vibron model: plain text
Algebraic techniques in molecular spectroscopy: Abstract
Renewed attention has been recently devoted to
molecular spectroscopy both from experimental and theoretical stand
points. This field which is related to many important applications of modern physics, physical chemistry and bio-
chemistry, has a long history of continuing developments and improvements. Nonetheless, this history is still far from
its conclusion.
Present day experimental techniques provide spectroscopic data (in both electronic and rotovibrational regimes) of
extremely high resolution. With these results at disposal, the key for the interpretation of phenomena related to a
very detailed picture of the physical system is not so far as it was a few years ago. In order to correctly use this
key, an enormous theoretical effort is needed: the wealth of information carried by new experimental results demands for
a deeper understanding of molecular structure and dynamics. Such a demand, in view also of the complexity of typical
molecules under study, often results to be beyond the possibilities of standard theoretical approaches. These can be
roughly divided in two families: (1) methods based on the numerical solution of the Schroedinger equation, making use
of more or less effective ab-initio potential surfaces;(2) semiempirical techniques, like the Dunham expansion
approach, in which powers series in the rotovibrational quantum numbers are introduced and fitted to experimental
data. Both techniques encounter serious difficulties when applied to medium and large size molecules. The most evident
trouble arises when dealing with many interacting roto-vibrational modes as it happens in molecules with more than
just three atoms. Diagonalization of very large matrices, control over many free parameters as well as book-keeping of
thousands of states is then needed.
In recent years, a new systematic approach to these problems has been introduced, namely an algebraic technique called
vibron model. This model can be thought as an adapted version to the molecular problem of the corresponding
algebraic model for nuclear spectroscopy, namely the interacting boson model, nowadays widely accepted and used
for its completeness and efficacy.
In the vibron model, rotations and vibrations are quantized in an abstract model space by making explicit use of boson
creator and annihilation operators which at the same time can be thought as generators of specific algebraic
structures. This kind of technique is somehow equivalent to a second quantization procedure specialized to the roto-
vibrational problem. As a second step, starting from the Hamiltonian operator expressed in this algebraic language,
a dynamical symmetry is e xtracted: this corresponds in practice to selecting among many different combinations of
creation and annihilation operators only invariant or Casimir operators. This results in a Hamiltonian operator
which is diagonal in a proper basis and analytical in its quantum numbers. The algebraic Hamiltonian suited for
molecular rotovibrational problems makes use of dynamical symmetries based on unitary algebras usually in four or two
dimensions. After its original formulation for simple diatomic molecules, the vibron model has been largely
extended to cover more and more complex situations. The result of these investigations is that, in comparison to
other methods, the algebraic technique very often offers better results with less computational effort. Any kind of
three-atomic molecule and a large class of four-atomic molecules have been investigated by using algebraic
techniques. The results obtained include data on vibrational levels, IR and Raman transition intensities and roto-
vibrational coupling analysis.
A new, simplified but still powerful version of the algebraic approach has been also introduced. This model
deals with purely vibrational modes (i.e. disregarding rotational contributions), but it seems nonetheless to
reproduce with unexpected accuracy very complex situations otherwise inaccessible to traditional methods. As a specific
aspect, a new mathematical theorem concerning the well established discrete group theory has been demonstrated
which allows one to further simplify any theoretical attack to highly symmetric vibrating systems.
All this work is done in collaboration with:
F. Iachello (Yale),
R. Lemus (Mexico City),
K. Lehmann and G. Scoles (Princeton),
L. Wiesenfeld and R. Jost (Grenoble),
D. Bassi, M. Scotoni and L.Lubich (Trento),
M. Herman (Bruxelles).
References
F. Iachello, Chem. Phys. Lett.78, 581 (1981);
F. Iachello and S. Oss, J. Mol. Spectrosc. 142, 85 (1990);
F. Iachello and S. Oss, Phys. Rev. Lett. 66, 2976 (1991);
F. Iachello and S. Oss, J. Mol. Spectr. 153, 225 (1992);
F. Iachello and S. Oss, J. Chem. Phys. 99, 7337 (1993);
F. Iachello, S.Oss and L.Viola, J. Chem. Phys. 101, 3531 (1994);
F. Iachello and S.Oss, J. Chem. Phys. 102, 1141 (1995).
... to my home page ...