The “Decisive” Role for Secondary Coordination Sphere Nucleophiles on Hydrogen Atom Transfer (HAT) Reactions: Does it Exist and What is its Origin? Yumiao Ma*a and Yishan Li b a. BSJ Institute, Haidian, Beijing, People’s Republic of China, 100084 b. Department of Chemistry, Tsinghua University, Haidian, Beijing, People’s Republic of China, 100084 [email protected]

Abstract: Although it has been reported that some radical reactions are possibly promoted by external ions, the origin of this phenomenon is unclear. In this work, several hydrogen atom transfer (HAT) reactions in the presence of anions were studied by density functional theory (DFT) calculations, electronic structure analysis and other methods, and it is concluded that both the electrostatic interaction and polarization of the transition state (TS) by the electric field generated by anions play a fundamental role in the TS stabilization effect, whereas the “charge shift bonding” that was previously presumed to be a major contributor is ruled out. Although the stabilization toward TSs in terms of electronic energy (and thus enthalpy) is significant, it should be noted that the effect is almost completely cancelled by entropy and solvation, and further cancelled by the formation of stable resting states. Thus there is still a long way for this effect to be used in actual catalysis.

Introduction The “electrostatic catalysis” or “salt effect” is a long-standing and well-established concept. Early in 1990s, the catalytic effect of ions that seem inert at the first glance toward organic chemical transformations has been studied by Craig Wilcox1-3. Later on, the promotion of cobalt-carbon bond dissociation by a nearby charge was found in a biochemistry-related Vitamin B complex4. In the recent years, the catalytic effect of charged groups toward Diels-Alder reaction was studied by Michelle Coote5, 6, and Kendall Houk7. The catalytic effect of charged groups is believed to have an electrostatic nature, proceeding through interaction between the dipolar moment of transition states (TSs) and the electric field generated by nearby charges, and thus is closely relevant to the external electric field effect in chemical reactions, which has been documented extensively in many cases8- 13. It is noteworthy that hydrogen atom transfer (HAT) reactions have also been reported to be affected by metal ions and ligands14-17, which is believed to be a field-induced phenomenon (charge- induced catalysis). On the other hand, however, Thomas Cundari and coworkers reported that external anions provide “decisive” stabilization to the TS for the hydrogen atom transfer (HAT) reaction between methane and hydroperoxyl radical very recently18. The authors concluded that the interaction between anions and the HAT TS is due to “charge shift bonding19, 20” originating from a 2-center-3- electron interaction, which is a brand new explanation for the influence of external ions. Thus it is interesting how much role charge shift bonding plays in the reported reactions, and also in other examples that were previously believed to be field-originated. In this work, we conducted a more detailed investigation on the “salt effect” for HAT reactions, which will provide new understanding toward this long-standing concept.

Computational Methods The geometry optimization of all structures were performed with the Gaussian 16 program21, at M11/6-311+G(d,p) level22-26, if not specially mentioned. DLPNO-CCSD(T) calculations were carried out with the ORCA 4.2 program27, 28, in combination with the aug-cc-pVTZ basis set29-31. All electronic structure analysis, including but not limited to bond critical point (BCP) properties, electron localization function (ELF), electron density Laplacian, were performed using the Multiwfn program32, based on the wavefunction obtained at M11/ma-def2-TZVPP level33. The GAMESS-US program34 was employed for LMO-EDA calculations35. It is found that the GAMESS-US program gave wrong results with the M11 functional, and thus M06-2X/6-311+G(d,p) level36 was selected to perform energy decomposition with the M11-optimized geometry. The SMD implicit solvation model37 was used for calculations with solvation effect, and the solvation free energies were obtained by G(M05-2X38/6-31G(d), with SMD(DMSO)) – G(M05- 2X/6-31G(d), gas phase). The final Gibbs free energies were obtained by the sum of DLPNO- CCSD(T) single point energy, M11/6-311+G(d,p) correction to free energy, and solvation free energy (the last term only for calculations in DMSO). Particularly, the solvation free energies for Cl-, Br- and proton are taken from experimental reports39, and those for F-, HO- and HS- were derived 40 41 42 from experimental pKa of HF, H2O and H2S in DMSO, which is 15.0 , 31.4 and 13.7 respectively.

