Perspective on “An extended Hückel theory. I. Hydrocarbons”

 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH⁺ ₃ and N⁺ ₂ using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two ²A₁ states, very similar and showing great mixing of the (2a _l ⁻¹) and (3a _l ⁻²5a _l ¹) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH₃. The possible contribution of a ²Π _g (3σ _g ⁻²1π _g ¹) state to the A shake-up peak of N₂ at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH₃ and 37 eV for N₂. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Ab initio study of the structure of 2,2-difluoroethanal in the ground and lowest excited triplet electronic states

The molecular structure of 2,2-difluoroethanal (DFE) in the ground (S₀) and lowest excited triplet (T_i) electronic states was investigated byab initio quantum-chemical methods. In the S₀ state, the DFE molecule exists as the only stablecis conformer. The T_i↓S₀ electronic excitation is accompanied by the rotation of the top and the deviation of the carbonyl fragment from planarity. For the DFE molecule in the T_i state, six minima corresponding to three pairs of enantiomers were found on the potential energy surface. Based on this potential energy surface, the problems on torsion and inversion nuclear motions were solved in the one- and two-dimensional approximations, and the interaction between these motions was revealed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 989–995, June, 2000.     

Structure and charge-state dependence of the gas-phase ionization energy of proteins

Photoionization of protein ions: The ionization energy of polyprotonated protein cations in the gas phase measured using VUV synchrotron radiation appears to be correlated with the charge state z of the protein and its tertiary structure. A simple electrostatic model accounts for the results and also shows predictive capabilities to derive a mean radius R(m) of the protein ion from the ionization energy, and vice versa.     

The Antiepileptic Lamotrigine and Its Analogues: Comparative Theoretical Electronic Properties

Electronic properties of lamotrigine (LTG) and two analogues (A1 and A2) are compared through MOPAC-AM1 calculations. Two stable conformers of LTG are calculated to exist in agreement with X-ray crystallography. In the three compounds and the two conformers for each of them, the more favorable protonation sites are N₂ and N₄; these should then be the sites appropriate for interaction with a receptor, and group valence reinforces the supposition. The molecular electrostatic potentials show that a region between the two chlorine atoms in LTG could be the site for an electrostatic interaction with a corresponding site in the receptor. The fluorine atom in A1 would play an equivalent role. A simple model for LTG-receptor interaction is proposed.     

Electronic absorption spectra of charge-transfer complexes and effects of substituents in radical cations

The effects of X substituents on the energies of charge-transfer bandshv _CT in electronic absorption spectra of charge-transfer complexes of π-, n-, or σ-donors (DX) with π- or σ-acceptors (A) as well as on the ionization potentialsI _D of individual DX molecules are described by the equationhv _CT(l _D)=a +bσ₁ +cσ _R ⁺ +dσ_α. When DX and A are fixed, the inductive (bσ₁), resonance (cσ _R ⁺ ), and polarization (dσ_α) contributions tohv _CT andI _D are virtually identical. The electronic structure of the D^.+X donor component of the compact [A^.−, D^.+X] radical-ionic pair in a solution is similar to that of the radical cation generated upon photoionization of the individual DX molecule in the gaseous phase. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1002–1006, June, 2000.     

Synthesis, ionisation potentials and electron affinities of hexaazatrinaphthylene derivatives

Several hexaazatrinaphthylene derivatives and a tris(thieno)hexaazatriphenylene derivative have been synthesised by reaction of the appropriate diamines with hexaketocyclohexane. The crystal structure of 2,3,8,9,14,15-hexachloro-5,6,11,12,17,18-hexaazatrinaphthylene has been determined by X-ray diffraction; this reveals a molecular structure in good agreement with that predicted by density functional theory (DFT) calculations and pi-stacking with an average spacing between adjacent molecular planes of 3.18 A. Solid-state ionisation potentials have been measured by using UV photoelectron spectroscopy and fall in the range of 5.99 to 7.76 eV, whereas solid-state electron affinities, measured using inverse photoelectron spectroscopy, vary in the range -2.65 to -4.59 eV. The most easily reduced example is a tris(thieno)hexaazatriphenylene substituted with bis(trifluoromethyl)phenyl groups; DFT calculations suggest that the highly exothermic electron affinity is due both to the replacement of the outermost phenylene rings of hexaazatrinaphthylene with thieno groups and to the presence of electron-withdrawing bis(trifluoromethyl)phenyl groups. The rather exothermic electron affinities, the potential for adopting pi-stacked structures and the low intramolecular reorganisation energies obtained by DFT calculations suggest that some of these molecules may be useful electron-transport materials.     

Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff

Abstract

For regularized hard potentials cross sections, the solution of the spatially homogeneous Boltzmann equation without angular cutoff lies in Schwartz's space 𝒮(? ^N ) for all (strictly positive) time. The proof is presented in full detail for the two-dimensional case, and for a moderate singularity of the cross section. Then we present those parts of the proof for the general case, where the dimension, or the strength of the singularity play an essential role.     

倒向随机微分方程及其应用

本文将介绍一类新的议程：倒向随机微分方程，为了便于理解，我们将首先通过与常微分方程和经典的随机微分方程的对比，并通过数理经济和数学金融学中的一个典型的例子来引入倒向随机微分方程。     

On approximation properties of a family of linear operators at critical value of parameter

We introduce the family of linear operators

associated to a certain “admissible bunch” of operators S_t, t>0, acting on , and investigate the approximation properties of this family as α→0⁺. We give some applications to the Riesz and the Bessel potentials generated by the ordinary (Euclidean) and generalized translations.