A theoretical conformational study on the structural parameters involved in the ring strain of exo-unsaturated four-membered heterocycles,Y = CCH2CH2X

The effect of ring-puckering angle on the structural parameters (bond lengths and angles) involved in the ring strain of a series of four-membered heterocycles (1–16) was theoretically demonstrated by using the ab initio methods MP2 and HF, and the DFT methods PBE1PBE, B3LYP, SVWN5 with 6-31+G(d,p) as basis set. The results revealed that the bonds within the ring (C–X and C–C) are the most sensitive to puckering angle changes. The variation of the C–X and C=Y bond lengths as function of puckering angle are determined by a balance between the 1,3 repulsive interactions and the electronic nature of the heteroatoms X and Y. Particularly, for azetidines and phosphetanes, the C–X and C=Y bond lengths exhibit a major increase at axial conformations. In general, the C–C bond length decreases with the puckering angle for all heterocycles. While the heteroatom–H bonds (in the ring skeleton) are very sensitive to geometric changes, exhibiting an increasing behaviour for equatorial conformations and a decreasing behaviour for axial conformations highly puckered (? > ?20°). The C–X–C angle decreases monotonically with the puckering angle, increasing the Baeyer strain on the studied molecules. Finally, all methods predicted a similar behaviour for the studied parameters as function of the puckering angle, although some smaller differences in the predictions of their respective values, especially at HF level, were observed.     

CNDO/2 and INDO all-valence-electron calculations on the dipole moment of iodine compounds

An application of the semi-empirical CNDO/2 and INDO methods to calculate the molecular dipole moment of iodine compounds has been made with all-valence electron scheme. Equilibrium geometries are obtained using experimental bond lengths and the various semi-empirical parameters required inscf-mo scheme are obtained from atomic Hartree-Fock calculations and by comparison withab initio calculations. Bothsp andspd valence basis sets are used.     

Dipole ordering and ionic conductivity in NASICON-Type Na<Subscript>3</Subscript>Cr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> structures

The aspects of structure, dipole ordering, and ionic conductivity of the Na₃Cr₂(PO₄)₃ crystal with the four polymorphic phases (α, α', β, and γ) have been investigated. The features of the α-Na₃Cr₂(PO₄)₃ crystal structure and its dipole ordering and relaxation polarization in the low-temperature α and α' phases have been refined. The occurrence of Na₃Cr₂(PO₄)₃ dipole ordering in the α and α' phases and high ionic conductivity in the β and γ phases is attributed to the structural changes in the rhombohedral [Me₂(PO₄)₃]^–3_3∞ crystal frame upon phase transformations α → α', α' → β, and β → γ. A model for explaining the dipole ordering and ionic conductivity phenomena in Na₃Cr₂(PO₄)₃ is proposed.     

Structural,elastic and thermodynamic properties of tetragonal and orthorhombic polymorphs of Sr2GeN2: an ab initio investigation

The structural, elastic and thermodynamic properties of the α (tetragonal) and β (orthorhombic) polymorphs of the Sr₂GeN₂ compound have been examined in detail using ab initio density functional theory pseudopotential plane-wave calculations. Apart the structural properties at the ambient conditions, all present reported results are predicted for the first time. The calculated equilibrium lattice parameters and inter-atomic bond-lengths of the considered polymorphs are in good agreement with the available experimental data. It is found that α-Sr₂GeN₂ is energetically more stable than β-Sr₂GeN₂. The two examined polymorphs are very similar in their crystal structures and have almost identical local environments. The single-crystal and polycrystalline elastic parameters and related properties – including elastic constants, bulk, shear and Young’s moduli, Poisson’s ratio, anisotropy indexes, Pugh’s criterion, elastic wave velocities and Debye temperature – have been predicted. Temperature and pressure dependence of some macroscopic properties – including the unit-cell volume, bulk modulus, volume thermal expansion coefficient, heat capacity and Debye temperature – have been evaluated using ab initio calculations combined with the quasi-harmonic Debye model.     

