Scalar waves in a one-dimensional randomly inhomogeneous medium: Allowance for spatial dispersion in pair-interaction approximation

The Helmholtz equation for the average field in an ubounded one-dimensional randomly inhomogenous medium described by the normalized binary correlation function (z₁, z₂)=exp(–/z//a), where a is the correlation scale and zz₁–z₂, is solved in a pair-interaction approximation (Bourret approximation). Allowance for the macroscopic spatial dispersion (caused by the inhomogeneity of the medium) expands the applicability range of the Bourret approximation by including ultrashort waves. The scattering indices y_± and phase v_± and group c_± propagation velocities of monochromatic waves corresponding to two roots x of the dimensionless wave numbers x_± of the dispersion equation are calculated. It is shown that, unlike in the three-dimensional case [1], the scattering index has the same asymptotic dependence on frequency for long and short waves: V₊ ²a. The wavelength-dependent applicability conditions of the pair-interaction approximation (M criterion) and negligibility of the macroscopic spatial dispersion (N criterion) are investigated for each of the roots. The field of a point source is represented as a superposition of divergent waves defined by roots x₊ and x_–. The absolute values of the amplitudes of these waves reach maximum values at the boundary of the short-wave and ultrashort-wave ranges. Anomalous properties of y_±, v_±, and c_± are observed in this region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Vol. 37, No. 4, pp. 407–421, April, 1994.     

Which electron count rules are needed for four-center three-dimensional aromaticity?

A series of charged and neutral four-center n-electron (4c-ne, n = 1-4) molecules based on the adamantane framework, but which include combinations of boron, nitrogen, and phosphorus atoms at bridgehead positions, were studied computationally at the B3LYP/6-31G* level of density functional theory (DFT). The three-dimensional aromaticity, observed earlier for the 1,3,5,7-bisdehydroadamantane dication (1), is found to be general for 4c-2e electron systems. The degree of electron delocalization, evaluated by energetic, geometric, and various magnetic criteria, is quite independent of the molecular symmetry (point groups vary from Td to Cs), the degeneracy of the orbitals, the molecular charges, and the nature of the atoms participating in the delocalized bonding. Although the multiple positive (e.g., in 1 and some of the heteroatom systems) and multiple negative charges are strongly repulsive, the rigid adamantane frameworks help hold the bridgehead atoms within bonding distances with the fewer available electrons. The corresponding 4c-1e doublets are approximately half as aromatic as the 4c-2e singlets based on the same criteria. However, the three-electron systems may either adopt distorted but still four-center delocalized structures, or alternative 3c-2e two-dimensional arrangements in which the fourth bridgehead atom is more distant. There is no need to derive special rules for each point group for 4c-ne systems. Although the three-dimensional stabilization is computed to be quite appreciable, ranging between 10 and 50 kcalmol(-1), this delocalization energy is generally not sufficient to overcome distortion due to strain in higher homologues of 1 and in analogous noncage systems. Among the various 4c-2e homoadamantanedehydro dications studied, only the 1,8-dehydrohomoadamandiyl-3,6-dication forms a three-dimensional aromatic system.     

The reactions of polyfluorocarbonyl compounds with phenylhydrazines

Methyl trifluoropyruvate (II) reacts with phenylhydrazine andp-nitrophenylhydrazine to give the corresponding phenylhydrazones (III) and (IV). The reaction of phenylhydrazine with hexafluoroacetone (I) at 20°C leads to the product of the C²-hydroxyalkylation of the aromatic ring (V). The hydroxyalkylation of hydrazobenzene under the same conditions is complicated by a benzidine rearrangement.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 948–950, April, 1990.     

A vinyl substitution reaction in fluoroalkenes

Based on the results of CNDO and INDO quantum-chemical calculations, the possibility of a vinyl substitution (along with an addition) upon reaction of perfluoropropylene, perfluoroisobutylene, and trifluorochloroethylene with alcohols, thiols, and amines, and the absence of a similar reaction in the case of tetrafluoroethylene is explained. The calculations allow the prediction that a vinyl substitution should take place in similar reactions of 1,1-di- and trifluoroethylenes, but not with mono- and 1,2-difluoroethylenes.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2802–2805, December, 1991.     

