Dissecting the Temperature Dependence of Electron-Proton Transfer

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Dissecting the Temperature Dependence of Electron-Proton Transfer Reactivity Daniel Bím, Mauricio Maldonado-Domínguez, Radek Fucik, and Martin Srnec J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b07375 • Publication Date (Web): 07 Aug 2019 Downloaded from pubs.acs.org on August 7, 2019

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The Journal of Physical Chemistry

Dissecting the Temperature Dependence of Electron-Proton Transfer Reactivity Daniel Bím,‡,a,b Mauricio Maldonado-Domínguez,‡,a Radek Fučík,c and Martin Srneca,*

aJ.

Heyrovský Institute of Physical Chemistry, The Czech Academy of Sciences, Dolejškova 3, Prague

8, 18223, Czech Republic. bInstitute

of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Prague 6, 16610, Czech

Republic cDepartment

of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical

University in Prague, Czech Republic

ABSTRACT The rate of elementary reactions usually rises with increasing temperature. In rare cases, however, a slowdown is observed instead. One example of this is hydrogen-atom abstraction from the iron(II)-tris[2,2’-bi(tetrahydropyrimidine)] complex, [FeII(H2bip)3]2+, by the TEMPO radical. So far ascribed to a strongly temperature-dependent equilibrium constant Keq, this description does not fully account for the observed rate deceleration. In this work, we dissect the activation barriers of four electron-proton transfers including this exceptional case, by employing the concept of asynchronicity, derived as an extension to Marcus theory, together with the classical Bell-Evans-Polanyi effect. By also accounting for tunneling and statistics, the presented theoretical model yields near-quantitative accuracy. Based on chemically welldefined quantities, this method offers a detailed insight into temperature-dependent kinetics of hydrogen-atom abstraction reactions and may serve as an alternative to the established Eyring plot analysis.

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Control over reaction rates (and thus chemical reactivity and selectivity) is a dream of many chemists.1-7 In practice, it means a search for optimal reaction conditions by balancing many variables including, among others, the choice of a solvent, pH, ionic strength, concentration, and temperature. As for the effect of temperature on chemical reactivity, textbooks teach us that an elementary chemical reaction proceeds faster at higher temperatures (T), which is, however, not always true.8-9 An example of such a rare exception was observed by Mayer for the H-atomabstraction reaction (HAA) between the FeII(H2bip)3 complex (H2bip ≡ 2,2′-bi-1,4,5,6tetrahydropyrimidine) and the TEMPO radical (2,2,6,6-tetramethyl-1-piperidinoxyl), which is referred to as reaction 1 in Scheme 1.10 In this case, the observed second-order rate constant k decreases from 308 to 171 M-1 s-1 as T raises from 278 to 328 K, corresponding to a temperatureinduced change of activation free energy (TG≠) of +2.9 kcal mol-1. Importantly, this value exceeds the ‘threshold’ of +2.5 kcal mol-1, above which reaction 1 gets slower as T elevates from 278 to 328 K. This threshold can be readily determined from experimental data considering Eyring equation:

(

)

(

∆𝑇

ℎ

)

≠ = 𝑅[𝑇0 + ∆𝑇] × 𝑙𝑛 1 + 𝑇0 ―𝑅∆𝑇 × 𝑙𝑛 𝑘0 × 𝑘𝐵𝑇0 Δ𝑇∆𝐺𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

(1)

with k0 corresponding to the rate constant at T0 (= 278K). Employing the Marcus cross relation,11 Mayer et al. attributed the unusual deceleration of reaction 1 to a strongly temperature-dependent equilibrium constant Keq,10 which is directly connected to the free energy of reaction G0 (≡ −RT  ln(Keq)). However, we notice that the barrier for this reaction (1 in Scheme 1) increases with T approximately two times faster than the corresponding G0 (cf. TG≠ ≈ +2.9 vs. TG0 ≈ +1.5 kcal mol-1). This clearly violates the Bell-Evans-Polanyi (BEP) principle,12-13 according to which a more exergonic (or endergonic) reaction yields a lower (or higher) G≠ roughly proportional to one half of the change in G0. Although the BEP principle is only approximate, it was many times successfully


