3 calculations on the system C2H+7

CHEMICAL PHYSICS LETTERS

Volume 58. number2

AI3 INiT10 CALCULATIONS INCLUD~G AND hUNDO/

15 September 1978

ELECTRON CORRELATION,

CALCULATIONS ON THE SYSTEM C&

Hans-Joachim KGHLER Arbeitmppe Quantenchemie. Sektion Chemie, Ka&Uarx-UniversitZt, DDR-701 Leipzig. GDR and Hans

LISCHKA

Institut fir Theoretiche A-1090 Vienna, Ausirti

G emie und Strahlenchemie, Universitn”t&Yen,

Received 24 April 1978

Ab initio SCF and CEPA PNO calculationshave been performed togetherwith hHNDO/3 c&uJations on the system CzH;. In agreementwith experimentalassjgnment,but in contradictionto MIND0/3 results, the ab initio methods show the CC protonated structureto be more stable than the CH protonated structure.The energy differenceis 8.5 kcal/molat the SCF level and 6.3 kcal/molwith inclusionof electron correlation.Additionally, AH&,-, for the reactionCzH; + H2 = CzH?jand the proton affiity of etbane are computed-

1. Introduction The xnokcular ion CH; was one of the first carbocations found by mass spectrometric investigations of ion-molecule reactions [I]. Later on, the next higher analogue C,e h= also been observed [2] _ &G shown below, two different structures may be derived for C2$ from C$: in one case a ‘%H3” hydrogen is replaced by a methyl group Ieading to structure I whereas in the other case the substitution occurs at the “Hz” hydrogen (structure II)_

Ab i&t& SCF calculations (STO_3G, 431G and 6-51G) have been performed for both isomers [3,4] Structure II was found to be more stable by 10-l 1 kcal/mol. However, results obtained with the semiempirical MPJDO/3 method favored structure I by

= 16 kcal/mol[5] _More recently, Hiraoka and Kebarle [6] studied the kinetics and equilibria of the following reaction:

They report the errtence of two isomeric species of Czh?, one present at low temperature (-130 to -160°C) and the other one at high temperarure (+- 40 to 2!10°C). The low temperature species (A& = 215 kcal/mol) was identified as structure I whereas structure II was attributed to the high temperature species (if = 203.2 kcal/mol). Jir -view of the present situation it is the purpose of our work to study systematically a series of structures of C&. Previously, we found for the moleculesC& and C2H4X+, X = H, F, Cl, CHa [7,8] that in the case of the pure hydrocarbon systems MiNDO/3 results agreed well with ab initio calcdations including electron correlation_ In the present paper we continue our investigations and also reinvestigate the MIND0/3 calculations by Bischof and Dewar IS]. 175

VoIume

58. number

2

CHEMICAL

2. Method of calculation The ab in&o computations were performed both at the SCF level and with inclusion of valence shell correlation energy. Starting from localized SCF MO’s [9] we calculate electron correlation effects tl the framework of the CEPA PNO method [ 10, 11] . We use the same contracted Huzinaga gaussian basis sets [12,13] as in refs. [7,8] : Basis set A: 7s3p contracted to [411 l/21] on carbon and 3s contracted to 1211 on hydrogen. The 3s tinctions were scaled by a factor 1.44. Basis set B: a d-set (exponent o = l-0) on each carbon atom and a p-set (a = 0.65) on hydrogen were added to basis set A. The MNDO/S computations were performed with the program no_ 279 distributed by QCPE [14]_ This program was extended by one of us (IX-J-K.) to enable a characterization of the stationary points on the potential energy hypersurface by the eigenvalues of the matrix of force constants [15-171 according to the McIver-Komornicky treatment [ 181 _

3. Results and discussion The Newman projections of the C2q structures investigated are shcwn in fig_ 1_We discuss the MNDO/3 results first_ The geometries of the rotamers Ia, Ib, IIa- Lid have been optimized with respect to all geometrical variables. Bischof and Dewar [5] and W. Thiel (see reference 23 in ref. [5]) investigated only the stationary points Ia, UC and IId In agreement with these authors we fmd a local minimum for the structure Ia (Mf = 199.84 kcalimol). The rotamer Ib (AH, = 200.99 kcal/mol) is a saddle point for the internal rotation of the methyl group. However, neither structure IIc nor lid proposed by the above authors corresponds to a local minimum. The true MNDOI3 minimum of this isomer is given by structure IIa (Af!if = 211.18 kcal/mol)_ Inspection of the eigenvalues and eigenvectors of the matriX of force constants shows the following situation: structure iId is a maximum (n-0 negative eigenvalues, UC= 215.57 kcal/mol)_ One of the corresponding eigenvectors indicates a rotation of the two methyl groups clockwise and counter-clockwise resulting in the minimum structure IIa. The other vector leads to structure Ilb (AfXf = 2 11.31 kcal/moI) _ 176

