Ab initio calculations on the isomerization of C4H4 radical cations

and Ion Processes

ELSEVIE R

International Journal of Mass Spectrometry and Ion Processes163 (1997) 169-175

Ab initio calculations on the isomerization of

C4H4 radical cations

G. Koster, W.J. van der Hart* Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden Universi~, PO Box 9502, 2300 RA Leiden, The Netherlands

Received 17 September 1996; revised 1 December 1996

Abstract

Ab initio calculations at the MRCI//ROHF/6-31G** level on the possible isomerization pathways of C4H4 radical cations give a clear explanation of experimental results obtained from neutralization-reionization mass spectrometry and from photodissociation experiments. The observed photon-induced isomerization of vinyl acetylene radical cations to the methylene cyclopropene structure is in excellent agreement with the calculated results. It is suggested that the methylene cyclopropene radical cation is not a primary product of fragmentation of C6H 6 precursor ions but is formed via a low-energy isomerization of ions having a non-classical structure. This isomerization presumably takes place within the ion/molecule complex before the fragments go apart. © 1997 Elsevier Science B.V.

Keywords: C4H4 radical cations; Ab initio; Isomerization

1. Introduction The structures of C4H4 radical cations from different neutral precursors have been the subject of a large number of publications (see [ 1,2] and references cited therein). It is now generally assumed that C 4 H 4 radical cations obtained by fragmentation of C 6 H ~ a r e a mixture of ions having the vinyl acetylene structure (2 in Fig. 1) or the methylene cyclopropene structure 1. Ions having one of the other classical structures butatriene 3 and cyclobutadiene 4 can only be obtained by fragmentation of precursors having structures close to 3 or 4 [1]. In the accompanying paper [3] we have shown that the photodissociation of C4H 4 radical cations in the visible region is unusually complicated. This is due to both a transition from one- to * Corresponding author.

two-photon dissociation and competition between two-photon dissociation and photoninduced isomerization from structure 2 to structure 1. In order to understand the isomerizations involved, ab initio calculations on the possible interconversions between structures 1 to 4 have been performed. In previous work [4,5] some ab initio calculations o n C 4 H 4 have been published, but in these papers only some stable ion structures were considered.

2. Methods Ab initio calculations using the 6-31G** basis set were performed with both the GAMESS-UK[6] and the GAUSSIAN94 [7] program packages. In previous work on similar radical cations [810], we found that unrestricted Hartree-Fock

0168-1176/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved Pll S 0 1 6 8 - 1 1 7 6 ( 9 6 ) 0 4 5 3 9 - 9

170

G. Koster, W.J. van der Hart~International Journal of Mass Spectrometry and Ion Processes 163 (1997) 169-175

f 7÷"

H

/ H

\

H

.-°--°-°

H 1

7"

\

kk

/

/C -- H 2

H

/

H

H7 + •

H\

H

H/

/ 0=0=0=0

H 3

\

/ c=o I I c=c

.7"

~H 4

Fig. 1. Classical C4H 4 radical cation structures.

wavefunctions can have a very large spin contamination with S 2 values as high as 1.0 for crucial points on the potential energy surface. For this reason we considered UHF wavefunctions not to be a good starting point for correlated optimizations. With G A M E S S - U K o r G A U S S I A N 94, correlated optimizations are not possible after a restricted open-shell SCF (ROHF) calculation. Therefore, stable ion structures and transition states were optimized without symmetry at the ROHF level. In these calculations the start structures were taken from a previous MNDO investigation of the possible reaction paths [11]. The optimized geometries were tested by a calculation of the vibrational frequencies. The transition states had one negative force constant whereas a visualization of the corresponding vibration, using VmRAM [12], showed that this vibration corresponds with the assumed reaction coordinate. In all cases where the optimized geometry appeared to be symmetric, further calculations were based on symmetric structures. For the optimized structures, single-point multireference configuration interaction (MRCI) calculations with single and double excitations were done with the Table CI ([13] and references cited therein) option of GAMESS-UK. In these calculations, configurations involving a transition from the lowest 6 occupied or to the highest 15 virtual molecular orbitals were not included (these latter orbitals have an orbital energy higher than 2.5 Hartree). All configurations having a coefficient squared higher than 0.0025 in the final ground state wavefunction or higher than 0.0030 in the wavefunction for the second root (of the same symmetry) were used as reference

configurations. The threshold, used in Table CI calculations, was set at 5.0/~Hartree. The number of configurations in the final diagonalization was of the order of 25 000. In Table CI the contribution of the remaining configurations is calculated by perturbation theory. The final MRCI values given in the tables below include a generalized Davidson size-consistency correction [14].