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applied in HAA chemistry by Mayer and by others.14-18 Especially, the BEP principle was shown to hold relatively well for HAAs with small |G0|, which is the case for all of the reactions 1-4 in Scheme 1.14 Further, the use of the ΔG≠/ΔG0 = 1/2 ratio can be justified by the remarkable success of Marcus theory and its extensions to HAAs.11, 14, 19-20 The discrepancy between TG0 and TG≠ thus suggests that ΔTKeq is not the major influence on the change of k, opening the pertinent question on what other factors contribute to the large TG≠ value responsible for this unusual temperature dependence of the reaction rate (Scheme 2). We are convinced that understanding these factors is an important step toward the rational search of suitable HAA catalysts as well as the optimal conditions necessary for controlling efficient and selective chemical transformations.

Scheme 1. Four HAA reactions (labeled as 1-4) taken from Refs. 10 and 11.

Herein, we present the computational study of the temperature dependence of four experimentally well-characterized HAA reactions (labeled as 1-4 in Scheme 1), with the aim to elucidate all key contributions to TG≠ apart from the BEP effect such as, inter alia, tunneling and asynchronicity factor η; the latter describes the disparity in proton and electron transfer thermodynamic driving forces and was recently identified by us as an integral part of



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Marcus reorganization energy.21 The presented approach offers a viable and chemically intuitive alternative to the traditional Eyring plot analysis of temperature dependences of reaction rates.

Scheme 2. An increase of the bimolecular HAA reaction barrier (TG≠) determines a change of the rate constant, as temperature is increased from T0 to T1. For a T-independent reaction rate constant, the corresponding value of TG≠ reaches the threshold (TG≠threshold) below/above which the HAA reaction gets faster/slower in passing from T0 to T1. The elucidation of key contributions to TG≠ is a subject of the presented work.

To derive the methodology allowing the analysis described in Scheme 2, let us start by considering a general bimolecular electron-proton transfer reaction: AH + B•  A• + BH

(2)

that is composed of three steps: (i) formation of the reactant complex (RC) from two separate AH and B• reactants, (ii) transformation of RC into the product complex (PC) through one transition state (TS), (iii) and dissociation of PC into two separate A• and BH products. These steps, along with quantities controlling kinetics and thermodynamics of the process, are described in Scheme 3.


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Scheme 3. Bimolecular electron-proton transfer reaction, including all steps – formation of the reactant complex (RC) followed by H-atom/proton-coupled electron transfer involving one transition state (TS) and leading to the product complex (PC) which dissociates into separate products. All relevant free-energy changes: wR, G0, G≠, G0,R, and wP – are described in the text. According to Marcus theory, the free-energy barrier for an elementary bimolecular electron-proton transfer reaction (G≠) reads as: ∆𝐺 ≠ (𝑇) = 𝑤𝑅(𝑇) +

(

𝜆(𝑇) 4

1+

Δ𝐺0,𝑅(𝑇) 2 𝜆(𝑇)

)

(3)

where wR is the free energy of formation of RC from two separate reactants, AH and B•, whereas G0,R stands for the free-energy difference between RC and PC (cf. Scheme 3), and  is the reorganization energy required to diabatically perturb the structure of RC into the structure of PC, i.e., without H+/e− transfer taking place. All terms in Eq. (3) are dependent on temperature. Assuming that 4  G0,R|2, which is frequently the case in HAA chemistry,22 Eq. (3) can be approximated, after expansion and first-order truncation, as the sum of three contributions: ∆𝐺 ≠ (𝑇) = 𝑤𝑅(𝑇) +

𝜆(𝑇) 4

+

Δ𝐺0,𝑅(𝑇)

