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171.
Maurice A. de Gosson 《Foundations of Physics》2009,39(2):194-214
We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which is at the origin of the definition of symplectic capacities, and which provides an interesting link between classical and quantum physics. 相似文献
172.
D.H. Delphenich 《Annalen der Physik》2009,18(4):206-230
The mechanics of wave motion in a medium are founded in conservation laws for the physical quantities that the waves carry, combined with the constitutive laws of the medium, and define Lorentzian structures only in degenerate cases of the dispersion laws that follow from the field equations. It is suggested that the transition from wave motion to point motion is best factored into an intermediate step of extended matter motion, which then makes the dimension‐codimension duality of waves and trajectories a natural consequence of the bicharacteristic (geodesic) foliation associated with the dispersion law. This process is illustrated in the conventional case of quadratic dispersion laws, as well as quartic ones, which include the Heisenberg–Euler dispersion law. It is suggested that the contributions to geodesic motion from the non‐quadratic nature of a dispersion law might represent another source of quantum fluctuations about classical extremals, in addition to the diffraction effects that are left out by the geometrical optics approximation. 相似文献
173.
This paper introduces Bohmian mechanics (BM) into the
intense laser-atom physics to study high-order harmonic generation.
In BM, the trajectories of atomic electron in an intense laser field can
be obtained with the Bohm--Newton equation. The power spectrum with the
trajectory of an atomic electron is calculated, which is found to be irregular.
Next, the power spectrum associated with an atom
ensemble from BM is considered, where the power spectrum becomes
regular and consistent with that from quantum mechanics. Finally,
the reason of the generation of the irregular spectrum is discussed. 相似文献
174.
The spin-weighted spheroidal equation in the case of s = 1 is studied. By transforming the independent variables, we make it take the Schrdinger-like form. This Schrdinger-like equation is very interesting in itself. We investigate it by using super-symmetric quantum mechanics and obtain the ground eigenvalue and eigenfunction, which are consistent with the results previously obtained. 相似文献
175.
E. G. Gal'pern I. V. Stankevich A. L. Chistyakov L. A. Chernozatonskii 《Russian Chemical Bulletin》1999,48(11):2039-2045
Molecular and electronic structure of four polyhydrogenated (n,0)-tubulenes, namely, [−C24H4−]
m
(1), two isomers of composition [−C28H4−]
m
(2 and3), and [−C32H4−]
m
(4) withn benzene rings in the cross section (n=6, 7, 7, and 8, respectively), was simulated atm>1 (m is the number of repeating fragemnts). It was assumed that hydrogen atoms are attached to all carbon atoms lying on the two
most distant elements of the cylinders of the corresponding tubulenes. The energy band structures of macromolecules1–4 and their Li-intercalated analogs [−C24H4Li−]
m
(5) [−C28H4Li−]
m
(two isomers,6 and7), and [−C32H4Li−]
m
(8), containing one Li atom per repeating unit at each center, were obtained in the EHT approximation by the crystal orbital
method. Geometric parameters of repeating units of structures1–8 were found after MNDO/PM3 optimization of the energies of hydrocarbon molecules C72H24, C84H26 (two geometric isomers), and C96H28, containing three repeating units of corresponding tubulenes1–4 each. The conductivity types of polyhydrogenated tubulenes1–4 are the same as those of their precursors, (6,0)-, (7,0)-, and (8,0)-tubulenes. Dispersion curves of systems5–8 are much the same as those of macromolecules1–4; however, electron energy spectra of5–8 possess metallic conductivity type and the positions of Fermi levels for these systems are higher than for compounds1–4.
Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2061–2067, November, 1999. 相似文献
176.
