Dimers of the Major Components of the Atmosphere: Realistic Potential Energy Surfaces and Quantum Mechanical Prediction of Spectral Features.

E. Carmona-Novillo, V. Aquilanti

New accurate potential energy surfaces for the dimers O2-O2, N2-N2 and N2-O2  are available from analysis of scattering experiment for our laboratory, the only degrees of freedom which are frozen being the intramonomer vibrations, supposedly ininfluent in low energy dynamics.

In particular the novel technique developed in our group, first reported in Nature in 1994 [1] , for cooling oxygen to the lowest vibro-rotational state and for aligning the rotational angular momentum, allows the control of the relative orientation of the colliding molecules and so permit observation of a quantum-mechanical interference effect (the "glory"). Analysis of the velocity dependence of the integral cross-section for the scattering showing the glory oscillations provides data which together with accurate second virial coefficient yields the intramolecular potential and thus information on the dimer structure. So it is possible to obtain the anisotropy of the potential energy surfaces, namely the dependence on relative orientation for the dimers O2-O2, N2-N2 [2,3] and N2-O2.  These results indicate that most of the bonding in the dimer comes from electrostatic (van der Waals) forces. However chemical (spin-spin) contributions for (O2)2 are not negligible in this open-shell-open-shell.

The used potential energy surfaces are such that their handling and the physical interpretation of its terms make them "realistic" in the sense that they reproduce micro and macroscopic quantities experimentally available. In the case on integral cross-sections it is observed that both their absolute values and the features of "glory oscillations" are determined by the depth of the well and by its position and also from the long range dependence according to the C6/R6 law. In the case of the second virial coefficient it is observed that low temperature data are mainly reproduced by the anisotropic term of the potential (which can be described as a the pseudoatomo-diatom interaction) while at high temperature only the spherical part of the interaction is operative. Considering these aspects, a fit of potential is made so that the potential obtained agree with experimental cross-section and second virial coefficient data.

It is interesting to observe how for the two van der Waals complexes geometry
and the nature of the three dimers differ. In the case of oxygen the equilibrium geometry obtained for the ground singlet state is the H-configuration. A role is played for the equilibrium configuration from the spin-spin interaction , in spite that its contribution to the bond is approximately only 15 % . This leads to a geometry where the two O2 molecules are parallel. In the case of N2 (no electronic spin) the basic feature which determines the equilibrium geometry is the quadruple moment, which favors the T-configuration, and also the bond forces are stronger in the oxygen case because the strength of the spin spin interaction.  Finally a X-configuration is found for N2-O2, because no role is played by spin interaction and the quadrupole interaction is not enough strong to make stable the T-configuration.

We report calculations of the bound rovibrational states of the dimers for J lower or equal to 6 by solving the secular problem over the exact Hamiltonian, considering the monomers as rigid rotors. The full quantum mechanical calculations of bound states are carried out using the program BOUND [4], where one coordinate (here the intermolecular distance R) is treated as a scattering coordinate, and the Schrödinger equation is written using a basis set expansion for the remaining N-1 degrees of freedom. The coupled equations are then solved using the standard techniques of scattering theory, but with bound state boundary conditions, using the logarithmic derivative method for propagating the solutions along R. This method has been found to be particularly useful for van der Waals complexes, where there is wide-amplitude vibrational motion along the intermolecular coordinate. Surprisingly we have seen that although an exhaustive analysis of the used potential energy surfaces in the various calculations shows that they are topologically very different [5,6] , even when they fail to reproduce experimental data (integral cross-sections and second virial coefficient) they lead to comparative results for spectroscopic observables, in spite that absolute values of the well depths and well positions differ significantly.

On the other side, we calculated the harmonic frequencies through the second derivative of the potential around the equilibrium geometry of the dimers. From these values we obtain the energy levels of each vibrational level (harmonic), and the values calculated are very different from the exact results. We can say that the harmonic approximation fails in the case of these  van der Waals molecules because interaction forces are very weak and the potential anisotropy is important.


We can conclude that the three dimers O2-O2, N2-O2 and N2-N2 present characteristics more of a cluster than of a weakly bound molecule and that the interaction between the monomers is very anharmonic. Implications for the interpretation of recent laboratory [7,8] and atmospheric spectroscopic observations [9] will be discussed, as well as of current measurements of high pressure behavior of oxygen [10].

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