Density Functional Studies on the Lone Pair Effect of the Trivalent Group (V) Elements: I. Electronic Structure, Vibronic Coupling, and Chemical Criteria for the Occurrence of Lone Pair Distortions in AX3 Molecules (A=N to Bi; X=H, and F to I)

The energetic, steric, and bonding properties of molecules AX 3 (A=N to Bi; X=H, F to I) are analyzed using density functional theory. It is found that the “lone pair” in the initial D 3 h geometry is of central atom p z character for the NX 3 and AH 3 molecules, whereas it possesses s symmetry in all other cases − here generally with a strong delocalization toward the ligands. The stabilization of the distorted C 3 v geometry is due mainly to covalency effects, whereas steric interaction forces according to the Gillespie−Nyholm model do not seem to play a significant role. The application of the conventional vibronic pseudo Jahn−Teller coupling approach (PJT), here for the D 3 h → C 3 v transition [A 1 ‘⊗(α 2 ‘ ‘ + α 1 ‘)⊗A 2 ‘ ‘ interaction], is an appropriate means for inorganic chemists to predict trends for the extent of distortion and for the corresponding energy gain. The vibronic coupling constants and the vibronic stabilization energies, which mainly determine the total D 3 h → C 3 v energy gain, vary according to the sequences F > H > Cl > Br > I (A: N to Bi), and N > P > As > Sb > Bi (X: H,F), the dependence on A being only small or not present (X: Cl to I). Thus, the hardest molecules are the most susceptible to vibronic coupling, the latter energy being approximately imaged by the hardness difference η( C 3 v ) − η( D 3 h ). A roughly inverse trend is observed if the extent of the angular distortion τ α from D 3 h to C 3 v symmetry is considered; here, the softest molecules such as Sb(Bi)Br 3 exhibit the largest and NH 3 the smallest deviations from D 3 h geometry. The different sequences for τ α are due to the strong influence of the force constant, which represents the C 3 v → D 3 h restoring energy. It is remarkable that the vibronic coupling energy is strongly correlated with the chemical hardness η (an observable quantity), while the stabilization energy for the D 3 h → C 3 v transition is not directly reflected by η, in contrast to what is generally called the “principle of maximum hardness”.