Structural Characterization of Chemical Species in Solution by a Theoretical Analysis of XANES Spectra

A theoretical analysis method using a discrete variational X (DV-X) molecular orbital (MO) calculation, based on electron transition from an inner orbital to an unoccupied orbital, is introduced to analyze X-ray absorption near-edge structure (XANES) spectra in a lower energy region below the X-ray absorption edge. The computational procedure is described in detail and the evaluation of an obtained result is also explained. Applications of this method are presented for Cu(II) ions in liquid ammonia, macrocyclic Cu(II) complex in aqueous solution, and Al(III) ions in aqueous solution.     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

SCF perturbation theory for unimolecular reactions

A CNDO/2 SCF perturbation theory is presented for interpreting the form of CNDO/2 potential energy surfaces of unimolecular reactions. The analysis is performed by calculating the energy change E arising from a distortion of the molecular geometry along the reaction coordinate. E is decomposed into different perturbational contributions which are appropriate for an interpretation of the perturbation energy E. Moreover, E is resolved into energy parts arising from a single occupied orbital and contributions due to pairwise orbital interactions. In this way one evaluates numerically how the form of the occupied and unoccupied orbitals determines the magnitude of E. If the distortion occurs along a definite symmetry coordinate, group-theoretical arguments can be applied to discuss the magnitude of characteristic components of the perturbation energy. The SCF perturbation theory is used to analyze the isomerization of ethylene, cis-2-butene and cis-2-butenenitrile.This work was partially supported by Nato-Grant No. 1072     

Geometry optimization inab initio SCF calculations

The floating orbital geometry optimization (FOGO) described previously [1, 2] for atoms without polarized inner-shell electrons, is extended to the general case. Instead of the Hellmann-Feynman force a special gradient is calculated analytically and utilized in a variable metric procedure simultaneously with the ordinary energy gradient. Test calculations on a sample of 12 molecules were performed to check the efficiency of the method. The geometries obtained are better than those obtained with the corresponding double-zeta basis set. The most striking results, however, are excellent dipole moments.     

Ab initio calculation of some low-lying electronic excited states of methane

The energies of some low-lying electronic excited states of methane are calculated by using wave functions built up in terms of plane waves modulated by multicenter Gaussian factors. The wave functions of the various states are evaluated by a two steps iterative process. In the first step, each excited orbital is determined while keeping all other rigid; in the second, rearrangement effects are introduced. Final results are in good agreement with experimental data and allow to enhance an assignement hypothesis for the first electronic transitions.     

Binding of α-hydroxy-β-amino acid inhibitors to methionine aminopeptidase. The performance of two types of scoring functions

The binding mode of a recently described set of -hydroxy--amino acid inhibitors of methionine aminopeptidase type 2 is suggested in the present work. The binding mode is supported by analysis of published structures of transition state analogues co-crystallised with E. coli methionine aminopeptidase and by a comparison of molecular interaction fields calculated using GRID for E. coli and human methionine aminopeptidase. Based on the suggested binding mode two types of scoring functions have been evaluated and compared. These are the commercially available consensus score, CScore, and scoring of the ligands employing energies calculated using the Merck Molecular Force Field (MMFF). Enriched subsets of ligands were obtained when using CScore, but these scores could not be used to assess the relative affinities of individual compounds. Although still not sufficiently accurate for reliable predictive purposes, an improved correlation was obtained between structure and affinity using a combined force field energy including contributions from solvation and conformational energy penalty for binding.     

Conformational behaviour and molecular similarity of some β1-adrenergic ligands

Summary The conformational behaviour of a series of aryloxypropanolamines was investigated by means of a new procedure which allows the sampling of the molecular torsional surface in a very efficient way. The combination of such a procedure with the standard molecular mechanics algorithms for the geometry optimization gives, as a result, the definition of a powerful computational scheme for the detailed analysis of the potential energy surface of complex molecules. The compounds studied show a remarkable tendency to form intramolecular hydrogen bonds, which seem to play a key role in determining the lowest energy structures. The indices of molecular similarity proposed by Carbó, computed for the most stable conformers, do not account for differences between diastereoisomers, and, as a consequence, can hardly be used to attempt a structure-activity correlation.     

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V _xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V _xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.Dedicated to Professor H. Hartmann on the occasion of his 65th birthday.     

Calculation of vertical ionization potentials of ketene by perturbation corrections to Koopmans' theorem

The vertical ionization potentials of ketene are calculated by perturbation corrections to Koopmans' theorem. The present results are compared with those from the pseudonatural orbital coupled electron pair approach and the experimental values.     

