method. The harmonic vibrational frequencies were calculated at the same level of theory used for the characterization of stationary points and zero‐point vibrational energy corrections. The condensed Fukui functions have been calculated to find the favorable reactive site for the electrophilic (f), nucleophilic (f), and radical (f) attacks in the reactants. The transition states were connected with reactants, intermediate, and products, and the minimum energy paths have been confirmed through intrinsic reaction coordinate calculation. The potential energy barrier between each step of the reactions has been calculated to find the most favorable reaction path. The binding nature of cysteine model compound with diketone substrate has been studied through the interaction energies, bond lengths, electron density, natural bond orbital, and atoms in molecules theory analysis. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Schwingungsspektren und Kraftkonstanten der Übergangsreihe O2PF—S2PF— S2P(CH3)

Vibration spectra and force constants of the series O₂PF — S₂PF — S₂P(CH₃). The vibrational spectra of OSPF, S₂PF, S₂PF(CH₃) and S₂P(CN) are reported and discussed with O₂PF and S₂P(CH₃). On the basis of a simplified valence-force-field the force constants are calculated and the bonding relations are discussed. In the ions, f PF is lower than in corresponding molecules. The ionic charge is distributed over nearly all atoms of the ions.     

Study of chemical bonding in H2 and HF molecules: Wave function and density functional theory (DFT) parameters approach

Balint Kurti's Fourier grid Hamiltonian method is employed to obtain the molecular wave function and equilibrium bond length for H₂ and HF molecules. The density functional theory parameter, namely, the chemical hardness (η) value, was determined for some diatomic hydride molecules using this wave function and the results are found to be in good agreement with the values obtained from the ab initio HF–SCF method. A new formula for chemical hardness (η=1/2Dr, where D is the proportionality constant and r is the internuclear distance) is introduced in binding energy and change of hardness equations to determine the chemical hardness and chemical potential values for different bond lengths. The binding energy and change of hardness values are calculated for H₂, H, H, HF, HF⁺, and HF⁻ molecules and the bond stability is discussed. Finally, the concept of an atom in a molecule is examined in the context of DFT parameters and comparison is made between an atom in a molecule and the isolated atom. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 662–669, 2000     

19F-NMR-spektroskopischer Nachweis und statistische Untersuchung zur Bildung der gemischten Clusteranionen [(Mo6ICl)F]2−, n = 0–7, und Darstellung von (TBA)2[(Mo6I)F]

¹⁹F NMR Spectroscopic Evidence and Calculation of the Statistical Formation of Mixed Cluster Anions [(Mo₆I Cl )F ]^2?, n = 0–7, and Preparation of (TBA)₂[(Mo₆I )F ] The octa-μ₃-iodo-hexafluoro-hexamolybdate(2?)ion [(Mo₆I)F]^2? is prepared for the first time. The system of the 21 innersphere mixed clusters (Mo₆ICl)⁴⁺, n = 0–7 is formed by exchange of innersphere bound Clⁱ against outersphere bound I^a on tempering solid [(Mo₆Cl)I] at 400°C. Prolonged tempering leads to increasing average n values of the mixture, which is converted into the tetrabutylammonium salt (TBA)₂[(Mo₆ICl)F]. Using increments of chemical shifts and integral peak intensities the 54 ¹⁹F-nmr signals of the 21 species (compound n = 8 is absent) are assigned and confirmed by the 2 D-¹⁹F/¹⁹F-COSY spectrum. From the measured intensities the distribution of the different compounds is determined and proves significant deviation from statistical occupation, revealing the preference of isomers with iodine atoms occupying edges of the innersphere cube and discrimination of those sharing diagonals of the faces. Moreover all compounds with n = 3 and 4 are present overaverage in comparison to the others.