Spin-Free configuration-interaction study of molecules using single-parameter alternat molecular orbitals

A procedure is outlined for a programmable spin-free configuration-interaction (CI ) study in molecules using single-parameter alternant molecular orbitals for generating various configurations. The configurations were chosen to form bases for the irreducible representation {2^N/2–2, 1^2S} of the general linear group GL(n). Using a transformation to biorthogonal space the CI matrix elements of a spin-free Hamiltonian were generated. The procedure has been used to obtain the π-electron energies for the ^3,1A_g and ^3,1B_u states of cis- and trans-butadiene.     

Energy expressions for atomic configurations in the L–S coupling scheme

The matrix elements of the spin-free Hamiltonian between two atomic configuration state functions (CSF 'S ) in the L–S coupling scheme are expressed in terms of the atomic integrals F^k's and G^k's. Using these general expressions, the matrix elements have been obtained for all the atomic configurations with three valence electrons that have not been solved so far by earlier methods. The scope for applying this new approach to obtain the Auger line energies and the promotion energies of metals that involve more than two partially filled shells is indicated. The energy expressions for some of the relevant configurations are tabulated.     

Synthesis Characterization and Crystal Structure of 2-(3,4,5-trimethoxyphenyl)-1-(4-fluorophenyl)-4,5-diphenyl-1H-imidazole

The title compound, C₃₀H₂₅FN₂O₃, was prepared from the four-component one-pot condensation reaction and the product crystallized using dimethylformamide. The structure of the compound was established by elemental analysis, Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), UV-Visible, and single-crystal X-ray diffraction. The compound crystallizes in the triclinic crystal system with the space group Pī, with unit cell parameters a = 10.286(2) Å, b = 11.795(2) Å, c = 21.331(4) Å, α = 100.270(3)°, β = 90.093(3)°, γ = 90.062(3)°, and Z = 4. The crystal and molecular structure of the title molecule is stabilized by intra-molecular interactions of types C–H···N and C–H···O.     

Synthesis,Crystal Structure,and Characterization of New 2,4,5-Triphenyl Imidazole: 4,5-Diphenyl-2-(3,4,5-trimethoxyphenyl)-1H-imidazole

The substituted triarylimidazole, C₂₄H₂₂N₂O₃, was prepared from the three-component one-pot condensation reaction and the product was crystallized by using dimethylformamide. The structure of the compound was confirmed by elemental analysis, FT-IR, thermogravimetric analysis (TGA), UV-Visible and single-crystal X-ray diffraction. The compound crystallizes in the monoclinic crystal system in the space group P2₁/c with unit cell parameters a = 10.509(3) Å, b = 18.748(5) Å, c = 22.016(6) Å, β = 90.844(5)°, and Z = 8. The crystal structure of the compound was stabilized by the inter-molecular interactions of types N–H???N, C–H???O, and C–H???N, and intra-molecular interactions of the type C–H???O. The structure also involves C–H???π interactions.     

Preparation and Characterization of Modified Cellulose Fiber-Reinforced Polyvinyl Alcohol/Polypyrrolidone Hybrid Film Composites

In this work, cellulose was modified by using 2-(trifluromethyl)benzoylchloride by base catalyzed reaction. Modification of cellulose was confirmed by IR studies. The biodegradable composite films were developed by a film casting method using modified cellulose with poly(vinyl alcohol) and polypyrrolidone in different compositions. Film composites showed good biodegradability. Better barrier and mechanical properties showed by film composites as the percentage of modified cellulose increased. This indicates the importance of modified cellulose as a reinforcing agent. After analyzing these properties of film composites we came to the conclusion that, these biocomposites can be used for membrane and packaging applications.     

Subduction coefficients for 〈2N/2–S, 12S〉 ↓ 〈2, 1〉 ⊗ 〈2, 1〉 of U(n) ↓ U(n1) ⊗ U(n2)

The determination of the subduction coefficients for states of the unitary group U(n) under the restrictions U(n) ↓ U(n₁) ? U(n₂) have been considered for the spin free states of many electron systems. Using the transformation properties of the tensor basis spanning the irreducible representation 〈2^N/2–S, 1^2S〉 of U(n) under the permutations of electron coordinates, a simple programmable procedure has been developed for the determination of these coefficients. The procedure has been illustrated using a simple example.     

Synthesis,characterization, single crystal X-ray diffraction and DFT studies of ethyl 5-methyl-1-phenyl-1H-pyrazole-4-carboxylate

The present study describes the synthesis, spectroscopic, and single crystal X-ray structural analysis of ethyl 5-methyl-1-phenyl-1H-pyrazole-4-carboxylate. The pyrazole ester of formula [C₁₃H₁₄N₂O₂] was prepared from the three-component one-pot condensation reaction of ethyl acetoacetate, N,N-dimethyldimethoxymethanamine, and phenyl hydrazine. The product was crystallized by using ethanol as solvent. The structure of the compound was confirmed by elemental analysis, Fourier transforms infrared (IR), thermogravimetric analysis, UV-visible (UV-Vis), ¹H NMR, and single-crystal X-ray diffraction studies. The gas-phase molecular geometry and the electronic structure-property of the molecule were calculated at the density functional theory. The frontier molecular orbitals, theoretical UV-Vis, and IR stretching vibrations were also reported. The compound crystallizes in the monoclinic system with the space group P2₁/c and Z = 4. The unit cell parameters are a = 12.141(3) Å, b = 13.934(4) Å, c = 7.2777(18) Å, and β = 97.816(14)⁰. The structure is stabilized by an intermolecular interaction of type C-H···O and the structure also involves C-H···π interactions.     

Synthesis,Crystal Structure and Characterization of (Z)-2-N′-hydroxyisonicotinamidine

The compound (Z)-2-N′-hydroxyisonicotinamidine, (2) was synthesized and characterized by ¹H NMR, FT-IR, FAB-Mass, UV-Visible Spectra, and elemental Analysis. Its molecular structure was solved by single crystal X-ray diffraction method. The title molecule, C₆H₇N₃O is crystallized in the orthorhombic crystal system with the space group Pna2₁ and with unit cell parameters a = 12.5664(8) Å, b = 8.8622(6) Å, c = 5.7953(4) Å, α = 90°, β = 90°, γ = 90°, and Z = 4. The molecular and crystal structure of the title molecule is stabilized by an intramolecular interaction of the type N—H···O, and the intermolecular interactions of types N—H···N and O—H···N.