35 resultados para Energy levels (Quantum mechanics)


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Variation calculations of the vibration–rotation energy levels of many isotopomers of HCN are reported, for J=0, 1, and 2, extending up to approximately 8 quanta of each of the stretching vibrations and 14 quanta of the bending mode. The force field, which is represented as a polynomial expansion in Morse coordinates for the bond stretches and even powers of the angle bend, has been refined by least squares to fit simultaneously all observed data on the Σ and Π state vibrational energies, and the Σ state rotational constants, for both HCN and DCN. The observed vibrational energies are fitted to roughly ±0.5 cm−1, and the rotational constants to roughly ±0.0001 cm−1. The force field has been used to predict the vibration rotation spectra of many isotopomers of HCN up to 25 000 cm−1. The results are consistent with the axis‐switching assignments of some weak overtone bands reported recently by Jonas, Yang, and Wodtke, and they also fit and provide the assignment for recent observations by Romanini and Lehmann of very weak absorption bands above 20 000 cm−1.

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High-resolution vibration-rotation spectra of monofluoroacetylene are reported for many bands in the region 1700 to 7500 cm−1. The spectra were observed on Nicolet 7199 and Bruker IFS 120 Fourier spectrometers, with resolutions of about 0.06 and 0.003 cm−1, respectively. About 130 bands have been observed in this region, of which about 80 have been rotationally analyzed. The assignment of vibrational labels to the higher energy levels is complicated by the effects of strong Fermi resonances, and many weak localized rotational resonances are observed.

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In this work preliminary results are reported on an extensive vibrational analysis of the molecules HCCX and DCCX with X = F and Cl, in which a number of anharmonic resonances are analysed. The importance of quartic anharmonic resonances in these molecular types is reported involving the effective constants K1244 and K1255, and these are related to the corresponding resonances in acetylene and its isotopomers. The correct analysis of Fermi resonances and quartic anharmonic resonances is important not only in reproducing the high overtone energy levels, but also in fitting the observed rotational constants, and in determining the αr constants and hence the equilibrium rotational constants. In this paper we revise our recent analysis of the equilibrium structure of HCCF in the light of these effects.

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A program has been developed to calculate the energy levels and corresponding wavefunctions for a two‐dimensional anharmonic potential surface of at least C2v symmetry. This program has been employed to explain the high resolution splittings observed in the far infrared spectrum of 2,5‐dihydrofuran. The magnitude of the cross term connecting the ring‐twisting and ring‐puckering modes of 2,5‐dihydrofuran is sufficiently large to be significant. The potential surface determined also suggests that the ring‐twisting mode may be slightly anharmonic.

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Rovibrational energy levels, transition frequencies, and linestrengths are computed variationally for the sulfur hydrides D2S and HDS, using ab initio potential energy and dipole surfaces. Wave-numbers for the pure rotational transitions agree to within 0.2 cm−1 of the experimental lines. For the fundamental vibrational transitions, the band origins for D2S are 860.4, 1900.6, and 1912.0 cm−1 for ν2, ν1, and ν3, respectively, compared with the corresponding experimental values of 855.4, 1896.4, and 1910.2 cm−1. For HDS, we compute ν2 to be 1039.4 cm−1, compared with the experimental value of 1032.7 cm−1. The relative merits of local and normal mode descriptions for the overtone stretching band origins are discussed. Our results confirm the local mode nature of the H2S, D2S, and HDS system.

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The vibrational spectrum of dimethyl acetylene has been remeasured with better resolving power than hitherto, and the rotational fine structure of some perpendicular type bands has been partly analyzed. The energy levels of a molecule of this kind in which internal rotation of methyl groups may arise have been re-examined theoretically and the rotational structure of the absorption bands has been more clearly defined than previously. The experimental results are consistent with the assumption of unrestricted internal rotation of the methyl groups, and the Coriolis factors $\zeta _{i}$ for several vibrations have been determined.

