chemistry journal of moldova

N.Gorinchoy et al./Chem.J.Mold. 2008, 3 (1), 105-111K 2F /( E E)v . (3)2is the vibronic coupling contribution to the curvature of the AP arising from the mixing of the ground ( ) with theexcited ( ) states in the second order perturbation theory, andF ( Hˆ ( r , q ) q ) 0 , (4)is the constant of vibronic coupling between the mixing states. In eqs. (2)-(4) is the electronic Hamiltonian of thesystem, and E and E are the total energies of the ground and excited states respectively. Derivatives in these equationsare taken in the reference configuration at q =0. Note that the vibronic constants F , and therefore the vibroniccontribution K to the curvature of the AP, are nonzero only if contains .vIt was proved analytically and confirmed by a series of numerical calculations [2-7] that for any molecularsystem the contribution to the curvature of AP of the ground state is always positive,K 0.(5)0This means that structural instabilities and distortions of high-symmetry configurations of any polyatomic system innon-degenerate states are due to, and only to the PJTE, the mixing of the electronic state under consideration withhigher in energy (excited) states under the nuclear displacements in the direction of distortion. The instability takes place if the inequality K K holds, i.e. when the vibronic coupling is strong enough and/or the energy gapv 0between the mixing states is relatively small. To answer the questions whether the system in the reference nuclearconfiguration is stable or not with respect to any low-symmetry coordinateE , and the matrix elementsunder consideration.F andq , the wave functions, energy gaps E -K should be calculated for the states that are mixed under the displacement0Coordinates of instabilityInvestigation of the possible spatial structures of the system should be started with its highest possible symmetry.In the case of the H 2O 2molecule the linear configuration of D h symmetry is the reference one. In this configurationthe four-atom molecular system H 2O 2has seven vibrational degrees of freedom, which transform according to theirreducible representations 2 g u g u. Two modes, uand g, correspond to the bending of the moleculeand transform the linear nuclear configuration into the cis- (C 2v) and trans- (C 2h) transition states, leaving them, however,planar. Schematic illustration of these two modes is shown in Fig.1, a,b.After separating of the center of masses we come to the following symmetrized displacements of the type,describing the internal motions of the atoms under the bending distortion:qgxqg yquxqu ym( xO2( M m)1m( yO2( M m)1m( xO2( M m) x1m( yO2( M m) y1O2 xO2 yO2) O2) ) ) M( x1 x2),2( M m)M( y1 y2),2( M m)M( x1 x2),2( M m)M( y1 y2),2( M m)(6)106