Ming Huang Timothy J. Giese Darrin M. York 《Journal of computational chemistry》2015,36(18):1370-1389
Semiempirical quantum models are routinely used to study mechanisms of RNA catalysis and phosphoryl transfer reactions using combined quantum mechanical (QM)/molecular mechanical methods. Herein, we provide a broad assessment of the performance of existing semiempirical quantum models to describe nucleic acid structure and reactivity to quantify their limitations and guide the development of next‐generation quantum models with improved accuracy. Neglect of diatomic differential overlap and self‐consistent density‐functional tight‐binding semiempirical models are evaluated against high‐level QM benchmark calculations for seven biologically important datasets. The datasets include: proton affinities, polarizabilities, nucleobase dimer interactions, dimethyl phosphate anion, nucleoside sugar and glycosidic torsion conformations, and RNA phosphoryl transfer model reactions. As an additional baseline, comparisons are made with several commonly used density‐functional models, including M062X and B3LYP (in some cases with dispersion corrections). The results show that, among the semiempirical models examined, the AM1/d‐PhoT model is the most robust at predicting proton affinities. AM1/d‐PhoT and DFTB3‐3ob/OPhyd reproduce the MP2 potential energy surfaces of 6 associative RNA phosphoryl transfer model reactions reasonably well. Further, a recently developed linear‐scaling “modified divide‐and‐conquer” model exhibits the most accurate results for binding energies of both hydrogen bonded and stacked nucleobase dimers. The semiempirical models considered here are shown to underestimate the isotropic polarizabilities of neutral molecules by approximately 30%. The semiempirical models also fail to adequately describe torsion profiles for the dimethyl phosphate anion, the nucleoside sugar ring puckers, and the rotations about the nucleoside glycosidic bond. The modeling of pentavalent phosphorus, particularly with thio substitutions often used experimentally as mechanistic probes, was problematic for all of the models considered. Analysis of the strengths and weakness of the models suggests that the creation of robust next‐generation models should emphasize the improvement of relative conformational energies and barriers, and nonbonded interactions. © 2015 Wiley Periodicals, Inc. 相似文献
177.
QM/MM modeling of the hydroxylation of the androstenedione substrate catalyzed by cytochrome P450 aromatase (CYP19A1) 下载免费PDF全文
Ignacio Viciano Raquel Castillo Sergio Martí 《Journal of computational chemistry》2015,36(23):1736-1747
CYP19A1 aromatase is a member of the Cytochrome P450 family of hemeproteins, and is the enzyme responsible for the final step of the androgens conversion into the corresponding estrogens, via a three‐step oxidative process. For this reason, the inhibition of this enzyme plays an important role in the treatment of hormone‐dependent breast cancer. The first catalytic subcycle, corresponding to the hydroxilation of androstenedione, has been proposed to occur through a first hydrogen abstraction and a subsequent oxygen rebound step. In present work, we have studied the mechanism of the first catalytic subcycle by means of hybrid quantum mechanics/molecular mechanics methods. The inclusion of the protein flexibility has been achieved by means of Free Energy Perturbation techniques, giving rise to a free energy of activation for the hydrogen abstraction step of 13.5 kcal/mol. The subsequent oxygen rebound step, characterized by a small free energy barrier (1.5 kcal/mol), leads to the hydroxylated products through a highly exergonic reaction. In addition, an analysis of the primary deuterium kinetic isotopic effects, calculated for the hydrogen abstraction step, reveals values (~10) overpassing the semiclassical limit for the C? H, indicating the presence of a substantial tunnel effect. Finally, a decomposition analysis of the interaction energy for the substrate and cofactor in the active site is also discussed. According to our results, the role of the enzymatic environment consists of a transition state stabilization by means of dispersive and polarization effects. © 2015 Wiley Periodicals, Inc. 相似文献
178.
A general molecular mechanics (MM) model for treating aqueous Cu2+ and Zn2+ ions was developed based on valence bond (VB) theory and incorporated into the atomic multipole optimized energetics for biomolecular applications (AMOEBA) polarizable force field. Parameters were obtained by fitting MM energies to that computed by ab initio methods for gas‐phase tetra‐ and hexa‐aqua metal complexes. Molecular dynamics (MD) simulations using the proposed AMOEBA‐VB model were performed for each transition metal ion in aqueous solution, and solvent coordination was evaluated. Results show that the AMOEBA‐VB model generates the correct square‐planar geometry for gas‐phase tetra‐aqua Cu2+ complex and improves the accuracy of MM model energetics for a number of ligation geometries when compared to quantum mechanical (QM) computations. On the other hand, both AMOEBA and AMOEBA‐VB generate results for Zn2+–water complexes in good agreement with QM calculations. Analyses of the MD trajectories revealed a six‐coordination first solvation shell for both Cu2+ and Zn2+ ions in aqueous solution, with ligation geometries falling in the range reported by previous studies. © 2012 Wiley Periodicals, Inc. 相似文献
179.
Summary A model is devised using molecular mechanics to simulate chromatographic separations of enantiomers. Theoretical results derived from this model are compared with experimental findings obtained using supercritical fluid chromatography. The model is then developed to incorporate the effects of binding the stationary phase to a matrix. Computed results show that addition of the matrix into the model has significant effects on the ability of the stationary phase to separate racemic mixtures. 相似文献
180.