4 Discussion

A. Summary

In the present study, the potential energy diagram for the hydrogen dissociation reactions from HCNH, $\rm HCNH \to HCN + H$ (I) and $\rm HCNH \to HNC + H$ (II), were calculated by means of extensive ab-initio MO calculations. The activation barrier for channel I was always lower in energy than that of channel II. The energetics derived form the present calculations are essentially similar to the energy diagram for $\rm H + CNH \to HCN + H$ obtained by Talbi et al. (Talbi et al. 1996). Using the energetics data obtained, the reaction rates were calculated on the basis of RRKM theory including tunneling effects. The reaction rates for channel I were larger than those of channel II at lower internal energies of HCNH, below E = 48 kcal/mol, whereas channel II became dominant at higher energy. The branching ratio HCN/HNC was estimated to be 0.3 at an internal energy of 4.4 eV, which corresponds to the adiabatic electron affinity of HCNH⁺ (Shiba et al. 1998).

B. Reaction model

It is known that the observed abundance ratios of HCN and HNC are dependent on the temperature of the molecular clouds. The ratios in OMC-1 range from 1 to 100 (Schilke et al. 1992). Figure 4 shows the observed HCN/HNC ratios in various sources plotted against the reciprocal of temperature of the molecular clouds (Hirota et al. 1998).

Figure 4: Reaction rates for channels I and II plotted as a function of internal energy of HCNH calculated by means of RRKM theory including tunneling effects.

At high temperature, the ratios lie on a straight line. The ratios are not dependent on temperature at lower temperature regions, although the values are widely distributed. It is considered that HNC is destroyed by reactions with the other atoms: $\rm HNC + H \to HCN + H$ and $\rm HNC + O \to NH + CO$ for example (Schilke et al. 1992; Talbi et al. 1996). These reactions have activation energies and rate constants strongly dependent on temperature.

For a mechanism in the low temperature region, some theoretical calculations have been carried out by several groups (Shiba et al. 1998; Herbst 1979; Talbi & Ellinger 1998, 1996; Tachikawa 1999). Previous theoretical studies predicted that the branching ratio HCN/HCN formed via two $^2\Sigma$ states is closed to 1. This ratio was calculated on the basis of Franck-Condon (FC) model of electron capture of HCNH⁺ with the assumption that the reaction occurs via excited states of HCNH ($^2\Sigma$ states). This value was schematically illustrated by a dashed line in Fig. 5 (i.e., the line of $\rm Log(HCN/HNC) = 0$, and shown by $^2\Sigma$).

Figure 5: Observed HCN/HNC ratio in various sources is plotted against 1/T. Data are taken from Hirota et al. (1998, ApJ 503, 717). The OMC-1 data (Schilke et al. 1992) are fitted to the function [HCN]/[HNC] $= A \exp (-\Delta E/T)$, where $\Delta E$ is the potential barrier drawn as a solid line. The dashed line ($^2\Sigma$) is the ratio predicted by the Franck-Condon model via two $^2\Sigma$ states. The dotted line ($^2\Pi$) is the ratio predicted by the present model which the reaction occurs via the HCNH ($^2\Pi$ and 2A') state.

The ratio is not dependent on temperature. This FC model can reasonably explain almost all observed abundance ratios in low temperature. However, as clearly seen in this figure, the observed ratios seem to be widely distributed in the range $\rm Log(HCN/HNC) = -0.64 {-} 0.25$ in lower temperature regions, indicated by a circle in Fig. 5.

The present value obtained by RRKM theory is schematically plotted by a doted line ($^2\Pi$ state) in Fig. 5. If a reaction occurs via the ground state potential energy surface, the branching ratio is calculated to be $\rm HCN/HNC = 0.3$ $\rm (Log(HCN/HNC) = -0.52$ at E=4.4 eV). This model can also explain some observed branching ratios in the circle region in Fig. 4. This agreement may imply that some of the HCN and HNC molecules are formed via the ground state of HCNH ($^2\Pi$ state) after the electron capture of HCNH⁺.

The isotope effects on the branching ratios were also investigated by means of ab-initio and RRKM calculations for the H and D dissociation reactions in DCND, HCND and DCNH. The values obtained are consistent with the observed differences in DCN/HCN branching ratios as reported by Turner (2001).

Our main results can be summarized as follows,

(1)

In the temperature dependent region, the formation and decomposition of the HCN and HNC molecules occurs via $\rm HNC + H \to HCN + H$ or $\rm HNC + O \to NH + CO$.

(2)

In the temperature independent region, in particular the region where the ratio of HCN/HNC is close to 1.0, the electron capture reaction

$$\begin{eqnarray*}\rm HCNH^+ + e^- \to \left[HCNH\left(^2\Sigma\right)\right]^* &\to&\rm HNC + H\\ &\to&\rm HCN + H \end{eqnarray*}$$

may be dominant.

(3)

In the temperature independent region, in particular the region where the ratio of HCN/HNC is below 1.0, the decomposition reaction on the ground state PES,

$$\begin{eqnarray*}\rm HCNH^+ + e^- \to \left[HCNH\left(^2\Pi\right)\right]^* &\to& \rm TS1 \to HNC + H\\ &\to& \rm TS2 \to HCN + H \end{eqnarray*}$$

would be dominant. Thus, the present model could explain the relation between the branching ratio (HNC/HCN) and temperature.

Acknowledgements

The authors are indebted to the Computer Center at the Institute for Molecular Science (IMS) for the use of the computing facilities. H.T. also acknowledges a partial support from a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan.