3 Results

A. Structures and energetics of the HCNH system

The present calculations showed that two reaction channels are involved in the hydrogen atom dissociations from HCNH on the ground state potential energy surface ($^2\Pi$ or ²A' states) expressed by

$$\begin{eqnarray*}\rm HCNH~ \left(^2\Pi\right)&\to& \rm TS1\to HCN + H~~~ channel~I\\ &\to&\rm TS2 \to HNC + H~~~ channel~II. \end{eqnarray*}$$

Channels I and II are pathways for the N-H and C-H bond cleavage reactions of HCNH, respectively. Each channel has a transition state expressed by TS1 or TS2. The structures of HCNH at the stationary points along the H-atom dissociation reactions (channels I and II) were fully optimized at the MP4SDQ/cc-pVTZ and MP4SDQ/6-311++G(d, p) levels of theory. Both calculations gave similar geometrical parameters. The optimized structures obtained at the MP4SDQ/cc-pVTZ level are illustrated in Fig. 1. The HCNH molecule has a bent structure with a trans form and a planar one ( $\phi= 180^\circ$). The structures of TS1 and TS2 are also illustrated in Fig. 2.

Figure 2: Optimized structures of HCNH system. The values were calculated at the MP4SDQ/cc-pVTZ level. Bond lengths and angles are in Å and in degrees, respectively. Experimental geometrical parameters are $r\rm (CH)=1.065$ and $r\rm (CN)=1.153$ Å for HCN (Herzberg 1966), and $r(\rm NH)=0.986$ and $r\rm (CN)=1.173$ Å for HNC (Harmony et al. 1979).

Both transition states have a cis form. The product molecules for channels I and II are HCN and HNC, respectively. The bond distances of HCN, r(C-H) and r(CN), were calculated to be 1.0648 and 1.1551 Å, respectively, in good agreement with experimental values (1.065 and 1.153 Å). For the HNC molecule, a reasonable structure was also obtained. These results strongly indicate that the MP4SDQ/cc-pVTZ calculation would give reasonable structures for the HCNH system.

The total energies and potential energy curve calculated at the MP4SDQ/cc-pVTZ, QCISD/aug-cc-pVTZ, MP4SDQ/aug-cc-pVTZ, QCISD/6-311++G(2df, 2pd), and QCISD/6-311++G(3df, 3pd) levels are given in Fig. 3.

Figure 3: Potential energy curve for the hydrogen atom decomposition of HCNH calculated for several levels. The structures at each stationary point were obtained at the MP4SDQ/cc-pVTZ level (see Fig. 1).

The structure at each stationary point was fully optimized at the MP4SDQ/cc-pVTZ level. Relative energies are given in Table 1. The calculations indicate that the barrier heights for channels I and II are close to each other, although that of channel II was always lower than that of channel I in all levels.

   

Table 1: Relative energies ( $E_{\rm rel}$ in kcal mol^-1) calculated at various levels^a.

	HCNH	TS1	TS2	HCN + H	HNC + H
MP4SDQ/cc-pVTZ	0.0	34.8	38.5	23.0	34.4
MP4SDQ/aug-cc-pVTZ	0.0	34.8	39.1	20.8	35.4
QCISD/6-311++G(2df,2pd)	0.0	33.7	40.4	23.1	37.3
QCISD/6-311++G(3df,3pd)	0.0	33.8	40.7	23.4	37.6
QCISD/aug-cc-pVTZ	0.0	33.5	40.4	23.2	37.7

^a Geometries were fully optimized at the MP4SDQ/cc-pVTZ level.

Harmonic vibrational frequencies of HCNH, TS1, TS2, HCN and HNC were calculated at the MP4SDQ/6-311++G(d, p) level. The results are summarized in Table 2. Inclusion of zero-point vibrational energies changed relative energies to the low-energy region. However, TS1 is always lower in energy than that of TS2.

   

Table 2: Harmonic vibrational frequencies calculated at the MP4SDQ/6-311++G(d, p) level (in cm^-1). Zero point vibrational energies (ZPE in kcal/mol) and best estimated relative energies ( $E_{\rm rel} + \Delta ZPE$) are also given. $E_{\rm rel}$ were calculated at the QCISD/aug-cc-pVTZ//MP4SDQ/cc-pVTZ level.

