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3 Potential curves and transition moments

The potential curves and electric dipole transition moments are calculated by the multireference single- and double-excitation (MRD-CI) configuration interaction method (Buenker & Peyerimhoff [1974], [1975]; Buenker [1986]), with configuration selection and energy extrapolation using the Table CI algorithm (Buenker [1980], [1981]; Buenker & Phillips [1985]). During the CI excitation procedure, the five lowest molecular orbitals corresponding to 1s, 2s, and 2p orbitals of the heavy atoms are always doubly occupied, whereas some high virtual orbitals are discarded. The atomic orbital basis sets used in the present calculations contain at least one f-type function for the heavy atoms and one d-type function for the hydrogen atom. The basis sets consist of 73 contracted Gaussian functions for both PH+ and SH+, and 109 contracted functions for SiH+. Further details about our MRD-CI calculations on these species can be found in the following references: for SiH+ see Sannigrahi et al. ([1995]), for SH+ see Kimura et al. ([1997]), and for PH+ see Gu et al. ([1999]).

The potential curves of relevant states of the three ions are shown in Figs. 1 to 3, respectively. In the region $R \geq 2.0$ a0, the potentials are obtained from the ab initio calculations, whereas the potentials for R < 2.0 a0 are obtained by fitting the last few ab initio points using the form $a\exp(-bR) + c$. The asymptotic separated-atom and united-atom limits of these states can be found in Table 1. The electric dipole and transition moments are shown in Fig. 4. In the short R region (R < 2.0 a0), their curves (full lines) are obtained by extrapolating the form aR2 + bR to zero at the united-atom limit by using the last few ab initio points. The contributions of the transition moments in the very short R region to the final cross sections are expected to be quite small although the exact positions of the "turning point'' of the electric transition moments of PH+ and SiH+ are somewhat uncertain. Further details on SiH+ are given in Stancil et al. ([1997]).

In Table 2, the spectroscopic constants, $R_{\rm e}$ (equilibrium distance), $D_{\rm e}$ and D0 (dissociation energies), and $\omega_{\rm e}$ (vibrational frequency), of the ground states for the three ions are listed together with previous experimental and theoretical results. It can be seen that there is generally good agreement between the present calculations and previous results. We find that the ground states of SiH+, PH+, and SH+ support 22, 22, and 21 vibrational levels and 932, 760, and 731 rovibrational levels, respectively.

\end{figure} Figure 1: The $X~^1\Sigma^+$ and $A~^1\Pi$ potentials of SiH+

\end{figure} Figure 2: The $X~^2\Pi$ and $1~^2\Sigma^-$ potentials of PH+

\end{figure} Figure 3: The $X~^3\Sigma^-$ potential of SH+


Table 2: Spectroscopic constants of the ground states
  $R_{\rm e}$ (a.u.) $D_{\rm e}$ (eV) D0 (eV) $\omega_{\rm e}$ (cm-1) References
This work 2.84 3.354 3.22 2155.0  
Exp. 2.842 3.354 3.22 2157.15 Carlson et al. ([1980])
Exp. 2.842   3.17 2157.17 Huber & Herzberg ([1979])
Theory 2.844   3.30 2161.23 Matos et al. ([1988])
Theory 2.848 3.229   2155.35 Hirst ([1986])
Theory 2.853   3.24 2153.5 Rosmus & Meyer ([1977])
This work 2.708 3.41 3.27 2370  
Exp. 2.693   3.34 $\pm$ 0.2 2299.6a Narasimham ([1957])
Theory 2.692 3.41 3.26 2354 Bruna et al. ([1981])
Theory 2.704   3.31 2375.8 Rosmus & Meyer ([1977])
This work 2.581 3.52 3.36 2565  
Exp. 2.5772 (3.7) (3.54) 2547.7 Rostas et al. ([1984])
Theory 2.587 3.53 3.37 2535 Bruna et al. ([1983])
          Hirsch & Bruna ([1999])
Theory 2.585   3.73 2566.1 Rosmus & Meyer ([1977])

This value corresponds to $\Delta G_{1/2}.$
Values in paratheses are estimates.

\end{figure} Figure 4: Transition moments of SiH+ and PH+ and the dipole moment of SH+

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