A CNDO/2 localised orbital study of dipole moments of sila- and germa-ethylenes

CNDO/2 calculations have been performed to predict dipole moments for silaethylenes, with either Slater of Burns atomic orbitals, and for germaethylenes with Burns orbitals only. Trends on replacement of two hydrogen atoms at either end of the double bond by fluorine are similar in both sets for the silaethylenes and in accordance with expectation, but an anomalous trend is observed for fluorination of the carbon in germaethylenes.Localised orbitals have been examined to seek an explanation for this anomaly. In all cases the trends are in the unexpected sense for the π orbitals but in the expected sense for the others taken together and for most of these individually. The anomaly with the germaethylenes thus appears to be associated with the relative magnitudes of these opposing trends, where donation of electrons via the π bond to the germanium atom outweighs the accumulation of charge around the fluorine atoms attached to the carbon.     

The electronic structure of molecules by a many-body approach : II. Ionization potentials one-electron properties of pyridine and phosphoridine

The valence ionization potential (IPs) of pyridine and phosphoridine are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the Hartree-Fock approximation. For pyridine the order of the first three IPs is a₂(π), a₁(n), b₁(π), but the IPs of the a₂ and a₁ orbitals are so close together that they have to be regarded as identical in binding energy, which is also concluded from experiment. Whereas for pyridine the ordering of the IPs calculated in the HF approximation is incorrect, it is correct for phosphoridine. For this latter molecule the first three ionization potentials are due to ionization from the b₁(π), a₂(π), and a₁(n) orbitals. Several one-electron properties are calculated and compared with experimental and other theoretical data. The localized molecular orbitals are discussed as well.     

Heteroorganic derivatives of furan. 69. Analysis of electron structures of 2-furyltriethoxysilane and 1′-(2-furyl)-silatrane by the MO LCAO CNDO/2 method

The electron structures (charges on the atoms, additive populations of the atomic orbitals, and multiplicities of the chemical bonds) of 2-furyltriethoxysilane, 1-(2-furyl)silatrane, and the starting triethanolamine were analyzed by the MO LCAO CNDO/2 method taking into account the d orbitals. The localized molecular orbitals and the hybrid atomic orbitals that form them were constructed by the Polak projection method.see [1–3] for Communications 66–68.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1314–1321, October, 1989.     

DFT and CI Studies of Electronic Structure and Photoionization of Sc,Ti, V,Cr, and Co Tris-β-diketonate Complexes

Orbital structure calculations were performed in the density functional theory (DFT) approximation for neutral complexes of Sc, Ti, V, Cr, and Co tris-β-diketonates; for the first three compounds, the structures of the ground ionic states and ionization energies were calculated in the CI approximation with decomposition on the orbitals of DFT. The sequence of the highest occupied orbitals found by this procedure coincides with the order of bands in the PES spectrum, while in the SCF-HF ab initio method, it does not. After the electron removal, all orbitals are stabilized by about 4.5 eV; for the vanadium complex, the removal of one d electron leads to the greatest stabilization of the remaining occupied orbital, which is essentially a d orbital. In CI calculations, using the DFT orbitals for decomposition does not lead to significantly better agreement with experiment when compared to the single-determinantal approximation and to the CI method with orbitals of the ab initio approximation.Original Russian Text Copyright © 2004 by I. S. Osmushko and V. I. Vovna__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 783–791, September–October, 2004.     

Many body perturbation methods in a discrete orbital basis: Application to CH4 and Ne

Discrete basis many body perturbation calculations have been performed on Ne and CH₄ in a basis which mimics Boys' oscillator orbitals. The L-shell correlation energy obtained for Ne was –0.347 which is to be compared with the best numerical basis many body perturbation result of –0.336 ± 0.01 obtained by Lee, Dutta and Das and the best variational result of –0.322 obtained by Sasaki and Yoshimine. An analysis of 3- and 4-body corrections (pair-pair repulsions) and the effects of many body EPV renormalization for both localized and canonical SCF orbitals is presented.     

