Charge distributions and chemical effects. 23. The chemical bond, a theory of electron density

Abstract

The energy of atomization, ma*, of a hypothetical vibrationless molecule is conveniently partitioned into bonded and nonbonded contributions. The portion of Ma* associated with the bond formed by atoms i and j (Le., the "bond energy", t i j ) can be deduced from the derivatives of tij with respect to the nuclear charges of i and j . Bond energies derived for one molecule are not transferable to other molecules because, as a rule, the simple transfer of selected tij's would not satisfy the requirement for molecular electroneutrality. The appropriate charge renormalization accompanying the use of selected reference bond energies toij leads to a description of the "bonded part" of ma*, = xtoij + xiX,aijAqi, featuring the effects due to changes in net atomic charges (Aqi) with respect to the charges of the atoms forming the reference bonds. Theoretical expressions are given for the aii coefficients. Applications to saturated hydrocarbons indicate that the charge-dependent Xix,aiiAqi part is by far the leading term accounting for the energetic differences between isomers or conformers and that nonbonded coulomb interactions play an almost negligible role in that respect. The structural effects in linear and branched paraffins and in compounds containing chair or boat cyclohexane rings are deduced from the theoretical ai:s, indicating that 1 me e) of electronic charge added to hydrogen stabilizes a CH bond by 0.632 kcal/mol, whereas 1 me added to carbon has a stabilizing effect of 0.247 on a CH bond and of 0.488 kcal/mol on a CC bond. The calculated molecular atomization energies agree with their experimental counterparts within 0.16 kcal/mol (average deviation). IntroductionSeveral fundamental aspects of chemical binding are discussed in this paper, namely, the view that molecules can be regarded as assemblies of "chemical bonds" with energies of their own or, else, as collections of "atoms in the molecule" with energies differing from their free-state values. Various facets of energy partitioning are reviewed and expanded. The roles of electronic charge distributions and finally that of "steric effects" are analyzed in detail. The whole adds up to give a novel view of the important physical features governing molecular stabilities and casts a new light on relevant aspects facilitating the interpretation of organic chemistry. Numerical examples are worked out for saturated hydrocarbons in order to illustrate in a comprehensive way the detailed features of this unified picture of molecular energies. A qualitative description of the relevant results and implications in organic chemistry is offered in the Conclusions.

Charge distributions and chemical effects. XL. Chemical bonds in benzenoid hydrocarbons

“…The expression indicates how their energies depend on the charges of the bond-forming atoms (1)(2)(3): eg is for a reference bond with net charges qp and qy at atoms i and j, respectively, whereas eij corresponds to modified charges, q, = qy+ Aq, and qj = qy+ Aqj. The av and aji parameters, "measuring" the changes in bond energy accompanying unit charge variations at atoms i and j, respectively, are discussed further below, as well as the E~' s .…”

Charge distributions and chemical effects. XXXI. Molecular energies of ethylenic compounds

“…q; = -1 1.7 me (H atom in ethane) The energy of a molecule in its hypothetical vibrationless state at 0 K is conveniently described in terms of bond energy contributions depending on the charges of the bond-forming Finally, the aij's are given by the expression (1) (Appendix I) atoms (1). The appropriate expressions were successfully tested (1)(2)(3) in comparisons with experimental atomization energies, AE:, given by eq.…”

“…The appropriate expressions were successfully tested (1)(2)(3) in comparisons with experimental atomization energies, AE:, given by eq. [l] (see Appendix I: glossary).…”

“…These verifications were made for linear and branched paraffins, including saturated hydrocarbons constructed from chair and/or boat cyclohexane rings (1,2), as well as for ethers, aldehydes, and ketones (3). The present study offers a test for simple alkenes C,,H2,.…”

“…The ag's required in this study and the parameters from which they were derived are indicated in Table 1. For the CH and C C bonds involving sp3 carbon atoms, the average inverse distance between nucleus i and the center of u electronic charge on atom j (i.e., (r,Ti)O) is approximated in the usual manner (1) by the inverse of the internuclear distance, rcH = 1.08 and rcc = 1.53 A. This approximation locates the centroids of u charges at the nuclear positions.…”