单边条件下的 Taylor平均逼近

本文中 ,我们对函数加适当的条件 ,从而改进了 Taylor平均逼近的阶.     

Simulation of molecular and electronic structure of polyhydrogenated (n,0)-tubulenes and their analogs intercalated with lithium

Molecular and electronic structure of four polyhydrogenated (n,0)-tubulenes, namely, [−C₂₄H₄−] _m (1), two isomers of composition [−C₂₈H₄−] _m (2 and3), and [−C₃₂H₄−] _m (4) withn benzene rings in the cross section (n=6, 7, 7, and 8, respectively), was simulated atm>1 (m is the number of repeating fragemnts). It was assumed that hydrogen atoms are attached to all carbon atoms lying on the two most distant elements of the cylinders of the corresponding tubulenes. The energy band structures of macromolecules1–4 and their Li-intercalated analogs [−C₂₄H₄Li−] _m (5) [−C₂₈H₄Li−] _m (two isomers,6 and7), and [−C₃₂H₄Li−] _m (8), containing one Li atom per repeating unit at each center, were obtained in the EHT approximation by the crystal orbital method. Geometric parameters of repeating units of structures1–8 were found after MNDO/PM3 optimization of the energies of hydrocarbon molecules C₇₂H₂₄, C₈₄H₂₆ (two geometric isomers), and C₉₆H₂₈, containing three repeating units of corresponding tubulenes1–4 each. The conductivity types of polyhydrogenated tubulenes1–4 are the same as those of their precursors, (6,0)-, (7,0)-, and (8,0)-tubulenes. Dispersion curves of systems5–8 are much the same as those of macromolecules1–4; however, electron energy spectra of5–8 possess metallic conductivity type and the positions of Fermi levels for these systems are higher than for compounds1–4. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2061–2067, November, 1999.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

Theoretical investigation of the weak interactions of rare gas atoms with silver clusters by resonance Raman spectroscopy modeling

The interactions of rare gas atoms (Rg = Ar, Kr, and Xe) with small neutral and cationic silver clusters have been investigated by density functional methods and the effect of these weak interactions on the resonance Raman spectra of the complexes has been evaluated. The resonance Raman technique that depends on the properties of ground and excited state, seems deeply sensitive to the weak rare gas–metal cluster interactions, and the use of inert gases has been proven to be an excellent approach to recognize the ability of this technique to detect extremely weak interactions. In this work, for , and complexes the IR, normal and resonance Raman spectra have been calculated and the effect of rare gas–cluster stretching vibration ( ) on the pattern and the relative intensities of different spectra have been investigated. The resonance Raman spectra for the weakly interacted complexes (with the interaction energies less than ?2.0 kcal/mol) exhibit the vibration with the detectable intensity that its intensity increases by going from Ag₆–Ar to Ag₆–Xe complex. Moreover, the resonance Raman spectra (based on the excited state gradient approximation) for high intensity nearly degenerate excited states, proved the effect of accumulation of the excited state charge density on the relative intensity of vibration.     

Predicting ion selectivity in water purification by capacitive deionization: Electric double layer models

Ion-selective water treatment is needed to address emerging problems in an energy- and cost-efficient manner. Capacitive deionization (CDI) is a membraneless water treatment technology, which relies on storing ions in charged electric double layers (EDLs) of micropores. CDI has shown remarkable selectivity, with local density approximations (LDAs) showing some success in guiding selective separations. However, many underlying processes are represented by lumped fitting parameters in LDA models, hindering further progress. Atomistic models help unravel selectivity mechanisms, but are difficult to integrate with cell-level CDI theory. Here, we review and extend LDA models for CDI, highlight a knowledge gap in connecting between LDA and atomistic models for CDI, and emphasize and build upon analogies between micropore EDLs and nanofiltration membranes.     

A comparative quantum-chemical analysis of electronic structures and spectroscopic parameters of cycloalkanes and cyclopolysilanes

A comparative quantum-chemical analysis of the electronic structures and spectroscopic parameters of the cycloalkanes C₃H₆, C₄H₈, C₅H₁₀, and C₆H₁₂ and their silicon analogs Si₃H₆, Si₄H₈, Si₅H₁₀ and Si₆H₁₂ was performed in the framework of the SCF MO LCAO method in the INDO approximation. Qualitative interpretation of “abnormal” ionization potentials and energies of electronic absorption spectra of cyclopolysilanes has been given. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1997.     

New method for calculating the adsorption of noble gases on amorphous surfaces

A new approach to calculating the equilibrium characteristics of the adsorption of noble gases on the amorphous surfaces of adsorbents was developed and applied to the Ar−TiO₂(rutile) system. Intermolecular adsorbate-adsorbate interactions are taken into account for the nearest neighbors in the quasi-chemical approximation. The lattice energy parameters of all interactions of the model are determined from the Lennard-Jones potential (12-6). The formation of amorphous TiO₂(rutile) surface includes completion of the surface layers and partial removal of the surface oxygen ions. The quality of the amorphization procedure was confirmed by the experimentally measured heats and isotherms of adsorption of the system under study. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1109–1118, June, 1997.     

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.