Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations

Matrix elements of unitary group generators between spin-adapted antisymmetric states are shown to be proportional to spin matrix elements of so-called “line-up” permutations. The proportionality factor is given explicitly as a simple function of the orbital occupation numbers. If one bases the theory on ordered orbital products, the line-up permutations are given a priori. The final formulas have a very simple structure; this is a direct consequence of the fact that the spin functions have been taken to be geminally antisymmetric.     

Spherically symmetric axial Gaussian lobe 3d and 4f orbitals

The axial Gaussian lobe orbital (AGLO ) representations of 3d and 4f orbitals proposed by LeRouzo and Silvi have been angularly optimized to ensure spherical symmetry of filled 3d and 4f shells. The functions have been tested on the hydrogen atom in the presence of high quality s and p basis sets and found to provide excellent minimal Gaussian representations of polarization functions. Exact orbital degeneracy is not obtained within each shell, however. Tabulated values are given to allow arbitrary scaling of the 3d and 4f lobe mimic orbitals.     

Calculations of XPS spectra for oxyanions and related compounds by the discrete variational-Xα method

Calculations of molecular-orbital energies and x-ray photoelectron spectra have been carried out for the third-row oxyanions, transition-metal oxyanions, SiO₂ and TiO₂, by the discrete variational-Xα cluster method. The calculated orbital energies are consistent with those determined from the XPS experiments. Theoretical XPS line shapes with Gaussian are generally in good agreement with the observed spectra. However, underestimation has been found for the photopeak intensities in the low-binding-energy region of TiO₂. The discrepancy is partially attributed to the use of inaccurate photoionization cross-section for the Ti3d orbital.     

Second and third-order nonlinear optical properties and molecular parameters of azo chromophores: semiempirical analysis

The static and frequency dependent average polarizability (〈α〉), first- and second-hyperpolarizabilities (〈β〉 and 〈γ〉) and highest occupied molecular orbital (HOMO) and lowest occupied molecular orbital (LUMO) energies of nonlinear optical chromophores with nitro acceptors 1–5 have been investigated by using the Austin Model 1 (AM1), Modified Neglect of Diatomic Overlap (MNDO), MNDO with d orbitals (MNDO-d), Parameterization Method 3 (PM3), Recife Model 1 (RM1) and Parameterization Method 6 (PM6) methods within a time-dependent Hartree–Fock (TDHF) approaches. The electronic properties of chromophores 1–5 have been reported by employing two-state model calculated at Zerner's spectroscopic version of the Intermediate Neglect of Differential Overlap singly excited configuration interaction (ZINDO/S-SCI) method. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained by using molecular frontier orbital energies. The 〈α〉, 〈β〉, 〈γ〉 HOMO, LUMO energies, η and χ parameters have been investigated with respect to the choice of different semiempirical methods.     

14N nuclear quadrupole resonance study of substituted anilines and prediction of in vitro activity of sulfanilamides

¹⁴N nuclear quadrupole resonance (NQR) spectra of 22 monosubstituted anilines are reported and analyzed in the framework of the Townes and Dailey theory. Satisfactory correlations of the NQR data with both the Hammett σ parameters and the in vitro biological activities of the corresponding sulfanilamides have been found. The results obtained suggest that the nitrogen lone-pair orbital is more sensitive than the nitrogen–carbon sigma orbital is to substituent effects.     

Charge location and fragmentation under electron impact. IV—the behaviour under electron impact of some N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds

The ionization potentials of a series of N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds have been determined. The nature of the highest occupied orbital of the molecules and the use of empirical rules to rationalize the variations in the ionization potentials are discussed. The changes in the fragmentation patterns are related to the different low ionization potential site(s) in each molecule. The occurrence of various rearrangement ions are discussed on a similar basis.     

Molecular structure, vibrational spectra and HOMO, LUMO analysis of yohimbine hydrochloride by density functional theory and ab initio Hartree-Fock calculations

Yohimbine hydrochloride (YHCl) is an aphrodisiac and promoted for erectile dysfunction, weight loss and depression. The optimized geometry, total energy, potential energy surface and vibrational wavenumbers of yohimbine hydrochloride have been determined using ab initio, Hartree–Fock (HF) and density functional theory (DFT/B3LYP) method with 6-311++G(d,p) basis set. A complete vibrational assignment is provided for the observed Raman and IR spectra of YHCl. The UV absorption spectrum was examined in ethanol solvent and compared with the calculated one in gas phase as well as in solvent environment (polarizable continuum model, PCM) using TD-DFT/6-31G basis set. These methods are proposed as a tool to be applied in the structural characterization of YHCl. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) with frontier orbital gap are presented.     