Results and Discussions Although the meta-GGA M06-L functional43 was employed in Cundari’s report, it was found from a benchmark study involving M06-L, B3LYP-D3BJ44, 45, M06-2X, wB97xD46 and M11 that the performances of density functionals parallel their Hartree-Fock (HF) components (Table S1), and thus the range-separated functional M11 with a large HF component was chosen to be the functional used for geometry optimization in this work. The TSs were located for the HAT reactions between methane and hydroperoxyl radical (Scheme 1a), in the presence of various anions X-. The energetics and optimized C-X bond lengths at DLPNO-CCSD(T)/aug-cc-pVTZ//M11/6-311+G(d,p) level are listed in Table 1. Note that at this stage only the TSs, but not preactivation complexes or any other resting states are discussed. The full Gibbs free energy surface will be discussed later.

Scheme 1. The reactions studied in this work, and the definitions for some quantities discussed.

Table 1. The C-X distance (angstrom), TS stabilization energy (E in kcal/mol) and free energy (G in kcal/mol), EA, electron density on the C-X bond critical point (BCP), spin population on X for each TS of reaction (a) in Scheme 1. a b X C-X distance E E G EA ρBCP(C-X) Spin population on X F- 2.4875 -14.8 -12.7 -6.4 -43.1 0.0226 0.073 HO- 2.5459 -18.6 -14.3 -4.9 -6.9 0.0249 0.405 HCOO- 2.7385 -8.6 -7.2 1.9 -55.8 0.0157 0.028 Cl- 2.9875 -10.0 -8.6 -2.2 -47.8 0.0137 0.057 Br- 3.2168 -8.8 -8.1 -1.9 -45.2 0.0124 0.076 HS- 3.0130 -12.6 -8.5 1.3 -18.6 0.0176 0.335 MeS- 2.9020 -16.5 -13.0 -3.2 0.33 0.0222 0.525 a. At M11/6-311+G(d,p) level. b. At DLPNO-CCSD(T)/aug-cc-pVTZ//M11/6-311+G(d,p) level.

It is shown in Table 1 that all anions provide significant stabilization (i.e. negative E) to TS1 in terms of electronic energy, although largely cancelled by entropy. The second-row anions, fluoride and hydroxyl anion, are among the most stabilizing ones, whereas the HCOO- with delocalized negative charge exhibits much less stabilization. Interestingly, the heavier anions, Cl-, Br- and HS- provide similar stabilization energy at ~8.5 kcal/mol, while the E value becomes surprisingly much more negative upon replacement of the hydrogen in HS- with the methyl group. Overall, it is concluded that the combination of anions to TS1 is exothermic in most cases, and next we are about to figure out the reason. As suggested by Cundari’s work, we firstly examined the existence of charge shift bonding, which originates from the interplay between two resonance structures shown in Figure 1a. It has been proposed in the early research on the charge shift bonding in silicon-halogen bonds that resonance structures close in energy might lead to larger resonance energy47, and thus stronger charge shift bonding. Herein the energy difference between resonance structure 1 and 2 could simply be characterized by the difference in the vertical electron affinities (EA shown in Scheme 1) for the anion and the “bared” TS1(X=none). In addition, the magnitude of the involvement of 2 is reflected by the spin population on X. It is expected that a EA close to zero, as well as large spin population on X, should indicate strong charge shift interaction. The spin population values are listed in Table 1, and it is seen that for most anions the spin population on X- is negligible, except for OH-, HS- and MeS-, which also exhibit EAs closest to 0. Furthermore, the TS stabilization energy E correlates with both EA and spin population on X terribly. Thus it is questionable whether charge shift interaction could explain the observed energy change.

Figure 1. (a) A schematic representation of the resonance structures contributing to “charge shift interaction”. (b) The correlation of E with spin population on the anion. (c) The correlation of E with EA. (d,e) The ELF (d) and electron density Laplacian (e) Contour for TS1(X=HO-).

(f) The ELF contour for F2 molecule, a molecule with typical charge shift bonding. (g) The RDG isosurface for TS1(X=HO-), in which weak noncovalent interaction is shown in blue (stronger ones) and green (weaker ones).