(4)

2

According to Scheme 2, G0 is related to G0,R as: G0,R = G0 + wP − wR

(5)

with wP defined as the free energy of PC formation. Note that G0 = ―𝐹∆𝐸°𝐻, where 𝐹 5 ACS Paragon Plus Environment


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is the Faraday constant and ∆𝐸°𝐻 is the difference between proton-coupled reduction potentials of A• and B• [ = 𝐸°𝐻,𝐴• ― 𝐸°𝐻,𝐵•]. This allows for the transformation of Eq. (4) into: ∆𝐺 ≠ (𝑇) =

𝑤𝑅(𝑇) 2

+

𝑤𝑃(𝑇) 2

+

𝜆(𝑇) 4

―

Δ𝐸°𝐻(𝑇)

(6)

2

Recently, we introduced a descriptor reflecting the thermodynamic bias for asynchronicity in coupled H+/e− transfers (stemming from the reduction potentials of A• and B• and the acidity constants of AH• and BH•)23, the so-called asynchronicity factor .21 In ref. 21, the descriptor  is demonstrated to affect G≠ through its connection to Marcus reorganization energy , so that

 =  − F  |

(7)

where  is a reorganization energy at the synchronous limit of coupled electron and proton transfers. Considering the Marcus cross-relation theory,24-25 we postulate that  can be determined from knowing the barriers of two self-exchange reactions (i.e. AH + A = A + AH and BH + B = B + BH). This is described more in the SI. Noticeably, the connection between

 and the reaction rate was also experimentally implemented by Goetz and Anderson in a series of proton transfer-driven HAA reactions by CoIIIO oxidant.26 Substituting  by  − F| in Eq. (6), and considering the change of ∆𝐺 ≠ as T raises from T0 to T0+T, we get: ∆𝑇∆𝐺 ≠ =

∆𝑇𝜆0 4

―𝐹 

(

∆𝑇|𝜂| 4

+

∆𝑇Δ𝐸°𝐻 2

)+

1 2

(∆𝑇𝑤𝑅 + ∆𝑇𝑤𝑃)

(8)

Equation (8) describes the temperature-induced change of the free-energy barrier G≠ as a function of the T-dependence of five different thermodynamic factors, representing a simple but powerful tool in understanding differences in reactivity and selectivity of related electronproton transfer reactions. To achieve a quantitative accuracy, the T-dependent tunneling ≠ ≠ correction and statistical terms (∆𝑇∆𝐺𝑡𝑢𝑛 ) are incorporated in Eq. (9): and ∆𝑇∆𝐺𝑠𝑡𝑎𝑡


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∆𝑇∆𝐺

≠

=

∆𝑇𝜆0 4

―𝐹 

(

∆𝑇|𝜂| 4

+

∆𝑇Δ𝐸°𝐻 2

)+

1 2

≠ ≠ (∆𝑇𝑤𝑅 + ∆𝑇𝑤𝑃) + ∆𝑇∆𝐺𝑡𝑢𝑛 + ∆𝑇∆𝐺𝑠𝑡𝑎𝑡

(9)

where

(

≠ = ―𝑅𝑇0 × ln 1 + ∆𝑇∆𝐺𝑡𝑢𝑛

∆𝑇𝜏 𝜏0

) ―𝑅∆𝑇 × ln(𝜏

0

+ ∆𝑇𝜏)