Structural and vibrational properties of C36 and its oligomers (C36) M = 2, 3, 4 by tight-binding molecular dynamics

Non-orthogonal tight-binding molecular-dynamics is employed to calculate structural and vibrational properties of C₃₆ and its oligomers (C₃₆) _{M = 2, 3, 4} . The lowest energy configuration of the C ₃₆ cage is confirmed to have D _6h symmetry. For the dimer, too, the D _2h structure reported in the literature is found. The vibrational spectrum is identified with the power spectrum of the displacement autocorrelation function. Additional vibrational properties are extracted from the dynamical matrix. For the monomer, fair agreement with available ab initio calculations is achieved, with comparatively smaller deviations in the Raman-frequencies than for published semi-empirical calculations. The features of the vibrational modes are correlated with the structural properties of the oligomers. Received 24 November 2000 and Received in final form 24 August 2001     

Measurements of N2-broadening and -shifting parameters of the water vapor spectral lines in the second hexad region

The water vapor line broadening and shifting in the ν₁+ν₂+ν₃ band induced by nitrogen pressure are measured with Bruker IFS 125 HR FTIR spectrometer at the spectral resolution of 0.01 cm⁻¹ for the line with upper states angular momentum up to 11. Line contour parameters are calculated using a semi-empirical approach extended by the use of empirical data to determine some fitting model parameters. We use the complete set of high accuracy vibration-rotation dipole transition moments calculated for all possible transitions using wavefunctions determined from variational nuclear motion calculations and an ab initio dipole moment surface. Calculated values of line contour parameters are in a good agreement with observed parameters.     

Temperature dependence of ratio between dielectric anisotropy and order parameter in fluorinated nematic liquid crystals

Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.     

Temperature dependence of ratio between dielectric anisotropy and order parameter in fluorinated nematic liquid crystals

Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.     

Dispersion energy constants C 6(A,B), dipole oscillator strength sums and refractivities for Li,N, O,H2, N2, O2, NH3, H2O,NO and N2O

Accurate values for the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C ₆(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H₂, N₂, O₂, NH₃, H₂O, NO, and N₂O. The calculations have been carried out by employing dipole oscillator strength distributions for these species that have been constructed (except in the case of H) by using discrete oscillator strength, photo-absorption, and high energy inelastic scattering data and by requiring the distributions to reproduce the Thomas-Reiche-Kuhn sum rule and, in the case of the molecules, available accurate refractivity and dispersion measurements for the relevant dilute gases. These oscillator strength distributions were also used to evaluate the refractivity R(λ), as a function of wavelength λ in the visible and ultra-violet region below the ultra-violet absorption thresholds, and the dipole oscillator strength sums S _-2l , l = 1, 2, …, 7, for each atom and molecule. The calculated values of R(λ) provide refractivities for wavelengths, especially in the ultra-violet region, for which accurate experimental data are often not available. The accurate results for C ₆(A, B) and for various dipole oscillator strength sums are used to make self-consistent tests of the adequacy of (1) the C ₆(A, A) bounds provided by Padé approximant methods and (2) various semi-empirical formulae for C ₆(A, B). Some problems that can arise in using other procedures to evaluate the S _-2l and C ₆(A, B) are discussed briefly.     

Concentration effects on absolute depolarized Rayleigh ratios and effective polarizability derivatives of CS2 in liquid mixtures with CCl4

Experimental results are reported from polarized and depolarized Raman intensity measurements in combination with absolute depolarized Rayleigh ratios of liquid CS₂ in CCl₄ mixtures at 25°C. Using a calibrated Raman spectrometer it was possible to determine the concentration dependence of g ₂ · γ² _eff of CS₂. Intensity measurements of the polarized and depolarized Raman spectra of the symmetric stretching vibration of CS₂ under the same conditions allowed the determination of the effective values of α₀₁ and γ₀₁ respectively to the normal mode Σ⁺ _g in the liquid phase. In the neat liquid, α₀₁ = 0·19 ų and γ₀₁ = 0·22 ų. In mixtures with CCl₄ the values of α₀₁ decrease at lower CS₂ concentration whereas the values of γ₀₁ increase. These results indicate that the isotropic induced dipole field is increasingly cancelled as the environment becomes more isotropic while the anisotropic part is amplified in CCl₄. A report is also given of an anomalous concentration behaviour of the intensity of the combination mode v ₁ + v ₂-v ₂ on the low frequency side of the v ₁ transition which is amplified relative to the intensity of the v ₁ mode as the CCl₄ concentration increases.     