Cyclic Acetals. Structural Analysis of 1,3-Dioxepine and Related Compounds

The He(I) PE spectra of 1,3-dioxepine ( 1 ) and the related bicyclic acetals 1,3,7,7-tetramethyl-2,11-dioxabicyclo[4.41]undeca-3,5-dien-10-one ( 2 ) and 1,3,7,7-tetramethyl-10-methylidene-2,11-dioxabicyclo[4.4.1]undeca-3,5-diene ( 3 ) have been recorded and analyzed. Interpretation of the PE data indicate strong orbital interactions between the diene and acetal moieties in 1 . Different conformations have been evaluated by a joint MMP2 molecular mechanics and ab initio molecular orbital analysis, which shows 1 to prefer a slightly boat-shaped conformation with the diene part being planar and the CH₂ group placed considerably out-of-plane. The bicyclic acetals 2 and 3 show a frontier orbital picture similar to 1 superimposed with the characteristics of the C?O and C?C groups, respectively. The crystal structure of the keto-acetal 2 was determined by an X-ray analysis.     

Theory of lone pairs. II. A moment analysis of localized molecular orbitals in ten-electron hydrides

Ab initio double-zeta quality molecular orbital calculations have been carried out on an extensive series of ten-electron hydrides. The Edmiston–Ruedenberg energy-localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms of dipole moments, contour plots, and a simplified model for the orbital density involving analysis of the first and second moments. The simplified moment analysis model may be easily visualized in terms of threedimensional geometric objects, spheres, and ellipsoids. The model summarizes the information on the effective functional distribution inherent in the more detailed orbital contour plots in a clear and concise manner.     

The synthesis and the magnetic properties of perfluoroalkyl organometallic chromium(III) complexes containing n-substituted salicylaldimines and other ligands

Perfluoroalkyl derivatives of Cr^III containing tetradentate or bidentate ligands derived from N-substituted salicylaldimines have been prepared by the reaction between the ligands and dihaloperfluoroalkylchromium acetonitrile complexes. The compounds show considerable solid-state and solution stability. Their magnetic moments are all greater than the spin-only value for a d³ system, and a molecular orbital bonding scheme is suggested to explain this observation.     

Structure and energetic of Bn (n = 2–12) clusters: Electronic structure calculations

The electronic and geometric structures, total and binding energies, first and second energy differences, harmonic frequencies, point symmetries, and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps of small and neutral B_n (n = 2–12) clusters have been investigated using density functional theory (DFT), B3LYP with 6‐311++G(d,p) basis set. Linear, planar, convex, quasi‐planar, three‐dimensional (3D) cage, and open‐cage structures have been found. None of the lowest energy structures and their isomers has an inner atom; i.e., all the atoms are positioned at the surface. Within this size range, the planar and quasi‐planar (convex) structures have the lowest energies. The first and the second energy differences are used to obtain the most stable sizes. A simple growth path is also discussed with the studied sizes and isomers. The results have been compared with previously available theoretical and experimental works. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Theoretical Study of the trans-3,6-Dimethoxy-1,2,4-trioxane Molecule

The molecule of trans-3,6-dimethoxy-1,2,4-trioxane has been studied by the semiempirical molecular orbital AM1 and PM3 methods. The numerical results of the structural study have been analyzed in terms of several stereoelectronic effects and compared with available experimental data. Theoretical predictions derived from both methods are in a good agreement with each other.     

Isoelectronic smoothing of energy levels and calculations on the 2sns 1 S→2smp 1 P 0 transitions in the beryllium isoelectronic sequence

Oscillator strengths for 2sns ¹ S2smp ¹ P ⁰ transitions of several ions in the beryllium isoelectronic sequence (BeI- CrXXI) have been computed and analyzed. The quantum defect orbital method, including core-polarization effects through an effective dipole-moment transition operator, has been followed. Comparisons are made between various theoretical and experimental data and those predicted here. It is shown that the quantum defect orbital formalism adequately describes transitions in these atomic systems.     

