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Quantum mechanical calculations of theHCN-HNC isomerizationD. Booth a & J.N. Murrell aa School of Molecular Sciences, University of Sussex, Brighton, BN1 9QJ

Available online: 23 Aug 2006

To cite this article: D. Booth & J.N. Murrell (1972): Quantum mechanical calculations of the HCN-HNCisomerization, Molecular Physics: An International Journal at the Interface Between Chemistry andPhysics, 24:5, 1117-1122

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MOLECULAR PHYSICS, 1972, VOL. 24, No. 5, 1117-1122

Quantum mechanica l calculations of the HCN-HNC isomerization

by D. B O O T H and J. N. M U R R E L L

School of Molecular Sciences, University of Sussex, Brighton, BN1 9QJ

(Received 5 July 1972)

Ab initio calculations using a minimum basis of Slater orbitals have been carried out on the molecules HCN and HNC with optimization of geometry. The predicted geometry of HNC is compatible with an observed radio- emission line which has been attributed to this molecule. The reaction profile for the internal migration of the proton has been calculated. The transition state is approximately T shaped with an activation energy from HNC of 251 kJ/mole.

1. INTRODUCTION

Although alkyl cyanides are stable molecules, the species H N C has only been positively identified by Milligan and Jacox [1] in argon and nitrogen matrices at 4 K. Earlier assignment of a weak Raman line in liquid H C N due to the species H N C was later shown by Herzberg [2] to be due to HClaN, and McCrosky et al. [3] have obtained chemical evidence that H N C could only exist in H C N at ex- tremely small concentrations at room temperature. An emission line from the galactic sources W51 and DR21 at 9065 + 1 M H z has been tentatively assigned by Buhl and Snyder [4] to the J = 1 + 0 rotational transition of HNC, on the basis of an assumed geometry of Milligan and Jacox [1].

Van Dine and Hoffman [5] examined the potential surface for the internal migration of the hydrogen from one end of the CN group to the other using Extended Huckel methods. They found an activation energy from H N C of approximately 400 kJ/mole with a T-shaped transition state. Loew and Chang [6] also made Extended Huckel calculations and obtained the potential energy curve for the linear dissociation of both H C N and C N H as they considered this a com- petitive route for isomerization. However, their calculations predicted a hetero- lyric dissociation into H + and C N - whereas dissociation to radicals has the lower energy.

There have been many calculations on H N C both empirical and ab initio, but, to our knowledge, there have been no ab initio calculations on HNC. In view of the recent interest in this species we here report the results of such calculations. Our objectives are similar to those behind the Extended Huckel calculations, namely, both a study of the bonding in the two species and an investigation of the lowest energy route for migration of the proton. In addition a calculated structure for H N C will give support or otherwise to the assignment of the radio-emission band referred to above.

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1118 D. Booth and J. N. Murrell

2. METHOD OF CALCULATION

The calculations have been based on a non-empirical 8 C F M O procedure with minimum basis of Slater-type atomic orbitals, with the restriction that the 2s and 2p orbital exponents for the same atom were equal. Initial calculations were made using a fast integral package that gives approximate three and four-centre integrals. From earlier work on other molecules the results using this package have been found to be reasonably close to those obtained from accurate integral packages [8] (root mean square deviation from 15 calculations was 0.01 a.u.). After optimiza- tion of most parameters in the calculation the final energies were calculated using the 8teven's integral package [9].

Optimal geometries and exponents for the valence orbitals were obtained for three structures : linear HCN, T-shaped C H N and linear HNC. Each of these requires a minimization over seven non-linear parameters (two bond lengths and five orbital exponents) which for complete optimization can be very time-con- suming. Our approach was first to optimize independently the carbon and nitro- gen ls and 2s (2p) exponents for reasonable values of the other parameters. In doing this we are assuming that they are only weakly dependent on the other variables. The remaining variables, the two bond lengths and the hydrogen ls exponent were .jointly optimized by taking a grid of points which spanned the energy minimum and fitting these points to a harmonic function. Points on the grid were successively removed and replaced by points closer to the minimum. Our aim was to optimize the energy to an accuracy of 0.0005 a.u. and this requires bond lengths and exponents accurate to approximately 1 per cent. Our best parameters are quoted in table 1 to three decimal places, but the last figure cannot be taken to be accurate for the true optima. For other configurations of the mole- cule we define Rla as the distance of the hydrogen atom from the centre of the CN band, and 0 as the angle between the vectors R H and Rcz ~ (0 = 0 for H C N and ~r for HNC).

0 0 7r/2 ~r

RH(A.U.) 3"034 2"138 2"934 Rcz;(A.U.) 2"179 2"330 2'208 ~I~(ls) 1"235 1"271 1"370 ~c(2s, 2p) 1"685 1"643 1"610 ~i~(2s, 2p) 1 "940 1 "964 1 "990

T a b l e 1. Op t imized paramete r s for 0 = 0 ( H CN) , 0 = 7r/2 and 0 = ~r(HNC) based on approxi - ma te integrals. T h e ca rbon and n i t rogen l s exponen ts were op t imixed to 5'68 and 6"67 respect ively for all configurat ions.

