Temperature Dependence of the Outer-Sphere Reorganization Energy

Twisto-Electrochemical Activity Volcanoes in Trilayer Graphene

In this work, we develop a twist-dependent electrochemical activity map, combining a low-energy continuum electronic structure model with modified Marcus-Hush-Chidsey kinetics in trilayer graphene. We identify a counterintuitive rate enhancement region spanning the magic angle curve and incommensurate twists in the system geometry. We find a broad activity peak with a ruthenium hexamine redox couple in regions corresponding to both magic angles and incommensurate angles, a result qualitatively distinct from the twisted bilayer case. Flat bands and incommensurability offer new avenues for reaction rate enhancements in electrochemical transformations.

Predicting the Ion Desolvation Pathway of Lithium Electrolytes and Their Dependence on Chemistry and Temperature

To better understand the influence of electrolyte chemistry on the ion-desolvation portion of charge-transfer beyond the commonly applied techniques, we apply free-energy sampling to simulations involving diethyl ether (DEE) and 1,3-dioxoloane/1,2-dimethoxyethane (DOL/DME) electrolytes, which display bulk solvation structures dominated by ion-pairing and solvent coordination, respectively. This analysis was conducted at a pristine electrode with and without applied bias at 298 and 213 K to provide insights into the low-temperature charge-transfer behavior, where it has been proposed that desolvation dominates performance. We find that, to reach the inner Helmholtz layer, ion-paired structures are advantageous and that the Li⁺ ion must reach a total coordination number of 3, which requires the shedding of 1 species in the DEE electrolyte or 2-3 species in DOL/DME. This work represents an effort to predict the distinct thermodynamic states as well as the most probable kinetic pathways of ion desolvation relevant for the charge transfer at electrochemical interphases.

Reorganization Energies, Entropies, and Free Energy Surfaces for Electron Transfer

Reorganization energies for an intramolecular self-exchange electron-transfer reaction are calculated by quantum-classical molecular dynamics simulations in four solvents with varying polarity and at temperatures ranging from 250 to 350 K. The reorganization free energies for polar solvents decrease systematically with increasing temperature, indicating that they include substantial contributions from entropy changes. The variances of the energy gap between the reactant and product states have a major component that is relatively insensitive to temperature. Explanations are suggested for these observations, which appear to necessitate rethinking the free energy functions of a distributed coordinate that frequently are used in discussions of reaction dynamics.

Wiedemann-Franz Law for Molecular Hopping Transport

The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant transport mechanism in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear temperature dependence of their ratio as expressed in the standard WF law is replaced by a linear dependence on the nuclear reorganization energy associated with the electron hopping process. The robustness of the molecular WF relation is confirmed by examining the conductance properties of a paradigmatic molecular junction. This result opens a new way to analyze conductivity in molecular systems, with possible applications advancing the design of molecular technologies that derive their function from electrical and/or thermal conductance.

Electron-Transfer-Induced Thermal and Thermoelectric Rectification

Controlling the direction and magnitude of both heat and electronic currents using rectifiers has significant implications for the advancement of molecular circuit design. In order to facilitate the implementation of new transport phenomena in such molecular structures, we examine thermal and thermoelectric rectification effects that are induced by an electron transfer process that occurs across a temperature gradient between molecules. Historically, the only known heat conduction mechanism able to generate thermal rectification in purely molecular environments is phononic heat transport. Here, we show that electron transfer between molecular sites with different local temperatures can also generate a thermal rectification effect and that electron hopping through molecular bridges connecting metal leads at different temperatures gives rise to asymmetric Seebeck effects, that is, thermoelectric rectification, in molecular junctions.

Nuclear Quantum Effects on Aqueous Electron Attachment and Redox Properties

Nuclear quantum effects (NQEs) on the reduction and oxidation properties of small aqueous species (CO₂, HO₂, and O₂) are quantified and rationalized by first-principles molecular dynamics and thermodynamic integration. Vertical electron attachment, or electron affinity, and detachment energies (VEA and VDE) are strongly affected by NQEs, decreasing in absolute value by 0.3 eV going from a classical to a quantum description of the nuclei. The effect is attributed to NQEs that lessen the solvent response upon oxidation/reduction. The reduction of solvent reorganization energy is expected to be general for small solutes in water. In the thermodynamic integral that yields the free energy of oxidation/reduction, these large changes enter with opposite sign, and only a small net effect (0.1 eV) remains. This is not obvious for CO₂, where the integrand is strongly influenced by NQEs due to the onset of interaction of the reduced orbital with the conduction band of the liquid during thermodynamic integration. We conclude that NQEs might not have to be included in the computation of redox potentials, unless high accuracy is needed, but are important for VEA and VDE calculations.

