Rotation-Vibration of Polyatomic Molecules

Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

“…From Equation (37), the perturbed Hamiltonian matrix elements are, in general, functions of some power of the normal coordinate matrix, but Equation (45) deals only with Q'. To obtain formulae for integrals analogous to (45) but involving higher powers of Q, one employs matrix multiplication [ 171; for example, the matrix Q2 is simply the (matrix) product of two Q matrices,"…”

“…To a good approximation, the limits of integration in (37) and (38) may be interchanged; see [ 171 or [27] for discussion. The vibrational potential energy constants y$, and rotational potential energy constants y::: in (37) are simply the constant coefficients from (27):…”

Microwave spectrum of SiH3CCH in the 4ν10 state

“…From a treatment of the Hamiltonian up to the fourth order in vibration and the sixth order in rotation, Amat et al (8) have derived the diagonal and off-diagonal matrix elements of the vibration-rotation…”

“…These anomalies may be due to interactions with other vibrational modes; according to the infrared values of Refs. (5, 6), many states or combination states may be involved (8,9).…”

Analysis of Rotation--Vibration Relative Equilibria on the Example of a Tetrahedral Four Atom Molecule

“…Significant effort by mathematicians and molecular physicists to converge the two fields resulted in the qualitative theory of highly excited quantum molecular systems based on recent mathematical developments. We join the two approaches and demonstrate what kind of concrete results can be immediately obtained in molecular systems [1,2,3,4] by applying powerful methods of symmetric Hamiltonian systems [5,6,7,8,9,10,11]. We choose a concrete problem of rotation-vibration of a four-atomic molecule with tetrahedral equilibrium configuration [12,13] in order to explain the details of our approach.…”