From the optimum parameters derived above we assumed that on varying 0 all parameters (Q), except R m could be represented by the expression

Q(O)=A+B cos O+C cos z 0. (1)

The constants A, B, C were determined from the values at 0 = 0, w/2 and 7r. The reason for treating R E differently from the other parameters is that it shows a much larger variation with 0, as can be seen from table 1.

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Quantum mechanical calculations of the H C N - H N C isomerization 1119

Calculat ions were made for all values of 0 shown in table 2 wi th R H varied about the est imate der ived on the basis of (1). These calculat ions were repeated us ing Steven ' s S C F M O p rog ramme [9] and the results are shown in table 2.

0 0 rr/6 rr/3 ,'r/2 4rr/3 5~'/6 ~"

RH 3"034 2"993 2-523 2-138 2"330 2'791 2"934 - E 92'5967 92'5595 92.5166 92"5131 92-5432 92.5591 92-5707 Kl l 8"1 8"1 6"2 4-8 6"3 7"2 10"6 qK 0"153 0"186 0-199 0'213 0'235 0'273 0'280 qc 0.017 -0 '059 -0"136 - 0'074 0'012 - 0-006 - 0"041 q~ -0 .170 -0.125 -0.063 -0 .138 - 0.254 - 0.266 -0-238

R~ 3.128 2-965 2"520 2"133 2'339 2.785 2"970 - E 92"6024 92-5725 92-5131 92.5059 92-5349 92'5693 92'5890

Table 2. Calculated Rtt and energy (a.u.) as a function of angle, assuming that the other parameters satisfy equation (1). All values, except for the last two rows, were based on the approximate integral package. Kl l is the curvature (m dyne/A) in the direction of RH assuming all other parameters to be constant, q is the net atom charge defined by (3).

3. RESULTS

By fi t t ing the seven calculated poin ts in table 2 to a seven- t e rm po lynomia l in cos O, the react ion profiles were calculated and are shown in the figure. For the exact integrals the t rans i t ion state was fo und at 0 = 78 ~ with an energy of - 92.5054 a . u .

T h e potent ia l surface local to the equ i l i b r i um geometry of H C N and H N C is represented by a general Tay lo r expans ion in the d i sp lacement variables

R 1 = R x n ( X is C or N), R 2 = RCN ' and R a = 0 :

_ _ 0 1 2 1 2 1 2 E - E + ~-KllR 1 + K12RIR 2 + ~Kz2R, ~ + ~KzaR 3 + .... (2)

T h e values of K n , K12, K22 , Kza were found by a least squares cr i ter ion on the set of points , which were chosen to range over a doma in small enough to ensure that

HCN HNC Experiment This work Others Experiment (c) This work

Rxi~ (A) 1.062(b) 1.079 1.058(f) 1-01 0.987 RcN (A) 1-157(b) 1.153 1.157(f) 1.17 1.168 K11(a ) 6-258(e) 8.1 8'0(d) 7"1 10"6 KI~ - 0"19(e) - 1 "3 - - - - - 2"2 K~2 18'58(e) 27"4 26"9(d) 16'4 20"4 K33 0-26(e) 1"9 0"36 0'104 0"5

- - E(A.U.) 93"473 (g) 92"6023 92'6095 - - 92"5890

(a) K l l , g12, K22 are in mdynes/A. K3a in mdyne A/rad 2. These were calculated using the approximate integral package. (b) [t3]. (c) [1]. (d) [12]. (e) [10]. (f) [15], (g) [16].

Table 3. Equilibrium bond lengths and force constants for HCN and HNC.

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1120 D. Booth and J. N. Murretl

- 9 2 ' 5

L

I - Ul

~ 9 2 t 6 ( ! u n i p ~ 1

,n'16 ~/3 ~/a a . /3 5,r/6 ,r

Energy profiles along the reaction coordinate. (a) using approximate integrals. (b) Using accurate integrals.

the surface was predominantly quadratic but large enough so that the variation in energy was greater by some order of magnitude than the estimated random error. Using the cubic force constants determined by Suzuki et al. for HCN [10] the estimated range in bond lengths over which cubic terms would be no greater than 10 per cent of the quadratic terms was found to be approximately 0.1 a.u. for both RcI ~ and RcN. The results are shown in table 3.

We show in table 2 the pseudo force constant Kll for changing R H about its optimum, but keeping all the other parameters at the values estimated from (1). This gives the change in curvature in a direction approximately orthogonal to the reaction coordinate, which would be useful for any dynamical calculation of the rate of isomerization.

Table 2 also shows the net atom charges as a function of 0 defined by

f (3) &,q= 2 ~occ. CrpCrQ" _J

In HNC the CN bond is marginally more polar than in HCN and the proton is significantly more positive.

