Cyclic C3 structures

CHEMICAL

Volume 80, number 3

PHYSICS LETTERS

15 June 1981

CYCLIC C, STRUCTURES Robert A. WHITESIDE,

Raghavachari KRISHNAN, Michael J. FRISCH, John A. POPLE

Department of Chemistry, Carnegie-Mellon Urziversit~v, Pittsburgh. Pennsylvania 1.5213, USA

and Paul VON R. SCHLEYER Institut fiir Organische Chemie der UniversitZt Erlangen-Niirnberg. 8520 Erbmgen, FRG Received 6 February 1981;

in final form 18 March 1981

Alternative cyclic Ca structures are not competitive energetically with the linear ‘Xi ground state, 1. The Dab triplet, 4, is a local minimum on the potential energy surface. Cyclopropynylidene, a C av singlet (3) is a saddle point for the degenerate isomerization which permutes the order of carbon atoms in 1. The activation energy for this transformation is predicted to be 29 kcal/mole.

1. Introduction First discovered spectroscopically in the tail of a comet, C, is produced in stars, in hydrogen flows, and in carbon vapor produced by electric discharge, flash photolysis, radiofrequency induction, or by laser heating of graphite [l-4]. The IX; ground state of C, is known to prefer a D ah linear geometry_ This can be described by singlet valence structure, 1, with four deiocalized rr electrons

[41:c,

=

cz=

c3:

1

Even though 6, IS known to have a remarkably low bending frequency, there appears to be no experimental evidence for cyclic isomers [l-4] _Valence structures 2 and 3 can be written for singlet C3 rings; the cyclic triplet, 4, with two rr electrons, is a further possibility which merits attention_ __

c 3:

:c12

-_

,cz

/EZ Cl

w

,cz c3

3

-c,

----cs-

4

The tricarbene, 2, has zero ‘ITelectrons but cyclopropynylidene, 3, with a carbene attached to a triple bond, might, along -with 4, benefit from 2n electron aromatic delocalization. Even if cyclic structures do not correspond to local minima in the potential surface, they will be involved m paths for the degenerate rearrangement which exchanges central (C,) and terminal (C, and C,) nuclei in 1. In this paper, we report results of an ab initio molecular orbital study of structures 1-4, addressing the following questions: (1) Are there cyclic equilibrium structures corresponding to 2,3 or 4? (2) If such potential minima are not involved in the degenerate rearrangement, what is the transition structure for such transformations? (3) What is the activation energy for this isomerization? The C3 potential surface has been examined in previous ab initio theoretical work, Liskow, Bender, and Schaefer (LBS) [4 3 made a careful study of the CCC bending motion in 1, known to give rise to a low vibrational frequency [l-3] _They considered the bending motion all the way to a CCC angle of 6C” and noted that the ground state of 1 correlates with a degenerate (IE’) state for the equilateral triangle. The valence electronic configuration (D 3b) is then 547

(a;)”

(e’)4 (az)2 (a;)2

(e’)‘.

A triplet (3Ai)

state (4)

also arises from the same configuration. In another study, Lathan, Radom, Hariharan, Hehre and Pople (LRHHP) [5] obtained a Hartree-Fock structure for 3 using a minimal @TO-3G) basis. At this simple level of theory, 3 is found not to be an energy minimum. Lowering the symmetry by slight displacement led back down to the linear structure 1 upon geometrical optlmlzation. Since our recent study of C, suggested unexpectedly that a cyclic, rhomboid structure might be preferred over a linear geometry [6], we felt that a reexamination be retealing.