15 September 1978

PHYSICS LETTERS

H

H l-l

J?i

A

H H

H H

Ib

H IIC

IId

Fig. 1. Newman projections of the rotamers investigatedin this work. Hb is the bride_ proton.

which is a saddle point for the interconversion of Ha into its equivalent counterpart_ Another saddle point for the same interconversion is represented by structure IIc @I+ = 211.80 kcaI/moI). Structure IIb is more favorable than IIc by about 0.5 kcal/mol. MND0/3 predicts structure Ia to be more stable than IIa by = 11 kcal/mol. For the purpose of comparison with the ab initio results we also performed MINDO/3 calculations on D?&J(IIe) and Dsh(I’ff) struttures. These geometries (not shown in fig. 1) are characterized by a linear CH& bond (see also ref. 14)). ‘Ihe MND0/3 geometries agree quite well with the STO-3G values [4]_ However, IIe and IIf are significantly less stable than the other structures (wf = 218.67 and 218.72 kcallmol, respectively) and correspond to a local maximum and a transition state, respectively. In performing the SCF and CEPA P&IO computations we used the MIND013 geometries for all rotarners and the STO-3G optimized geometries for la, Pld and IIe [3,4] _ The results are collected in table 1_ Relative stabilities can be compared in table 2. As in previous investigations [7,8,19,25] we obtain a significant influence of polarization functions and electron correlation on relative stabilities, From a comparison of the

CHEMICAL

Volume 58, number 2

PHY SKIS LETTERS

Table 1 SCF and CEPA PNO results (auj for C,H; obtained with basis sets A and B, respectively. U&ss otherwise indicated the MIND013 geometries are used

Structure

BasissetA

Basis&B

-ESCF

E STO-3G aj b geometIy Ila Ub IIC

IId IId

STO-3G aj He bj’geometry

-ESCF

_ECEPA

79.38816 79.38219 79.38367 7938016 79.37783 79.37986

79.72514 79.70152 79.72072 79.72199 79.72015 79-72136

79.30636

79.37354

79-71375

79.34690 79.34999

79.40164 79.39971

79.73511 79.73348

79.3 1609 79.32615 79.31204 79.30868 79.30572 79.30961

a) See refs_ [3,4]_ bj D,d symmetry. For the definition of the geometry see text and ref. [4].

geometry for structure Ia calculated with the MIND0/3 [S] and ST03G [3,4] method, respectively, one finds that the ST03G computations yield a loose intermolecular complex between Ii2 and C&_ On tbe o*rher hand, MINDOj3 results in a CHH three-center bond similar to the one in CI-I$ [3,4,19,2(l). With basis set A the intermolecular complex is more stable *&an the MIND013 structure whereas inclusion of polarization functions and electron correlation effects reverses the order. Thus, for structure I the MINDO/3 results are confirmed.

IS September 1978

The situation is different for the CC protonated structures of type 11. The discrepancies found between the ab initio calculations in refs. [3,4] and the MIND013 results [S] remain. Calculations using the MIND013 geometries show the structures Da -1Id to be less stable than structure I. This fact still agrees with the MINDO/3 stabilities. But already at that stage the diferences in stability are much smaller than the MIND0/3 values_ Furthermore, the STO-3G geometry differs considerably from its MINDO/3 analogue. The CC bond distance in structure IId (STO-3G) is significantly stretched in comparison to MINDO/3 (3.33 au versus 4.46 au)_ As a consequence, the stability of Ud (STO3G geometry) with respect to Ia is increased. Structure IId is now the most stable one, in accordance with experimental fmdings [6]. In the investigations by Lathan et al. [4] structure IIe was found slightly more stable than IId. This fact is also reproduced by our basis A. On the other hand, with basis set B (SCF and CEPA) IId is more stable than IIe. However, the difference is small (= 1 kcal/mol). Thus we conclude that the potential energy surface is relatively flat wi-rh respect to a displacement of the bridging hydrogen atom. Further geometry optimization with larger basis sets than STO-3G are necessary in order to determine the minimum structure more preciselyIn table 3 AE and AH values for reaction (1) and the proton affinity of ethane are shown. In computing .&H values we combined energy differences obtained