On the Presumptive Similarity of Kohn–Sham and Brueckner Orbitals

For states of many-electron systems disclosing various degrees of quasidegeneracy, we have carried out comparative studies of Kohn–Sham orbitals (KSO) generated for several xc-potentials, Brueckner orbitals (BO) represented by the Brueckner-coupled cluster orbitals, and Hartree–Fock (HF) orbitals by means of criteria directly related to the orbital structure which are based on relative distance indices for various pairs of equidimensional subspaces defined by the KSO and BO basis sets. We have found that both for weak and strong quasidegeneracy there are systems for which the KSO–BO distances are larger than the BO–HF ones. For strongly quasidegenerate states it is found that the distance indices are the largest for hybrid potentials, and that the subspaces spanned by KSOs are closer to those spanned by HF orbitals than by BOs. Hence, our results do not support the recently formulated expectations concerning the similarity of Brueckner orbitals and Kohn–Sham orbitals, including those corresponding to purely local exchange-correlation potentials.     

Unrestricted CNDO-MO calculations. II. MnO 4 2− and CrO 4 3−

The electronic structures of the tetrahedral molecule ions MnO ₄ ^2– and CrO ₄ ^3– have been investigated within an unrestricted CNDO-MO approximation [Theoret. Chim. Acta (Berl.)20, 317 (1971)]. Calculations assuming the unpaired electron occupies the 3a ₁, 2e, and 4t2 molecular orbitals indicate that the 3a ₁ and2e orbitals have similar orbital energies and that the 4t ₂ orbital is at a higher energy. The experimentally indicated2e orbital for the unpaired electron is obtained with expanded O^1– type atomic orbitals for oxygen and valence metal orbitals of the expanded 3d and plus one ion 4p types. The metal 4s orbitals must be held to the neutral atom type. The optimum valence orbitals above with a slightly contracted 4s type metal orbitals yield the minimum total energy and places the unpaired electron in the 3a ₁ orbital. Since the contracted 4s metal orbital produces results that are not in agreement with experimental data, the method used apparently does not adequately take into account the increased electron-electron repulsions that contracted 4s orbitals produce.     

Electronic structure of Li− and F− calculated directly in momentum space

Summary A self-consistent field method is applied to compute directly in momentum space the electronic structures of the bound anions Li^– and F^– at the Hartree-Fock level. The convergence towards the Hartree-Fock limit, starting from STO-3G, 3–21G, 3–21+G and 6–311+G AO's, is stable and monotonous. Substantial improvement in the quality of the anion orbitals is noted already after one iteration. Particularly interesting is the efficiency with which the method modifies and improves the shape of the trial functions.     

Energies of Association of Carbenium and Silylium Cations with Oxygen-Containing Molecules

The energies of association of Me_nH_3-n X⁺ cations (n = 0-3) with molecules of oxygen-containing bases (water, methanol, dimethyl ether) were calculated by the B3LYP/6-31G(d) method. These energies decrease with an increase in the number n of methyl groups at the X atom; this trend is more pronounced for X = C, which is due to a lower degree of charge transfer in the cation from the occupied orbitals of the methyl group to the vacant orbital of X in the case of X = Si. An increase in the association energy with an increase in the number of methyl substituents at the oxygen atom is due to an increase in the energy level of lone electron pairs of oxygen upon methyl substitution. As a result, the energy gap between the electronic levels of the unoccupied orbital of the cation and orbitals of the oxygen lone electron pairs becomes narrower, which makes the interaction between the unoccupied and occupied orbitals more efficient.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 5, 2005, pp. 754–756.Original Russian Text Copyright © 2005 by Ignat’ev, Kochina.     