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Data on the vibrational energy levels and rotational constants of carbon suboxide for the low-wavenumber bending mode ν7 are reviewed, in the ground-state manifold, and in the ν2-, ν3-, ν4-, and ν2 + ν4-state manifolds. Following the procedure developed by Duckett, Mills, and Robiette [J. Mol. Spectrosc. 63, 249 (1976)] the data have been inverted to give the effective bending potential in ν7 for each of these five states. Values are obtained for various other parameters in the effective vibration-rotation Hamiltonian. The potential and rotational constants in ν2 + ν4 are given to a close approximation by linear extrapolation from the ground state through the ν2 and ν4 states.

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The Fourier-transform spectrum of CH3F from 2800 to 3100 cm−1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm−1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν1(A1), ν4(E), 2ν2(A1), ν2 + ν5(E), 2ν50(A1), and 2ν5±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm−1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.

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When formulating least-cost poultry diets, ME concentration should be optimised by an iterative procedure, not entered as a fixed value. This iteration must calculate profit margins by taking into account the way in which feed intake and saleable outputs vary with ME concentration. In the case of broilers, adjustment of critical amino acid contents in direct proportion to ME concentration does not result in birds of equal fatness. To avoid an increase in fat deposition at higher energy levels, it is proposed that amino acid specifications should be adjusted in proportion to changes in the net energy supplied by the feed. A model is available which will both interpret responses to amino acids in laying trials and give economically optimal estimates of amino acid inputs for practical feed formulation. Flocks coming into lay and flocks nearing the end of the pullet year have bimodal distributions of rates of lay, with the result that calculations of requirement based on mean output will underestimate the optimal amino acid input for the flock. Chick diets containing surplus protein can lead to impaired utilisation of the first-limiting amino acid. This difficulty can be avoided by stating amino acid requirements as a proportion of the protein.

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The iron oxyallyl carbocation generated from 2,7-dibromocycloheptanone was induced to undergo [4 + 3] cycloaddition reactions with various furans, affording a series of 12-oxatricyclo-[4.4.1.1(2,5)]-dodec-3-en-11-one adducts. Similar methodology was used to prepare two additional cycloadducts using menthofuran and two homologous aliphatic dibromoketones. Dipolar cycloaddition of ozone to the adducts afforded the corresponding secondary ozonides (i.e., 1,2,4-trioxolanes) in variable yields. Ozonides were investigated by quantum mechanics at the B3LYP/6-31+G* level to study structural features including close contacts which may be responsible for enhancing ozonide stability. The effect of these ozonides and their corresponding precursor cycloadducts upon radicle growth of both Sorghum bicolor and Cucumis sativus was evaluated at 5.0 x 10(-4) mol L-1. The most active cycloadducts and ozonides were also evaluated against the weed species Ipomoea grandifolia and Brachiaria decumbens, and the results are discussed. Compared to ozonides previously synthesized in our laboratory, the new ozonides described herein present improved plant growth regulatory activity.

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The rovibration partition function of CH4 was calculated in the temperature range of 100-1000 K using well-converged energy levels that were calculated by vibrational-rotational configuration interaction using the Watson Hamiltonian for total angular momenta J=0-50 and the MULTIMODE computer program. The configuration state functions are products of ground-state occupied and virtual modals obtained using the vibrational self-consistent field method. The Gilbert and Jordan potential energy surface was used for the calculations. The resulting partition function was used to test the harmonic oscillator approximation and the separable-rotation approximation. The harmonic oscillator, rigid-rotator approximation is in error by a factor of 2.3 at 300 K, but we also propose a separable-rotation approximation that is accurate within 2% from 100 to 1000 K. (C) 2004 American Institute of Physics.