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Quantum mechanical calculations of the H C N - H N C isomerization 1121

The only difference in the order (with respect to symmetry) of the occupied orbitals of HCN and HNC is that the n orbital is the highest occupied for HCN but is the second highest in HNC. There is no crossing of occupied and vacant orbitals at any point on the reaction coordinate so we do not anticipate any region in which there would be exceptional correlation energy.

4. DISCUSSION

The differences between the results of the approximate and accurate integral packages were slightly larger for HNC than those we have found in most other cases. We therefore base most of our conclusions on the accurate integrals al- though for these results we have less information available. The results of HCN are similar to those of Palke and Lipscomb [11] and we do not think it worth quoting further details.

Our optimal geometry for HCN (see table 3) slightly underestimates RCN and overestimates RcH with respect to the experimental values, but these results are comparable with those of other calculations on HC N [12, 15]. Our calculated geometry would give a J = 0 + - I transition frequency for HCN of 88032 MHz compared with the experimental value of 88631"4 + 0.5 MHz by Netherhurst et al. [13]. For the same transition the calculated frequency for HNC is 90670 MHz, which even when qualified by the small discrepancy for HC N would give support to the assignment of the observed band, already referred to, at 90655 MHz to HNC.

We predict that HNC is thermodynamically less stable than HC N by 35-2 kJ/mole. To give this figure some physical meaning, it corresponds to an equili- brium constant for the concentration of HNC in HCN of approximately 10 -l~ at 300 K.

Our calculated activation energy for the HNC ~ H C N reaction is 251 kJ/mole. If we adopt the values suggested by Berkovitz for the homo and heterolytic dis- sociation energy of HCN [14] and assume that our energy difference between HC N and HNC is correct, we conclude that the intramolecular route for isomerization has by far the lowest energy. Our calculated activation energy is also appreciably less than the Extended Huckel value [5].

The calculated force constants for HC N and HNC displayed in table 3 are systematically higher than the experimental values, a typical feature of ab initio calculations. Those for HNC are significantly lower than for HCN.

Our results on the structure and energy of the non linear molecule will be used as the starting point for calculations on the biologically important dimer of HCN. The semi-empricial CNDO method has been unsuccessful in explaining the rela- tively low binding energy of this dimer [17], and one cannot have much confidence in the structure predicted by the CNDO method.

We are indebted to Professor L. Salem of the University of Orsay for making arrangements for the calculations using the Steven's integral package, to Mr. V. Saunders for the use of the approximate integral package, and to Dr. A. J. Harget for assistance in the early part of this investigation.

REFERENCES

[1] M1LLmAN, D. E., and JACOX, M. E., 1967, J. chem. Phys., 47, 278. [2] H~RZBERG, G., 1945, Infrared and Raman Spectra of Polyatomic Molecules (V~n

Nostrand), p. 281.

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1122 D. Booth and J. N. Murrell

[3] McCRosKY, C. R., BERaSTROM, F. W., and WAITKINS, G. 1942, -7. Am. chem. Soc., 64, 722.

[4] BUItL, D., and SNYDER, L., 1971, Bull. Am. astr. Soc., 3, 388. [5] VAN DINE, G. W., and HOFFMANN, R., 1968, .7. Am. chem. Soc., 90, 3227. [6] LoEw, G. H., and CHANG, S., 1971, Tetrahedron, 27, 3069. [7] RICHARDS, W. G., WALKER, T. E. H., and HINKLEY, R. K., 1971, A Bibliography of

Ab initio Molecular Wave Functions (Oxford). [8] PEDLEu J. B., GUEST, M. F., and MURRELL, J. N., 1971, MoIec. Phys., 20, 81. [9] STEWNS, R. M., 1970, -7. chem. Phys., 52, 1397.

[10] SuzuKI, I., PARISEAU, M. A., and OVERENI), J., 1966, J. chem. Phys., 44, 3561. [11] PALKe, W. E., and LIPSCOMB, W. N., 1966,-7. Am. chem. Soc., 88, 2384. [12] NEWTON, M. D., LATHAN, W. A., HEHRE, W. J., and POPLE, J. A., 1970, -7. chem.

Phys., 52, 4064. [13] NETH~RCOT, A. H., KLEIN, J. A., and TowNEs, C. H., 1952, Phys. Rev., 86, 798. [14] Bm~KOWITZ, J., 1962, -7. chem. Phys., 36, 2533. [15] SWlTKES, E., STEVENS, R. M., and LIPSCOMB, W. N., 1969, -7. chem. Phys., 51, 5229. [16] HOPKINSON, A. C., HOLBROOK, N. K., YATES, K., and CSIZMADIA, I. G., 1968, -7.

chem. Phys., 49, 3596. [17] HOYLAND, J. R., and KIER, L. B., 1969, Theor. chim. Acta, 15, 1.

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