Direct metal–carbon bonding in symmetric bis(C–H) agostic nickel(i) complexes

Agostic interactions are examples of σ-type interactions, typically resulting from interactions between C–H σ-bonds with empty transition metal d orbitals. Such interactions often reflect the first step in transition metal-catalysed C–H activation processes and thus are of critical importance in understanding and controlling σ bond activation chemistries. Herein, we report on the unusual electronic structure of linear electron-rich d⁹ Ni(i) complexes with symmetric bis(C–H) agostic interactions. A combination of Ni K edge and L edge XAS with supporting TD-DFT/DFT calculations reveals an unconventional covalent agostic interaction with limited contributions from the valence Ni 3d orbitals. The agostic interaction is driven via the empty Ni 4p orbitals. The surprisingly strong Ni 4p-derived agostic interaction is dominated by σ contributions with minor π contributions. The resulting ligand–metal donation occurs directly along the C–Ni bond axis, reflecting a novel mode of bis-agostic bonding.

Symmetric Ni(i) agostic complexes reveal an unusual mode of bonding that is dominated by direct carbon-to-metal charge transfer.     

Characteristic features of excess charge localization in stepwise three-electron reduction of Ni-octaethylporphin

We have investigated the electronic structure of Ni-octaethylporphin anions (NiOEP) by¹H NMR. We have established that in (NiOEP)–, the excess electron is localized in the orbital of the nickel, while the second and third extra electrons in (NiOEP)^2- and (NiOEP)^3- are localized in the orbitals of the ligand. We conclude that spin density is transferred between the d orbitals of the Ni and the orbitals of the porphyrin ligand.Institute of Molecular and Atomic Physics, Academy of Sciences of Belarus, 70 Prospekt Frantsiska Skoriny, Minsk 220072, Belarus. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 6, pp. 345–347, November–December, 1996. Original article submitted February 22, 1996.     

One electron orbitals intrinsic to the reduced hamiltonian

One electron orbitals are determined from the reduced hamiltonian by a simple one-step diagonalization. These reduced hamiltonian orbitals (RHO's) are uniquely determined and virtual orbitals obtained in this procedure are on a par with filled orbitals. These RHO's appear well suited for CI calculations. Minimum basis set calculations are presented for H₂O and compared with similar SCF studies.     

Stereochemistry of eight-membered heterocycles. 4. Dipole moments of cyclic acetals with two planar fragments

An additive system of polarities in 12H-dibenzo(dinaphtho)[d,g][1,3]dioxocins is proposed, and alkyl—oxygen and phenyl—oxygen group dipole moments in these compounds were determined. The stereospecific relation of the polarity of the C _sp 2-O bond to the mutual orientation of p orbitals of unshared electron pairs of oxygen atoms and orbitals of the aromatic ring is shown.A. N. Butlerov Scientific-Research Chemical Institute, V. I. Ul'yanov-Lenin Kazan State University, Kazan 420008. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 607–612, March, 1992.     

Covalency in actinide(iv) hexachlorides in relation to the chlorine K-edge X-ray absorption structure

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinide^IV hexachlorides, [AnCl₆]²⁻ (An = Th–Pu), is calculated with relativistic multiconfiguration wavefunction theory (WFT). Of particular focus is a 3-peak feature emerging from U toward Pu, and its assignment in terms of donation bonding to the An 5f vs. 6d shells. With or without spin–orbit coupling, the calculated and previously measured XANES spectra are in excellent agreement with respect to relative peak positions, relative peak intensities, and peak assignments. Metal–ligand bonding analyses from WFT and Kohn–Sham theory (KST) predict comparable An 5f and 6d covalency from U to Np and Pu. Although some frontier molecular orbitals in the KST calculations display increasing An 5f–Cl 3p mixing from Th to Pu, because of energetic stabilization of 5f relative to the Cl 3p combinations of the matching symmetry, increasing hybridization is neither seen in the WFT natural orbitals, nor is it reflected in the calculated bond orders. The appearance of the pre-edge peaks from U to Pu and their relative intensities are rationalized simply by the energetic separation of transitions to 6d t_2gversus transitions to weakly-bonded and strongly stabilized a_2u, t_2u and t_1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn–Sham molecular orbitals.

