Structural Chemistry, Vol. 9, No, 1, 1998
Paradigms and Paradoxes
Dissociation Energies and Rotational Barriers About CC Single, Double, and Triple Bonds: A Hybrid HF-DFT Approach (Becke3LYP/6-311++G**) Ibon Alkorta1 and Jose Elguero1,2 Received April 21, 1997; revised May 26, 1997; accepted June 3, 1997 KEY WORDS: Ab initio calculations; dissociation energies; rotational barriers.
INTRODUCTION
high level calculations [12-15] which are outside our purpose to report and discuss. We have preferred to carry out calculations using the hybrid HF-DFT approach (Becke3LYP/6-311 + +G**), which gives very good results in many fields of chemistry [16-18], We represent in Scheme 1 the energy profiles and report in Tables I and II the molecules involved. Let us examine first the case of a C—C bond exemplified by ethane (D3d). In this case, the rotational barrier (2.9 kcal mol~') [19] is so small compared with the single-bond breaking energy that it can be neglected. The entities formed are two planar methyl radicals (D3h) and the calculated CC single-bond-breaking energy is 91.7 (without), 82.3 (with zero-point energy, ZPE, correction), and 73.0 kcal mol~' (with thermal correction). The last two values, 82.3 and 73.0 kcal moP1, should be compared with experimental values at 0 K (97 kcal mol~') and at 25°C (83-85 kcal mol"1), showing that calculations underestimate the experimental results by 10-15 kcal mol'1. In the following discussion it is necessary to bear in mind that we are discussing thermodynamic values and that compounds of intermediate energy are not necessarily kinetic "intermediates." As pointed out by Nicolaides and Borden [15], in the case of ethane and ethylene there is no ambiguity, but in the case of acetylene it is necessary to take into account the diabatic bond breaking into two quartets, 4E, which is not the ground state of CH.
According to Miller, the difference in bond dissociation energies (BDEs) between a single bond, say C—C, and the corresponding double bond is the amount of energy necessary to cause rotation around the double bond [1], This partition of BDEs allows one to discuss the intriguing case of the barrier to the rotation about a CC triple bond. Intuitively, one expects that the barrier around a C=C bond should be higher than around a C=C bond, but that barrier is not a physical observable. Miller's paper of 1978, although discussed in a very popular reference book [2], has only been quoted six times in the literature [3-8] and none of these papers discusses the aspect which is relevant for the present work. Other authors, however, have used a similar approach [e.g., 9-11].
RESULTS AND DISCUSSION Rotational barriers around C—C and C=C as well as CC bond dissociation energies for ethane, ethylene, and ethyne (acetylene) have been computed with very 'Institute de Quimica McJdica, CSIC, Madrid, Spain. should be directed to Jose' Elguero, Instituto de Qufmica Me'dica, CSIC, Juan de la Cierva, 3, E-28006 Madrid, Spain; e-mail:
[email protected].
2Correspondence
59 l040-0400/98/0200-0059$15.00/0© 1998 Plenum Publishing Corporation
60
Alkorta and Elguero
Scheme 1. Energy profiles with ZPE correction (in kcal mol ') of the single (ethane), double (ethylene), and triple (acetylene) carbon-carbon bonds.
