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41.
The rearrangement of phenylcarbene (1) to 1,2,4,6-cycloheptatetraene (3) has been studied theoretically, using SCF, CASSCF, CASPT2N, DFT (B3LYP), CISD, CCSD, and CCSD(T) methods in conjunction with the 6-31G, 6-311+G, 6-311G(2d,p), cc-pVDZ, and DZd basis sets. Stationary points were characterized by vibrational frequency analyses at CASSCF(8,8)/6-31G and B3LYP/6-31G. Phenylcarbene (1) has a triplet ground state ((3)A") with a singlet-triplet separation (DeltaE(ST)) of 3-5 kcal mol(-)(1). In agreement with experiment, chiral 3 is the lowest lying structure on this part of the C(7)H(6) potential energy surface. Bicyclo[4.1.0]hepta-2,4,6-triene (2) is an intermediate in the rearrangement of 1 into 3, but it is unlikely to be observable experimentally due to a barrier height of only 1-2 kcal mol(-)(1). The enantiomers of 3 interconvert via the (1)A(2) state of cycloheptatrienylidene (4) with an activation energy of 20 kcal mol(-)(1). The "aromatic" (1)A(1) state, previously believed to be the lowest singlet state of 4, is roughly 10 kcal mol(-)(1) higher in energy than the (1)A(2) state, and, in violation of Hund's rule, (3)A(2) is also calculated to lie above (1)A(2) in energy. Thus, even if (3)A(2) were populated, it is likely to undergo rapid intersystem crossing to (1)A(2). We suggest (3)B(1)-4 is the metastable triplet observed by EPR.  相似文献   
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B3LYP/6-31G(d) calculations have been performed on the ring opening of cyclopropylcarbinyl radical 1 to 3-buten-1-yl radical 2. The dynamics of the reaction have been computed with canonical variational transition state theory (CVT), both with and without inclusion of small-curvature tunneling (SCT). The CVT + SCT calculations predict that 1 should undergo rapid and temperature-independent ring opening to 2 at cryogenic temperatures, by tunneling from the lowest vibrational level of 1.  相似文献   
45.
UB3LYP/6-31G(d) calculations have been performed in order to predict the ground states, 2A2 or 2B1, of cyclopentadienyl radicals that are mono- and bis-annelated with a wide variety of substituents. Unlike the case in the annelated cyclooctatetraenes, studied by Baldridge and Siegel, our calculations find that the sizes of the coefficients of the degenerate MOs at the annelated carbons are more important than the symmetries of the substituent's frontier orbitals in determining the mode of bond localization in the annelated cyclopentadienyl radicals.  相似文献   
46.
CO2 injected into porous formations is accommodated by reduction in the volume of the formation fluid and enlargement of the pore space, through compression of the formation fluids and rock material, respectively. A critical issue is how the resulting pressure buildup will affect the mechanical integrity of the host formation and caprock. Building on an existing approximate solution for formations of infinite radial extent, this article presents an explicit approximate solution for estimating pressure buildup due to injection of CO2 into closed brine aquifers of finite radial extent. The analysis is also applicable for injection into a formation containing multiple wells, in which each well acts as if it were in a quasi-circular closed region. The approximate solution is validated by comparison with vertically averaged results obtained using TOUGH2 with ECO2N (where many of the simplifying assumptions are relaxed), and is shown to be very accurate over wide ranges of the relevant parameter space. The resulting equations for the pressure distribution are explicit, and can be easily implemented within spreadsheet software for estimating CO2 injection capacity.  相似文献   
47.
First year mathematics degree students at Leicester Polytechnic attend a course in mathematical modelling. The aim is to introduce the students to mathematical modelling concepts and to model development. Work is set and marked during the course and this forms a vital part of the students' assessment. In addition to this, however, the students are assessed by means of a three hour examination at the end of the year. This examination is significantly different from the normal ‘five out of eight’ type. The philosophy and organization of the examination are discussed in this paper. An example of a particular examination, that for June 1986, is included as an appendix to illustrate the points made in the discussion.  相似文献   
48.
The newly synthesized phosphorus‐ and arsenic‐containing analogues of the thio‐ and seleno‐cyanate anions, PCSe?, AsCS?, and AsCSe?, as well as the known ion NCSe? were investigated in the gas phase by negative‐ion photoelectron spectroscopy (NIPES), velocity‐map imaging (VMI) spectroscopy, and quantum‐chemical computations. The electron affinities (EA), spin–orbit (SO) splittings, and “symmetric”/“asymmetric” stretching frequencies of the neutral radicals ECX. (E=N, P, As; X=S, Se), generated by electron detachment from the corresponding anions, were obtained from the spectra. The calculated EAs, SO splittings, and vibrational frequencies are in excellent agreement with the experimental measurements. These newly obtained values, when combined with those previously determined for the lighter analogues, show interesting trends on descending the pnictogen and chalcogen series. These trends are rationalized based on electronegativity arguments, the electron distributions in the HOMOs, and NBO/NRT analyses.  相似文献   
49.
The newly synthesized phosphorus‐ and arsenic‐containing analogues of the thio‐ and seleno‐cyanate anions, PCSe?, AsCS?, and AsCSe?, as well as the known ion NCSe? were investigated in the gas phase by negative‐ion photoelectron spectroscopy (NIPES), velocity‐map imaging (VMI) spectroscopy, and quantum‐chemical computations. The electron affinities (EA), spin–orbit (SO) splittings, and “symmetric”/“asymmetric” stretching frequencies of the neutral radicals ECX. (E=N, P, As; X=S, Se), generated by electron detachment from the corresponding anions, were obtained from the spectra. The calculated EAs, SO splittings, and vibrational frequencies are in excellent agreement with the experimental measurements. These newly obtained values, when combined with those previously determined for the lighter analogues, show interesting trends on descending the pnictogen and chalcogen series. These trends are rationalized based on electronegativity arguments, the electron distributions in the HOMOs, and NBO/NRT analyses.  相似文献   
50.
Hydrogen is produced by the reaction between zinc and hydrochloric acid. This reaction is used to illustrate the importance of considering thermodynamics when designing a chemical reactor. The gas released is collected in soap bubbles that rise in the air, indicating that a lighter than air gas has been produced. The bubbles can be lit to add a dramatic effect to the demonstration. The reaction is highly exothermic, raising the temperature of the reaction materials and the reactor. Batch operation of this reactor would require short cooling periods between reactions. Alternatively, a modification of the design is suggested to allow for continuous cooling of the vessel, which would allow semicontinuous operation of the reactor. (Zinc would have to be periodically replenished as it is consumed in the reaction.) The consequences associated with the cooling of the vessel are discussed.  相似文献   
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