No-barrier theory: calculating rates of chemical reactions from equilibrium constants and distortion energies

Easy and accurate computation of energy barriers for carbocation solvation: an expeditious tool to face carbocation chemistry

An expeditious procedure for the challenging computation of the free energy barriers (ΔG≠) for the solvation of carbocations is presented. This procedure is based on Marcus Theory (MT) and the popular B3LYP/6-31G(d)//PCM method, and it allows the easy, accurate and inexpensive prediction of these barriers for carbocations of very different stability. This method was validated by the fair mean absolute error (ca. 1.5 kcal mol-1) achieved in the prediction of 19 known experimental barriers covering a range of ca. 50 kcal mol-1. Interestingly, the new procedure also uses an original method for the calculation of the required inner reorganization energy (Λi) and free energy of reaction (ΔG). This procedure should pave the way to face computationally the pivotal issue of carbocation chemistry and could be easily extended to any bimolecular organic reaction.

Rate constants for formation of bisulfite addition compounds: an examination in terms of No Barrier Theory

We report a study of the rates of sulfite addition to carbonyl compounds. This reaction is useful in separating compounds (aldehydes react more extensively than ketones, thus becoming water soluble) because the reaction is readily reversible. Although the reaction is mainly by addition of sulfite dianion, the equilibrium is much more favorable for the addition of bisulfite to give a monoanionic adduct. It is also of interest because bisulfite addition is very favorable; thus, we are dealing with a very strong nucleophile. This work demonstrates that No Barrier Theory can calculate rates for good nucleophiles (cyanide and now sulfite) as well as poor nucleophiles such as water. It has been necessary to develop good ways to handle the anionic tetrahedral adducts (in the case of sulfite as nucleophile, dianionic), which tend to break down in the gas phase unless explicitly solvated, and modified procedures for crowded transition states to allow for some relief of steric congestion while maintaining the essential definition of the distorted species resulting from bond formation without geometry change.

Dichotomous hydrogen atom transfer vs proton-coupled electron transfer during activation of X-H bonds (X = C, N, O) by nonheme iron-oxo complexes of variable basicity

We describe herein the hydrogen-atom transfer (HAT)/proton-coupled electron-transfer (PCET) reactivity for Fe(IV)-oxo and Fe(III)-oxo complexes (1-4) that activate C-H, N-H, and O-H bonds in 9,10-dihydroanthracene (S1), dimethylformamide (S2), 1,2-diphenylhydrazine (S3), p-methoxyphenol (S4), and 1,4-cyclohexadiene (S5). In 1-3, the iron is pentacoordinated by tris[N'-tert-butylureaylato)-N-ethylene]aminato ([H3buea](3-)) or its derivatives. These complexes are basic, in the order 3 ≫ 1 > 2. Oxidant 4, [Fe(IV)N4Py(O)](2+) (N4Py: N,N-bis(2-pyridylmethyl)bis(2-pyridyl)methylamine), is the least basic oxidant. The DFT results match experimental trends and exhibit a mechanistic spectrum ranging from concerted HAT and PCET reactions to concerted-asynchronous proton transfer (PT)/electron transfer (ET) mechanisms, all the way to PT. The singly occupied orbital along the O···H···X (X = C, N, O) moiety in the TS shows clearly that in the PCET cases, the electron is transferred separately from the proton. The Bell-Evans-Polanyi principle does not account for the observed reactivity pattern, as evidenced by the scatter in the plot of calculated barrier vs reactions driving forces. However, a plot of the deformation energy in the TS vs the respective barrier provides a clear signature of the HAT/PCET dichotomy. Thus, in all C-H bond activations, the barrier derives from the deformation energy required to create the TS, whereas in N-H/O-H bond activations, the deformation energy is much larger than the corresponding barrier, indicating the presence of a stabilizing interaction between the TS fragments. A valence bond model is used to link the observed results with the basicity/acidity of the reactants.

Farewell to the HSAB treatment of ambident reactivity

The concept of hard and soft acids and bases (HSAB) proved to be useful for rationalizing stability constants of metal complexes. Its application to organic reactions, particularly ambident reactivity, has led to exotic blossoms. By attempting to rationalize all the observed regioselectivities by favorable soft-soft and hard-hard as well as unfavorable hard-soft interactions, older treatments of ambident reactivity, which correctly differentiated between thermodynamic and kinetic control as well as between different coordination states of ionic substrates, have been replaced. By ignoring conflicting experimental results and even referring to untraceable experimental data, the HSAB treatment of ambident reactivity has gained undeserved popularity. In this Review we demonstrate that the HSAB as well as the related Klopman-Salem model do not even correctly predict the behavior of the prototypes of ambident nucleophiles and, therefore, are rather misleading instead of useful guides. An alternative treatment of ambident reactivity based on Marcus theory will be presented.

