Andreas A. Zavitsas

A comparison of methods for measuring relative radical stabilities of carbon-centred radicals

This article discusses and compares various methods for defining and measuring radical stability, including the familiar radical stabilization energy (RSE), along with some lesser-known alternatives based on corrected carbon-carbon bond energies, and more direct measures of the extent of radical delocalisation. As part of this work, a large set of R-H, R-CH(3), R-Cl and R-R BDEs (R = CH(2)X, CH(CH(3))X, C(CH(3))(2)X and X = H, BH(2), CH(3), NH(2), OH, F, SiH(3), PH(2), SH, Cl, Br, N(CH(3))(2), NHCH(3), NHCHO, NHCOCH(3), NO(2), OCF(3), OCH(2)CH(3), OCH(3), OCHO, OCOCH(3), Si(CH(3))(3), P(CH(3))(2), SC(CH(3))(2)CN, SCH(2)COOCH(3), SCH(2)COOCH(3), SCH(2)Ph, SCH(3), SO(2)CH(3), S(O)CH(3), Ph, C(6)H(4)-pCN, C(6)H(4)-pNO(2), C(6)H(4)-pOCH(3), C(6)H(4)-pOH, CF(2)CF(3), CF(2)H, CF(3), CCl(2)H, CCl(3), CH(2)Cl, CH(2)F, CH(2)OH, CH(2)Ph, cyclo-CH(CH(2))(2), CH(2)CH[double bond, length as m-dash]CH(2), CH(2)CH(3), CH(CH(3))(2), C(CH(3))(3), C[triple bond, length as m-dash]CH, CH[double bond, length as m-dash]CH(2), CH[double bond, length as m-dash]CHCH(3), CHO, CN, COCH(3), CON(CH(2)CH(3))(2), CONH(2), CONHCH(3), COOC(CH(3))(3), COOCH(2)CH(3), COOCH(3), COOH, COPh), and associated radical stability values are calculated using the high-level ab initio molecular orbital theory method G3(MP2)-RAD. These are used to compare the alternative radical stability schemes and illustrate principal structure-reactivity trends.

Enthalpies of Formation of Hydrocarbons by Hydrogen Atom Counting. Theoretical Implications.

Standard enthalpies of formation at 298 K of unstrained alkanes, alkenes, alkynes, and alkylbenzenes can be expressed as a simple sum in which each term consists of the number of hydrogen atoms n of one of eight different types (n1-n8) multiplied by an associated coefficient (c1-c8) derived from the known enthalpy of formation of a typical molecule. Alkylbenzenes require one additive constant for each benzene ring, accounting for a possible ninth term in the sum. Terms are not needed to account for repulsive or attractive 1,3 interactions, hyperconjugation, or for protobranching, rendering them irrelevant. Conjugated eneynes and diynes show thermodynamic stabilizations much smaller than that observed for 1,3-butadiene, bringing into question the usual explanation for the thermodynamic stabilization of conjugated multiple bonds (p orbital overlap, pi electron delocalization, etc.).

Determination of enthalpies (‘Heats’) of formation

Determination of enthalpies of formation, now well into its second century, continues to be an active research field. Classical combustion thermochemistry, known by Lavoisier, is carried out with precision in several laboratories, though usually on the microscale, as appropriate to the small quantities of rare or unstable species preparative chemists are able to win and purify. Nonclassical methods such as differential scanning calorimetry and proton emission techniques are practiced. Enthalpy estimation based on additivity has been brought to an improved level of accuracy, and its basis in molecular structure has been examined with the goal of achieving maximum simplicity. Discrepancies between experimental results and additive estimates due to ‘special effects’ have brought about a considerable amount of causative speculation in the literature. Quantum mechanical methods have enjoyed increased proliferation through new methods of finding enthalpies of formation and other thermochemical and molecular properties such as heat capacity and entropy. Powerful basis set and configuration interaction software is available within the Gaussian© suites of programs. New levels of accuracy, in the kilojoules per mole range, have been achieved by Wn methods, and wider generality is enjoyed by methods based on density functional theory. New tabulation methods have been introduced that use computer error estimation procedures to root out flawed experimental results and increase overall reliability of the data one selects from the compilation.

The potential energy curve of the ground state of lithium, Li2

Abstract Seven reported potential energy curves (RKR, IPA, and rotationless) are compared for the ground states of 7 Li 2 , 6 Li 7 Li, and 6 Li 2 . Discrepancies among them, particularly in the repulsive (inner) limb, are evaluated. Irregularities in the behavior of the “spectroscopic” parameter β of the Morse function are found with some of them. The “universal” potential energy function that produces a priori potentials, without prior knowledge of them [J. Am. Chem. Soc. 113 (1991) 4755], yields a curve that lies generally between the seven spectroscopic potentials over most of their domain. The a priori potential appears as a consensus and is judged to be the best estimate of the potential energy curve of Li 2 . Values of distances obtained from it are presented at the reported energy levels of 7 Li 2 .

A Single Universal Scale of Radical Stabilization Energies Does Not Exist : Global Bond Dissociation Energies and Radical Thermochemistries Are Described by Combining Two Universal Scales

Results from any single scale of radical stabilization energies are dependent on the species chosen for setting its zero. A scale of radical destabilization energies with a universal zero reference point is shown to exist, but it must be used in conjunction with a universal scale capable of describing the polarities of bonds broken and formed. The use of the two scales is demonstrated for calculating bond dissociation enthalpies, enthalpies of reactions, enthalpies of formation, and the magnitude of steric effects, resonance, and conjugation stabilization. Examples of applications include explanations of some observed effects in autoxidations and polymerizations.

