Chemistry Journal <strong>of</strong> Moldova. N.Gorinchoy General, et al./Chem.J.Mold. Industrial and Ecological 2008, 3 (1), Chemistry. 105-111 2008, 3 (1), 105-111VIBRONIC ORIGIN OF THE “SKEWED” ANTICLINE CONFIGURATIONOF THE HYDROGEN PEROXIDE MOLECULEN. N. Gorinchoy * , I. Ya. Ogurtsov and Ion ArseneInstitute <strong>of</strong> Chemistry, Academy <strong>of</strong> Sciences <strong>of</strong> Moldova, Academiei str. 3, MD 2028 Kishinev, Republic <strong>of</strong> Moldova*E-mail: ngorinchoy@yahoo.com; Phone 373 22 739649Abstract: The vibronic origin <strong>of</strong> instability <strong>of</strong> the symmetrical forms (D h, C 2hand C 2v) <strong>of</strong> the hydrogen peroxidemolecule H 2O 2was revealed using ab initio calculations <strong>of</strong> the electronic structure and the adiabatic potentialenergy curves. The vibronic constants in this approach were estimated by fitting <strong>of</strong> the ab initio calculated adiabaticpotential in the vicinity <strong>of</strong> the high-symmetry nuclear configurations to its analytical expression. It was shownthat the equilibrium “skewed” anticline shape <strong>of</strong> the C 2symmetry can be realized in two ways: D hC 2v C 2orD h C 2h C 2with the decreasing <strong>of</strong> the adiabatic potential energy at every step.Keywords: hydrogen peroxide, electronic structure, pseudo Jahn-Teller effect.IntroductionIt is known that molecules <strong>of</strong> the type ABBA have a different geometry in gaseous phase: acetylene HCCH is alinear molecule (D h), HNNH has a bent form with the C 2hsymmetry and hydrogen peroxide H 2O 2adopts a “skewed”anticline shape with
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 <strong>of</strong> the AP arising from the mixing <strong>of</strong> the ground ( ) with theexcited ( ) states in the second order perturbation theory, andF ( Hˆ ( r , q ) q ) 0 , (4)is the constant <strong>of</strong> vibronic coupling between the mixing states. In eqs. (2)-(4) is the electronic Hamiltonian <strong>of</strong> thesystem, and E and E are the total energies <strong>of</strong> 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 <strong>of</strong> the AP, are nonzero only if contains .vIt was proved analytically and confirmed by a series <strong>of</strong> numerical calculations [2-7] that for any molecularsystem the contribution to the curvature <strong>of</strong> AP <strong>of</strong> the ground state is always positive,K 0.(5)0This means that structural instabilities and distortions <strong>of</strong> high-symmetry configurations <strong>of</strong> any polyatomic system innon-degenerate states are due to, and only to the PJTE, the mixing <strong>of</strong> the electronic state under consideration withhigher in energy (excited) states under the nuclear displacements in the direction <strong>of</strong> 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 <strong>of</strong> instabilityInvestigation <strong>of</strong> the possible spatial structures <strong>of</strong> the system should be started with its highest possible symmetry.In the case <strong>of</strong> the H 2O 2molecule the linear configuration <strong>of</strong> D h symmetry is the reference one. In this configurationthe four-atom molecular system H 2O 2has seven vibrational degrees <strong>of</strong> freedom, which transform according to theirreducible representations 2 g u g u. Two modes, uand g, correspond to the bending <strong>of</strong> the moleculeand transform the linear nuclear configuration into the cis- (C 2v) and trans- (C 2h) transition states, leaving them, however,planar. Schematic illustration <strong>of</strong> these two modes is shown in Fig.1, a,b.After separating <strong>of</strong> the center <strong>of</strong> masses we come to the following symmetrized displacements <strong>of</strong> the type,describing the internal motions <strong>of</strong> 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
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