Increased Valence or Electronic Hypervalence for Symmetrical Three-Centre Molecular Orbital Configurations

摘要

With PSI_1= y + k_1 a + b,PSI_2 = y - b,and PSI_3 = y - k_3 a + b as Y-A and A-B bonding,non-bonding,and antibonding three-centre molecular orbitals for a symmetrical Y-A-B type bonding unit with overlapping atomic orbitals y,a,and b,it is deduced that the maximum value for the A-atom valence,(V_A = V_(ab)+ V_(ay)),is(a)4(3 - 2√2)= 0.6863 for the one-electron and five-electron configurations PHI(1)=(PSI_1)~1 and PHI(5)=(PSI_1)~2(PSI_2)~2(PSI_3)~1)~1;(b)8(3-2√2)= 1.3726 for the two-electron and four-electron configurations PHI(2)=(PSI_1)~2 and PHI(4)=(PSI_1)~2(PSI_2)~2;and(c)4/3 for the three-electron configuration PHI(3)=(PSI_1)~2(PSI_2)~1.Thus for each of the three-centre molecular orbital configurations,the A-atom can exhibit increased valence,or electronic hypervalence,relative to the valence for an A-atom in a two-centre molecular orbital configuration.When k_1≠ 0 for PHI(1)and k_3≠ 0 for PHI(5),the A-atom odd-electron charge is not equal to zero.This odd-electron charge is available for(fractional)electron-pair bonding to a fourth atom X,to give an additional contribution,V_a,to the valence.The resulting maximum value for the A-atom valence(V_A = V_(ab)+ V_(ay)+V_a)is equal to 1.2020 for each of PHI(1)and PHI(5).A-atom valencies are calculated for the three-centre bonding units for several molecules and ions.The expressions for V_A = V_(ab)+ V_(ay)were derived with atomic orbital overlap integrals omitted.The present paper shows how the theory is modified when these integrals are included.