2 Computational methods

All ab-initio molecular orbital (MO) calculations were carried out using the Gaussian 98 program package (Frisch et al. 1998). The geometry optimizations of molecules at the stationary points were made at the Møller-Plesset forth order perturbation theory with Dunning's correlation consistent basis set (valence triple-zeta): namely, MP4SDQ /cc-pVTZ level. Also, the MP4SDQ/6-311++G(d, p) calculation was carried out in order to obtain the geometry of the molecules. Using the optimized geometries, the energies were re-calculated by the quadratic configuration interaction including the single and double substitution (QCISD) calculation with standard Pople's basis sets: namely, the QCISD/6-311++G(2df, 2pd) and QCISD/6-311++G(3df, 3pd) levels. Also, total energies were calculated at the QCISD/aug-cc-pVTZ levels.

The electronic configuration of HCNH⁺ is illustrated in Fig. 1.

Figure 1: Schematic illustration for molecular orbitals of HCNH+.

The electrons occupy up to the double degerated $\pi$CN) molecular orbital (1$\pi$ orbital) of HCNH⁺. If an excess electron occupies $\pi^*$(CN) orbital (2$\pi$ rbital) by electron capture, $\rm HCNH^+ + e^- \to HCNH$, the electronic state of HCNH is expressed by the $^2\Pi$ state. This is the ground state of HCNH. HCNH has an excited state expressed by HCNH ($^2\Sigma$) if the excess electron occupies in the $\sigma^*$(CH) orbital. In the present study, we considered only the $^2\Pi$ state of HCNH (i.e., the ground state of HCNH). This state is changed to ²A' state if the molecular symmetry is reduced to the Cs symmetry.

Harmonic vibrational frequencies of the molecules at the stationary points along the reaction coordinates, HCNH, TS1, TS2, HCN and HNC, were calculated at the MP4SDQ/6-311++G(d, p) level. In addition, in order to estimate isotope effect on the reaction, the harmonic frequencies for the systems including deuterium, DCND, DCNH and HCND, were calculated with the same manner.

The reaction rates were calculated using RRKM theory as a function of excess energy of HCNH. In the RRKM calculations, the tunneling effect was included by Miller's method (Miller 1979)