J. Phys. Chem. B 2000, 104, 9887-9893
9887
Solvation of Carbanions in Organic Solvents: A Test of the Polarizable Continuum Model Tore Brinck,*,† Allan Godsk Larsen,‡ Kenneth Michael Madsen,‡ and Kim Daasbjerg*,‡ Physical Chemistry, Royal Institute of Technology, SE-10044 Stockholm, Sweden, and Department of Chemistry, UniVersity of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark ReceiVed: March 29, 2000; In Final Form: July 25, 2000
The solvation of carbanions in the solvents N,N-dimethylformamide (DMF) and tetrahydrofuran (THF) has been analyzed on the basis of experimental and theoretical data. Experimental solvation energies are obtained from present and previously reported electrochemical measurements of reduction potentials of the corresponding radicals. Theoretical solvation energies are obtained from quantum chemical calculations using the polarizable continuum model (PCM). It is found that the solvation energy is relatively independent of molecular size and structure for the saturated carbanions. This indicates that the negative charge is strongly localized to the anionic carbon. The conjugated carbanions have considerably lower absolute solvation energies (|∆G°sol|) than the saturated carbanions. This is a consequence of the strong delocalization of the negative charge in the former group. The propargyl anion is also found to have a surprisingly low absolute solvation energy. However, high-level quantum chemical calculations show that the electronic structure has large contributions from two different resonance structures, CHtCCH2- and -CHdCdCH2, which results in a significant charge delocalization. There is good agreement between calculated and experimental solvation energies for both the conjugated and nonconjugated primary anions. However, the PCM method consistently underestimates the absolute solvation energies of the secondary and tertiary carbanions. This is attributed to an insufficient treatment of first-layer solvation effects in the method. According to the experimental measurements, the absolute solvation energies are on average 2-3 kcal mol-1 lower in THF than in DMF. The theoretical data indicate a considerably larger solvent effect, 7-10 kcal mol-1. The discrepancy between theory and experiment may partly be attributed to the use of a supporting electrolyte in the measurements, but the main cause seems to be that the short-range interaction tendencies of the solvent cannot be fully characterized by its dielectric constant.
Introduction Solvation plays a tremendous role for the stability and reactivity of ions. For instance, the oxidation potential of hydroxide is diminished substantially, while the reactivity of hydroxide is raised if aqueous or other polar hydrogen-bonding solutions are replaced by aprotic solvents such as acetonitrile and dimethyl sulfoxide.1,2 Likewise, small differences in solvation provide the explanation of why the acidity order for 2-methyl-2-propanol, 2-propanol, ethanol, and methanol is reverted on going from the gas phase to aqueous solution.3 From a theoretical point of view different models and simulation procedures have been proposed and developed to improve the description of solvation phenomena.4-6 In particular, the combined quantum mechanical/continuum dielectric approaches have gained considerable interest in recent years.5 In these approaches, the solvent, represented by a dielectric continuum, is interacting with the quantum mechanically computed charge distribution of the solute. The polarizable continuum model (PCM) is one of the more successful approaches in this category.5,7-9 It combines a rigorous description of the molecular charge distribution with a rather flexible approach for defining the solute cavity. Using a parametrized description of the solute * To whom correspondence should be addressed. (T.B.) Fax: +4687908207. E-mail:
[email protected]. (K.D.) Fax: +4586196199. Email:
[email protected]. † Royal Institute of Technology. ‡ University of Aarhus.
cavities, it was shown for a set of 28 monovalent ions that the PCM method is capable of predicting solvation energies with an accuracy close to 1 kcal mol-1.9 In that study, as in many earlier theoretical studies, the focus was on the solvation of stable ions, e.g., halides in aqueous solution. The performance of the PCM method and other theoretical methods for prediction of less stable ions, such as carbanions, in organic solvents is relatively unknown. The reason for this is that there has been a considerable lack of reliable experimental data. However, recent developments10,11 have made it possible experimentally to extract solvation data for carbanions of high basicity from thermochemical cycles that incorporate the standard potential of the corresponding short-lived radicals. Initial studies using this method have displayed interesting behaviors in the solvation properties of carbanions with regard to changes in size and hybridization.11 The formal relationship between the solvation energy of the anion, ∆G°sol(R-), and the standard potential of the radical, E°R•, has long been recognized on the basis of a thermochemical cycle (see Scheme 1) and is given in eq 1.12 The parameter ∆G°sol(R•)
∆∆G°sol ≡ ∆G°sol(R-) - ∆G°sol(R•) ) -∆G°a - FE°R• - C (1) is the solvation energy of the radical R•, ∆G°a is the gas-phase Gibbs energy of electron attachment of R•, and C is a constant which depends on the reference electrode. Of the two solvation terms, the dominant term will be the one of the ion due to the
10.1021/jp0011948 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/03/2000
9888 J. Phys. Chem. B, Vol. 104, No. 42, 2000
Brinck et al.
