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
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  , 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 , 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
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  will be discussed, as well as of
current measurements of high pressure behavior of oxygen .
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