A simulation of the mixed spin 3–spin 3/2 ferrimagnetic Ising model

The mixed spin 3–spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals ?4 ≤ D_A/J ≤ 8 and ?4 ≤ D_B/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through D_A/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected D_A/J values (?2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α′ = 0, β = 0.125, β′ = 0.875 and γ = γ′ = 1.75).     

Calculations of molecular multipole electric moments of a series of exo-insaturated four-membered heterocycles,Y = CCH2CH2X

The influence of ring puckering angle on the multipole moments of sixteen four-membered heterocycles (1-16) was theoretically estimated using MP2 and different DFTs in combination with the 6-31+G(d,p) basis set. To obtain an accurate evaluation, CCSD/cc-pVDZ level and, the MP2 and PBE1PBE methods in combination with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were performed on the planar geometries of 1-16. In general, the DFT and MP2 approaches provided an identical dependence of the electrical properties with the puckering angle for 1-16. Quantitatively, the quality of the level of theory and basis sets affects significant the predictions of the multipole moments, in particular for the heterocycles containing C=O and C=S bonds. Convergence basis sets within the MP2 and PBE1PBE approximations are reached in the dipole moment calculations when the aug-cc-pVTZ basis set is used, while the quadrupole and octupole moment computations require a larger basis set than aug-cc-pVTZ. On the other hand, the multipole moments showed a strong dependence with the molecular geometry and the nature of the carbon-heteroatom bonds. Specifically, the C-X bond determines the behavior of the μ(?), θ(?) and ?(?) functions, while the C=Y bond plays an important role in the magnitude of the studied properties.     

Conformational and Structural Analysis of 6‐(4‐Methoxy‐phenyl)‐1,5,7a‐triphenyl‐tetrahydro‐imidazo[1,5‐b][1,2,4]oxadiazol‐2‐one

Abstract

The cis stereochemistry of 6‐(4‐methoxy‐phenyl)‐1,5,7a‐triphenyl‐tetrahydro‐imidazo[1,5‐b][1,2,4]oxadiazol‐2‐one was studied by use of a PM3 semi‐empirical quantum mechanical model, and x‐ray crystallographic analysis. It crystallizes in the monoclinic space group P2 ₁ /n with a = 10.812(1) Å, b = 16.464(2) Å, c = 13.379(1) Å, α = 90.00°, β = 98.39(1)°, γ = 90.00°, V = 2356.07(4) Å³, Z = 4, D _calc = 1.3067 g cm^?3, F(0 0 0) = 976.41, and μ = 0.086 mm^?1. The structure was solved by direct methods and refined to R = 0.066 for 1257 independent reflections [I > 4σ (I)]. The results from x‐ray diffraction were seen to be generally consistent with the results from previously reported spectroscopic investigations, beside theoretical calculations, except for conformations of five‐membered fused heterocycles. Two inter‐ and intramolecular weak interactions in addition to carbon atoms (C1 and C3) with different chiralities were found in the structure. The conformational study was performed by randomly scanning the potential energy surface belonging to the title compound with respect to selected torsion angles.     

Oscillator strengths for the Schumann-Runge bands of 16O2

Experimental oscillator strengths are presented for the (1-0)-(22-0) and (3-1)-(17-1) Schumann-Runge bands of ¹⁶O₂. A wavelength resolution of ~0.04 Å enabled individual rotational lines to be studied and an equivalent width data analysis method was used. The now established decrease in equivalent band oscillator strength with increased rotation is observed. The mean band oscillator strengths of this work for the (1-0)-(12-0) bands are in excellent agreement with recent ultra-high resolution absolute measurements, and the oscillator strength density is found to be continuous across the dissociation limit. The dipole moment deduced from the present oscillator strengths agrees well with recent ab initio and semi-empirical determinations.     