Spectroscopic and quantum chemical investigation on non-covalent interaction in chromophore appended fullerene complexes of calix[4]arene

The present paper describes the spectroscopic and theoretical insights on non-covalent interaction of a calix[4]arene molecule, namely, 4-iso-propyl-calix[4]arene (1) with chromophore appended fullerenes, namely, tert-butyl-(1,2-methanofullerene)-61-carboxylate (2) and [6,6]-phenyl-C(71)- butyric acid methyl ester (3) in solvents having varying polarity, viz., toluene and benzonitrile. Absorption spectrophotometric studies reveal appreciable ground state interaction between fullerenes and 1. The most fascinating feature of the present study is that 1 binds very effectively with both 2 and 3 as obtained from binding constant (K) data of such complexes; i.e., K(2-1) and K(3-1) exhibit value of 4.53 × 10(5) dm(3) mol(-1) (7.95 × 10(5) dm(3) mol(-1)) and 13.35 × 10(5) dm(3) mol(-1) (27.62 × 10(5) dm(3) mol(-1)) in toluene (benzonitrile), respectively. The effect of solvent over the complexation between fullerenes and 1 is clearly observed from the trend in the K values. Estimation of solvent reorganization energy (R(S)) evokes that both 2-1 and 3-1 complexes are stabilized more in toluene compared to benzonitrile. Molecular mechanics force field (MMMF) calculations in vacuo evoke geometrical structures of the 2-1 and 3-1 complexes and reveal interesting feature regarding binding pattern of fullerenes toward 1 in terms of heat of formation value of the respective complexes.

Absorption spectrophotometric, NMR and theoretical investigations on ground state non-covalent interaction of C₆₀ and C₇₀ with a designed trihomocalix[6]arene in solution

The present paper reports the spectroscopic investigations on non-covalent interaction of fullerenes C(60) and C(70) with a designed trihomocalix[6]arene (2) in toluene. UV-vis studies reveal appreciable ground state interaction between fullerenes and 2. Jobs method of continuous variation establishes 1:1 stoichiometry for fullerene-2 complexes. Binding constant (K) data reveals that 2 binds C(70) more strongly compared to C(60), i.e. K(C60-2)-47,540 dm(3)mol(-1) and K(C70-2)-86,360 dm(3)mol(-1). Proton NMR studies provide very good support in favor of strong binding between C(70) and 2. Estimation of solvent reorganization energy (R(S)) evokes that C(70)-2 complex is stabilized more compared to C(60)-2 complex as R(S(C60-2))- -1.162 eV and R(S(C70-2))- -1.244eV. Semiempirical calculations at third parametric level of theory in vacuo evoke the single projection structures of the fullerene-2 complexes and interpret the stability difference between C(60) and C(70) complexes of 2 in terms of enthalpies of formation values.

Free energy, entropy and volume of activation for electron transfer reactions in a polar solvent

A continuum theory with account of cavity size fluctuations is employed to study free energy, volume and entropy of activation for nonadiabatic electron transfer (ET) reactions in polar solvents. By using a two-sphere cavity description, model calculations are performed for charge separation and recombination processes in acetonitrile under ambient conditions. It is found that the cavity size at the transition state varies with the free energy of reaction as well as with the thermodynamic conditions. In contrast to the Marcus theory predictions, the volume and entropy of activation show a monotonic behavior with the free energy of reaction and a strong correlation with each other. For example, for a given ET process, the volume and entropy of activation have the same sign. Their values for the charge separation and recombination processes are opposite in sign. These findings are in good qualitative agreement with measurements.

Solvent Reorganization Entropy of Electron Transfer in Polar Solvents

We report the results of molecular dynamics simulations of the solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile at varying temperatures. The simulations confirm the prediction of microscopic solvation theories of a positive reorganization entropy in polar solvents. The results of simulations are analyzed in terms of the splitting of the reorganization entropy into the contributions from the solute-solvent interaction and from the alteration of the solvent structure induced by the solute. These two contributions mutually cancel each other, resulting in the reorganization entropy amounting to only a fraction of each component.

