Collision of an Atom with a CH₂(X ³B₁) (0,v₂,0) bender vibrational level

BASISTYPE = 17

System subroutine: sych2x

Basis subroutine: hiba17_ch2x.F90

The definition of the system dependent parameters is as follows:

• NTERM: the number of potential surfaces involved. This parameter should equal the number of MU terms in the angular expansion of the potential.. This parameter can not be changed

• NUMPOT: an index representing the particular potential used. This variable is passed to the POT subroutine

• IPOTSY: cylindrical symmetry of potential. The variables (theta,phi) describing the angular expansion of the potential should be defined with the a inertial axis defined as the body-frame z axis and, if possible, the xz plane as a plane of symmetry of the molecule (in this case, POTSY = 2). If the flag IHOMO = .True., only terms with LAMBDA + MU equal to an integer multiple of IPOTSY can be included in the potential. Example: for H₂O, IPOTSY = 2

• IOP: ortho/para label for molecular states of the asymmetric top. If IHOMO =.True. then
  • if IOP = 1: only para states included in channel expansion
  • if IOP = −1: only ortho states included in channel expansion
• IVBEND: the v2 bending vibrational quantum number [0 <= IVBEND <= 3]
• JMAX: the maximum rotational angular momentum included in the channel expansion
• EMAX: the maximum energy of a state to be included in the rotational state basis

The CH₂(X ³B₁) molecule has a low barrier to linearity, and its rotational energies are not at all well described by the standard rotational energy formulas. Bunker and Jensen have developed a Morse oscillator-rotating bender internal dynamics Hamiltonian (MORBID) to compute the rovibrational energies in this electronic state [see P. Jensen and P. R. Bunker, J. Chem. Phys. 89, 1327 (1988); P. R. Bunker, P. Jensen, W. P. Kraemer, and R. Beardworth, J. Chem. Phys. 85, 3724 (1986)]. Rather than compute the rotational energies in a given vibrational level, here we look up the energies in a table provided by Jensen [P. Jensen, private communication (2010)]. The CH₂(X ³B₁) state is well described by Hund’s case (b) coupling, in which the electron spin [S=1] is weakly coupled to the molecular frame. As a result, the rotational rotational angular momentum n is coupled to the electron to yield states of total angular momentum j = n − 1, n, n + 1 [if n >= 1]. This subroutine sets up a calculation of spin-free cross sections, for transitions between states of differing n.

Because of the large effective A rotational constant in the bender levels, the rotational wave functions are well approximated by symmetric top wave functions. The latter can be expressed in a symmetrized basis as [S. Green, J. Chem. Phys. 64, 3463 (1976)]

| n k m s > = [2(1+δ_k0)]−1/2 [ | n k m > + s | n −k m >] where s is the symmetry index (+1 or −1). By setting BASTST = .TRUE., you can output the values of n, s, the values of the asymmetric top prolate and oblate projection quantum numbers [k_p and k_o], and the internal energies.