Theoretical analysis on structural,spectroscopic, and electronic properties of some 2-aminobenzimidazole complexes by using PBE1PBE,B3LYP,and HF methods

The molecular geometry, vibrational frequencies, gauge including atomic orbital (GIAO) ¹H and ¹³C chemical shift values of ABZ-TNB [ABZ-TNB: 2-aminobenzimidazole-trinitrobenzene] and ABZ-PA [ABZ-PA: 2-aminobenzimidazole-picric acid] in the ground state were calculated by using density functionals (B3LYP and PBE1PBE) and Hartree-Fock (HF) methods with the 6–31 ++ G(d,p) basis set. Furthermore, the electronic spectrum of title complexes was calculated with the time dependent DFT levels (TD-PBE1PBE and TD-B3LYP) and HF (TD-HF) method starting from the ground state geometry optimized in the gas phase. A detailed assignment of vibrational spectra was made on the basis of the calculated potential energy distribution (PED). Total static dipole moment (μ), the mean polarizability (〈α〉), the anisotropy of the polarizability (Δα), the mean first-order hyperpolarizability (〈β〉), highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, chemical hardness (η) and electronegativity (χ) of ABZ-TNB and ABZ-PA complexes were also investigated with quantum chemical calculations. Additionally, data obtained from quantum chemical calculations were compared with the experimental ones.     

Susceptibility and electric dipole in metal C 60 compounds

The permanent electric dipole moment of metal atom-C₆₀ compounds is measured. A column (alkali) and a row (transition metals) of the periodic table are systematically investigated. Most of the experimental results are obtained at high temperature when the atom is mobile on the C₆₀ cage. For a given example (NaC₆₀), the dipole moment is also measured by a different method at low temperature and both results are consistent. For alkali, the results are compared to ab initio calculations. A good agreement is obtained, both for absolute values and for the evolution of the bonding in the alkali column. For transition metals, the relative values of the dipole moments are in qualitative agreement with the ionic character of the compounds.     

Synthesis,phase stability and oxide ion conductivity of Ce(IV)–Cd(II) double substituted bismuth vanadate

Bi₄V₂O_11-δ has been doped with Ce and Cd to study double substitution. The system with various dopant concentrations (0.07 ≤ x ≤ 0.30) was prepared by the standard solid-state reaction method. The correlation between the polymorphism and oxide ion performance was well investigated as a function of temperature and composition with the help of thermal analysis, X-ray diffraction (XRD) and AC impedance spectroscopy. From XRD results it is seen that the high oxide ion conducting tetragonal γ-phase is stabilized for x = 0.17. For the compositions x ≤ 0.10, monoclinic α-phase is retained at room temperature with clear evidence for two successive phase transitions α ? β and β ? γ. For x = 0.13, β ? γ phase transition is seen. However, the existence of order–disorder, γ' ? γ transition was confirmed for x = 0.17. It is seen that the highest low-temperature ionic conductivity at 320 °C is 3.19 × 10^?4 S cm^?1 which was observed for x = 0.17.     

An ab initio calculation of the vibrational energies and transition moments of HSOH

We report new ab initio potential energy and dipole moment surfaces for the electronic ground state of HSOH, calculated by the CCSD(T) method (coupled cluster theory with single and double substitutions and a perturbative treatment of connected triple excitations) with augmented correlation-consistent basis sets up to quadruple-zeta quality, aug-cc-pV(Q+d)Z. The energy range covered extends up to 20 000 cm⁻¹ above equilibrium. Parameterized analytical functions have been fitted through the ab initio points. Based on the analytical potential energy and dipole moment surfaces obtained, vibrational term values and transition moments have been calculated by means of the variational program TROVE. The theoretical term values for the fundamental levels ν_SH (SH-stretch) and ν_OH (OH-stretch), the intensity ratio of the corresponding fundamental bands, and the torsional splitting in the vibrational ground state are in good agreement with experiment. This is evidence for the high quality of the potential energy surface. The theoretical results underline the importance of vibrational averaging, and they allow us to explain extensive perturbations recently found experimentally in the SH-stretch fundamental band of HSOH.     