Table I. Computed Total Energies (in Hartrees) for the Molecules of Scheme 1 with the Corresponding ZPE and Thermal Corrections in kcal mol~ ' at the Becke3LYP/6-31 1 + + G**//Becke3LYP/6311 + +G** Level
Molecule
Total energy (Hartrees)
Zero-point energy (kcalmor 1 )
Thermal correction (kcal mol - 1 )
C2H6 C2H4 C2H2 CH3 CH2 (t) CH2 (s) C2H4 (t) CH(d) CH(q) C2H2 (t) trans C2H2 (t) cis C2H2 (q5)
-79.8 657 -78.61554 -77.35666 -39.85519 -39.16612 -39.14674 -78.51333 -38.49410 -38.46118 -77.20013 -77.21827 -77.10547
46.62 31.86 16.94 18.60 10.75 10.35 28.45 4.03 4.35 14.70 14.90 13.64
13.45 13.10 11.89 11.35 11.52 11.10 14.00 10.54 10.92 13.71 13.69 14.24
Consider now ethylene (D2h), which was the case discussed by Miller [1], The CC bond breaking leads to two carbenes (methylenes) which could exist as singlets (1A2) or triplets (3B2). The triplets are of lower energy and for a pair of these last entities, the calculated CC double-bond-breaking energy is 177.8 (without), 167.4 (with ZPE correction), and 157.5 kcal moP1 (with thermal correction), excellent values taking into account the experimental information (Table II), since the underestimation is reduced to 4-9 kcal mol~'. Remember that ethylene dissociates diabatically, as well as adiabatically, to two 3B2 CH2 molecules [15] [see also 20, 21], its diabatic and adiabatic CC BDEs being the same, 171 kcal mol~' (Table II). The total energy gap can be partitioned into two terms: the rotational barrier around the C=C bond and the CC single-bond-breaking energy. Rotation of the ethylene produces a singlet ethylene twisted at 90° (each —CH 2 - moiety is planar) (D2d),
61
BDEs and Rotational Barriers About CC Bonds
Table IL Calculated (Becke3LYP/6-31 1 + +G**//Becke3LYP/6-31 1 + +G**) and Experimental Data for the Processes Depicted in Scheme 1"
Process
Energy
Energy +ZPE at OK
C 2 H 6 ->2xCH 3 C 2 H 4 -»2xCH 2 (s) C 2 H 4 ->2xCH 2 (t) C2H4 - C2H4 (t) C2H2-»2xCH(d) C 2 H 2 ->2xCH(q) C2H2 -> C2H2 (t) cis C2H2 -» C2H2 (t) trans C2H2 (t) cis -> C2H2 (q5)
91.74 202.09 177.77 64.13 231.21 272.53 86.84 98.22 70.78
82.31 190.93 167.41 60.72 222.34 264.30 84.81 95.99 69.52
Energy +ZPE + T at 298 K 73.05 181.82 157.48 59.83 213.15 254.35 83.01 94.17 68.98
Other calculations [13]
Experimental data at 298 K [12]
94.4
83-85
177.3
146-151
228.3
199-200
Experimental data at OK
97 [22] 171.0 ± 1.2 [14,23] 65 [19, 22, 24] 228.8 ± 0.7 [14, 23]
"All values in kcal mol~'. ZPE, zero-point energy correction; TC, thermal correction.
but this structure is 8.5 kcal mol ' is higher than the perpendicular triplet ethylene [25]. This last structure is 64.1-60.7 kcal mol~' higher in energy and can be directly compared with the experimental value (at room temperature) of 65 kcal mol"1, although the D2d triplet is a local minimum, while the barrier corresponds to a transition state [26]. Thus, the difference (113.6-106.7 kcal mol"1) should represent the CC single-bond-breaking energy, which increases compared with ethane, as is apparent in Scheme 1. Finally, we will consider the most interesting case, that of acetylene (Dxb). The dissociation leads to two carbynes (methylidynes) (D^) which can exist as a doublet or a quartet, the first one, 2II, being of lower energy; the calculated CC triple-bond energy (adiabatic process) is 213.2 (298 K)-222.3 (0 K) kcal mol"', in good agreement with the experimental values of 199200 (298 K) and 228.8 (0 K) kcal mol"1 (Table II). The energy to be partitioned is that corresponding to the diabatic process leading to two 4E CH (264.30 kcal mol~'). This last energy can be pardoned into three terms: the triple-bond rotational barrier, a double-bond rotational barrier, and the CC single-bond-breaking energy. The first barrier leads to a triplet diradical which can exist in two isomers, the less stable, the trans (C2h), and the more stable, the cis (C2v), with an increase in energy of 86.8-84.8 kcal mol ~'. The second barrier leads to a biscarbene (C2) which exists as a quintet, 70.8-69.5 kcal mol"1 still higher in energy. Note also that the single CC bond-breaking energy increases from ethane (82.3 kcal mol~') to perpendicular triplet ethylene (106.7 kcal mol"1) to bis-carbene (110.0 kcal mol"1; Scheme 1). The experimental energies at RT are proportional to the corrected energies at 0 K,
which allows an estimation of the barrier around the C=C bond at 0 K as being 75.4 kcal mol"1. The E + ZPE values must be compared with the experimental values at 0 K [Eq. (2)]. This equation predicts for the CH2 (D2d) triplet a relative value at 0 K of 75.2 kcal mol"', similar to our estimation of the barrier [assimilating both energies, Eq. (3) is obtained]:
On the other hand, comparing thermally corrected values at 298 K (E + ZPE + thermal correction [TC], Table II) with experimental values at 298 K [2], we obtain
It appears that the thermal corrected values are systematically underestimated. Finally, we have carried out a topological analysis of the nature of the CC bonds of the different species of Scheme 1 using the AIM (Atoms in Molecules) methodology [27] with the AIMPAC program package [28].
