The Unrestricted Hartree-Fock Theory of Chemical Reactions. IV: Singlet Radical States with "Antiferromagnetic" Spin Orderings in Four-Center Exchange Reaction of Hydrogen Molecules

Abstract

A UHF theoretical analysis is carried out on four-center exchange reaction of two hydrogen molecules in reaction paths with D. symmetry including D.,, D •• and T, confor. mations as special cases. It is shown that the UHF singlet ground state of the H. system consists of ten distinct UHF configurations which appear at different regions of nuclear con­ figuration space. Three among the ten configurations are closed shell type and the other seven correspond to singlet radicals with distinct antiferromagnetically ordered spin structures. Three among the seven singlet radical configurations have spin structures modulated one dimensionally, the other three have those modulated two dimensionally and are very similar to Overhauser's helical spin density wave. Another configuration has tetra-hedrally modulat­ ed spin structure. The adiabatic potentials of the UHF configurations are calculated and their interconnection relation is studied. The electronic correlation effects underlying these singlet radical states are discussed in connection with orbital co;rrelation diagrams. · § I. Introduction In previous papers/>-'> we have discussed chemical significances of the instabilities and the broken symmetry solutions in the unrestricted Hartree-F.ock (UHF) theory and shown· that the electronic state of a singlet biradical can be well represented by a spin density wave (SDW) type solution which emerges from an instability of a restricted Hartree-Fock (RHF) solution. We consider, in this paper, the four-center exchange reaction of two hydrogen molecules in the conformations with D 2 symmetry including those with D2h, D 2rt and Trt symmetries as special cases. · We shall show from a detailed UHF theoretical analysis of the H 4 system that there are singlet radicals with more complex electronic structures than the simple biradicals with two unpaired electrons. The H 4 system may enter into seven different singlet radical states, which· are characterized by distinct antiferromagnetic spin structures, in the regions near the transition conformations. Three of them are similar to the alternant orbital of Uiwdin,5l Itoh and Yoshizumi,6l the other three to the helical SDW of Overhauser 7l and another one has a spin structure modulated in a three-dimensional way. Possibility of such plentiful kinds of singlet radicals and their interconversion in reacting molecular systems has not been recognized so