Collisions of an asymmetric top with a closed-shell linear molecule

BASISTYPE = 30

System subroutine: syastp3

Basis subroutine: hiba30_astp3.F90

Refs. T. R. Phillips, S. Maluendes, and S. Green, J. Chem. Phys. 102, 6024 (1995); P. Valiron et al., J. Chem. Phys. 129, 134306 (2008).

This basis subroutine pertains to collisions of an asymmetric top molecule of $C_{2v}$ or $C_s$ symmetry with a closed-shell diatomic molecule. For a $C_{2v}$ molecule, the body-frame z axis is taken to lie along the $C_{2}$ axis,, following Green’s convention.

For a molecule with $C_{v}$ symmetry, the body-frame z axis is taken to lie along the an inertial axis.

The definition of the integer system dependent parameters is as follows:

• NTERM: the number of potential surfaces involved. This parameter can not be changed
• NUMPOT: an index representing the particular potential used. This variable is passed to the POT subroutine
• IOP: ortho/para label for molecular states of the asymmetric top of $C_{2v}$ symmetry. If IHOMO =.true. then
  • if IOP = 1: only para states included in channel expansion
  • if IOP = −1: only ortho states included in channel expansion IOP is not needed if IHOMO =.false. (for a molecule of $C_{s}$ symmetry, but a number should be entered for this parameter nevertheless.

• JMAX: the maximum rotational angular momentum included in the channel expansion

• IPOTSY2: symmetry of potential. Set equal to 2 for homonuclear molecule 2, or 1 for heteronuclear molecule.

The definition of the real system dependent parameters is as follows:

• AROT, BROT, CROT: rotational constants of the asymmetric top
• EMAX: the maximum energy of a level to be included in the rotational state basis

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The rotational eigenfunctions of an asymmetric top are expanded in a symmetrized symmetric top basis as [S. Green, J. Chem. Phys. 64, 3463 (1976)]

$

jkms > = [2(1+ \delta k_0)]^{1/2} [

jkm> + s

j-km>] $

where $s$ is the symmetry index (+1 or −1). In this basis, the asymmetric top hamiltonian block diagonalizes into 4 groups: (1) $k$ even, $s$ = +1, (2) $k$ even, s = −1, (3) $k$ odd, s = +1, and (4) $k$ odd, s = −1.

The expansion coefficients are stored in the array c as:

• $c(k=0)$, $c(k=2)$, … $c(k=j)$, for even $k$
• $c(k=1)$, $c(k=3)$, … $c(k=j)$, for odd $k$

By setting BASTST=.TRUE., you can output the values of $j$, $s$, the values of the prolate and oblate projection quantum numbers [ $k_p$ and $k_o$], and the internal energies, as well as the expansion coefficients.