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 AX(3) molecules (A=N toBi; 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 th at the "lone pair" in the initial D-3h geometry is of central atom p, chara cter for the NX3 and AH(3) molecules, whereas it possesses s symmetry in al l other cases - here generally with a strong delocalization toward the liga nds. The stabilization of the distorted C-3 upsilon geometry is due mainly to covalency effects, whereas steric interaction forces according to the Gi llespie-Nyholm model do not seem to play a significant role. The applicatio n of the conventional vibronic pseudo Jahn-Teller coupling approach (PJT), here for the D-3h-->C-3 upsilon transition [A(l)'x(alpha (2)'' + alpha (1)' )xA(2)'' interaction], is an appropriate means for inorganic chemists to pr edict trends for the extent of distortion and for the corresponding energy gain. The vibronic coupling constants and the vibronic stabilization energi es, which mainly determine the total D-3h-->C-3 upsilon energy gain, vary a ccording 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: C1 to I). Thus, the hardest molecules are the most susceptible to vibronic coupling, the latter energy being approximately imaged by the hardness diff erence eta (C-3 upsilon) - eta (D-3h) A roughly inverse trend is observed i f the extent of the angular distortion tau (alpha) from D-3h to C-3 upsilon symmetry is considered; here, the softest molecules such as Sb(Bi)Br-3 exh ibit the largest and NH3 the smallest deviations from D3h geometry. The dif ferent sequences for tau (alpha), are due to the strong influence of the fo rce constant, which represents the C-3 upsilon-->D-3h restoring energy. It is remarkable that the vibronic coupling energy is strongly correlated with the chemical hardness eta (an observable quantity), while the stabilizatio n energy for the D-3h-->C-3 upsilon transition is not directly reflected by eta, in contrast to what is generally called the "principle of maximum har dness".