An ab initio and molecular mechanical investigation of ureas and amide derivatives

Ab initio molecular orbital theory with the 6-31G* basis set has been used to investigate the geometries and preferred conformations for urea, derivatives of urea, and a few complicated amide derivatives. The results from the ab initio calculations provide insight into the gas-phase rotational barrier about the C? N bond and have been used to generate parameters for the MM2(87) molecular mechanics program. When applicable, theoretical structures are compared with corresponding previously reported experimental geometries. Urea is predicted to be nonplanar with pyramidal amino groups.     

Semiempirical study of electronic and bonding properties of iron silicide clusters

Summary Molecular orbital calculations of iron, silicon, and iron silicide clusters have been carried out using the UHF-MINDO/SR method. The nature of the bonding in these compounds has been investigated by analyzing the importance of bonding indexes and diatomic components of the total energy. It has been found that in iron silicide the strongest bond is formed between Fe-Si and that it arises mainly as the result ofsp-sp type orbital interactions. Althoughd orbitals show very little overlap withs-p orbitals, they do contribute significantly to bonding through electrostatic type diatomic interactions. By means of a detailed analysis ofsp, andd orbitals and total density of states (DOS) of Fe₇Si₇, Si₇Fe₇, Fe₁₅, and Si₁₇ clusters, the present calculations have permitted us to explain the origin of the iron silicide UPS experimental peaks.     

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

Configuration Interaction (CI) calculations on the ground ²P state of boron atom are presented using a wave function expansion constructed with L‐S eigenfunction configurations of s‐, p‐, and d‐Slater orbitals. Two procedures of optimization of the orbital exponents have been investigated. First, CI(SD) calculations including few types of configurations and full optimization of the orbital exponents led to the energy ?24.63704575 a.u. Second, full‐CI (FCI) calculations including a large number of configuration types using a fixed set of orbital exponents for all configurations gave ?24.63405222 a.u. using the basis [4s3p2d] and 2157 configurations, and to an improved result of ?24.64013999 a.u. for 3957 configurations and a [5s4p3d] basis. This last result is better than earlier calculations of Schaefer and Harris (Phys Rev 1968, 167, 67), and compares well with the recent ones from Froese Fischer and Bunge (personal communication). In addition, using the same wave functions, CI calculations of the boron isoelectronic ion C⁺ have been performed obtaining an energy of ?37.41027598 a.u. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals

The original idea of the model applied to HeH⁺ excited states is: One electron occupies a diatomic orbital similar to the HeH⁺⁺ ground state 1s function. The other electron occupies an orbital which can be represented by a linear combination of functions similar to H ₂ ⁺ excited state functions. One or two screening parameters are variationally optimized to compensate for the smallness of the one-electron basis.CI calculations have been performed for five excited HeH⁺ states covering a wide range of internuclear distances. The CI wave functions have been submitted to a natural spin orbital analysis. The strongly occupied NSOs are compared with the original model functions.Dedicated to Professor Hermann Hartmann on occasion of his 65th birthday on May 4th, 1979.     

Synthesis,mesomorphic, photophysical and computational studies of new achiral four-ring unsymmetrical bent-core mesogens and their Copper(II) complexes

New achiral four-ring unsymmetrical bent-core mesogens derived from 2,5-dihydroxybenzaldehyde and their copper(II) complexes have been synthesised as a new design with an imine and ester linkage. These new bent-core molecules resemble hockey-stick shape, which possesses 4-n-alkyloxy chain (4-n-hexyloxy and 4-n-decyloxy) at one end and methyl or methoxy group at the other end of the molecule. The synthesis, spectroscopic characterisation, phase transition temperature and characterisation of phase behaviour are reported. The bent-core molecules exhibited monotropic nematic and smectic A phase depending on the terminal chain length. Interestingly, copper(II) complexes of bent-core molecules displayed monotropic nematic phase. This is the first report on copper(II) complexes of bent-core molecules that exhibited nematic phase. The four-ring bent-core molecule exhibited fluorescence with large stoke shift. The density functional theory calculations of bent-core molecules and their copper(II) complexes are carried out using Gaussian 09 program at B3LYP level to obtain the stable molecular conformation, dipole moment, highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) energies and bending angle of the compounds. The natural atomic charges and electronic configurations of the atoms of free ligands as well as the complexes have been evaluated.