	HCNH	TS1	TS2	HCNa + H	HNCb + H
1	3541.1(a')	1801.9i(a')	931.8i(a')	3475.9($\sigma$)	3860.9($\sigma$)
2	3070.3(a')	3491.0(a')	3853.7(a')	2121.5($\sigma$)	2053.3($\sigma$)
3	2246.3(a')	2359.6(a')	2043.5(a')	739.6($\pi$)	484.5($\pi$)
4	1203.5(a')	881.9(a $\hbox{$^{\prime\prime}$ }$)	518.9(a $\hbox{$^{\prime\prime}$ }$)	739.6($\pi$)	484.5($\pi$)
5	982.5(a $\hbox{$^{\prime\prime}$ }$)	774.2(a')	423.8(a')
6	859.8(a')	559.7(a')	355.3(a')
ZPE	17.0	11.6	10.3	10.1	9.8
$E_{\rm rel} + \Delta ZPE$	0.0	28.1	33.7	16.3	30.5

^a Experimental values were measured to be 3311.5, 2096.9 and 712.0 cm^-1 (Shimanouchi et al. 1992).
^b Experimental values were measured to be 3652, 2023.9 and 464.2 cm^-1 (Pettersson 1998).

For comparison, vibrational frequencies of the molecules at the stationary points for the deuterium dissociation reactions,

$$\begin{eqnarray*}\rm DCND^+ ~ \left(^2\Pi\right)+ e^- &\to&\rm [DCND]^* \\ &\to&... ...~ channel~I(D)\\ &\to& \rm TS2(D) \to DCN + D~~~ chennel~II(D) \end{eqnarray*}$$

were calculated in the same manner. The results are given in Table 3. The stretching modes of DCND (modes 1-3) were largely shifted to low-energy region. The imaginary frequencies at the transition states TS1(D) and TS2(D) were calculated to be 1337.1i and 683.5i cm^-1, respectively, which are more blue-shifted than that of HCNH (1801.9i and 931.8i cm^-1). The zero point vibrational energies (ZPEs) were lowered by the isotope effect. The vibrational frequencies of the molecules at the stationary points for the HCND and DCNH were also calculated and the results are summarized in Table 4. The imaginary frequencies for the D atom dissociation were lower than that of hydrogen.

 

 

Table 3: Harmonic vibrational frequencies of the DCND system calculated at the MP4SDQ/6-311++G(d, p) level (in cm^-1). Zero point vibrational energies (ZPE in kcal/mol) and best estimated relative energies ( $E_{\rm rel} + \Delta ZPE$) are also given. $E_{\rm rel}$ was calculated at the QCISD/aug-cc-pVTZ//MP4SDQ/cc-pVTZ level.

	DCND	TS1(D)	TS2(D)	DCN + D	DNC + D
1	2642.0(a')	1337.1i(a')	683.5i(a')	2723.3($\sigma$)	2905.7($\sigma$)
2	2399.2(a')	2816.8 (a')	2899.7(a')	1950.6($\sigma$)	1964.8($\sigma$)
3	2039.3(a')	2075.2(a')	1955.4(a')	589.7($\pi$)	383.2($\pi$)
4	954.8(a')	718.7(a $\hbox{$^{\prime\prime}$ }$)	410.1(a $\hbox{$^{\prime\prime}$ }$)	589.7($\pi$)	383.2($\pi$)
5	720.7(a $\hbox{$^{\prime\prime}$ }$)	639.7(a')	353.6(a')
6	630.4(a')	410.6(a')	257.7(a')
ZPE	13.4	9.5	8.4	8.4	8.1
$E_{\rm rel} + \Delta ZPE$	0.0	29.6	35.4	18.2	32.4

 

 

Table 4: Harmonic vibrational frequencies of the HCND and HCND systems calculated at the MP4SDQ/6-311++G(d, p) level (in cm^-1).

Stationary point		frequency
	Reaction of HCND
HCND	3553.6	2448.3	2058.6	1079.1	865.6	742.8
TS1	1353.9i	3499.7	2328.1	891.3	744.5	452.6
TS2	933.9i	2907.0	1958.1	417.3	412.0	279.4
	Reaction of DCNH
DCNH	3083.2	2629.8	2204.2	1153.9	863.9	685.3
TS1	1794.8i	2836.5	2099.9	724.0	696.6	492.9
TS2	688.3i	3867.2	2042.7	519.9	390.0	309.2

B. Reaction rates

On the basis of the energetics and vibrational frequencies, reaction rates for channels I and II were calculated as a function of internal energy (E) of HCNH using RRKM theory including tunneling effects. The results are given in Fig. 3. At lower internal energy, channel I was significantly dominant. The curves of reaction rates for channel I and II crossed each other at E = 48 kcal/mol. Channel II becomes dominant at higher energies. At E = 4.4 eV, which corresponds to the electron affinity of HCNH⁺ (Shiba et al. 1998), the branching ratio for HCN/HNC was calculated to be 0.3. The corresponding branching ratio for DCN/DNC was calculated to be 2.8 at E = 4.4 eV, which is significantly larger than the reaction of the hydrogen atom. This is due to the isotope effect in deuterium.

For comparison, the ratios for the H or D atom dissociation reactions of DCNH and HCND were calculated. The ratio of DNC/HCN is calculated to be 5.9 for HCND, is 0.63 in DCNH.