4 resultados para 2-methyl-3-methoxy-4-phenylbutanoic acid

em Bucknell University Digital Commons - Pensilvania - USA


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The title compound, C(34)H(24)Cl(4)N(4)O(8)S, is a linear penta-cyclic system formed of two substituted benzoxazinyl groups fused to 2-n-butyl-tetra-hydro-thio-phene. The oxazine ring, which is fused to the n-butyl-substituted side of the thio-phene ring, is in a boat conformation. The other fused oxazine ring and the tetra-hydro-thiene ring are each in an envelope conformation. The bridgehead C atom alpha to both the S and N atoms forms the flap of each envelope. This results in a twist of the penta-cyclic system such that the dihedral angle between the terminal dichloro-benzene rings is 82.92 (8)°. In the crystal, inversion-related mol-ecules form a weakly hydrogen-bonded dimer, with two C-H⋯O inter-actions between an H atom on the oxazine ring and an amide O atom. Additionally, C-H⋯O inter-actions occur between an H atom on a screw-related nitro-benzene ring and an O atom on the nitro-benzene ring of one mol-ecule. One of the Cl atoms and the butyl group are disordered over two sets of sites with occupancy ratios of 0.94 (2):0.06 (2) and 0.624 (4):0.376 (4), respectively.

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The Gaussian-2, Gaussian-3, complete basis set- (CBS-) QB3, and CBS-APNO methods have been used to calculate ΔH° and ΔG° values for neutral clusters of water, (H2O)n, where n = 2−6. The structures are similar to those determined from experiment and from previous high-level calculations. The thermodynamic calculations by the G2, G3, and CBS-APNO methods compare well against the estimated MP2(CBS) limit. The cyclic pentamer and hexamer structures release the most heat per hydrogen bond formed of any of the clusters. While the cage and prism forms of the hexamer are the lowest energy structures at very low temperatures, as temperature is increased the cyclic structure is favored. The free energies of cluster formation at different temperatures reveal interesting insights, the most striking being that the cyclic trimer, cyclic tetramer, and cyclic pentamer, like the dimer, should be detectable in the lower troposphere. We predict water dimer concentrations of 9 × 1014 molecules/cm3, water trimer concentrations of 2.6 × 1012 molecules/cm3, tetramer concentrations of approximately 5.8 × 1011 molecules/cm3, and pentamer concentrations of approximately 3.5 × 1010 molecules/cm3 in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.

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The Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO methods have been used to calculate geometries of neutral clusters of water, (H2O)n, where n = 2–6. The structures are in excellent agreement with those determined from experiment and those predicted from previous high-level calculations. These methods also provide excellent thermochemical predictions for water clusters, and thus can be used with confidence in evaluating the structures and thermochemistry of water clusters.

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Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.