Nonstandard tools of nonsmooth analysis

This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.     

On combining non-standard methods. I. Monadology

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 69–78, September–October, 1990.     

Symmetry measures

The reconstruction of a superminimal measure of symmetry is considered on the basis of its values on indecomposable polyhedra.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 615–622, April, 1976.     

Conformational analysis of singlet-triplet state mixing in Paternò-Büchi diradicals

Conformational dependence of spin-orbit coupling (SOC) in flexible Paternò-Büchi (PB) diradicals has been studied with high-level ab initio methods using both (i) one-electron spin-orbit Hamiltonian with parametrized (effective) nuclear charges in conjunction with a state-averaged MCSCF wave function as implemented by Robb in Gaussian 98 and (ii) complete one- and two-electron SOC with a fully optimized MCSCF triplet wave function and frozen core singlet as implemented by Furlani in the GAMESS computational package. The ab initio results revealed two distinct areas of elevated SOC values, one corresponding to the region whereby a cisoid conformation in the C-C-O-C fragment brings the two odd-electron orbitals closer to each other, and the other area corresponding to the partially eclipsed conformation lacking direct overlap between the spin centers. In this second region the 1,4-electronic communication is mediated by the oxygen's 2p-lone pair, which is suitably oriented to play the role of a "relay-antenna". The other critical factor affecting the rate of intersystem crossing (ISC)--singlet-triplet energy separation--was computed utilizing a multireference CASSCF-MP2 method to include dynamic correlation effects. The largest singlet-triplet energy gap, approximately 2 kcal/mol, was found for a gauche conformer (also a minimum SOC conformation). Rotation about the central C-O bond either toward the fully eclipsed (0 degrees ) or the partially eclipsed (120 degrees ) conformations decreases the singlet-triplet gap while increasing the value of the SOC matrix element. These computational findings support the Griesbeck model for stereochemistry of triplet PB reactions and provide a rigorous basis for predicting the probability of ISC in diradicals separated by a partially conjugated spacer.     

S-tosylsulfenamides,new electrophilic sulfosulfenylating agents

A method has been developed for the synthesis of thiosulfonates by the electrophilic addition of S-tosylsulfenamides to olefins or their electrophilic substitution in aromatic systems. SO₃, Py·SO₃, and BF₃·Et₂O were used as activators. The addition of S-tosylsulfenamides to olefins proceeds through electrophilic trans addition.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2623–2629, November, 1991.