104,688 research outputs found
Hohenberg–Kohn theory including spin magnetism and magnetic fields
No full textBeginning with work by U. von Earth and L. Hedin in 1972 and continuing with recent papers in 2001 by K. Capelle and G. Vignale and by H. Eschrig and W. E. Pickett, questions have been raised about the meaning and validity of Hohenberg-Kohn theory when spin magnetism and/or magnetic fields are present. This article offers clarifications of some of these questions. in particular, it also concludes that these questions do not affect spin-density functional theory for nondegenerate ground states as currently practiced. © 2004 Wiley Periodicals, Inc
The second order Caffarelli-Kohn-Nirenberg identities and inequalities
No full textThis paper focuses on optimal constants and optimizers of the second order
Caffarelli-Kohn-Nirenberg inequalities. Firstly, we aim to study optimal
constants and optimizers for the following second order
Caffarelli-Kohn-Nirenberg inequality in radial space: let , ,
\begin{equation}\label{0.1} \left(\int_{\mathbb{R}^N} \frac{|\Delta
u|^p}{|x|^{p\alpha}} \mathrm{d}x\right)^{\frac{1}{p}} \left[\int_{\mathbb{R}^N}
\frac{\left|\nabla u\right|^{\frac{p(t-1)}{p-1}}}
{|x|^{\frac{p(t-1)}{p-1}\beta}} \mathrm{d}x\right]^{\frac{p-1}{p}} \ge
C(N,p,t,\alpha,\beta) \int_{\mathbb{R}^N} \frac{\left|\nabla
u\right|^t}{|x|^{t\gamma}} \mathrm{d}x. \end{equation} Secondly, we establish
second order -Caffarelli-Kohn-Nirenberg identities, and obtain optimal
constants and optimizers of the second order -Caffarelli-Kohn-Nirenberg
inequalities (i.e., in \eqref{0.1}) in general space. Lastly, under some
more general assumptions, we consider the optimal weighted second order
Heisenberg Uncertainty Principles, which complements the recent work [``The
sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates
for the sharp second order uncertainty principle'', 2022, arXiv:2102.01425].
This paper's main novelty lies in the fact that we research the optimal
versions of the second order Caffarelli-Kohn-Nirenberg inequalities \eqref{0.1}
in radial space or in general space, and also establish the second order
-Caffarelli-Kohn-Nirenberg identities
Kohn–Sham fragment energy decomposition analysis
No full textWe introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations
A new species of Triepeolus (Hymenoptera: Apidae), with comments on T. utahensis (Cockerell) and T. melanarius Rightmyer
No full textRightmyer, Molly G., Kono, Yoshiaki, Kohn, Joshua R., Hung, Keng-Lou James (2014): A new species of Triepeolus (Hymenoptera: Apidae), with comments on T. utahensis (Cockerell) and T. melanarius Rightmyer. Zootaxa 3872 (1), DOI: 10.11646/zootaxa.3872.1.
Letter, [Author unclear] to Paulina T. Merritt
No full textHandwritten letter to Paulina Merritt from an unknown author, October 1, 1876.
Hartree-Fock and Kohn-Sham time-dependent response theory in a second-quantization atomic-orbital formalism suitable for linear scaling
No full textWe present a second-quantization based atomic-orbital method for the computation of
time-dependent response functions within Hartree-Fock and Kohn-Sham density-functional
theories. The method is suited for linear scaling. Illustrative results are presented for excitation
energies, one- and two-photon transition moments, polarizabilities, and hyperpolarizabilities for
hexagonal BN sheets with up to 180 atoms
Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections
No full textWe report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies
Breakdown of lung framework and an increase in pores of Kohn as initial events of emphysema and a cause of reduction in diffusing capacity
No full textPurpose: Pulmonary emphysema is the pathological prototype of chronic obstructive pulmonary disease and is also associated with other lung diseases. We considered that observation with different approaches may provide new insights for the pathogenesis of emphysema. Patients and methods: We reviewed tissue blocks of the lungs of 25 cases with/without emphysema and applied a three-dimensional observation method to the blocks. Based on the three-dimensional characteristics of the alveolar structure, we considered one face of the alveolar polyhedron as a structural unit of alveoli and called it a framework unit (FU). We categorized FUs based on their morphological characteristics and counted their number to evaluate the destructive changes in alveoli. We also evaluated the number and the area of pores of Kohn in FUs. We performed linear regression analysis to estimate the effect of these data on pulmonary function tests. Results: In multivariable regression analysis, a decrease in the number of FUs without an alveolar wall led to a significant decrease in the diffusing capacity of the lung for carbon monoxide (DLCO) and DLCO per unit alveolar volume, and an increase in the area of pores of Kohn had a significant effect on an increase in residual capacity. Conclusion: A breakdown in the lung framework and an increase in pores of Kohn are associated with a decrease in DLCO and DLCO per unit alveolar volume with/without emphysema
The trust-region self-consistent field method in Kohn–Sham density-functional theory
No full textThe trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.</p
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