ChemicalPhysics 68 (1982) 155-170
NorthHoll;tnd publishing Company
PERWRBED ROTATIO_NAL STATE METHOD FOR COLLISIONS
BETWEEN AN ION AND AN ASYMMETRIC-TOP RIGID ROTOR
Kamhiro SAKtMOTO
Tne ZnstirureofSpace and Astronautical Science,
Konuzba. Meguro-Au,Tokyo J-53.Japan
Received 13 November 1981
The theory of low-energy coU.isions between an ion and an asymmetric-top rotor is formulated in the adiabatic (perturbed rotational state) representation. Some symmetry properties of the system which give useful schemes for cakulations
are discussed. For numerical examples, the adiabatic potential curves and the nonadiabatic couplings are presented for ionHz0 and HDO, and the rotationally inelastic cross section is calculated for the ion-HDO system. A perturbative treatment
in the adiabatic representation, in which the CorioJ.5 transition is taken into account, and the first Born approximation are
also applied.
1. Introduction
Hitherto, we have investigated the theory of slow collisions between an ion and a polar molecule which is assumed a linear or symmetric-top rotor [l-3]. The previous studies demonstrated that the rotational state of the
molecule during collision is well described by the adiabatic (PRS: perturbed rotational state) representation. In
the PRS theory, two important notions are introduced, that is, oni is the adiabatic potential curves, which is useful for the calculation of the chemical reaction and the transport processes [4,5], and the other is the nonadiabatic
coupling by which the rotational inelastic processes are induced among the adiabatic potential curves. Whether the
adiabatic representation is appropriate is judged by the smallness of the nonadiabatic transition probability during
collision. If we describe the state of the low-velocity collision system of an ion and a polar molecule in terms of
the free-rotor basis, we fmd that a large number of free-rotor states must be taken into account although the net
transition probability after collision is very small 131. On the other hand, in the adiabatic representation, only inclusion of the mkimum basis for the transition under consideration, or even the perturbative treatment gives reliab!e results [l-3,6].
For the system of an ion and a polar molecule, the most important interaction is au ion-dipole interaction. At
low-velocity the collision with very large impact parameters contributes to the rotationally inelastic transition except for weakly polar molecules such as CO, NO, etc. This allows us to neglect the short-range forces and to assume the point-dipole interaction [3]. Furthermore, the distortion of the relative motion is negligibly small, and
the reIative trajectory can be assumed a straight line [2]. Under these assumptions, we can obtain a scaling law for
the rotationally inelastic cross section when the molecub is a linear or symmetric;top rotor [ 1,3]. For an asymmetric-top rotor, this scaling Iaw can no longer be obtained. This is because the rotational state of an asymmetrictop rotor depends on the three rotational constants, and the direction of the dipob moment relative to the principal axes differs for different molecules.
The collision-induced rotational transition is one of the most dominant inelastic processes at low temperature
gases. Recently, in the interstellar cloud, many molecules (about 50 species) have beeo found 171. The radio lines
from these molecuIes are important observational means to estimate the molecular abundances and to diagonose
the interstellar conditions [8]- For this reason, the theory of the rotationa! excitation at low temperatures has
0301-~lW/82/0000-0000/S
02.75 0 1982 North-Holland