Traditionally the existence of charge shift bonding is characterized by the properties at bond critical point (BCP), such as the electron density, electron density Laplacian, and electron localization function (ELF). Typical charge shift bonds, such as that in F2 molecule, exhibit large electron density, positive Laplacian, and slightly accumulated ELF at BCP. The electron densities at the BCP located between the carbon atom and anion are recorded in Table 1, and all TSs exhibit negligible electron densities at BCPs. The contours for ELF and electron density Laplacian for TS1(X=HO-) clearly show that there is no accumulation of ELF, and only near-zero Laplacian in the C-X interatomic region (Figure 1d and e). Furthermore, the reduced density gradient (RDG) analysis48, a method that directly shows the region with noncovalent weak interaction and filters covalent interaction, directly shows that the C-X interaction lies in the region of weak interaction, even with OH- as the anion. All these results indicate that there is negligible chemical bonding between C atom and anions. The ELF, Laplacian and RDG analysis results for TS1(X=MeS-) are shown in Figure S3, and there is no different conclusion. However, it still cannot be concluded that there is no charge shift interaction that contributes to the TS stabilization, although charge shift bonding has been ruled out. Next, however, we will focus on alternative ways to explain the observed energy change, and then reconsider the existence of charge shift interaction. There are three possible types of interaction that may contribute to the TS stabilization besides charge shift bonding, namely hydrogen bonding, intrinsic dipole-anion interaction, and polarization effect due to the electric field generated by anion. It has been reported by Tian Lu et al that the electron density at the BCP between a hydrogen acceptor and the corresponding hydrogen atom is a good indicator of hydrogen bond strength49. Unfortunately, in all TSs studied there is no BCP between X and H atoms. Thus we turned to core-valence bifurcation (CVB)50, another well-known hydrogen bonding indicator. The CVB values for all anions except HS- and OH- indicate very weak hydrogen bonding (Table S2). Based on these observations, it is proposed that hydrogen bonding contributes only little to the total E. In order to clarify how much role electric field plays in the TS stabilization, a uniform electric field model was employed (Figure 2). In this model, the bared TS1(X=none) is placed in a uniform electric field simulating the influence of external anions, and an “effective” field strength is defined by the electric field at the midpoint of TS1(X=none) along z-axis. TSs were re-optimized in the presence of varied external field (Figure 2b) and the stabilization energies of external field along z- axis at M11/6-311+G(d,p) level exhibit quadratic correlation with field strength. Interestingly, field along y-axis, which is perpendicular to the hydrogen atom transfer path (and also the intrinsic dipole moment of TS1), affords stabilization effect in similar magnitude, and thus it seems that the stabilization originates from polarization, but not intrinsic dipole interaction. The effective field strength resulted from each anion is calculated from the restrained electrostatic potential (RESP) atomic charge51 on the electronegative atom, and the E predicted using the fitted relationship in Figure 2b is in very good consistence with the M11-calculated E in the presence of anions (since the relationship is fitted with M11 data, it is considerable that it is more comparable with Es at M11 level), with only X=MeS- as an exception. Since the field model above is able to provide pretty good explanation for the observed E, the contribution of charge shift interaction is further precluded, and it is suggested that it is the “field effect” that plays the major role in the TS stabilization.

Figure 2. (a) A schematic description for the uniform electric field model. (b) The energy change of TS1 in the presence of varied external field. (c) The correlation betweenE observed and predicted with the electric field model. (d) The change of energy and spin population on the sulfur atom upon elongation of the C-S distance of TS1(X=MeS-). Distances are in angstrom.

Further investigation on the role of spin population delocalization is performed for the MeS- case (Figure 2d). Upon re-optimization of TSs at elongated C-S distance, the spin population on S atom drops to zero rapidly, and the energy raises by about 2.5 kcal/mol. It is then concluded that the radical delocalization, or “charge shift interaction”, contributes around 2.5 kcal/mol for the stabilization in TS1(X=MeS-), in consistence with the ~3 kcal/mol underestimation of E by electric field model. Since TS1(X=MeS-) is the one with largest spin population on X among all cases studied, it is concluded that charge shift bonding plays only a minor role in “salt effect” for TS1, and its contribution should be even less for anions other than MeS-. On the other hand, however, the full Gibbs free energetics give a different scene of the salt effect, although it is established that external anions combine with TS1 significantly. All anions combine even more strongly with the OOH radical by hydrogen bonding, affording stable resting states, and increasing overall barrier, which is not mentioned in Cundari’s work. The overall Gibbs free energy surface is shown in Figure 3. The energies for X-HOO complexes are raised upon solvation, but the overall barriers for all reactions still raise. Moreover, the solvation effect further cancels the TS-stabilization effect. As a result of all the effects above, the reaction is actually inhibited by external anions.