Re-examination of the NDDO approximation and introduction of a new model beyond it

The NDDO (neglect of diatomic differential overlap) approximation, a widely used basis for many semi-empirical molecular orbital (MO) approaches, is re-examined based on non-empirical frozen-core calculations on small molecules. An improvement going beyond the NDDO approximation is proposed. Our study shows that under the NDDO approximation, when the remaining non-DDO-type two-electron repulsion integrals (TERIs) are calculated using the basis set from the Löwdin orthogonalization of the valence atomic orbitals, the resulting total energies are much higher than those from the corresponding frozen-core ab initio calculations. On the other hand, when the remaining non-DDO TERIs are calculated using non-orthogonal valence atomic orbitals (similar to the Roby model), for most of the molecules calculated, the total energies are significantly lower than those from the corresponding ab initio calculations. Furthermore, we also find that for some molecules, the total energies thus calculated are higher than the corresponding ab initio results. The nonsystematic variation of the absolute errors in the total energy calculations is due to the fact that the core-electron and the electron-electron interactions are not treated in a balanced way in the NDDO approximation. A new model, which overcomes the deficiencies in the NDDO model, is proposed. In this model, a first-order correction term is added to the electron-electron Coulomb interactions, thereby improving the balance between the core-electron and the electron-electron interactions. Non-empirical test calculations show that the total energies from the new model are consistently higher than those from the ab initio calculation but closer to the ab initio results. We expect that the proposed new model would be useful in developing new high-quality semi-empirical MO approaches.     

Potential use of small basis set on the calculations of electronic properties of some four-membered heterocycles: a conformational study

The potential use of small basis sets upon a low level of theory was studied on the calculations of electronic properties (dipole moment, static polarisability and static hyperpolarisabilities) of a series of 16 four-membered heterocycles with an exocyclic double bond at the position 3 (1–16). First, the calculations were performed within the Hartree–Fock (HF) approximation using 6-31G, 6-31G(d,p) and 6-31+G(d,p) as basis sets for the different conformational states of each molecule, and the results obtained were compared with the MP2/6-31+G(d,p) results reported. In the second place, in order to know the real potential of HF calculations, these were compared with those calculated using larger approaches such as MP2/6-311+G(d,p), MP2/aug-cc-pVDZ, CCS/6-311+G(d,p), CCS/aug-cc-pVDZ, CCS/aug-cc-pVTZ, CCSD/6-31+G(d) and CCSD/cc-pVDZ, taken into account only the planar and equilibrium geometries of each molecules. The HF approaches permit us to obtain a good qualitative representation of the dipole moment as a function of puckering angle in comparison with MP2, CCS and CCSD levels for all tested molecules. However, only HF/6-31+G(d,p) provides quantitative values of dipole moment for the heterocycles 1, 5 and 13 in comparison with MP2, CCS and CCSD levels. On the other hand, the polarisability and hyperpolarisabilities were quite sensitive to the quality of level of theory and basis sets. In particular, HF/6-31+G(d,p) predicted a representative approximation of alpha for the molecule 16 in comparison with larger methods as MP2/aug-cc-pVDZ, CCS/aug-cc-pVDZ and CCS/aug-cc-pVTZ, while a detailed analysis showed that HF can be used in the calculation of alpha for the molecules 3, 7, 11 and 15, but it requires the use of extended basis sets. Also, HF/6-31+G(d,p) predicted values of beta very similar to those calculated at the MP2 and CCSD levels used, for the planar and equilibrium geometry of the molecules 10 and 14. Furthermore, HF/6-31+G(d,p) described a representative dependence of this property with the puckering angle for the heterocycles 9, 10 and 14, compared with the MP2 curves.