3. Results Fig. 2 shows the reaction pathways considered in the calculations. The scheme in Fig. 2 is based on a systematic investigation at the semiempirical (MNDO) level of all possible C 4 H 4 radical cations (excluding structures with pentavalent carbon atoms) and their possible interconnections [11]. The results of the present ab initio calculations are given in Table 1 and the relative energies in kcal mol -~ at the MRCI level are included in Fig. 2. These latter values are corrected for the SCF zero-point energy scaled with a factor of 0.89. From the energy values in Table 1 and Fig. 2 it is clear that the classical ion structures 1 to 4 have a lower energy than the non-classical structures 5 to 8. The heats of formation of the classical ion structures are not very well known. According to the values tabulated in [15], both the butatriene and the vinyl acetylene structures have a heat of formation 5 kcal mo1-1 higher than that of the methylene cyclopropene structure. This is in reasonable agreement with the calculated values of 6 and 11 kcal mol -l, respectively (Fig. 2). The non-classical ion structures 5 and 6 have a substantially lower energy than structures 7 and

R

C) m

C'~

/

/\

,C'~+

i

÷

_._i

~*" /°--°\ II li

\

o~

II

/\

\/

o~

I +

I

+

~

-r

"I-

°AT /

II

C)"

~.--

I

I

÷

___1

I

-1"

,N

y

I

-r

o~

II

II

II

i ~o/T

T

• /

4-

"';/-r

___1

I

"I-

172

G. Koster, W.J. van der Hart~International Journal of Mass Spectrometry and Ion Processes 163 (1997) 169-175

Table I S C F , M R C I a n d Z P E e n e r g i e s (in H a r t r e e ) o f the r e l e v a n t ion s t r u c t u r e s a n d transition states a n d r e l a t i v e e n e r g i e s at the M R C I level (in kcal mol -~) i n c l u d i n g the z e r o - p o i n t e n e r g i e s s c a l e d b y a f a c t o r o f 0 . 8 9 Structure

SCF

MRCI

ZPE

AE

Methylene cyclopropene 1

- 153.447016

- 153.793563

0.064532

0

Vinyl acetylene 2

- 153.412201

- 153.775908

0.064445

11

Butatriene 3

- 153.406974

- 153.780962

0.061285

6

Cyclobutadiene 4

- 153.418468

- 153.780855

0.066720

9

5

- 153.387504

- 153.742801

0.062376

30

6

- 153.376223

- 153.745149

0.061850

29

7

- 153.34169

- 153.693786

0.060765

61

8

- 153.346710

- 153.707547

0.061472

52

Tt

- 153.361507

- 153.734020

0.061384

36

T2

- 153.306386

- 153.661845

0.059187

73

T3

- 153.325666

- 153.696190

0.058146

58

T 4

-

153.339670

- 153.701787

0.059824

55

T5

- 153.335589

- 153.697537

0.058667

57 53

T6

- 153.346067

- 153.706103

0.062049

T7

- 153.339064

- 153.698732

0.058748

56

T8

- 153.337663

- 153.691526

0.060564

62

8. This is not surprising. Both structures 5 and 6 can be described as consisting of a charged oddmembered r-electron system with the unpaired electron in a localized o-orbital. The prototype of such an ion structure is an allyl cation with one of the terminal hydrogens removed [8]. It has been shown before that this type of ion structure has a relatively low heat of formation. In calculations on the isomerization of the 1,3-hexadien-5-yne radical cation [10] it was even found that comparable non-classical C 6 H 6 ion structures have heats of formation significantly below that of the classical 1,3-hexadien-5-yne structure. In the present case especially structure 5 is of vital importance because it is the intermediate in isomerizations between the classical ion structures (Fig. 2). The existence of ion structures 7 and 8 is highly questionable. The ring-opened cyclobutadiene structure 7 is only a minimum at the SCF level but has an energy higher than that of the SCF transition state T7 to structure 5 at the MRCI level. In the same way, the energy difference between structure 8 and the transition state T 6 for a ring expansion to the cyclobutadiene structure is lower than the accuracy of the calculations. The reason for the inclusion