Chlorine K-edge XANES of An(iv) hexachlorides, calculated with multiconfiguration wavefunction theory, is interpreted in terms of similar metal–ligand covalency along the An = Th–Pu series.     

Influence of the symmetry of frontier orbitals on the height of the barriers to redox reactions of stable free radicals

An analysis of the symmetry of frontier molecular orbitals makes it possible to determine the molecular orbitals which take part in the redox conversions of stable radicals of various classes. In agreement with experimental data, it has been shown that the lowest barrier to reactions involving the electron disproportionation of stable phenoxyl, nitroxide, and verdazyl radicals is realized only when high-lying excited MO's participate. Conversely, the redox reaction between free verdazyl and phenoxyl radicals is allowed for the doublet ground states of the radicals, but the analogous reaction between verdazyl and nitroxide radicals requires the participation of excited molecular orbitals.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 1, pp. 86–91, January–February, 1987.     

Induced representations of point groups and symmetry of localized orbitals

Complete representation tables are constructed for crystallographic symmetry point-group representations induced by local subgroups. We discuss the applicability of induced representations of point groups to the analysis of symmetry and to the construction of orbitals localized on atoms and bonds in a molecule. As an example, canonical and localized orbitals in tetrahedral hydroxyanion MnO₄ ^– are considered.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 6, pp. 641–650, December, 1986.     

Ionization of fluoromethanes: CHF3 and CF4. A Greens̀ function study and an (e, 2e) spectroscopic investigation

A Green's function study has been performed on CHF₃ and CF₄. Theoretical results are compared with (e 2e) spectral data. Previous assignment of valence-shell orbitals is confirmed and a splitting of the innermost ionizations over many shake-up terms in experimental and theoretical results on both molecules.     

The use of population localised orbitals to interpret molecular orbital calculations

An efficient and general method is derived to calculate population localised molecular orbitals (LMO's) from a given SCF eigenvector matrix, by reduction to an eigenvalue problem. Applications to both localised molecules (NH₃ and C₂H₂) and delocalised ones (B₂H₆, C₆H₆ and butadiene) are discussed in some detail. It is shown that unequal occupation of atomic energy levels leads to non-orthogonal LMO's. The consequences of non-orthogonal atomic hybrid orbitals are discussed, formulas for their overlap in terms of atomic occupation numbers are derived and it is shown that the occupation numbers are connected to LMO atomic orbital coefficients by various sum rules.     

Calculation of Multicenter Nuclear Attraction and Electron Repulsion Integrals over Slater Orbitals by Fourier Transform Method Using Gegenbauer Polynomials

In this study, using complete orthonormal sets of exponential type orbitals (ETOs), a single closed analytical relation is derived for a large number of different expansions of overlap integrals over Slater type orbitals (STOs) with the same screening parameters in terms of Gegenbauer coefficients. The general formula obtained for the overlap integrals is utilized for the evaluation of multicenter nuclear attraction and electron repulsion integrals appearing in the Hartree–Fock–Roothaan equations for molecules. The formulas given in this study for the evaluation of these multicenter integrals show good rate of convergence and great numerical stability under wide range of quantum numbers, scaling parameters of STOs and internuclear distances.     

Hulthén and slater type 2d functions in some excited configurations of sulphur and phosphorus

It is shown that a substantial energy improvement is gained by the variational use of Hulthén orbitals, instead of single Slater orbitals, in the 3d shells of some excited configurations of sulphur and phosphorus. The energies obtained are close to those attained with two-term Slater functions. In some cases the radial distribution functions from Hulthén orbitals are as good an approximation of SCF radial distributions as those from two-term Slater orbitals. Single term 2d functions with only one parameter are found to give almost identical energies and radial distribution functions as those obtained from two-parameter Hulthén orbitals. It is shown that the relationship between one-term 2d orbitals and Hulthén orbitals gives a method of enforcing nuclear cusp conditions on the former with little effect on the energy.