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1.
For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 相似文献
2.
3.
Ranjana Yadav 《European Polymer Journal》2007,43(8):3531-3537
Models capable of predicting the maximum extent of conversion (p) of cardanol-based novolac-type phenolic resin, have been developed using response surface methodology to determine the optimum reaction conditions. Three-dimensional response surface and their contour plot were drawn. The maximum extent of conversion (98.93%) was predicted when the cardanol was condensed with formaldehyde (molar ratio 1:0.652) at 119.84 °C for a time period of 3 h with the catalyst (e.g., citric acid) concentration of 1.988% of total volume of cardanol and formaldehyde. The pH of the reaction mixture was maintained at 3.0. These predicted values for optimum process conditions were in good agreement with experimental data. 相似文献
4.
We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy vxc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be vxc(z → ∞) = ?αKS,xc/z, and its exchange and correlation components to be vx(z → ∞) = ?αKS,x/z and vc(z → ∞) = ?αKS,c/z, respectively. The analytical expressions for the coefficients αKS,xc and αKS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient αKS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of vxc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli Wx(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy vx(z → ∞), and the Coulomb Wc(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy vc(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
5.
Ram Parkash S. C. Ahluwalia S. C. Sud R. N. Sahni R. C. Paul 《Monatshefte für Chemie / Chemical Monthly》1981,112(6-7):707-711
Heats solution of someLewis acids and bases in acetic anhydride have been determined and the following order of their relative strengths is proposed: SbCl5>SO3>SnCl4>TiCl4>AsCl3 and piperidine>
n-butylamine>potassium acetate>sodium acetate -picoline>quinoline. Heats neutralization of theseLewis acids and bases in acetic anhydride suggest that the major enthalpy change in these neutralization reactions is due to the combination of a proton and the (CH2COOCOCH3)-ion, resulting in the formation of acetic anhydride.
Lösungs- und Neutralisationswärmen von Lewis-Säuren und-Basen in Essigsäureanhydrid
Zusammenfassung Es wurden die Lösungswärmen einigerLewis-Säuren in Essigsäureanhydrid bestimmt und folgende Reihung nach ihrer relativen Stärke vorgeschlagen: SbCl5>SO3>SnCl4>TiCl4>AsCl3 und Piperidin> n-Butylamin>KAc>NaAc-Picolin>Chinolin. Die Neutralisationswärmen dieserLewis-Säuren und-Basen legen nahe, daß der Hauptanteil daran auf die Reaktion eines Protons mit (CH2–COOCOCH3)-zurückzuführen ist.相似文献
6.
Israel Cabasso Suresh K. Sahni David Vofsi 《Journal of polymer science. Part A, Polymer chemistry》1988,26(11):2997-3014
Phosphonic acid ester derivatives of glycerol, D -mannitol, D -sorbitol, pentaerythritol, and dipentaerythritol have been synthesized by transacetalation reactions with diethyl 2,2-diethoxyethylphosphonate. These phosphonated derivatives of polyols and carbohydrates have been esterified to from the corresponding methacrylates. All these compounds have been characterized on the basis of their elemental analysis and spectroscopic (infrared including FT–IR, 1H-, 13C-, 31P-NMR, and mass) methods. Transacetalation reactions with dialkyl 2,2-dialkoxyethylphosphonate lead to the synthesis of 1,3-dioxane derivatives in the case of D -mannitol, pentaerythritol, and dipentaerythritol, whereas a mixture of both 1,3-dioxane and 1,3-dioxolane derivatives is obtained with D -sorbitol and glycerol. The methacrylates of phosphonylated polyol derivatives show the capacity to dissolve and interact with metal salts such as bismuth bromide and uranyl nitrate. Some of the polymers obtained from these monomers have been characterized on the basis of their spectral and thermal (differential scanning calorimetry) properties. 相似文献
7.
Suresh K. Sahni 《Transition Metal Chemistry》1979,4(2):73-76
Summary Complexes of 2,6-dipicolinic acid hydrazide, DPH, with ZnII, CdII and HgII have been prepared and characterized by elemental analysis, i.r. and electronic spectra and by electrical conductance measurements. The ligand is terdentate, having coordination sites at two deprotonated amide-nitrogen and pyridine-nitrogen atoms. The ZnII and HgII complexes are pentacoordinate whereas the CdII complexes are hexacoordinate and have trigonal bipyramidal and pseudooctahedral stereochemistries, respectively. The Zn, Cd and Hg ions induce cyclization of DPH complexes upon reaction with-diketones. The complexes of macrocyclic ligands so formed have the same stereochemistries as those of DPH. 相似文献
8.
Bhagwan S. Garg Ranjana Dixit Asha L. Singh 《Journal of Thermal Analysis and Calorimetry》1990,36(7-8):2567-2582
Three different types of iron(III) complexes, Fe(A)3, Fe(A)2(A') and Fe(A)(A')2, whereA is either piperidyldithiocarbamate or morpholyl dithiocarbamate andA' is glycine(oxine) acetylacetone have been prepared by reacting Fe(III) salt with sodium salt of piperidinedithiocarbamic acid or morpholine-dithiocarbamic acid and acetylacetone(oxine)-glycine in different ratios. The mixed ligand complexes have been characterised by elemental analysis, magnetic susceptibility measurements, infrared, electronic spectral techniques and by thermal analysis. Electronic spectral studies suggests that all the complexes possess distorted octahedral geometry. The magnetic moment of the high spin iron(III) complexes lies in the range of 5.88–6.00 and for low spin lies in the range of 3.36–4.34 B.M. TG studies show one step decomposition of complexes and formation of Fe2O3 at the end of the step. 相似文献
9.
Ashok K. Singh Amar Singh Ranjana Gupta Madhu Saxena Bharat Singh 《Transition Metal Chemistry》1992,17(5):413-416
The kinetics of oxidation of three aldoses (glucose, mannose and galactose) byN-bromoacetamide (NBA) in the presence of an alkaline solution of RuO4 as catalyst and Hg(OAc)2 as co-catalyst and as a scavenger for bromide have been investigated. The main products of the oxidation are the corresponding
aldonic acids. The reaction is zero order with respect to aldose and OH−. First order dependence of the reaction on both NBA and RuO4 at low concentrations shifts to zero order at higher concentrations. Addition of acetamide decreases the reaction rate, while
addition of Hg(OAc)2 has the opposite effect. No significant effect of ionic strength was observed. OBr− is postulated as the reactive oxidising species and a mechanism involving co-catalysis by RuO4 and HgII is proposed.
TMC 2588 相似文献
10.
Devendra K. Rastogi Suresh K. Sahni Vidya B. Rana Satendra K. Dua 《Transition Metal Chemistry》1978,3(1):56-60
Summary Dimeric manganese(II)and iron(II)complexes, (ML)2, derived from benzoyl hydrazones ofo-hydroxyaryl aldehydes and ketones arc described and characterised by elemental analyses and by conductance, molecular weight, magnetic, electronic and i.r. spectral measurements. The dimeric nature of the complexes is revealed by i.r. spectra which show bands atca. 885 Mn2+ and 820 cm–1 Fe2+, characteristic of ring vibrations. The i.r. spectra reveal the terdentate nature of the ligands. The electronic spectra in dimethylformamide are consistent with the tetrahedral nature of the complexes. The appreciable lowering in
eff is attributed to the presence of exchange interactions between two paramagnetic atomsvia oxygen bridges.Reprints of this article are not available. 相似文献