(10)

and ≠ = ―𝑅∆𝑇 × ln(𝑛𝑠𝑖𝑡𝑒) ∆𝑇∆𝐺𝑠𝑡𝑎𝑡

(11)

with  from Eq. (10) being a transmission coefficient at T (a detailed description of tunneling is given in the SI), and nsite from Eq. (11) corresponding to the number of equivalent sites available for reaction. For purposes of the following discussion, we finally rewrite Eq. (9) into: ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠ ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 = ∆𝑇∆𝐺𝜆0 + ∆𝑇∆𝐺𝑎𝑠𝑦𝑛 + ∆𝑇∆𝐺𝐵𝐸𝑃 + ∆𝑇∆𝐺𝑅𝐶 + ∆𝑇∆𝐺𝑃𝐶 + ∆𝑇∆𝐺𝑡𝑢𝑛 + ∆𝑇∆𝐺𝑠𝑡𝑎𝑡 (12)

where the subscript “implicit” emphasizes the absence of an explicit calculation of the TS (with ≠ ≠ ≠ an exception of the ∆𝑇∆𝐺𝜆0 and ∆𝑇∆𝐺𝑡𝑢𝑛 contributions), which contrasts to ∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡

obtained from the standard approach (see SI). The method presented herein, condensed into Eq. (12), is an analytical tool that decomposes ∆𝑇∆𝐺 ≠ into seven individual contributions arising ≠ from reorganization energy at the synchronous coupled electron-proton transfer limit (∆𝑇∆𝐺𝜆0 ), ≠ ≠ asynchronicity (∆𝑇∆𝐺𝑎𝑠𝑦𝑛 ), the BEP effect (∆𝑇∆𝐺𝐵𝐸𝑃 ), formation of reactant and product ≠ ≠ ≠ ≠ complexes (∆𝑇∆𝐺𝑅𝐶 and ∆𝑇∆𝐺𝑃𝐶 ), tunneling (∆𝑇∆𝐺𝑡𝑢𝑛 ) and statistics (∆𝑇∆𝐺𝑠𝑡𝑎𝑡 ). This

methodology goes beyond the classical Eyring plot analysis by providing a detailed information on key physicochemical contributions to the reaction barrier changes. Notably, all the contributions are in principle attainable by experiments and, except for reorganization energy and tunneling, are derived from thermodynamics. ≠ To demonstrate the robustness of our approach, we first calculated the ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 and ≠ quantities for a prototypical series of 18 HAA reactions between cyclohexa-1,4∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡



diene and (X)(TMC)FeIVO complexes (Figure 1) and for a series of 40 HAA reactions between simple organic substrates and the methoxy radical (Figure S2). In all cases, we found a nice agreement between ‘explicit’ and ‘implicit’ ∆𝑇Δ𝐺 ≠ values.

≠ ≠ Figure 1. Comparison of ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 and ∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 in a series of HAA reactions between

(X)(TMC)FeIVO complexes (X denotes various trans-axial ligands to the oxo group) and cyclohexa-1,4-diene (CHD) substrate over the range of T = 278-328 K. Note that only the ∆𝑇∆ ≠ contribution from CHD is considered, since the self-exchange reactions for FeIVO 𝐺𝜆0

complexes were not calculated.27

Having such a comparison, we now turn our attention to reactions 1-4 from Scheme 1. The results are presented in Figure 2 and Tables S1-S4. First, the figure shows an excellent ≠ ≠ agreement between ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 and ∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 for all reactions 1-4, with a difference that ≠ does not exceed 0.3 kcal mol-1. Since ∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 comes from a well-established theoretical

approach, such an agreement gives credence to Eq. (12) to capture all important contributions to the temperature dependence of electron-proton transfer activation barriers. We note in ≠ ≠ passing that we have also compared ∆𝑇∆𝐺𝜆0 contributing to ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 with the result reported

by Hammes-Schiffer,28 who calculated 𝜆 for the self-exchange ‘FeIII(H2bim)3 + FeIII(Hbim)(H2bim)2’ reaction using a more sophisticated multistate continuum theory for charge transfer processes. Hammes-Schiffer showed that 𝜆 is ~22 kcal mol-1 at 298 K, and ∆𝑇𝛥𝜆


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= 0.1 kcal mol-1 for T = 298-324 K.28 This agrees well with our calculated values: 𝜆 = 21.1 kcal mol-1 and ∆𝑇𝛥𝜆 = 0.04 kcal mol-1 for T = 298-324 K. ≠ ≠ The agreement of calculated ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 with the experimentally-derived ∆𝑇∆𝐺𝑒𝑥𝑝𝑡 is ≠ also remarkable: ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 for reactions 1 and 3 differ from experimental data by less than