The influence of vibronic interactions on the chiroptical spectra of dissymmetric pseudo tetragonal metal complexes

The influence of vibronic interactions on the chiroptical spectra associated with a threesome of nearly degenerate electronic excited states in a dissymmetric molecular system is examined on a formal theoretical model. The model considers two vibrational modes to be effective in promoting pseudo Jahn-Teller (PJT) type interactions between the three closely spaced electronic excited states. Formal expressions are developed for the rotatory strengths of individual vibronic levels derived from the coupled electronic states. Two mode (vibrational)-three state (electronic) vibronic Hamiltonians are constructed (basis set size, 63–108, depending upon interaction parameters used) and diagonalized for a large number of different parameter sets representative of various vibronic coupling strengths, electronic energy level spacings, oscillator (vibrational mode) frequencies, and electronic rotatory strengths. Diagonalization of these vibronic Hamiltonians yields vibronic wave functions and energies which are then used to calculate rotatory strength spectra for the model system. The calculated results demonstrate the profound influence which vibronic interactions of the PJT type may have on the sign patterns and intensity distributions within the rotatory strength spectrum associated with a set of nearly degenerate electronic states. The implication of these results for the interpretation of circular dichroism spectra of chiral transition metal complexes with pseudo tetragonal symmetry are discussed.     

Chiroptical properties of cyclic α-diketones

The chiroptical properties of dissymmetric cyclopentanedione, 3-methylcyclopentane-1,2-dione, and glyoxal structures are examined on a theoretical model in which the electronic wave functions are obtained from semiempirical all-valence-shell molecular orbital calculations. Excited state wave functions are constructed in the virtual orbital-configuration interaction approximation. The rotatory strengths, dipole strengths, oscillator strengths, and dissymmetry factors of the lower energy singletsinglet transitions in eleven cyclopentanedione and ten glyoxal structures are calculated and reported. The signs and relative magnitudes of the rotatory strengths associated with the two lowest energy singlet transitions are found to be extraordinarily sensitive to ring substituents and ring conformational parameters as well as to inherent chirality within the -dicarbonyl moiety of the cyclopentanedione structures. Vicinal effects play a significant role in determining the signs and magnitudes of the electronic rotatory strengths. For a given configurational isomer of an inherently dissymmetric -dicarbonyl group (i.e., P or M), the signs of the electronic rotatory strength of the lowest energy transition in glyoxal and in cyclopentanedione are opposite. This result suggests that cisoid glyoxal structures may not be useful models for the chiroptical properties of cyclic -diketone systems with cisoid dicarbonyl moieties.This work was supported in part by a grant from the Petroleum Research Fund administered by the American Chemical Society, the Camille and Henry Dreyfus Foundation, and a computing grant from the University of Virginia Computer Science Center.     

Gas chromatographic and IR spectroscopic characteristics of tri- and tetramethylcyclohexenyl butenyl ketones

Infrared spectroscopic characteristics and gas chromatographic retention indices of tri- and tetramethylcyclohexenyl butenyl ketones were determined at different temperatures of analysis. Thermodynamic characteristics of sorption on the apolar stationary phase were calculated. The sorption characteristics of tri- and tetramethylcyclohexenyl butenyl ketones show that under conditions of capillary gas chromatography these compounds are retained due to the dispersive energy. It was shown by FTIR spectroscopy that the formation of conjugation systems of double bonds is responsible for the higher retention of the -isomers compared with that of the -isomers. The shortening of the distance between the carbonyl and trimethylcyclohexenyl groups was found to be accompanied by a decrease in the retention of the isomeric compounds.     

MNDO calculations on diazirines

The MNDO molecular orbital method gives good agreement between experimental geometries and, when available, heats of formation of diazirines. MNDO and ab initio calculations have been performed on a novel intermediate, methylenediazirine, proposed in a reaction of 3-chloro-3-methyl-diazirine. The relation of this intermediate to its diazo-isomer, its dimer and the products of the reaction are discussed on the basis of MNDO calculations.     

Semiempirical studies of core-electron binding energy shifts

The inner-core binding-energy shifts (BEs) of boron and carbon atoms in various chemical environments were studied by the semiempirical Self-Consistent Charge Molecular Orbital (SCC MO) method. The calculations are based on the initial ground state electrostatic potential model. The main feature of our approach is the empirical treatment of the coefficient relating BEs with the orbital populations of the host atom and the Madelung energy term. These adjustable parameters absorb a large portion of relaxation energy. The so obtained results are in good agreement with experimental data. They are better than earlier CNDO/2 results obtained by using either ground state or relaxation potential models. Present results indicate that semiempirical methods like SCC MO are able to account for changes in BE(1s) with a fair accuracy although the inner-shell electrons are not explicitly considered in the actual calculations.     

