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In this paper we consider the existence and stability of multi-spike solutions to the fractional Gierer-Meinhardt model with periodic boundary conditions.In particular we rigorously prove the existence of symmetric and asymmetric two-spike solutions using a Lyapunov-Schmidt reduction. The linear stability of thesetwo-spike solutions is then rigorously analyzed and found to be determined by theeigenvalues of a certain $2 × 2$ matrix. Our rigorous results are complemented byformal calculations of $N$-spike solutions using the method of matched asymptoticexpansions. In addition, we explicitly consider examples of one- and two-spikesolutions for which we numerically calculate their relevant existence and stabilitythresholds. By considering a one-spike solution we determine that the introductionof fractional diffusion for the activator or inhibitor will respectively destabilize orstabilize a single spike solution with respect to oscillatory instabilities. Furthermore,when considering two-spike solutions we find that the range of parameter valuesfor which asymmetric two-spike solutions exist and for which symmetric two-spikesolutions are stable with respect to competition instabilities is expanded with the introduction of fractional inhibitor diffusivity. However our calculations indicate thatasymmetric two-spike solutions are always linearly unstable. 相似文献
54.
Tymofii Y. Nikolaienko Leonid A. Bulavin 《International journal of quantum chemistry》2019,119(3):e25798
We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found. 相似文献
55.
针对光催化过程中的低光利用率和低催化效率,采用光化学还原法将Ag纳米颗粒均匀修饰在BaTiO3纳米压电材料表面,制备了xmol/L-Ag/BaTiO3(x=0.01、0.02、0.04,x为Ag的浓度)等离激元压电光催化剂.研究了压电光催化过程中的反应机理及等离激元颗粒负载的浓度对光催化剂性能的影响.研究结果显示,0.02mol/L-Ag/BaTiO3在全光谱光辐照和超声激发的压电场的辅助下,在75min内可降解91%的罗丹明B,将降解效率提升了21%,证实了纳米复合结构中压电势对表面等离激元光催化活性的重要影响.催化性能的提升源于压电效应和表面等离子体共振效应的协同作用.Ag纳米颗粒的等离子体共振效应(LSPR),使光吸收范围从紫外光区扩大至可见光波段.超声驱动可使BaTiO3纳米压电体发生形变而于表面产生压电电荷,压电势的存在进一步增强了LSPR诱导的光生载流子分离,促进羟基自由基的生成,加速有机染料的降解.本工作将BaTiO3的压电效应引入等离子体光催化中,可推广到其他材料和催化系统中,为环境净化提供一种有效的技术. 相似文献
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《Journal of computational chemistry》2018,39(20):1517-1530
Novel measures of electron (de)localization within the Quantum Theory of Atoms in Molecules (QTAIM) atomic basins are presented which, unlike orthodox localization indices (LIs), are fully exclusive and can be easily visualized. This work shows that QTAIM‐defined LIs describe a portion of interatomic delocalized electrons; hence, the chemical/physical interpretation of orthodox LIs is misleading. Using the recently introduced Fragment, Atomic, Localized, Delocalized, and Interatomic (FALDI) density decomposition technique we derive two novel sets of LIs and delocalization indices (DIs), by accounting for the overlap between localized and delocalized density functions. The FALDI‐based LIs and DIs perfectly recover chemically expected core and bonded electron count. Usefulness of new (de)localization indices and their 3D representations were demonstrated on a number of examples, including formamide and benzene. We therefore expect that the scheme reported in this work will provide a valuable stepping stone between classical conceptual chemistry and quantum chemical topology. © 2018 Wiley Periodicals, Inc. 相似文献
58.
The concept of resonance-assisted hydrogen bonds(RAHBs)highlights the synergistic interplay between theπ-resonance and hydrogen bonding interactions.This concept has been well-accepted in academia and is widely used in practice.However,it has been argued that the seemingly enhanced intramolecular hydrogen bonding(IMHB)in unsaturated compounds may simply be a result of the constraints imposed by theσ-skeleton framework.Thus,it is crucial to estimate the strength of IMHBs.In this work,we used two approaches to probe the resonance effect and estimate the strength of the IMHBs in the two exemplary cases of the enol forms of acetylacetone and o-hydroxyacetophenone.One approach is the block-localized wavefunction(BLW)method,which is a variant of the ab initio valence bond(VB)theory.Using this approach,it is possible to derive the geometries and energetics with resonance shut down.The other approach is Edmiston’s truncated localized molecular orbital(TLMO)technique,which monitors the energy changes by removing the delocalization tails from localized molecular orbitals.The integrated BLW and TLMO studies confirmed that the hydrogen bonding in these two molecules is indeed enhanced byπ-resonance,and that this enhancement is not a result ofσconstraints. 相似文献
59.
《Journal of computational chemistry》2017,38(13):981-997
A novel approach for calculating deformation densities is presented, which enables to calculate the deformation density resulting from a change between two chemical states, typically conformers, without the need for radical fragments. The Fragment, Atom, Localized, Delocalized, and Interatomic (FALDI) charge density decomposition scheme is introduced, which is applicable to static electron densities (FALDI‐ED), conformational deformation densities (FALDI‐DD) as well as orthodox fragment‐based deformation densities. The formation of an intramolecular NH⋅⋅⋅N interaction in protonated ethylene diamine is used as a case study where the FALDI‐based conformational deformation densities (with atomic or fragment resolution) are compared with an orthodox EDA‐based approach. Atomic and fragment deformation densities revealed in real‐space details that (i) pointed at the origin of density changes associated with the intramolecular H‐bond formation and (ii) fully support the IUPAC H‐bond representation. The FALDI scheme is equally applicable to intra‐ and intermolecular interactions. © 2017 Wiley Periodicals, Inc. 相似文献
60.
《Journal of computational chemistry》2017,38(30):2618-2631
We present an automated quantum chemical protocol for the determination of preferred protonation sites in organic and organometallic molecules containing up to a few hundred atoms. It is based on the Foster–Boys orbital localization method, whereby we automatically identify lone pairs and π orbitals as possible protonation sites. The method becomes efficient in conjunction with the robust and fast GFN‐xTB semiempirical method proposed recently (Grimme et al ., J. Chem. Theory Comput . 2017, 13 , 1989). The protonated isomers that are found within a few seconds to minutes of computational wall‐time on a standard desktop computer are then energetically refined using density functional theory (DFT), where we use a high‐level double‐hybrid reference method to benchmark GFN‐xTB and low‐cost DFT approaches. The proposed DFT/GFN‐xTB/LMO composite protocol is generally applicable to almost arbitrary molecules including transition metal complexes. Importantly it is found that even in electronically complicated cases, the GFN‐xTB optimized protomer structures are reasonable and can safely be used in single‐point DFT calculations. Corrections from energy to free energy mostly have a small effect on computed protomer populations. The resulting protomer equilibrium is valuable, for example, in the context of electrospray ionization mass spectrometry where it may help identify the ionized species and assist the interpretation of the experiment. © 2017 Wiley Periodicals, Inc. 相似文献