Syntheses based on (N,N-difluoroamino)dinitroacetonitrile

High reactivity of the nitrite group in (NN-difluoroamino)dinitroacetonitrile was demonstrated. Based on its reaction with HN₃, a new preparative method for the synthesis of 5-[(N,N-difluoroamino)dinitromethylltetrazole was developed; some derivatives of the latter compound have been obtained.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8. pp. 2056–2058, August, 1996.     

Paths for the formation of dioxin-type xenobiotics: Quantum-chemical treatment 1. Formation of polychlorobiphenylenes from polychlorobenzenes

The heats of formation of polychloroarynes (PCA's) from polychlorobenzenes (PCB's) have been calculated by the AMI method as a function of the composition and structure of the PCB's according to a two-step scheme including deprotonation with the formation of carbanions (PCCA's, H₁) and dechlorination to PCA's (H₂). The influence of the solvent on H₁ and H₂ has been evaluated in the framework of the solvaton model. It has been shown that the value of H₁ decreases as the number of C1 atoms in the PCB is increased, while H₂ increases along the same series due to the increase in the relative stability of the PCCA as the number of C1 atoms is increased. Although the dimerization of PCA's with the formation of polychlorobiphenylenes (PCBP's) is forbidden by orbital symmetry rules, calculations of fragments of the potential-energy surface have shown that this reaction takes place with an energy barrier amounting to about 1 kcal/mole.A. N. Nesmeyanov Institute of Organometallic Compounds, Russian Academy of Sciences, 117813 Moscow. Institute of Organic Chemistry, Bulgarian Academy of Sciences, 1113 Sofia. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 350–355, February, 1992.     

Non-solvated aluminum hydride. Crystallization from diethyl ether-benzene solutions

Crystallization of non-solvated aluminum hydride from a diethyl ether-benzene mixed solvent was studied. The desolvation of AlH₃·(Et₂O)_x etherate in solution and the crystallization of α-AlH₃ during polythermal heating of the solution occur only in the presence of ≥10 wt.% LiAlH₄. The process is multistage, and the crystallization begins with the formation of the AlH₃·0.25Et₂O solvate, which recrystallizes in the solid phase into γ-AlH₃ and then α-AlH₃. Four crystalline modifications of aluminum hydride were characterized by X-ray diffraction and electron microscopy. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1259–1265, July, 2007.     

Crystal Structure of Cu(hfac)2 Complexes with Organomercury Binitroxide

The organomercury biradical HgL₂ (L is deprotonated 4,4,5,5-tetramethyl-2-imidazoline-3-oxide-1-oxyl) is capable of performing the bridging function for design of multinuclear heterospin systems. This paper describes synthesis and crystal structure of HgL₂ and the first multinuclear complexes of Cu(hfac)₂ with HgL₂.     

Reactions of diarylamines with hexafluoroacetone

Diphenylamine reacts with hexafluoroacetone to give a mixture of products, of which 2-(1-hydroxy-1-trifluoromethyl-2,2,2-trifluoroethyl)diphenylamine (II) was isolated. N-Arylanthranilic acids modify the 1,1,1,3,3,3-hexafluoro-2-hydroxy-2-propyl group upon the reaction of its sodium salt with the hydrate of hexafluoroacetone (I) under mild conditions. This method gave 4-(1-hydroxy-1-trifluoromethyl-2,2,3-trifluoroethyl)-N-(2,3-xylyl)anthranilic acid from N-(2,3-xylyl)anthranilic acid in 93% yield.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 952–954, April, 1991.     

Synthesis of α, α, ω-trihydropolyfluoroalkyl chlorophosphates by the reaction between α,α,ω-trihydropolyfluoroalkyl phosphites and sulfuryl chloride

Conclusions An efficient method for the synthesis of ,,-trihydropolyfluoroalkyl chlorophosphates is by reacting ,,-trihydropolyfluoroalkyl dichlorophosphites and bis-(,,-trihydropolyfluoroalkyl) phosphites with sulfuryl chloride. It has been found that in three-coordinated polyfluoroalkyl phosphites, the high electronegativity of the polyfluoroalkyl groups hinders cleavage of the latter on reaction with sulfuryl chloride, thereby facilitating the formation of oxidation products.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 146–149, January, 1988.