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The ability of new hydrophobic tridentate ligands based on 2,6-bis(benziinidazol-2-yl)pyridine, 2,6-bis(benzoxazol-2-yl)pyridine and 2,6-bis(benzothiazol-2-yl)pyridine to selectively extract americium(III) from europium(III) was measured. The most promising ligand-2,6-bis(benzoxazol-2-yl)-4-(2-decyl-1-tetradecyloxy)pyridine L-9 was found to give separation factors (SFAm/Eu) of up to 70 when used to extract cations from 0.02-0.10 M HNO3 into TPH in synergy with 2-bromodecanoic acid. Six structures of lanthanide complexes with 2,6-bis(benzoxazol-2-yl)pyridine L-6 were then determined to evaluate the types of species that are likely to be involved in the separation process. Three structural types were observed, namely [LnL(6)(NO3)(3)(H2O)2], 11-coordinate only for La, [LnL(6) (NO3)(3) (CH3CN)], 10-coordinate for Pr, Nd and Eu and [LnL(6) (NO3)(3)(H2O)], L 10-coordinate for Eu and Gd. Quantum Mechanics calculations were carried out on the tridentate ligands to elucidate the conformational preferences of the ligands in the free state and protonated and diprotonated forms and to assess the electronic properties of the ligands for comparison with other terdentate ligands used in lanthanide/actinide separation processes.

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We have favoured the variational (secular equation) method for the determination of the (ro-) vibrational energy levels of polyatomic molecules. We use predominantly the Watson Hamiltonian in normal coordinates and an associated given potential in the variational code 'Multimode'. The dominant cost is the construction and diagonalization of matrices of ever-increasing size. Here we address this problem, using pertubation theory to select dominant expansion terms within the Davidson-Liu iterative diagonalization method. Our chosen example is the twelve-mode molecule methanol, for which we have an ab initio representation of the potential which includes the internal rotational motion of the OH group relative to CH3. Our new algorithm allows us to obtain converged energy levels for matrices of dimensions in excess of 100 000.

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Currently microporous oxidic materials including zeolites are attracting interest as potential hydrogen storage materials. Understanding how molecular hydrogen interacts with these materials is important in the rational development of hydrogen storage materials and is also challenging theoretically. In this paper, we present an incoherent inelastic neutron scattering (INS) study of the adsorption of molecular hydrogen and hydrogen deuteride (HD) in a copper substituted ZSM5 zeolite varying the hydrogen dosage and temperature. We have demonstrated how inelastic neutron scattering can help us understand the interaction of H-2 molecules with a binding site in a particular microporous material, Cu ZSM5, and by implication of other similar materials. The H-2 molecule is bound as a single species lying parallel with the surface. As H-2 dosing increases, lateral interactions between the adsorbed H-2 molecules become apparent. With rising temperature of measurement up to 70 K (the limit of our experiments), H-2 molecules remain bound to the surface equivalent to a liquid or solid H-2 phase. The implication is that hydrogen is bound rather strongly in Cu ZSM5. Using the simple model for the anisotropic interaction to calculate the energy levels splitting, we found that the measured rotational constant of the hydrogen molecule is reduced as a consequence of adsorption by the Cu ZSM5. From the decrease in total signal intensity with increasing temperature, we were able to observe the conversion of para-hydrogen into ortho-hydrogen at paramagnetic centres and so determine the fraction of paramagnetic sites occupied by hydrogen molecules, ca. 60%. (c) 2006 Elsevier B.V. All rights reserved.

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The three lowest (1(2)A('), 2(2)A('), and 1(2)A(')) potential-energy surfaces of the C2Cl radical, correlating at linear geometries with (2)Sigma(+) and (2)Pi states, have been studied ab initio using a large basis set and multireference configuration-interaction techniques. The electronic ground state is confirmed to be bent with a very low barrier to linearity, due to the strong nonadiabatic electronic interactions taking place in this system. The rovibronic energy levels of the (CCCl)-C-12-C-12-Cl-35 isotopomer and the absolute absorption intensities at a temperature of 5 K have been calculated, to an upper limit of 2000 cm(-1), using diabatic potential-energy and dipole moment surfaces and a recently developed variational method. The resulting vibronic states arise from a strong mixture of all the three electronic components and their assignments are intrinsically ambiguous. (c) 2005 American Institute of Physics.