Journal of Molecular Structure (Theo&m), 184 (1989) 391-397 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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AN AB INITIO MOLECULAR ORBITAL STUDY OF THE t&H+ POTENTIAL ENERGY SURFACE

JON BAKER*

University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW (Gt. Britain)

SIU-CHEUK CHAN, KAM-YUEN WU and WAI-KEE LI*

Department of Chemistry, The Chinese University of Hong Kong, Shutin, N.T. (Hong Kong)

(Received 10 June 1988)

ABSTRACT

The C&H+ potential energy surface has been studied using ab initio molecular orbital calcula- tions. Full geometry optimization has been performed for equilibrium and transition structures at both Hartree-Fock (I-IF) and correlated (MP2) levels with the 6-31G* basis set, and improved energy comparisons obtained at the MP4 level with the 6-31G** basis set. Two stable C&H+ equi- librium structures have been found; they correspond to protonation of neutral C3 at a terminal carbon (l,Cmv) and on the central carbon (2,&v), with 2 being 253 kJ mol-’ higher in energy than 1. In addition, two saddle points have been located on the surface. They correspond to the transition structures for the rearrangement of 2+ 1 (3,Cs) and the 1,3-hydrogen migration of 1 ( 4,CzV). The barriers to these reactions are calculated to be 83 and 100 kJ mol- ‘, respectively.

INTRODUCTION

C&H+ is a stable cation of considerable interest because of its postulated role in interstellar hydrocarbon synthesis and chemical evolution [ 1,2]. It has been studied both mass spectroscopically [ 3,4] and with the aid of ab initio molec- ular orbital calculations [5,6]. The most recent ab initio study appears to be that of Pople et al. [ 71 who looked at C&H+ as part of a general study of the structure and energetics of Ci-CI carbocations. They determined two equilib- rium structures at the HF/6-31G* level, corresponding to protonation of neu- tral C, at a terminal carbon ( 1) and on the central carbon (2), respectively. The linear form ( 1) is more stable at HF/6-31G* by 173 kJmol_l, rising to 220 kJmol-’ with the inclusion of correlation incorporated via single point MP4 (SDQ) /6-31G** calculations at the 6-31G* geometries. The heat of for- mation of 1 was calculated to be 1602 kJ mol-‘, in very good agreement with the experimental determinations of 1607 [ 31 and 1619 kJmol-’ [ 41.

*Authors for correspondence

0166-1280/89/$03.50 0 1989 Elsevier Science Publishers B.V.

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In the present work the transition structures for the 1,2- (i.e. l-2) and 1,3- hydrogen migrations of 1 are determined. In addition we have recalculated all stationary points at the MP2/6-31G* level to determine the effects of corre- lation on the optimized geometries. Also our best energies are calculated at the

TABLE 1

Calculated total energies (hartree) for C,H+ structures

Level Structure

1 2 3 4 6

HF/4-31G” - 113.49654 HF/6-31G*b - 113.65480 MP2/6-31G**b - 113.99442 MP3/6-31G**b - 114.00390 MP4/6-31G**b - 114.04285

- 114.00485 - 113.99778 - 114.00423 - 114.04715

- 113.42331 - 113.58872 - 113.89133 - 113.92097 - 113.94741

- 113.89767 - 113.89164 - 113.92113 - 113.94811

- 113.35544 - 113.53222 - 113.85790 - 113.88224 - 113.91341

- 113.86010 - 113.85712 - 113.88207 - 113.91242

- 113.38508 - 113.59746 - 113.96813 - 113.97405 - 114.00776

- 113.97717 - 113.97606 - 113.97004 - 113.96896 - 113.97456 - 113.97496 - 114.01030 - 114.00910

‘Geometries optimized at the HF/4-31G level. bGeometries optimized at the HF/6-31G* level. “Geometries optimized at the MP2/6-31G* level. dThie calculation included all orbitals in the optimization; all other single point correlated calculations are with frozen core.

TABLE 2

Calculated relative energies (kJ mol-‘) and zero-point vibrational energies (ZPVEs) for C3H+ structurese

Level Structure

1 2 3 4 5

HF/4-31G” 0 192 370 293 HF/6-31G*b 0 174 322 151 MP2/6-31G**b 0 271 358 69 MP3/6-31G**b 0 218 319 78 MP4/6-31G**b 0 251 340 92 ZPvEb 57 48 37 53 MP2/6-31G*“vd 0 281 380 73 76 MP2/6-31G**= 0 279 369 73 76 MP3/6-31G**= 0 218 321 78 77 MP4/6-31G**= 0 260 354 97 100 ZPWW 52 45 34 55 50

a,b*csdSee footnotes under Table 1. ‘Calculated from the total energies in Table 1.

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TABLE 3

Calculated hermonic vibrational frequencies (HF/6-31G*; cm-‘) C,H+ structures

211 (n) 359 (a,)

3158 (al) 1406i (a’)

2393 (a’) 1172i (b,) 3434 (al)

959 (k) 1302 (a) 2343 (a) 3534 (a) 597 (b,) 938 (bz) 1342 (a,) 1707 (b,)

190 (av) 320 1187 (a’) 2044 (a’ )

(aO) 945 (b,) 1536 (a,) 1907 (al)

1084 (b,)

TABLE 4

Calculated harmonic vibrational frequencies (MP2/6-31G*; cm-‘) for C3H+ structures

204 (1~) 315 (aI)

2974 (al) 1511i (a’) 2214 (a’)

722 (5,) 3276 (a,) 815i (a’ )

3276 (a’)

759 (n) 1213 (CI) 2168 (u) 3354 (a) 495 (5,) 752 (5,) 1264 (al) 1697 (b.J

143 (a”) 230 (a’) 1100 (a’) 2048 (a’)

887 (b,) 1062 (b,) 1402 (al) 1791 (al)

872 (a”) 998 (a’) 1481 (a’ ) 1757 (a’)

full MP4 (SDTQ)/G-31G** level. This should therefore complete the study of the C&H+ potential energy surface, as far as rearrangements of the stable spe- cies are concerned.