62
Alkorta and Elguero
Table HI. Bond Lengths, Bond Critical Points, and Bond Orders of the Different Molecules of Scheme 1 Bond length r
(A)
Molecule C2H6 C2H4 C2H2 C2H4 (t) C2H2 (t) cis C2H2 (q5)
1.5305 1.3288 1.1994 1.4473 1.3278 1.5482
Pbcp
(ea.u.~ 3 ) 0.23780 0.34378 0.41172 0.27558 0.33228 0.22301
Bond order n
1.000 1.966 3.032 1.272 1.827 0.910
ing to a double bond) or 154 kcal mol l (leading to a single bond). This kind of approach can be used for other XY systems, X and Y being different atoms, where BDE have been reported (N or P [12]; Si [32]; Ge or Sn [33]).
SUPPLEMENTARY MATERIAL AVAILABLE All geometries are available on simple request to either author.
REFERENCES The bond orders n have been calculated using the electron density at the bond critical points pbcp and the following equation, proposed by Bader [27, p. 75]:
where A and B are evaluated to fit the values of 1 for ethane, 2 for ethene, and 3 for acetylene. The resulting bond orders for all the compounds studied are gathered in Table III. According to Pauling [29, 30], there exists a linear relationship between the bond length r and the logarithm of the bond order [r(A) = r 0 (A) - c log n), where c is usually taken as 0.56 A. A statistical analysis of the data at Table III shows a Pauling-type relationship with c = 0.68:
It has been postulated that, in general, for a bond between two given atoms, the bond length r decreases as the bond energy increases [31]. The following equation shows that this is the case for compounds of Table
III:
The linear relationships between r, log n, and bond energies is a guarantee of the consistency of our HF/ DFT approach. Moreover, Eq. (7) should provide a simple tool to estimate other bond energies.
CONCLUSION In conclusion, the rotational barrier around a CC triple bond can be estimated to be 85 kcal mol~' (lead-
1. Miller, S. I. J. Chem. Educ. 1978, 55, 778-780. 2. March, J. Advanced Organic Chemistry, 4th ed. Wiley: New York, 1992, p. 24. 3. Taube, R.; Seyfert, K. J. Organomet. Chem. 1983, 249, 365369. 4. Agranat, I.; Skancke, A. J. Am. Chem. Soc. 1985, 107, 867871. 5. Pestana, D. C.; Power, P. P. J. Am. Chem. Soc. 1989, 111, 6887-6888. 6. Toullec, J. J. Chem. Soc. Perkin Trans. 2 1989, 167-171. 7. Lindford, L.; Kruger, G. J.; Hattingh, J. T. Z. J. Chem. Soc. Dalton Trans. 1989, 1565-1577. 8. Pestana, D. C.; Power, P. P. Inorg. Chem. 1991, JO, 528-535.
