chemistry journal of moldova

N.Gorinchoy et al./Chem.J.Mold. 2008, 3 (1), 105-111Consider in more detail the nature of the mixing states. In the linear configuration the first excited uterm arisesfrom the excitation of one electron from the fully occupied gmolecular orbital (formed almost solely from the 2p AOs of the oxygen atoms) to the unoccupied uMO which is an antisymmetrical linear combination of the 2p AOsof the oxygen atoms and 1s AOs of hydrogens. The second excited gstate is formed by one-electron excitation fromthe same occupied gMO to the virtual gone which is a symmetrized linear combination of the 2p AOs of the Oatoms and 1s AOs of the H atoms (Table 1 and Fig. 3). Thus the determinants in the CI wavefunctions of the ground+ gand corresponding excited uand gelectronic states differ by one spin-orbital only. Taking into account that theHamiltonian H in eq. 4 is a sum of one-particle operators, the vibronic constants F uand F g can be calculated asone-electron matrix elements of the type g x ( Hˆ( r , q ) / q u x ) 0 u and g x ( H / q g x ) 0g. Forthe planar bent C 2hand C 2vconfigurations corresponding vibronic constantsFa Ag( Hˆr q qu ( , ) / au) 0Auand Fa A1 ( Hˆ( r,q) / q)2a20 A2are reduced to the matrix elements bg( Hˆ( r , q ) / qabu ) 0 u anda2 ( Hˆ( r,q) / qa)2 0 a1respectively.Fig. 3. MO energy level scheme for the H 2O 2molecule in linear (D h), bent (cis-C 2vand trans-C 2h)and equilibrium “skewed” anticline (C 2) nuclear configurationsThe large values of the vibronic constants are due to the nature of the mixing MOs determining the essentialchanges of the binding by the distortion. Indeed, for example, in the linear configuration the overlap of the occupied gand unoccupied u( g) orbitals is zero by symmetry restrictions (Fig. 4), and hence these orbitals do not contributeto oxygen-hydrogen bonding. Under the g( u) type nuclear displacements the gMO split and one of its componentbecome of the same symmetry as the respective admixing virtual orbital. Now their overlap is nonzero resulting in theadditional bonding of the 2p AOs of the oxygen atoms with the orbital of the nearest hydrogen atom.(a) (b)Fig. 4. Schematic illustration to the covalence origin of the vibronic instability of the linear configuration of H 2O 2: (a) g u, (b) g g. The overlap integral between the vibronically mixing molecular orbitals (white areas) is zero in thelinear D hconfiguration and becomes nonzero by g( u) distortions bending the H 2O 2molecule towards to the cis-C 2v(a) and trans-C 2h(b) transition states109