A partially projected wave function for radicals

Abstract

A partially projected wave function for odd electron systems with quantum number M=1/2, containing µu spin functions α and µ spin functions α, with fractional spin component αS_z=1/2 and 3/2 are derived from the totally projected wave function. To obtain these wave functions new symmetry relations between Sanibel coefficients for the odd electron case have been found, as well as the relations between primitive spin functions and their spin permutations. The wave function for the doublet state is shown not to contain contamination of the quadruplet state, and the wave function for the quadruplet does not have contamination of the duplet. Both wave functions exhibit equal forms except in the signs of their summation terms. The number of primitive spin functions depends on the number of electrons (n_s), it grows linearly as n_s=(N+3)/2. It can be considered as a generalization of the half projected Hartree–Fock wave function to the odd electron case. The HPHF wave function is defined for even electron systems and consists of only two Slater determinants, it has been shown to introduce some correlation effects and it has been successfully applied to calculate the low-lying excited states of molecules. Therefore, this investigation is the first step to propose a method to calculate the excited states of radicals when other methods are impracticable.