0.8 kcal mol-1; in the case of 2 and 4 the differences are 0.1 and 0.6 kcal mol-1. As for 1, the ∆𝑇 ≠ ≠ exceeds the calculated Δ𝑇∆𝐺𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 from Eq. (1) (note that ‘DFT threshold’ ∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡/𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 ≠ is determined from the ∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 activation barrier), which is in line with the observation of a ≠ rate deceleration as T increases. Contrary, the ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡/𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 calculated for 2-4 are

considerably lower than both DFT and experimental threshold values as marked in Figure 2. This is also in accord with the observed ‘usual’ temperature dependence of the reaction rate. ≠ In 1, all but the statistical factor (∆𝑇∆𝐺𝑠𝑡𝑎𝑡 ) are of the same sign and comparable

magnitude (ranging from +0.1 to +0.6 kcal mol-1), collectively pushing up the reaction barrier as T raises (Figure 2). Importantly, none of them has a prevalent character and omitting any of the six contributions in Eq. (12) would predict the acceleration of the rate of reaction 1 in response to a T increment. For reaction 3, all of the contributions are smaller than those in 1, which results in a ≠ slower growth of the barrier (1 vs. 3: ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 = +2.2 vs. +1.6 kcal mol-1), faithfully ≠ reproducing the difference in the temperature dependence of experimental data (cf. ∆𝑇∆𝐺𝑒𝑥𝑝𝑡 =

+2.9 vs. +2.4 kcal mol-1 in Figure 2).



Figure 2. Explicitly and implicitly calculated temperature-induced changes of the reaction ≠ ≠ barriers (∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 and ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 given by Eq. (S2) and Eq. (12)) and their comparisons ≠ with ∆𝑇∆𝐺𝑒𝑥𝑝𝑡 for reactions 1-4, derived from experimental data taken from Refs. 10 and 11.

The barriers of ‘forward’ reactions 1 and 3 grow faster with T than their ‘backward’ ≠ counterparts 2 and 4. From Figure 2, the critical difference between ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 of ‘forward’

and ‘backward’ reactions consists in the temperature dependence of the BEP factor, which has ≠ an opposite effect on 1 vs. 2 (and on 3 vs. 4). In this respect, ∆𝑇∆𝐺𝐵𝐸𝑃 despite not playing a


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dominant role in any of the studied reactions, tips the balance. This finding is comprehensible ≠ ≠ ≠ ≠ ≠ since other contributions such as ∆𝑇∆𝐺𝜆0 , ∆𝑇∆𝐺𝑎𝑠𝑦𝑛 , ∆𝑇∆𝐺𝑡𝑢𝑛 and [∆𝑇∆𝐺𝑅𝐶 ] must + ∆𝑇∆𝐺𝑃𝐶

remain the same upon the change of reaction direction (from forward to backward). Using the traditional Eyring plot analysis, Mayer et al attributed the unusual T dependence of reaction 1 to negative activation enthalpy (∆𝐻 ≠ = 2.7 kcal mol-1).10 While we do not contradict this conclusion (our calculated value of ∆𝐻 ≠ is 1.7 kcal mol-1), we believe that the alternative analysis presented here provides a more comprehensive insight into the key contributions to activation barriers. Specifically for this study, it suggests the behavior of reaction 1 is mostly ≠ ≠ ≠ governed by four approximately equally large components ∆𝑇∆𝐺𝑎𝑠𝑦𝑛 , ∆𝑇∆𝐺𝐵𝐸𝑃 , ∆𝑇∆𝐺𝑅𝐶 and ≠ . In our opinion, the presented analysis has a great potential to facilitate a rational ∆𝑇∆𝐺𝑃𝐶