The activation strain model of chemical reactivity

Herein, we provide an account of the activation strain model of chemical reactivity and its recent applications. In this model, the potential energy surface DeltaE(zeta) along the reaction coordinate zeta is decomposed into the strain DeltaE(strain)(zeta) of the increasingly deformed reactants plus the interaction DeltaE(int)(zeta) between these deformed reactants, i.e., DeltaE(zeta) = DeltaE(strain)(zeta) + DeltaE(int)(zeta). The purpose of this fragment-based approach is to arrive at a qualitative understanding, based on accurate calculations, of the trends in activation barriers and transition-state geometries (e.g., early or late along the reaction coordinate) in terms of the reactants' properties. The usage of the activation strain model is illustrated by a number of concrete applications, by us and others, in the fields of catalysis and organic chemistry.

A test of various computational solvation models on a set of “difficult” organic compounds

Various dielectric continuum models in Gaussian 03, based on the SCRF approach, PCM, CPCM, DPCM, IEFPCM, IPCM, and SCIPCM, have been tested on a set of 54 highly polar, generally polyfunctional compounds for which experimental solvation energies are available. These compounds span a range of 13 kcal/mol in ΔGt. The root-mean-square (RMS) errors for the full set of compounds range from 2.48 for DPCM to 1.77 for IPCM. For each method, classes of compounds which were not handled well could be identified. If these classes of compounds were omitted, the performance improved, and ranged from 1.58 (PCM, 39 compounds) to 1.02 (IPCM, 42 compounds). Models in the PCM family (PCM, CPCM, DPCM, and IEFPCM) with the recommended UAHF or UAKS sets of radii rely on a highly parameterized definition of the solvent cavity. Where this parameterization was inadequate, the calculated solvation energies were less reliable. This has been demonstrated by devising a new parameterization for PCM and halogen compounds, which markedly improves performance for polyhalogen compounds. The effective radius for the portion of the cavity centered on a halogen atom was assumed to be linear in the electron-withdrawing or -donating properties of the rest of the molecule as measured by Hammett σ (for halogens on aromatic rings) or Taft σ* (for halogens on aliphatic carbons). This new parameterization for PCM was tested on a set of 45 aliphatic and 22 aromatic polyhalogen compounds and shown to do well. IPCM, which was already the best of the methods in Gaussian, can be considerably improved by a parameterization to allow for cavitation, dispersion, and hydrogen bonding. A large set of compounds was used for the parameterization to have multiple examples for each parameter and as far as possible to have molecules with multiple instances of each structural feature. In the end, 15 parameters were found to be defined by the data for 241 compounds. With this parameter set, the RMS error for the set used for fitting was 0.81 kcal/mol, and the RMS error for the original set of 54 compounds was 0.85. With this new parameterization, IPCM is clearly the best of the methods available in Gaussian 03.

Inverse Solvent Effects in Carbocation Carbanion Combination Reactions: The Unique Behavior of Trifluoromethylsulfonyl Stabilized Carbanions

Second-order rate constants for the reactions of the trifluoromethylsulfonyl substituted benzyl anions 1a-e (CF3SO2CH(-)-C6H4-X) with the benzhydrylium ions 2f-j and structurally related quinone methides 2a-e have been determined by UV-vis spectroscopy. The reactions proceed approximately 10-40 times faster in methanol than in DMSO leading to the unique situation that these carbocation carbanion combinations are faster in protic than in dipolar aprotic media. The pK(a) values of some benzyl trifluoromethylsulfones were determined in methanol (1c-H, 17.1; 1d-H, 16.0; 1e-H, 15.0) and found to be 5 units larger than the corresponding values in DMSO. Rate and equilibrium measurements thus agree that the trifluoromethylsulfonyl substituted benzyl anions 1a-e are more effectively solvated by ion-dipole interactions in DMSO than by hydrogen bonding in methanol. Brønsted correlations show that in DMSO the trifluoromethylsulfonyl substituted carbanions 1 are less nucleophilic than most other types of carbanions of similar basicity, indicating that in DMSO the intrinsic barriers for the reactions of the localized carbanions 1 are higher than those of delocalized carbanions, including nitroalkyl anions. The situation is reversed in methanol, where the reactions of the localized carbanions 1 possess lower intrinsic barriers than those of delocalized carbanions as commonly found for proton-transfer processes. As a consequence, the relative magnitudes of intrinsic barriers are strongly dependent on the solvent.