SCHEME 1
solvation of a charge. The electron attachment energy can to a good approximation be set equal to -EA, where EA is the electron affinity of R•. For the constant C, 109.3 kcal mol-1 is used, which originates from the value of the absolute potential of the standard calomel electrode ()-4.74 V) determined as an average of five separate measurements.13 In this paper our intention is to provide a description of the fundamental aspects of the solvation of carbanions in aprotic media on the basis of experimental and theoretical studies. In addition, the carbanion systems will be an excellent test of the performance of the theoretical methods for quantitative prediction of the solvation of complex ions. The following series of ions were selected, including both small localized systems and larger delocalized and sterically hindered systems: methyl, ethyl, propyl, butyl, 2-propyl, 2-butyl, tert-butyl, cyclopentyl, allyl, propargyl, and benzyl. For all these ions experimental solvation energies are available in the literature obtained in the solvent N,N-dimethylformamide (DMF).11 The present study was extended to include data for the butyl, allyl, and benzyl anions in tetrahydrofuran (THF) to elucidate the solvating properties of a nonpolar solvent. The relevant experimental data were extracted from the measurement of standard potentials of the corresponding radicals using two electrochemical approaches developed in the past 10-15 years, the indirect method14 and photomodulated voltammetry.15 Theoretical solvation energies have been computed using the PCM method. Methods and Procedure All quantum chemical calculations have been performed using the Gaussian 98 suite of programs.16 Molecular geometries have first been optimized at the HF/6-31G* level. Since a proper description of the electronic structures of anions requires the use of diffuse functions, the subsequent single-point PCM calculations were done at the HF/6-31+G* level. The selection of the size and shape of the cavity is of crucial importance for the result of the PCM calculations.5,8 Normally the cavity is built up by overlapping spheres centered at the nuclei of the solvated molecule. The radii of the spheres are often taken from the van der Waals radii of the constituting atoms and are scaled by an empirical factor.5 Recently, Tomasi and co-workers have developed a more elaborate empirical scheme where the radius of an atom in a molecule not only depends on the atomic number but also on the formal charge, hybridization state, and neighboring groups.9 This scheme has been parametrized to reproduce the solvation energies of a large number of small molecules and ions.9 In this work we have chosen the simpler approach of defining the size of the overlapping spheres from the van der Waals radii rather than using the new scheme of Tomasi. There are several reasons for this choice. First of all, we prefer to use as few empirical parameters as possible, since it otherwise may be hard to determine if the outcome of a calculation is physically significant or just an effect of the parametrization. Second, the hybridization states and the formal charges of the atoms in some of our ions, e.g., the propargyl and benzyl anions, cannot be unambiguously determined. Third, since carbanions were not included in the
Figure 1. ∆G°sol,el for the methyl anion as a function of the cavity scale factor. Computations were performed at the PCM-HF/6-31+G*// HF/6-31G* level of theory.
original parametrization of the Tomasi scheme,9 it is not obvious that it would work for our systems. Preliminary calculations did also indicate that the accuracy was not improved compared to that of the simple van der Waals scheme. In this work we have used the van der Waals radii of Pauling (1.50 Å for all C, including C-, and 1.20 Å for H) as implemented in Gaussian 98, and scaled them by the empirical factor 1.2.5 This scale factor has been found to be suitable for prediction of hydration free energies of organic molecules.5 As can be seen from Figure 1, the calculated solvation free energy (∆G°sol,el) is strongly dependent upon the size of the scale factor. This type of strong dependence of the solvation energy on the cavity size is common to all continuum methods. However, the behavior of increasing solvation energy with decreasing cavity size for very small cavities (scale factor