Table 2 Relative stabilities (in kcal/mol) with respect to structure ia (MINIJo/ Stmcture

MIND013

geometry)

Basis set A

Basis set B

&SCF ra aj Ia STO-3G lb geometry

1Ic IId

0 1.16 11.34 11.48 1197 15.73

STO-3G aj IId Ue bj’geometry

-

0 -6.31 254 4.65 6.50 4.06 6-11 -1934 -21.27

+XIF

MCEPA

0 3.75 2.82 5.03 6.48 5.21 9-17 --8_46 -7.25

0 14.82 2-77 1.97 3.13 2.37 7.14 -626 -5.23

aj STG3G optimized geometry [3,4]. bj D9d symmetry. Far the definition of the geometry see text and ref- [4]-

177

Vduzze

CHEhfICAL

58, number 2

PHYStCS LElTERS

15 September 1978

Table 3 Tkoretical energy differences and thermodynzmic quantities for the reactionGH; (noncJ.assical) + Hz = GH;, and the wmputed proton &in&y of ethane in compariron with expezimentd results- The AH and dG v&es are computed with respect to aE (CJZPA). The energetic vahes are given in kc&/mol, the entropy in cal deg-* moT1 qH+5 + H, = GH; AI.?(SCF) al

a)

aE(CEPA)

aEo b, A&$-AHp

Ud

-32

-11.6

-9.0

-15.2

5.6

6.8 =I

zy)(Z-=

Affp’ AH(eup) d)

4-O

9 asO (exp) ‘)

5

143 K) 0.5

-215

(T=

-19.6

= 1.5

24

Gso AC?&-, (ev) GH;

ra

143 K)

-11.8

i 0.4

-26.8

(T = 400 K)

-X*1 -2.1

1.8

= CzH6 + H”

aE(SCF)

a)

aE(CEPA) AE,, b,

@Go-@,

a)

138.0

146.5

141-4

147-7

4.2 0.49

-5.4

=)

0.57

PA(calcJ

138.3

143-4

PA (exp) d,

131.8

139.6

a) Energies for GHz (nonclassical). basis 3: E(SCF) = -78.25680 au, E(CEPA) = -78.54904 au (see ref. [S]); Ha : I.4 au+E(SCFl= -1.12631 au.E(CEPA) = --1.16184 au;C,H,rE(SGF) = -79.16824 au,E(CEPA) = -79.49978 table 8 in ref- [ 245). b)Computed fkom MIXDO/ results_ Aeo are the differences h ZeiO point energy=) MIND0/3 restdts from structure Ih. d)Ref. 161.

from the CFPA PNO method and zero-point energies cakuiated by MIIWO/3_ The temperature dependence was computed from standard thermodynamical formulas for the ideal gas and from a rigid-rotator/barmonk oscfiator appro.ximation. In a number of cases vibrational frequencies and thermodynamic properties have been calculated successfully on the basis of MIXi/ results [2223] _ In view of the large computational effort for an ab initio calculation of the harmonic force field we regard it as useful to correct the ab initio AE’s with the semi-empirical vibrational frequencies. When comparing with experimental 4.kYvatues this procedure is certainly more satisfactory than taking simply AE from an ab initio calculation_ Since for structure II MINDO/3 does not predict the correct geometry, we expect in this case the results for M to 178

3s lp, R = au (see

be somewhat less reliable than in case of structure I. Let us comment on only one point in more detail. If one compared AE(SCF) and AE(CEPA) for the reaction C& f H2 = C&(ia) (table 3) directly with the experimental AW one would come to the somewhat kurprising conclusion that the SCF approximation is much better than CJZPA; However, if zero-point energy corrections and temperature dependence are taken into account, the results based on CEPA energy differences are much closer to experiment. The same is true for the reaction leading to IId. The correlation energy contributions to the proton affinity of etbane are less pronounced and not quite consistent with the situation discussed above. In the case of the proton affinity with respect to structure Ia agreement with experiment is slightly worse than in the other examples

Volume 58, number 2

CHEMICAL

PHYSICS

4_ Conchlsion From our ab initio results we fmd structure II to be more stable than I. Although MIND0/3 has been used succe.sst%liyfor the discussion of other carbocations (see refs. [7,8] and references therein) this method is not appropriate for the correct description of structure and stability of the pentacoordinated, CC protonated form II. However, MINDO/3 is still useful for the computation of zero-point energy corrections and the temperature dependence of AH.

