Article pubs.acs.org/JPCA
The Correct Physical Basis of Protobranching Stabilization Lawrence S. Bartell* Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States ABSTRACT: The source of the extra stability of branched hydrocarbons over unbranched (hereafter referred to as protobraching stabilization) has been explained in several different self-consistent ways. Gronert, basing his arguments on well-established properties of organic molecules, namely that geminal atoms strongly repel each other, formulated a model which accounted for this “protobranching” stability simply and very well. However, careful quantum computations were found to yield correct protobranching energies only if they properly took electron correlation into account. Such a source of stability would not have been needed in Gronert’s model. The present article analyzes what is correct and what is uncertain about Gronert’s atomic repulsion model, and concludes that the computations of Wiberg, Bader, Grimme, Schleyer, and their colleagues overturn Gronert’s model and that bond− bond electron correlation energies provide the correct explanation of protobranching.
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INTRODUCTION The concept of “protobranching” was introduced by Schleyer and colleagues1 to refer to the number or 1,3 alkyl−alkyl interactions in hydrocarbon molecules. So, for example, there are three such interactions in isobutane and only two in nbutane. In this article, the term protobranching will refer to the extra stability, for whatever reason, of branched hydrocarbons compared with1,4−8 unbranched. There are two essentially different, hotly contested, rationalizations to account this stabilization. Gronert,2,3 on the one hand, attributes the stabilization to the deceased 1,3 nonbonded repulsions in more highly branched alkane isomers. Illustrated in the graphical abstract are some experimental examples of the consequences of strong 1,3 nonbonded repulsions and with effects of the ligand-close-packing model to be discussed in the following. The main opposition to Gronert’s interpretation comes from those who have carried out quantum computations which they have interpreted in various ways.1,4−8 The literature in the area is wide-ranging but this note will focus primarily on those articles directly related to the argument herein advanced. Schleyer and colleagues have published very articulate discussions of mutually consistent alternative models in the thermochemistry of organic molecules.6−8 It has even been suggested by several chemists that it is a matter of taste and convenience which model is used since all are self-consistent and accurate. It is my contention that the various models are not equally probable and that a correct physical basis exists to account for what I will continue to call protobranching stabilization. Before comparing the two interpretations we first note that one of the major participants in this dispute is Schleyer. A feature article in C&E News9 begins with an epiphany Schleyer © 2012 American Chemical Society
experienced when he was lecturing to students in a class on the structure and energy of organic molecules. He realized that protobranching stabilization could be accounted for if geminal methyl groups attracted each other. The article called this a “mysterious attraction”. As will become clear, such an attraction would indeed account for protobranching stabilization if it actually occurred. However, the situation turns out to be rather more complex. Let us first consider Gronert’s model2,3 to show that the 1,3 atom−atom repulsions he considers are indeed strong in hydrocarbons and quite sufficient to account for his result provided that certain conditions are met. To add perspective to the problem we will examine such an approach in some detail including physical evidence not discussed by Gronert. This will show how plausible such treatment is and confirm that his model is correct at least up to a certain point.