Heats of Formation of Organic Compounds by a Simple Calculation

Heats (enthalpies) of formation of organic compounds are obtained by adding a constant for a functional group to the heat of formation of its hydrocarbon precursor obtained by counting hydrogens, as previously described. A single molecule is used to obtain the contribution of each functional group. Unlike all other empirical schemes, no global fitting is used. The calculation is done with pencil and paper or a hand calculator. The accuracy of the results is demonstrated by their agreement with more than 360 species of experimentally known heats of formation with a mean average deviation of 0.75 kcal mol(-1), very nearly equal to the mean experimental uncertainty. Alcohols, hydroperoxides, ethers, amines, ketones, aldehydes, carboxylic acids, esters, chlorides, phenols, anilines, aryl ethers, nitriles, amides, and alkyl radicals are used as examples of the method. This success allows the calculation of experimentally unknown heats of formation. The method is limited to compounds that are not subject to strain or effects of conjugation. In such cases, the experimental heat of formation of the hydrocarbon precursor may be used. The method can be extended to functional groups not treated here.

Electrophilic aromatic substitution: enthalpies of hydrogenation of the ring determine reactivities of C6H5X. The direction of the C6H5-X bond dipole determines orientation of the substitution.

There are still some secrets left to this well-studied reaction. Previously unreported relationships discovered are as follows. The ordering of reactivities of C6H5X is the same as that of enthalpies of hydrogenation of the ring to the correspondingly substituted cyclohexane. The orientation of substitution (meta or ortho/para) is controlled by the dipole direction of the ipso-C-X bond, like an ON/OFF switch. The difference between the halogens and other deactivating groups is that the bond between the atom bonded to the ipso carbon has the positive end of the dipole on the ipso carbon for the halogens (C(δ+)-X(δ-)) but in the opposite direction (C(δ-)-X(δ+)) for other deactivating groups. This reverses the directing effect. For all X, including the halogens, ipso-C(δ+)-X(δ-) results in ortho/para substitution. p-(13)C NMR shifts of C6H5X greater than that of benzene predict meta substitution. A linear relationship exists between p-(13)C NMR shift and ΔHhyd, except for X = halogen. With halobenzenes, the ortho/para ratios of the products are linearly related to the ipso/ortho ratios of the (13)C shifts of C6H5X for chlorinations, brominations, nitrations, and protonations. The relative reactivities of the halobenzenes are linearly related to the p-(13)C NMR shifts. The electronegativities of X are linearly related to the (13)C NMR shifts of the ipso carbon.

Whence the energy term of the rate constant

Insights into the causes of energy barriers to reactions are obtained from our E* model for hydrogen abstractions. Results of the model are in good agreement with all eight experimentally studied symmetrical reactions of the type X-H + (*)X --> X(*) + H-X. The E* energy is broken down into three components: energy needed to overcome triplet repulsion between the terminal Xs, energy needed to bring the H-X bonds to their transition state distances, and energy gain by the resonance stabilization of delocalization of the odd electron over three atoms. The strength of the X-H bond is a minor factor. The conclusion that triplet repulsion is a major factor is supported by the London equation and by results of recent high level theoretical calculations. The E* model requires inputs of bond dissociation energies, bond lengths, and infrared stretching frequencies of X-H and X-X. Some reported failures of E* are shown to have been caused by use of input values subsequently found to be incorrect.

Destabilization of Conjugated Systems of α-Dicarbonyls and of Cyanogen

The formally conjugated system of α-carbonyls in 2,3-butanedione does not impart thermodynamic stabilization, but significant destabilization of 5.9 kcal mol–1. The conjugated triple bonds of cyanogen cause a large thermodynamic destabilization of 11.4 kcal mol–1, which is the difference in the enthalpies of hydrogenation of the first and second triple bonds. Experimental thermochemical and structural measurements and theoretical ab initio (G3) calculations support the destabilizations being reported. This work focuses only on the observable thermodynamic effects (enthalpies of hydrogenation), which are not necessarily related to the ability of conjugated groups to transmit electronic effects.

Effects of Molecule Stabilization Energies on Radical Reactions: G3 and G3(MP2) Model Chemistries Applied to Benzylic Systems

We have carried out G3 and G3(MP2) calculations of the molecule stabilization energies (MSEs) brought about by 11 common substituent groups in the meta and para positions of benzyl fluoride. We find that MSE is a function of the tendency of the substituent to donate or to withdraw electrons, such that a classic Hammett plot can be drawn. We propose that, in general, the direction of the benzylic Z-X dipole of YC6H4ZX is the major factor controlling the sign of the slope of Hammett plots of benzylic atom abstractions by radicals. When the Z-X dipole is pointed away from the substituted ring, electron withdrawing substituents destabilize the molecule, contributing to a decrease of the Z-X bond dissociation energy, and electron donating substituents stabilize it. The reverse is true when the dipole is reversed. This proposal is supported by 13C NMR results and by a survey of relevant benzylic and quasi-benzylic hydrogen or halogen atom abstractions studied experimentally. Calculations at the G3 level of theory demonstrate an increase in the bond dissociation energy of p-YC6H4CH2-H with increasing electron withdrawing ability of Y, contrary to results of previous lower level calculations. MSE values of substituted benzyl fluorides (p-YC6H4CH2F) correlate well with allylic MSE (trans-YCH=CHCH2F) and quantify the relative efficacy of transmission of electronic effects by vinylogy.