AcknowIedgement The computations were performed on the CDC CYBER 73/74 computers of the University of Vienna and the Technical University of Vienna and on the ESER 1040 computer of the University of Leipzig.

References [I] [2]

[3] [41 [S]

V-L. Talroze and A.L. Lyubimova, DokL Akad- Nauk SSSR 86 (1952) 509. S. Wexler and N. Jesse, J. Am. Chcm. Sot. 84 (1962) 3425; F-H. Field, J-J__Franklin and MS-B_ Munson, J. Am. Chem. sot. 85 (1963) 3575; P. Kebarile and E-W. GodboIe. J. Chem- Phys 39 (1963) 1131; M.S.B. Munson and F-H. Field, J. Am. Chem. Sot. 87 (1965) 3294. W.k Latban, W.J. Hehre and J.k PopIe, J. Am. Chem. sot. 93 (1971) 808. W.A. Latban, LA. Curtiss, W.J. Hehre, J.B. Lisleand J.A. Pople, in: Progr. Phys_ Org. C&em, 11 (1974) 175. PX Bischof and XJS_ Dewarm J. Am_ Chen~ Sot. 97 (1975) 2278_

LETTERS

15 September i978

[6] & Hiioka and P. Kebarle, J. Am. Chem. Sot. 98 (1976) 6119. [7] H.-J. KGhIer, D. Heidrich and H. Lischka, 2. Chem. 17 (1977) 67. [S] H. L.ischka and H.-J. Ki5ihkq J. Am. Chem. Sot-, to be published. 191 S.F. Boys, in: Quantum theory of atoms, molecules and the solid state, ed P--O_ L&din (Interscience, New York, 1967) p. 253. [lo] W. Meyer, Inrem. J. Quantum Chem. 1s (1971) 59; J. Chem. Phys. 58 (1973) 1017. [ 111 R Ahhichs, H. Lischka, V. Staemmler and W. Kutzeinig, J. Chem. Phys. 62 (1975) 1225. [12] S. Huzinaga, Apprcximate Atomic Functions I and II, University of Alberta (1971). [13] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [14] Program no. 279, Quantum Chemistry Progam Exchange- Indiana ?Jniversity. Bloomington, Indiana [1.5] RE. Stanton and J-W_ McIver Jr., J. Am. Chem. Sot. 97 (1975) 3632s [ 161 P.G. Mezey, Chem. Phys- Letters 47 (1977) 70, and references therein. 1171 M.J.S. Dewar, F-day Discussions Chem. Sot. 62 (1977) 197. [18] J.W. McIver Jr. and A. Komomicki, J. Am. Chem. Sot. 94 (1972) 2625. [19] P.C. Hariharan, W.A. Lathanand J-A. Pople, Chem. PhysLetters 14 (1972) 385. 1201 V. Dyczmons, V. Staemmier and W. Kutzw, Chem. Phys. Letters 5 (1970) 361; V_ Dyczmons and W_ K&&n&, Theoret Cl&n_ Acta 33 (1974) 239_ [21] RC. Bingham, M.J.S. Demand D.H. Lo, J. Am. Chem. Sot. 97 (1975) 1285. 1221 M.J.S. Dewar and G.P. Ford, J. Am. C&m. Sot. 99 (1977) 1685. [23] XLJ.S. Dewar and G-P_ Ford, J. Am. Chem- Sot. 99 (1977) 7322. [24] R Ahhichs, H_ Lischka, B. Zurawski and W_ Kutzeln@, J. Chem. Phys. 63 (1975) 4685. [25] B. Zurawski, R Ahhichs and WV? Kutzeh@g, Chem. Phys. Letters 21<1973) 309_

179