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EVIDENCE FOR LIGAND REPULSIONS To begin, note that there is much physical evidence that indicates that geminal atoms surrounding carbon repel each other strongly, which casts doubt on the “mysterious attraction”9 between geminal methyls. This primary source of information on ligand repulsion has been largely ignored. For one thing, ligands bonded to carbon have such short bond lengths that the separation between them is substantially shorter than the sum of their Pauling van der Waals radii10 implying that the geminal atoms strongly repel each other. By contrast, for molecules such as lanthanum trihalides, the central atom in the equilibrium D3h structure is so large that the Received: August 21, 2012 Revised: September 21, 2012 Published: September 26, 2012 10460
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ligand−ligand separation exceeds the sum of their van der Waals radii. The consequent attraction of the ligands for each other is revealed in the very soft out-of-plane mode.11 Additional evidence for the repulsions between ligands surrounding relatively small central atoms is provided by spectroscopic results and by the structures themselves. The spectroscopic evidence is suggested by results of the approximate force field, the Urey−Bradley field.12 This field is based on the direct interactions between geminal atoms, whereas in the popular diagonal force field, bending constants are, instead, based on displacements of angles. Although neither model field incorporates a full force constant matrix, it is suggestive that the Urey−Bradley field turns out to account for molecular vibrational frequencies better than the popular valence force field. This has been shown for a variety of molecules particularly by Shimanouchi and co-workers13,14 where the derived force constants are found to be of the magnitude implied by the repulsive potential energies expected between geminal atoms. It is fair to point out that this generalization appears not to be true for methane and certain other hydrocarbons. The reason why hydrocarbons differ from other molecules was shown by Kuchitsu and Bartell15 who found that a modified Urey−Bradley force field is superior to the valence force field even for hydrocarbons when certain stretch−stretch contributions are included, which are expected to be particularly strong for bonds involving hydrogen atoms. Moreover, the repulsions between hydrogens inferred from the vibrational spectra using a Urey−Bradley force field incorporating the stretch−stretch interactions are of the magnitude suggested by the 1960 field16 proposed to treat geminal H−H repulsions in hydrocarbons and related hydrides. Next, consider the fact that the shapes and stabilities of simple molecules have been shown beyond doubt to be determined by the close-packing of the repelling ligands (lcp) when the central atom is as small as carbon. This lcp packing was first noted in hydrocarbon molecules and their nitrogen, oxygen, fluorine, and chlorine derivatives,16 and later found to apply generally to molecules with central atoms of moderate size.17−27 In the lcp model, bond angles are dictated solely by ligand packing radii with no consideration of “hybridization”. Therefore, “hybridization theory” and even the popular VSEPR model28 (despite its apparent similarity to the lcp model) have very little to do with the molecular structures under consideration here.29 As mentioned earlier, the distances between the ligands, namely the sum of their lcp radii, are far shorter than the sum of their van der Waals radii, again indicating substantial, but balanced, ligand repulsions. Moreover, adding further confirmation that ligands repel, is a repelling points on a sphere model.30−33 In this model the points on a sphere represent ligands in the coordination sphere of a central atom. This simple model has been shown, particularly in ref 32, to be astonishingly good at accounting for diagonal and off diagonal quadratic, cubic, and higher-order force constants in molecules. It would seem to be clear then that, when the central atom is small, the interactions between geminal atoms are repulsive, not attractive. If this is true, it immediately invalidates the “mysterious attraction”9 between carbon atoms in geminal methyl groups initially proposed to explain protobranching.
Article
DISCUSSION
In the “molecular mechanics” representation of molecules, a model force field is constructed to create a molecular potential energy function of sufficient generality to cover any substance of concern. Minimizing the potential energy with respect to molecular deformations is supposed to yield the equilibrium structure of the molecule under consideration. Note that the difference between normal and iso potential energies in hydrocarbons can be expressed as: Vnormal − Viso = 2VC − H − (VC − C + VH − H)
(1)