Figure 3. The Gibbs free energy surface for reaction a in the presence of anions.

Although it has been revealed that anions cannot catalyze the HAT from methane to hydroperoxyl radical in the above work, the reaction studied above gives good insight into the physical picture of “salt effect”. After establishment of the field-originated nature, we next moved to the HAT from methane to phenyl and methyl radical (reaction b and c in Scheme 1). The absence of strongly hydrogen bond donating hydroperoxyl radical is expected to avoid the formation of stable resting states. It is noticed that both TS2 and TS3 adopt different geometry: the anions are no longer collinear with the methane carbon center and the coming radical, but form a triangle shape to maximum the hydrogen bonding, which could be understood considering the largely reduced intrinsic dipole in these two cases. However, it is believed that there is no particularity for TS1, and further comments could be found in Supporting Information. Again, all anions provide strong stabilization in terms of electronic energies, while most of them are cancelled by entropy. For both TS2 and TS3, there are no longer spin densities on all anions, and the involvement of charge shift interaction is further precluded. BCPs appear in the interatomic region between anions and nearby hydrogen atoms, and thus the contribution of hydrogen bonding is easily estimated from Lu’s work, indicating that HB contributes about 50% of E for these cases. The total E for TS3 can again be predicted by the uniform electric field model (while the effective field strength is hard to define for TS2). Since both TS2(X=none) and TS3(X=none) have negligible dipole moments, the field effect must come from either polarization or interaction with partly charged atoms, whereas the latter is also the origin of hydrogen bonding. In addition, energy decomposition methods further support the major role of electrostatic and polarization interaction (Supporting Information). The full Gibbs free energy surfaces for reaction b and c are shown in Figure 5. Despite the fact that the combining of anions with methyl or phenyl radical is much weaker than in reaction a, the overall barriers are still not lowered with only X=OH- for reaction b as an exception. Therefore, for the three reactions examined in this work, the catalytic effect of anions for HAT reactions previously reported by Cundari et al does not exist considering the full Gibbs free energy surface.

Figure 4. (a) Geometries for the geometry of TS2 and TS3, and the definition of effective field strength for TS3. (b, c) The energy changes in the presence of anions for TS2 (b) and TS3 (c). (d). The correlation between observed Es for TS3 and those predicted by the electric field model.

Figure 5. The Gibbs free energy surface for reaction b and c. Except for X=F- and X=OH-, no anion affords preactivation complex with lower energy than separated substrates for TS3.

Conclusion With computational methods, we studied the influence of external anions on the HAT reactions from methane to hydroperoxyl radical (reaction a), phenyl radical (reaction b) and methyl radical (reaction c). Although it was previously proposed by Cundari that it was charge shift bonding that made the major contribution to the stabilization effect toward HAT TSs, detailed electronic structure analysis shows that there is no chemical bonding between anions and methane carbon atom, and the spin delocalization is negligible for most anions. For the case with MeS-, which the anion bears the largest spin population among all reactions studied, the spin delocalization only contributes around 2.5 kcal/mol to the total energy. In contrast, a uniform electric field model gains quantitative success in interpreting the transition stabilization energy. By combining all these results, as well as energy decomposition study, it is believed that the electrostatic and polarization effect due to charged species play a major role. On the other hand, although TSs are stabilized in terms of electric energy (and thus enthalpy), the effect cannot compensate the unfavorable entropy. As a result, the overall barrier, which is further influenced by stable resting states formed by substrates and anions, is not lowered or even raised in the presence of anions. In a summary, in contrast to the well-known existence of salt effect for polar cycloaddition or other reactions with polar TSs, our results are strongly against the presence of the Cundari-type “salt-effect” in HAT reactions. Strategical design, such as spatially constrained anions in order to compensate the entropy effect, is highly in need to further make use of the salt effect in the design of real “salt-catalyzed” HAT reaction in the future.

Supporting Information Benchmark data, CVB values, further discussion on TS geometry and the uniform electric field model, results for energy decomposition analysis, electronic structure analysis for TS1(X=MeS-), and all geometries involved in this work can be found in Supporting Information.

Acknowledgement Thank all students in Department of Chemistry, Tsinghua University for their great love and encouragement toward the authors.

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