9. Benson, S. W.; Cruikshank, F. R.; Golden, D. M.; Haugen, G. R.; O'Neal, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R. Chem. Rev. 1969, 69, 279-279. 10. Doering, J. P.; Me Diarmid, R. J. Chem. Phys. 1981, 75, 8791; 2687-2692. 11. Roth, W. R.; Adamczak, O.; Breukkmann, R.; Lennartz, H.W.; Boese, R. Chem. Ber. 1991, 124, 2499-2521. 12. Schleyer, P. von R.; Kost, D. J. Am. Chem. Soc. 1988, 110, 2105-2109. 13. LanghorT, S. R.; Bauschlicher, C. W.; Taylor, P. R. Chem. Phys. Lett. 1991, 180, 88-94. 14. Ervin, K. M.; Gronert, S.; Barlow, S. E.; Giles, M. K.; Harrison, A. G.; Bierbaum, V. M.; DePuy, C. H.; Lineberger, W. C.; Ellison, G. B. J. Am. Chem. Soc. 1990, 112, 5750-5759. 15. Nicholaides, A.; Borden, W. T. J. Am. Chem. Soc. 1991, 113, 6750-6755. 16. Jiao, H.; von R. Scheleyer, P. Angew. Chem. Int. Ed. Engl. 1996, 35, 2383-2386. 17. Pidun, U.; Boehme, C.; Frenking, G. Angew. Chem. Int. Ed. Engl. 1996, 35, 2817-2820. 18. Alkorta, 1.; Elguero, J. Tetrahedron, 1997, 53, 9741-9748. 19. Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds. Wiley: New York, 1994, pp. 539, 628. 20. Carter, E. A.; Goddard, W. A. J. Phys. Chem. 1986, 90, 9981001, and references therein; Yamaguchi, Y.; Schaeffer, H. F. J. Chem. Phys. 1997, 106, 1819-1826. 21. Trinquier, G. J. Am. Chem. Soc. 1990, 112, 2130-2137, and references therein. Berson, J. A.; Birney, D. M.; Dailey III, W. P.; Liebman, J. F. Ethylenedione: Its ions and Analogues, in Modem Models of Bonding and Delocalization, Liebman, J. F.; Greenberg, A. eds.; VCH: New York, 1988, pp. 391-441. Liebman, J. F.; Yee, S. O.; Deakyne, C. A. Systematics and Surprises in Bond Energies of Fluorinated Reactive Intermediates in Effect of Selective Fluorination on Reactivity in Organic andBioorganic Chemistry, Welch, J. T. ed.; American Chemical Society: Washington DC (ACS Symposium Series, 456), 1991, pp. 36-54.
BDEs and Rotational Barriers About CC Bonds 22. Hehre, W. J.; L. Radom, L.; Schleyer, P. von R.; Pople, J. A. Ab Mtio Molecular Theory. Wiley: New York, 1986, pp. 278, 426. 23. Wu, C. J.; Carter, E. A. J. Am. Chem. Soc. 1990, 112, 58935895. 24. Kalinowski, H.-O.; Kessler, H. In Topics in Stereochemistry, Vol. 7; Allinger, N. A.; Eliel, E. L.; eds.; Wiley: New York, 1973, p. 304. 25. Merer, A. J.; Mulliken, R. S. Chem. Rev. 1969, 69, 639-656. 26. Salem, L.; Rowland, C. Angew Chem. Int. Ed. Engl 1972, //, 92-111. 27. Bader, R. F. W. Atoms in Molecules. A Quantum Theory, Oxford University Press: New York, 1990.
63 28. Bieger-Konig, F. W.; Bader, R. F. W.; Tang, T. H. /. Comput. Chem. 1982,5,317-328. 29. Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals. Cornell University Press: Ithaca, New York, 1945, p, 174. 30. Biirgi, H.-B.; Dunitz, J. D.; eds. Structure Correlation, Vol. 2. VCH: Weinheim, Germany, 1994, pp. 195, 204, 225, 305. 31. Hine, J. Physical Organic Chemistry, McGraw-Hill: New York, 1962, p. 32. 32. Koseki, S.; Gordon, M. S.; Schmidt, M. W. Chem. Phys. Lett. 1992, 200, 303-310. 33. Windus, T. L.; Gordon, M. S. J. Am. Chem. Soc. 1992, 114, 9559-9568.