Where Vij’s are nonbonded interactions evaluated at their appropriate geminal nonbonded distances. It is immediately apparent, then, why the suggestion of a strong “mysterious attraction” between geminal methyl groups would make the iso isomer more stable than the unbranched isomer. In view of the evidence for the validity of the ligand-closepacking model (which is firmly supported by the literature cited17−27) it would seem that the atom−atom interactions involved in protobranching are strongly repulsive although, to be sure, they would contain some London dispersion forces, which would contribute modest attractive components. Therefore, protobranching energies can be easily accounted for if C− H interactions are more repulsive than the average of C−C and H−H interactions as in Gronert’s explanation,2,3 Gronert’s conclusion seems to be closely related to the potential energies proposed in the 1960 publication.16 Such a choice of potentials not only accounts quite well for the protobranching energies of a substantial number of molecules but, incorporated into a 1967 molecular mechanics model force field (hereinafter called the JTB field),34 it also yields remarkably accurate trends in bond lengths and bond angles over a series of molecules with different structures. Therefore, it would appear that Gronert’s explanation of protobranching energies is based on convincing experimental evidence. Therefore, the case is closed? Not yet. So far, all of the evidence cited has been based on empirical lines of reasoning and depends crucially upon the “if ” mentioned a few lines above. What has been ignored in the foregoing are the results of careful quantum computations.1,4−8 If nonbonded forces between geminal atoms were the correct source of protobranching stabilization, these would have been reasonably well represented by Hartree−Fock or conventional DFT computations. But such computations fail to yield results in accord with experiments. Computations properly incorporating electron correlation are required. This has been shown by such meticulous scientists as Wiberg,4 Bader,4 Grimme,5 and Schleyer,1 who found that electron correlation energy is crucial and must be considered to establish the correct basis for protobranching. Moreover, according to Ess et al.,35 Grimme was able to partition the electron correlation effects into regions of space and show that the electron correlation effects, which stabilize branched alkanes result from interpair electron correlations between bond orbitals of similar type, that is C−C with C−C and C−H with C−H. Comparable stabilization did not occur in electron correlations between C−C and C−H. Although the relative values, and also signs for energies corresponding to C−C and C−H pairs in comparison with (C−C, C−H) pairs are opposite to those in the 1960 potential energies used in the J.T.B. article,34 they also obviously favor iso over normal according to eq 1. Such a conclusion settles the dispute between the quantum chemists and Gronert. 10461
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(22) Gillespie, R. J.; Bytheway, I.; Robinson, E. A. Inorg. Chem. 1998, 37, 2811−2825. (23) Robinson, E. A.; Heard, G. L.; Gillespie., R. J. J. Mol. Struct. 1999, 48, 305−319. (24) Gillespie, R. J.; Robinson, E. A E. A..; Heard, G. L. Inorg. Chem. 1998, 37, 6884−6989. (25) Gillespie, R. J. Coord. Chem. Rev. 2000, 197, 51−62. (26) Gillespie, R. J.; Popelier, P. L. A. Chemical Bonding and Molecular Geometry: from Lewis to Electron Densities; Oxford Univ. Press: Oxford; 2001. (27) Robinson, E. A.; Gillespie, R. J. Inorg. Chem. 2003, 42, 3865− 3872. (28) Gillespie, R. J. J. Chem. Educ. 1963, 40, 295−301. (29) Here, it should be noted that MO computations excluding any interaction between ligands reproduce qualitatively the qualitative predictions of VSEPR. Bartell, L. S. Inorg. Chem. 1966, 5, 1635−1636 . However, the lcp model reproduces quantitatively correct molecular structures. Hence, the VSEPR and lcp models appear to be distinct models with VSEPR applying to cases where the central atom is large and ligand ineractions are weak. (30) Thompson, H. B.; Bartell., L. S. Inorg. Chem. 1968, 7, 488−491. (31) Bartell, L. S.; Plato, V. J. Am. Chem. Soc. 1973, 95, 3097−3104. (32) Bartell, L. S. Croatica Chem. Acta 1984, 57, 927−933. (33) Bartell, L. S.; Barshad, Y. Z. J. Amer. Chem. Soc. 1984, 106, 7700−7703. (34) Jacob, E. J.; Thompson, H. B.; Bartell, L. S. J. Chem. Phys. 1967, 47, 3736−3737. (35) Ess, D. H.; Liu, S.; De Proft, F. J. Phys. Chem. A 2100, 114, 12952−12957.
CONCLUSIONS Iiasmuch as Gronert’s theory is simple, self-consistent, and expressed in terms of intuitively appealing quantities, what is wrong with it? Gronert placed too much confidence in potential energy functions proposed by the experimentalist Bartell16 over a half-century ago on the basis of the very limited information available at the time. Quantum computations at the time were far too primitive to treat electron correlation and its partitioning in molecules. Those 1960 potential energy functions had been deliberately biased to yield plausible protobranching energies on the basis of atom - atom interactions instead of the bond−bond electron correlation energies now recognized as the correct source of protobranching energy. This originally introduced bias forced C−H repulsions to exceed those of C−C and H−H despite the fact that no a priori reason existed to justify this bias. The presently recognized ligand-close-packing model, however, implies a balance of ligand repulsions. Such a balance suggests a corresponding near balance of potential energies which would lead to a near cancelation of terms in eq 1. This completes the case against the Gronert interpretation.
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AUTHOR INFORMATION
Corresponding Author
E-mail: *
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Social Security Administration. REFERENCES
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