of C3 at higher levels of theory

2. Theoretical

15 June 1981

CHEhlICAL. PHYSICS LETTERS

Volume 80, number 3

could

methods

3. Results and discussion Optimized structures are listed in table 1 and the corresponding energies in tables 2 and 3. At all levels of theory, the linear structure 1 is found to be most stable with the valence electron configuration (c@~ (~,)~(a~)~ (o,)~ (T~)~, Liz_ This agrees with previous conclusions [l-4] _For the D,, equilateral triangle, several electron configurations were considered at the HF/STO-3G level. The tricarbene structure 2 (no n-electrons) has the electron configuration (a; )2 (e’)4 (a; )2 (e’)4, A lower singlet energy of electrons from one the symmetric n-type

and is relatively high in energy. is obtained by moving a pair of the degenerate e’ orbitals to orbital of symmetry a;_ This

Hartree-Fock theory is used for exploration of the potential surface and determination of geometries corresponding to stationary points. Closed-shell theory

gives the configuration (a;)2 (e’)4(a;)2 (az)2(e’)2 _As noted by LBS [4], use of real orbitals leads to a singledeterminant wavefunction which does not have proper symmetry for the D,, point group. We have nevertheless labeled the state 1 E’ in tables 1 and 2 since there

is used for singlet surfaces and spin-unrestricted theory (UHF) for triplets. The minimal STO3G [7] and split-valence 3-2 1 G [S] basis sets are used for preliminary studies and are followed by structure optimition with the 6-3 1 G * basis [9] _ This is the HF/6-3 1G * theoretical model. Force constants and harmonic fre-

which is an upper bound for the 1 E’ energy. The same electron configuration also gives rise to a triplet state. 3A;_ This gives a lower energy (UHF) than the singlet wavefunction, as expected from Hund’s rule. Since this triplet state has two 7relectrons’(symmetry a;)

are two possible determinants

with the same energy

quencies at this level are found by analytic second derivatives [lo] _ Single-point calculations including electron correlation are then carried out to the fourthorder M@ler-Plesset level in the space of single, double, triple and quadruple substitutions (excluding mnershell orbitals) [l l] _The Hartree-Fock geometries are used, so the fmal energies may be denoted by

and two unpaired o-electrons, it corresponds to structure 4 with resonance between the three equivalent possibilities_ Evaluation of second derivatives shows that the D,, triplet structutre is a local minimum in the potential surface. The degenerate ‘E’ state is not a potential minimum

MP4SDTQ/6-3lG*//HF/6-31G*.

plies to the real single determinants of the D,, structure to an isosceles

Table 1 Hartree-Fock Structure

548

since the Jahn-Teller

theorem

applies. The same apused. Distortion triangle (point

structures for C3 Point group

State

Electronic configuration

ST0 -3G

6-3 1G *

3-21G

Rl2

R13

Rl2

R13

R12

R13

D3h

‘Af

(ai )2 (e’): (ai )* (e’)4

1647

-

1.743

-

1.603

-

D3h %h

‘E’ 3A;

(ai)* (e’)4 (g’,2 (a;)* (e’)2 (a;)* (e’)4 (g’,2 (a;)2 (e’)2

c2v

“41


Da+

'Zg'

(~~)2~~o,)*(~~)2(~u)2(~u)4

1.417 1.385 1.501 1.282

1.287 -

1.361 1.506 1.275

1.259 -

1.346 1.46 1 1.278

1.250 -

Volume 80, number 3 Table 2 Optimized Hartree-Fock

15 June 1981

CHEMICAL PHYSICS LETTERS

energies (bartree) for

C3

Structure

Point group

State

ST0 -3G

3-21G

6-3lG*

2

JJ3!,

IA;

-111.63985

-112.40375

-113.07672

D3h

‘E

-111.78086 -111.81969 -111.84785 - 111.90660

-112.60568 -112.63225 - 112.72275

-113.29868 -113.32637 -113.35510

3 4 1

GV

‘A1

D3h D-h

3A; lx* g

Table 3 lM$Uer-PIesset energies a) (6-3 lG* basis) for C3 Structure

Point group

State

MP2

MP3

MP4SDQ

MWSDTQ total

relative

2 3

D3h

‘A;