Temperature- and Pressure-Dependence of the Outer-Sphere Reorganization Free Energy for Electron Transfer Reactions: A Continuum Approach

The outer-sphere reorganization free energy for electron-transfer reactions in polar solvents and its variations with temperature and pressure are studied in the dielectric continuum framework by extending the recent fluctuating cavity description [J. Chem. Phys. 2005, 123, 014504]. The diabatic free energies are obtained as a function of three variables, i.e., radii of two spherical cavities for the donor and acceptor moieties of an electron-transfer complex and a solvent coordinate that gauges an arbitrary configuration of solvent orientational polarization. Equilibrium cavities relevant to the reactant and product states are determined via the variational principle. This incorporates cavity size readjustment accompanying electron transfer and related electrostrictive effects. Another important consequence of the variational determination of equilibrium cavities is that their size depends on thermodynamic conditions. The application of the theoretical formulation presented here to electron self-exchange shows that in contrast to the prediction of the standard Marcus theory, the solvent reorganization free energy decreases with temperature. This is in excellent accord with a recent experiment on a mixed valence dinuclear iron complex in acetonitrile [J. Phys. Chem. A 1999, 103, 7888]. It is also found that electrostriction makes a significant contribution to outer-sphere reorganization. Model calculations for the dinuclear iron complex system show that about 25-30% of the total solvent reorganization free energy arises from cavity size changes, while solvent repolarization is responsible for the rest.

On the temperature and pressure dependences of cavities in the dielectric continuum picture

Cavity size at equilibrium and its variations with thermodynamic conditions are studied in the dielectric continuum framework of solvents. By employing Gibbs' theory of dividing surfaces, the fluctuating cavity description of Kim [H.J. Kim, J. Chem. Phys. 105, 6818 (1996)] is extended to include effects related to the local solvent density inhomogeneity near the cavity. The resulting theory is applied to study cavity size variations with temperature and pressure in dipolar and nondipolar solvents. Model calculations show that the cavity size tends to increase with temperature along an isobar and decrease with pressure along an isotherm.

Theory of torsional non-Condon electron transfer: A generalized spin-boson Hamiltonian and its nonadiabatic limit solution

The paper develops a theory of electron transfer with torsionally induced non-Condon (NC) effects. The starting point of the theory is a generalized spin-boson Hamiltonian, where an additional torsional oscillator bilinearly coupled to other bath modes causes a sinusoidal NC modulation. We derive closed form time dependent nonadiabatic rate expressions for both sudden and relaxed initial conditions, which are applicable for general spectral densities and energetic condition. Under the assumption that the torsional motion is not correlated with the polaronic shift of the bath, simple stationary limit rate expression is obtained. Model calculations of this rate expression illustrate the effects of torsional quantization and gating on the driving force and temperature dependences of the electron transfer rate. The classical limit of the rate expression consists of three Marcus-type terms, and is shown to agree very well with the exact numerical result.

Solvent reorganization energy of electron-transfer reactions in polar solvents

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.

Solvent-Dependent Dynamics of the MQ•→ReII Excited-State Electron Transfer in [Re(MQ+)(CO)3(dmb)]2+

The Re-->MQ(+) MLCT excited state of [Re(MQ(+))(CO)(3)(dmb)](2+) (MQ(+) = N-methyl-4,4'-bipyridinium, dmb = 4,4'-dimethyl-2,2'-bipyridine), which is populated upon 400-nm irradiation, was characterized by picosecond time-resolved IR and resonance Raman spectroscopy, which indicate large structural differences relative to the ground state. The Re-->MQ(+) MLCT excited state can be formulated as [Re(II)(MQ*)(CO)(3)(dmb)](2+). It decays to the ground state by a MQ*-->Re(II) back-electron transfer, whose time constant is moderately dependent on the molecular nature of the solvent, instead of its bulk parameters: formamides approximately DMSO approximately MeOH (1.2-2.2 ns) < THF, aliphatic nitriles (3.2-3.9 ns) << ethylene-glycol approximately 2-ethoxyethanol (4.2-4.8 ns) < pyridine (5.7 ns) < MeOCH(2)CH(2)OMe (6.9 ns) < PhCN (7.5 ns) < MeNO(2) (8.6 ns) <<< CH(2)Cl(2), ClCH(2)CH(2)Cl (25.9-28.9 ns). An approximate correlation was found between the back-reaction rate constant and the Gutmann donor number. Temperature dependence of the decay rate measured in CH(2)Cl(2), MeOH, and BuCN indicates that the inverted MQ*-->Re(II) back-electron transfer populates a manifold of higher vibrational levels of the ground state. The solvent dependence of the electron transfer rate is explained by solvent effects on inner reorganization energy and on frequencies of electron-accepting vibrations, by interactions between the positively charged MQ(+) pyridinium ring and solvent molecules in the electron-transfer product, that is the [Re(MQ(+))(CO)(3)(dmb)](2+) ground state.