of structure 8 is that all calculations on possible reaction pathways for ring opening of the cyclobutadiene radical cation 4 proceeded via this structure. This may be due to a change of symmetry in a more direct route between 4 and 7. In 4 the unpaired electron is in a r-orbital whereas in 7 it is in a a-orbital.

4. Discussion In the accompanying paper [3], it has been concluded that the barrier for the photon-induced isomerization between the vinyl acetylene structure 2 and the more stable methylene cyclopropene structure 1 is below the dissociation limit. The calculated value of 58 kcal mol -~ (47 kcal mo1-1 = 2.0 eV above the energy of the vinyl acetylene structure) for the barrier between these two structures (Fig. 2) is in excellent agreement with this conclusion. Except for the barrier for the transition between structures 5 and 1, all isomerization barriers are at least some 2 eV above the energies of the classical ion structures. It follows that if, for example, the different C 4 H 4 fragment ions from C6H6 are produced from the same precursor

173

G. Koster, W.J. van der Hart/International Journal of Mass Spectrometry and Ion Processes 163 (1997) 169-175

H\

,,Hq +" H--C~C--H

10 H

C--C

\ C:C=C:C /

H--C// C--H H

H

H

/ \

H7 +"

H 3

9 symmetric

antisymmetdc

Scheme

ion, then the formation of about equal amounts of methylene cyclopropene and vinyl acetylene ions is only possible if the major fraction of the fragment ions is formed with a very high internal energy. This seems very unlikely. Moreover, McLafferty and co-workers [1] have observed essentially different mixtures of isomeric C4H4 radical cations from different precursors. For these reasons we conclude that in all cases the different ion structures observed are produced from different precursor ions and that isomerizations after fragmentation, except for the interconversion of structures 5 and 1, have a negligible contribution to the fractions of the H\

/H -]+"

H H !

H

-C

C--

// C--C

C--C _-

\c~cc / /

-= ~o.,

\

H

/

H

N 12

0

34.6

\U H-I +" II

H\c/C~c f. H

//

/c--c\ H

15

H

H

/ H

\

/ H

13

34.3

H

\\

H

H

- ~ - q l , ~ 50.6

\

H

11

H

different ion structures observed. This same conclusion, except for the importance of structure 5, was reached in [1]. The authors suggested, for example, different pathways for the formation of the cyclobutadiene structure 4 and the butatriene structure 3 from 1,2- and 1,4-benzoquinone. In previous work from this laboratory, it has been shown that there are many isomerization barriers of C6H 6 radical cations below the dissociation limit [9,10,16,17]. In contrast to previous suggestions that the different isomeric C4H 4 fragment ions are formed from different C 6 H ~ excited states [1], we therefore believe that the fragment ions observed are formed

H

11.6

Scheme 2.

H

\ 14

36.1

H

174

G. Koster, W.J. van der Hart/International Journal of Mass Spectrometry. and lon Processes 163 (1997) 169-175

H

H

'1+"

H

\c/

H

that it is not surprising that cyclobutadiene ions are not observed as fragments from C6H6 precursors. The C6H6 precursor best suited for formation of the butatriene structure 3 seems to be the dimethylene cyclobutene radical cation 9 (see Scheme 1). The r-electron system of dimethylene cyclobutene is more or less comparable to that of hexatriene. This means that the unpaired electron in the radical cation should be in a molecular orbital symmetric with respect to the vertical symmetry plane. This is indeed found in ab initio calculations [17]. The singly occupied 7r-electron orbital in the butatriene radical cation, however, is comparable to the singly occupied z--electron orbital in the butadiene cation and, therefore, is antisymmetric (Scheme 1). This suggests that there is no simple direct route between C6H6 precursors and the butatriene radical cation. The remaining possible Call4 radical cation

q+"