Ab initio studies of the protonation of CO,N2 and NO+: Calculation of the minimum energy reaction paths

Ab initio molecular orbital calculations employing a 4-31G basis set have been used to study the minimum energy paths for the formation of HCO⁺, COH⁺, and HCOH²⁺ from CO by protonation. The protonation of N₂ to give NNH⁺ and HNNH²⁺ and of NO⁺ to form HNO²⁺ and NOH²⁺ have also been investigated. All species formed have linear equilibrium geometries and the minimum energy path for approach of the proton is along the line-of-centers of the heavy atoms. Energy barriers to the formation of the various species are given, where appropriate, and changes in geometry, ordering of molecular orbitals and orbital occupancy are discussed.     

Reactivity of pyrrole pigments. Part 9 MINDO/3 calculations on dipyrrolic partial models of bile pigments

The applicability of the MINDO/3 method is evaluated for calculations on dipyrrolic partial structures of bile pigments. It is shown that this method cannot be used for an accurate conformational analysis. However, when applying the frontier orbital model for reactivity parameters, a good picture of the HOMO and the LUMO distribution can be obtained in this type of molecules.

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Reaktivität von Pyrrolpigmenten, 9. Mitt. MINDO/3-Rechnungen von dipyrrolischen Partialmodellen von Gallenpigmenten

Zusammenfassung Es werden die Einsatzmöglichkeiten von MINDO/3 für den Fall dipyrrolischer Partialstrukturen der Gallenpigmente aufgezeigt. Die Methode ist für eine genaue Konformationsanalyse nicht geeignet. Unter Verwendung der Reaktionsparameter des Frontier-Orbital-Modells läßt sich jedoch ein gutes Bild der HOMO- und LUMO-Verteilung für diesen Verbindungstyp gewinnen.

     

Improving numerical integration through basis set expansion

Calculations are presented to assess a theorem presented by S.F. Boys [(1969) Proc. R. Soc. A. 309:195], regarding the accuracy of numerical integration in quantum chemical calculations. The theorem states that the error due to numerical integration can be made proportional to the error due to basis set truncation, and thus goes to zero in the limit of a complete basis. We test this theorem on the hydrogen atom, showing that with a solution-spanning basis, the numerically exact orbital energy can indeed be calculated with a small number of integration points. Moreover, tests for H and H₂⁺ demonstrate that even when only a near-complete basis is employed, Boys Theorem can significantly reduce integration error. However, for other systems, like the oxygen atom and the CO₂ molecule, the theorem yields no advantage for some occupied orbitals. It is concluded that the theorem would be most useful for calculations that demand large basis sets.     

Bonding criteria for diatomic molecular orbitals and inter-relations among them

Bonding criteria for molecular orbitals in diatomic molecules are discussed. An orbital force criterion is shown to have several conceptual and practical advantages, providing a basis for the investigation of inter-relations among many of the commonly employed criteria.It is found that interconsistency among those criteria is guaranteed, within the framework of Koopmans' Theorem, if the orbital energies are monotonic in the range (R _e, ).The application of the orbital force criterion to the second row homonuclear diatomics exhibits reasonable chemical trends concerning the valence-shell orbitals, as well as indications of a slightly antibonding nature of the inner orbitals.Based on a section of a thesis to be submitted by Y.T. to the Senate of the Technion-Israel Institute of Technology, in partial fulfilment of the requirements for the D.Sc. degree     

Calculations of the electronic structures of cage molecules using free-electron orbitals as a basis

A non-empirical molecular orbital method, particularly suitable for calculations on cage-like molecules, is described. The method uses as basis functions the set of free-electron functions which are the solutions of Schrödinger's equation for an electron confined between two concentric, spherical potential energy barriers. Application of the theory to the SCF calculation of the energies of the delocalized electrons in benzene and tetrasulphur tetranitride shows that the model is capable of interpreting the properties of such systems. However, it does highlight a difficulty in the calculation of excited state energies with one-centre models which appears to be largely unrecognized.Extension of the method to a consideration of all the valence electrons, using P₄ as an example, reveals problems the origin of which is an inadequate treatment of the core electrons. It is suggested that these problems may best be dealt with by use of a suitable pseudo potential.