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Efficient determination of accurate atomic polarizabilities for polarizeable embedding calculations 下载免费PDF全文
We evaluate embedding potentials, obtained via various methods, used for polarizable embedding computations of excitation energies of para‐nitroaniline in water and organic solvents as well as of the green fluorescent protein. We found that isotropic polarizabilities derived from DFTD3 dispersion coefficients correlate well with those obtained via the LoProp method. We show that these polarizabilities in conjunction with appropriately derived point charges are in good agreement with calculations employing static multipole moments up to quadrupoles and anisotropic polarizabilities for both computed systems. The (partial) use of these easily‐accessible parameters drastically reduces the computational effort to obtain accurate embedding potentials especially for proteins. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. 相似文献
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Characterizations of Sobolev spaces associated to operators satisfying off‐diagonal estimates on balls 下载免费PDF全文
Junqiang Zhang Der‐Chen Chang Dachun Yang 《Mathematical Methods in the Applied Sciences》2017,40(8):2907-2929
Let be a metric measure space of homogeneous type and L be a one‐to‐one operator of type ω on for ω ∈[0, π /2). In this article, under the assumptions that L has a bounded H ∞ ‐functional calculus on and satisfies (p L , q L ) off‐diagonal estimates on balls, where p L ∈[1, 2) and q L ∈(2, ∞ ], the authors establish a characterization of the Sobolev space , defined via L α /2, of order α ∈(0, 2] for p ∈(p L , q L ) by means of a quadratic function S α , L . As an application, the authors show that for the degenerate elliptic operator L w : =? w ? 1div(A ?) and the Schrödinger type operator with a ∈(0, ∞ ) on the weighted Euclidean space with A being real symmetric, if n ?3, with q ∈[1, 2], , p ∈(1, ∞ ) and with , then, for all , , where the implicit equivalent positive constants are independent of f , denotes the class of Muckenhoupt weights, the reverse Hölder class, and D (L w ) and the domains of L w and , respectively. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Salim A. Messaoudi Ala A. Talahmeh 《Mathematical Methods in the Applied Sciences》2017,40(18):6976-6986
We consider, in this paper, the following nonlinear equation with variable exponents: where a,b>0 are constants and the exponents of nonlinearity m,p, and r are given functions. We prove a finite‐time blow‐up result for the solutions with negative initial energy and for certain solutions with positive energy. 相似文献
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This paper offers a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on R~n. The authors use this idea to extend the result to real hyperbolic spaces H~n. 相似文献
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Grigoris Paouris Petros Valettas Joel Zinn 《Stochastic Processes and their Applications》2017,127(10):3187-3227
We study the dependence on in the critical dimension for which one can find random sections of the -ball which are -spherical. We give lower (and upper) estimates for for all eligible values and as , which agree with the sharp estimates for the extreme values and . Toward this end, we provide tight bounds for the Gaussian concentration of the -norm. 相似文献
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Eduardo M. Garau Pedro Morin 《Numerical Methods for Partial Differential Equations》2017,33(4):1266-1282
We develop an a posteriori error estimator which focuses on the local H1 error on a region of interest. The estimator bounds a weighted Sobolev norm of the error and is efficient up to oscillation terms. The new idea is very simple and applies to a large class of problems. An adaptive method guided by this estimator is implemented and compared to other local estimators, showing an excellent performance. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1266–1282, 2017 相似文献