C2v

‘Al

-

-113.35569 113.65042

-113.39813 -113.65888

-113.40761 -113-66689

-113.41682 -113.69219

202 7 29.9

4 1

D3h D-b

3A; ‘C;

-113.66848 -113.69047

-113 67404 -113.69795

- 113.67770 -113.70857

-113.70090 -113.73986

24.4

a) Total energies in bartree; relative energies in kcal/mole. HF/6-31G* group C,,)

with an angle at

to the valence electron

C2 greater than 60" leads

configuration

(a1)2(b2)2(a1)2@1)2(b2)2(a1)2 with lower energy_ Further optimization within Cav symmetry leads back to the linear structure 1.This is the path explored by LBS [4]. If the angle at C, is decreased from 60”) the second Jahn-Teller configuration (al)2(al)2(b2)2(bl)2(al)2(al)2 becomes lower m energy. Reoptimization of the geometry for this state (within C,, symmetry) leads to the cyclopropynylidene

structure 3 reported previously by LRHHF’ [5] _ Evaluation of the second-derivative matrix at this nuclear configuration shows a negative eigenvalue corresponding to symmetry-breaking b2 motion. Energy optirnization starting in this direction leads back to structure 1 via C, intermediate structures. Degenerate isomerization of C+ The three possible lmear structures 1 (with different nuclei in the central position) are three equivalent minima on the JahnTeller surface. Fig_ 1 shows a section of the crossing RHF/STO-3G surfaces for the isosceles triangles with unique angle at CZ (the equal bond lengths C, C2 and

geometries used_

C2C3 being optimized for each value of the angle)_ On the full surface there will be similar sections rotated by f 120” from this one, giving minima at the linear structures with Cl and C3 as central atoms. The cyclopropynylidene structure 3 is the transition structure for the isomerization: rc,=

c,=

c,:

-

:c,

/’

III

\, 1

%

3

:C,=

c,= c,:

1’

3 - 1 is the activation energy for this process. Refinement of the four structures l-4 at the HF/ 3-21G and dF/6-31G* levels does not appear to change these qualitative features of the potential surfaces. The tricarbene structure 2 remains very high 111 energy and is not considered further. The energy difference between 3 and 1 drops sharply on going from 3-21G to 6-31G* (from 73.5 to 35.4 kcal/mole). This is clearly due to the greater importance of d-functions The energy difference

549

CHEMICAL PHYSICS LE-IXERS

Volume 80, number 3

15 June 1981

)-

I-

)-

I-

)-

3

3c

Bond Angie

(C1C2C3)

In degrees

Fig. I. in highly strained carbon compounds. Evaluation of HF/6-31G* second derivatives for 3 confirms that this structure is still a saddle point at this level, the negative eigenvalue of the hessian matrix corresponding to b, motion_ The cyclic structure 4 is still a local minimum on the triplet surface. At the HF/6-31Glevel, its energy is Iti.0 kcal/mole above that of the linear structure 1.We have yet to find whether 4 is the lowest energy triplet on the HF/6-31G* surface. Preliminary calculations on triplet states [2] for the linear C, molecule suggest that they have comparable energies_ Inclusion of electron correlation (table 3) modifies these results slightly_ The rearrangement barrier (3 - 1) on the potential surface is calculated to be 299 kcal/ mole at the MP4SDTQ/6-3 lG* //HF/6-3 lG* level. It is noteworthy that the effect of triple substitutions is quite considerable (the corresponding barrier without such tripIes being 26.2 kcal/mole). The energy of the triplet structure 4 moves relatively higher (24.4 kcal/mole above l), in conformity with the expectation that triplet states have smaller correlation energies. The second derivatives found at the HF/6-31G* level lead to the predicted harmonic frequencies for the ground state and compare reasonably with experimental frequencies 1121 of 64 cm-1 (n,), 1230 cm-l (og) and 2040 cm-l (uu)_ We note that LBS found a 550

small negative bendmg force constant for C, with a basis set simrlar to ours, the principal difference being d-functions with two primitive gaussians rather than one as in 6-3 lG*. This indicates that such bending force constants are sensitive to details of the basis. The predicted frequencies for the tiiplet structure 4 are quite large, indicating that it might have an appreciable lifetime, if formed (see table 4)_