\c/

II

II

Hx /% /

/C\

C ~

C~--~-C~

H H--C-----C--H 10

- ~

H/

15 antisymmetric

I

symmetric

Scheme3. from different C6H~"isomers. In the following some possible pathways will be discussed. First of all, the only reasonable precursor of the cyclobutadiene structure 4 seems to be the Dewar-benzene structure obtained via a CI-C4 bond formation in the benzene radical cation. Although ab initio calculations on this latter isomerization have not been done, we believe

H\

I /H

C--C ~

H~ .~

/

C~C

H

13

H~

/

H

/

)C

C

2

H~

H

",,,,X

)o_H c--c'

\

\

HH /

Hq

H/c

//

C~C

/ C~CIo H

.÷

15

H

/ H q +°

/

/H ;~C.H

H--C~C--H 10

H

12

Scheme4.

H

\ /

H

C~

H-I*"

=c /\ 1

H

G. Koster, W.J. van der Hart~International Journal of Mass Spectrometry and Ion Processes 163 (1997) 169-175

structures, vinyl acetylene 2, methylene cyclopropene 1 and the non-classical structure 5 can, in principle, be obtained from the structures which are responsible for carbon and hydrogen scrambling in the benzene radical cation [9] (see Scheme 2, which includes the relative energies in kcal mol-1). On closer inspection, however, a direct formation of the methylene cyclopropene structure by fragmentation of the fulvene radical cation 15 seems unlikely. Ab initio calculations [9] show that in the fulvene radical cation 15, the singly occupied molecular orbital is antisymmetric with respect to the vertical symmetry plane, whereas the present calculations show that the corresponding orbital in the methylene cyclopropene is symmetric (Scheme 3). This result suggests that methylene cyclopropene fragment ions are not formed directly from C6H6 precursors but by a low-energy isomerization of the non-classical ion structure 5. From this discussion we arrive at the conclusion that, probably, the primary C4H 4 fragment ions from C6H6 precursors are formed in the way shown in Scheme 4. The vinyl acetylene structure 2 and the non-classical ion structure 5 are formed by fragmentation of structures 13, 12 and 15 in Scheme 4. Formation of structure 5 is followed by an isomerization to the methylene cyclopropene structure 1 via a low-energy barrier. This barrier is so low that the isomerization could very well take place within the ion/ molecule complex before the fragments go apart.

175

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Process., submitted for publication. [4] S.W. Staley, T.D. Norden, J. Am. Chem. Soc. I 11 (1989) 445. [5] W.T. Borden, E.R. Davidson, D. Feller, J. Am. Chem. Soc. 103 (1981) 5725. [6] M.F. Guest, P. Fantucci, R.J. Harrison, J. Kendrick, J.H. van Lenthe, K. Schoeffel, P. Scherwood, GAMESS-UKUser's Guide and Reference Manual, Revision C.0, Computing for Science (CFS) Ltd., Daresbury Laboratory, Daresbury, UK, 1992. [7] M.J. Friscb, G.W. Trucks, H.B. Schlegel, P M . W . Gill, B.G.

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[16] [17]

V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A.Nanayakkara, M.Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, GAUSSIAN94, Revision B.I, Gaussian, Inc., Pittsburgh, PA, 1995. W.J. van der Hart, Int. J. Mass Spectrom. Ion Process. 151 (1995) 27. W.J. van der Hart, J. Am. Soc. Mass Spectrom. 6 (1995) 513. W.J. van der Hart, J. Am. Soc. Mass Spectrom. 7 (1996) 731. G. Koster, Ph.D. Thesis, Leiden University, 1996. J. Dillen, Quantum Chemistry Program Exchange, Program no. QCMP 12010, 1992. R.J. Buenker, R.A. Philips, J. Mol. Struct. (Theochem) 123 (1985) 291. S.T. Elbert, E.R. Davidson, Int. J. QuantumChem. 8 (1974) 857. S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, R.D. Levin, W.G. Mallard, J. Phys. Chem. Ref. Data 17 (Suppl. 1) (1988). W.J. van der Hart, Int. J. Mass Spectrom. Ion Process. 130 (1994) 173. W.J. van der Hart, J. Am. Soc. Mass Spectrom., accepted for

publication.