COMPUTATIONAL METHOD

Standard ab initio molecular orbital calculations were carried out using the GAUSSIAN 82 [8] system of programs. Geometries of all structures were de- termined at the Hartree-Fock (HF) level with the 4-31G [9] and 6-31G* [lo] basis sets and at second-order in Meller-Plesset perturbation theory [ 11,121 with the 6-31G* basis set using gradient optimization techniques [ 13,141. In order to characterize the stationary points and to estimate the zero-point vi- brational energy (ZPVE ), harmonic vibrational frequencies were calculated at the HF and MP2 levels with the 6-31G* basis using geometries optimized at these levels. The effects of valence-electron correlation on the relative energies were determined from full fourth order Meller-Plesset perturbation theory (MP4) [ 11,121 calculations with the 6-31G** [lo] basis set.

Optimized geometries (HF/6-31G*, HF/4-31G in round parentheses and

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MP2/6-31G* in square parentheses) for all stationary points found are dis- played within the text. Bond lengths are given in angstroms and bond angles in degrees. Calculated total energies, ZPVEs and relative energies are sum- marized in Tables 1 and 2, and calculated frequencies for equilibrium and tran- sition structures are listed in Tables 3 (HF/6-31G*) and 4 (MP2/6-31G*). Unless otherwise stated, relative energies quoted within the text correspond to MP4/6-31G**//MP2/6-3lG* values, together with ZPVE corrections.

RESULTS AND DISCUSSION

As in the previous studies [ 5,6], only two stable minima were found on the C&H+ potential energy surface, corresponding to the following equilibrium structures

n

I

1.097 (1.098) Il. 1151

1.337 1.211 1.072 (1.336) (1.212) (1.068)

+c [1.3391 t1.2541

c-c Il.0851

l-l r123.21

2 (C2”)

Correlation lengthens all bond lengths to varying degrees (maximum 0.042 A for the central C-C bond in 1) but otherwise there are no major changes.

At least two resonance structures may be written for 1

+ + C=C= C-H- C-C=C-H

The linear structure found and its bond lengths indicate that the second struc- ture is more important than the first, while the contribution of the following resonance structure should be relatively small

+ C = C-C-H

Mulliken population analysis does indeed indicate that most of the charge is located on the terminal carbon atom.

Structure 2 is stabilized by charge delocalization; this is reflected in the C. I .C bond lengths which are significantly longer than in 1. Our best energy values indicate that 2 is less stable than 1 by 253 kJ mol-l, about 14% larger than the value previously reported (220 kJ mol-l, calculated at MP4 (SDQ) / 6-31G**//6-31G* [ 71).

Two saddle points were located on the HF/6-31G* C3H+ potential energy

395

surface, corresponding to the transition structures for the 1,2-hydrogen migra- tion of 1 (3) i.e. l-+2, and the 1,3-hydrogen migration (4). The calculated barriers at the SCF level are 322 and 151 kJ mol-‘, respectively.

w

1.233 (1.276) Il.2711

f173.81

1.079 (1.071) L1.0921

I

A

c: (1

C C 1.269

(1.280) f1.3071

.374

.392)

.3771

3 KS) 4 cc,“)

The barrier for the l- 2 rearrangement relative to 2 is 148 kJ mol-l. Single point MP4/6-31G**//6-31G* calculations reduce this to 89 kJ mol-l (see Ta- ble 2) which suggests that as far as unimolecular rearrangement is concerned, 2 is sufficiently stable to be detectable once formed. The barrier for 1,3-hydro- gen migration is reduced to 92 kJ mol-‘. (Note that, strictly speaking, the term 1,3-hydrogen migration is a misnomer since it is actually the C-H group which migrates rather than the hydrogen alone.)

A schematic potential energy profile for these rearrangements is given in Fig. 1 (including ZPVE corrections) which emphasizes that both 1 and 2 should be stable species.

The situation changes (at first sight quite dramatically) at the MP2/6-31G* level, since although the geometries of 3 and 4 are similar, vibrational analysis reveals that 4 is a minimum on the correlated surface. However, a slightly distorted Cs structure derived from 4 (5) was easily located using the

H

C L1.3101

C

eigenvector following algorithm [ 141 which represents the transition structure for the rearrangement 4+ 1 and lies only 3 kJ mol-l above 4. If zero-point vibrational energy is taken into account then 6 actually lies below 4 at all

396

320

0

1 1

Fig. 1. Schematic of the C&H+ potential energy surface (relative energies at MP4/6-3lG**//6- 31G*+ZPVE and in square parentheses MP4/6-31G**//MP2/6_3lG*+ZWE; kJ mol-*)

correlated levels considered (see Table 2). Thus, despite the vibrational anal- ysis, there is no real evidence to the effect that 4 is a minimum on the “real” potential energy surface.

A similar situation occurred in a recent ab initio study of N,...CO+ [15] where a cyclic C,, transition structure for CO+ migration was found to be a minimum at a higher level of theory; again a Cs distortion revealed a “transi- tion state” with a virtually identical energy.

Our best calculations (MP4/6-31G**//MP2/6-3lG* +ZPVE) indicate that 1 is more stable than 2 by 253 kJ mol-’ and has a barrier to 1,3-hydrogen migration of around 100 kJ mol-l. Although less stable than 1, the barrier for rearrangement (2-t 1) of 83 kJ mol-l suggests that, once formed, 2 should be sufficiently long-lived to be detectable experimentally.

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