optimization of temperature conditions for an H-atom abstraction catalyst of interest. In view of a number of sophisticated (quantum mechanical) theories of electron-proton transfer,22, 29-34 we aim to provide a simple yet robust methodology for a general use, which relies on quantities which are readily accessible by both experiment and computation. To conclude, the present computational study has been concerned with the elucidation of the thermodynamic factors causing the acceleration or deceleration of electron-proton transfer reactions in response to ΔT (Scheme 4). First, we propose a methodology to calculate independent contributions to reaction rates additional to the BEP effect: association of the RC, dissociation of the PC, the thermodynamic bias for asynchronicity embodied in the factor η, tunneling through the reaction barrier, and statistics associated with the number of equivalent reactive sites. Importantly, the magnitude of η not only quantifies the long-standing qualitative notion of asynchronicity in electron-proton transfer reactions but also proves to be a key component of the activation barrier.



Scheme 4. For a certain elevation of temperature (ΔT), reaction gets slower/faster if the ΔTinduced change of the reaction barrier height (ΔTΔG≠) falls above/below a ‘threshold’ value, which is defined by Eq (1). Utilizing the Eq. (12), the ΔTΔG≠ can be analyzed in terms of six major components (depicted schematically; here component in green/red contributes positively/negatively to ΔTΔG≠ ), allowing to assess which factor(s) is (are) key for a control of ΔT-induced change of rate constant (ΔT log k). Remarkably, by dissecting the different contributions to the reaction barrier, the present method represents a viable alternative to the classical Eyring plot analysis of H-atom abstraction reaction rates as a function of temperature. It provides detailed information based on thermodynamic descriptors whose fine-tuning will be, in our opinion, more intuitive than activation enthalpies and entropies for the design of chemical reactions and improved catalysts. The success of our analysis to describe the temperature dependence of a set of H-atom abstraction reactions, including a counterintuitive rate deceleration, serves as a proof of the concept and is a testament of the usefulness of the present approach. Finally, but equally important, this investigation raises awareness on the hitherto neglected contribution of asynchronicity to reaction rates and their temperature dependences.


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COMPUTATIONAL METHODS All computational details are provided in the Supporting Information. In brief, all geometry optimizations and energetic data discussed in the text were obtained from the DFT calculations, using M06L functional35 and COSMO-RS model of solvation36-37. The method was selected on the basis of an extensive benchmark against available experimental free energies of reaction and activation of reactions 1-4. Noticeably, the temperature dependent contributions to activation barriers were also evaluated using B3LYP- and HF-optimized geometries, but exhibited relatively low sensitivity to the choice of a method as presented in detail in the SI.

ASSOCIATED CONTENT Supporting Information: Coordinates of all calculated structures. (TXT) Full account of computational details, description of temperature dependent contributions to ≠ ≠ activation barriers for evaluation of ∆𝑇∆𝐺𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 and ∆𝑇∆𝐺𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 according to Eq. (12), raw

energetic data for reactions 1-4, comparison of different levels of theory for thermal contributions to Gibbs free energy, comparison of different levels of theory for electronic potential energies, description of tunneling correction to ∆𝑇∆𝐺 ≠ used in the work, derivation of λ0 from Marcus cross-relation theory. (PDF)

AUTHOR INFORMATION All authors have given approval to the final version of the manuscript. ‡These authors contributed equally. Corresponding Author: Martin Srnec; [email protected]



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ACKNOWLEDGMENTS The financial support of the Grant Agency of the Czech Republic (Grant No. 18‐13093S) is gratefully acknowledged. MMD acknowledges the co-finance between the EU and the Ministry of

Education,

Youth

and

Sports

of

the

Czech

Republic

for

the

project

CZ.02.2.69/0.0/0.0/18_070/. This work was supported by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations project „IT4Innovations National Supercomputing Center – LM2015070“.

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TOC Graphic


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Dissecting the Temperature Dependence of Electron-Proton Transfer

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