The HF/6-3 1G” harmonic frequencies may be used to calculate zero-point energies for 3,4 and 1. These are 4.8,5.7 and 5.7 kcal/mole respectively, ignoring the imaginary frequency for 3. After adding these corrections to the MP4SDTQ/6-31G* energies in table 3, the final prediction for the activation energy for degenerate isomerization is 29.0 kcal/mole. In conclusion,we may note that the general properties of the CS p otential surface are similar to some parts Table 4 Theoretical harmonic frequencies (cm-l) Structure

Point

State

a)

Frequencies

group

3

Czv

‘Ai

1402i(b&

4

bh

3A;

lOSl(e’),

1774(ai)

1

D-h

‘“;

154(7r&

1367(ug),

a) W/6-31G*

level of theory.

1339(al),

2013(al) 2311(0,)

Volume 80, number 3

CHEMICAL PHYSICS LETTERS

of the C,H2, recently investigated by Saxe and Schaefer [13]. They find that cyclopropyne, analogous to 3, re-

arranges without activation to propadienylidene, analogous to 1. They also predict the existence of a stable triplet form for cyclopropyne.

Acknowledgement Preliminary calculations on C3 were carried out by S. Godleski. This work was supported by the National Science Foundation under Grant CHE-8ti-01061-01, by the Fonds der Chemischen Industrie, and was facilitated by a NATO grant.

[4]

[5] [6] [7] [S]

15 June 1981

G_R J. Williams, Chem. Phys. Letters 33 (1975) 583; P.S. Skell, J J. Have1and M-J. McGIinchey, Accounts Chem. Res. 6 (1973) 97; R.T. Meyer, A.W. Lynch and J.M. Free+ J. Phys. Chem. 77 (1973) 1083. DSE. Liskow, CF. Bender and H-F. Schaefer III, J. Chem- Phys. 56 (1973) 5075; J. Riimelt, S.D. Peyerimhoff and R.J. Buenker, Chem. Phys. Letters 58 (1978) 1. WA_ Lathan, L. Radom, P-C. Hariharan, WJ. Hehre and JA. Pople, Topics Current Chem. 40 (1973). RAA. Whiteside, R. Krishnan, DJ. DeFrees, JA. Pople and P. vonR. Schleyer, Chem. Phys. Letters 78 (1981) 538. W-J. Hehre, RF. Stewart and JA. Pople, J. Chem. Phys. 51 (1969) 2657. J.S. BinkIey, JAA.Pople and WJ. Hehre, J_ Am. Chem.

Sot. 102 (1980) 4085. [9] P.C. Hariharan and JA. Pople, Theoret.

References [l ] K.H. Becker, T. Tatarayk

and J. Radi&Peri& Chem. Phys. Letters 60 (1979) 502. [2] J_ Radl&Peri& J. Rtimelt, S-D. Peyerimhoff and R J. Buenker, Chem. Phys. Letters 50 (1977) 344. [3] Z. Slanina and R_ Zahradnik, J_ Phys. Chem. 81 (1977) 2252;

Chlm. Acta 28 (1973) 213. [lo] JA_ Pople, R. Krishnan, H-B. Schlegel and J.S. Binkley, Intern. J. Quantum Chem. 13s (1979) 255. [ 111 R. Krishnan, M.J. Frisch and J A. Pople, J. Chem. Phys. 72 (1980) 4244. [12] W. Weltner Jr. and D. McLeod Jr., J. Chem. Phys. 40 (1954) 1305. [13] P. Saxe and H.F_ Schaefer III, J. Am_ Chem. Sot. 102 (1980) 3239.

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