Relationships between nonadiabatic bridged intramolecular, electrochemical, and electrical electron-transfer processes

Fermi's golden rule is used to develop relationships between rate constants for electron transfer in donor-bridge-acceptor and electrode-bridge-acceptor systems and resistances across metal-bridge-electrode and metal-bridge-tip junctions. Experimental data on electron-transfer rates through alkanethiolate, oligophenylene, and DNA bridges are used to calculate the electronic coupling matrix element per state through these moieties. The formulation is then used to predict the resistance of these bridges between two gold contacts. This approach provides a straightforward method for experimentalists to assess the self-consistency between intramolecular electron-transfer rate constants and low-bias resistances measured for molecularly bridged junctions between two metallic contacts. Reported resistances for alkanethiolate bridges vary by a factor of 20, with predicted resistances falling within this range. However, comparisons between carboxylato and directly linked alkanethiolate bridges suggest differences between the coupling at the interface to either the redox center or the gold electrode in such systems. Calculated resistances for oligophenylene bridges are close to those measured experimentally in a similar oligophenylene system.     

Theory of non-Markovian rate processes

Starting from a multidimensional reaction kinetic equation with a general time evolution operator and a reaction sink function K, we derive formally exact expressions for the survival probability, reaction time distribution, and mean reaction time by using the projection operator technique. These rate expressions are given in the rational function form, with the irreducible memory function Omegairr as the key ingredient. This approach has an advantage over the direct perturbation approaches that use the reaction term as the small parameter, in that Omegairr has a structure that can be perturbatively treated with (K - K) as the small parameter. The well-known Wilemski-Fixman-type rate expressions are reproduced as the zeroth-order approximation from the present theory. Practical methods for evaluating the formal rate expressions are presented, and the results calculated for a model of electron transfer in non-Debye solvents are compared with computer simulations. It is found that the present approach is very promising for the study of non-Markovian dispersive kinetics.     

The role of solvation in redox processes

In studying the role of solvation in redox processes we consider the influence of geometrical modifications in the discharge of monosolvated anion CN^?-H₂O. We define as “efficient” those modifications whose energy cost is less than the lowering which is produced in the ionization potential. we conclude that in the above-mentioned species the redox process is enhanced by desolvation. We try to generalise the results for the “stable” anions and cations.     

Thermodynamic aspects of solubility,solvation and partitioning processes of some sulfonamides

The thermodynamic aspects of sublimation processes of three sulfonamides with the general structures C₆H₅–SO₂NH–C₆H₄–R (R = 4-NO₂) and 4-NH₂–C₆H₄–SO₂NH–C₆H₄–R (R = 4-NO₂; 4-CN) were studied by investigating the temperature dependence of vapor pressure using the transpiration method. These data together with those obtained earlier for C₆H₅–SO₂NH–C₆H₄–R (R = 4-Cl) and 4-NH₂–C₆H₄–SO₂NH–C₆H₄–R (R = 4-Cl; 4-OMe; 4-C₂H₅) were analyzed and compared. A correlation was derived between sublimation Gibbs free energies and the sum of H-bond acceptor factors of the molecules. Solubility processes of the compounds in water, phosphate buffer with pH 7.4 and n-octanol (as phases modeling various drug delivery pathways) were investigated and corresponding thermodynamic functions were calculated as well. Thermodynamic characteristics of the sulfonamides solvation were evaluated. Also in this case a correlation between solubility/solvation Gibbs free energy values and the sum of H-bond acceptor factors was observed. For the sulfonamides with various substituents at para-position the processes of transfer from one solvent (water or buffer) to n-octanol were studied by a diagram method combined with analysis of enthalpic and entropic terms. Distinguishing between enthalpy and entropy, as is possible through the present approach, leads to the insight that the contribution of these terms is different for different molecules (entropy- or enthalpy-determined). Thus, in contrast to the interpretation of only the Gibbs free energy of transfer (extensively used for pharmaceuticals in the form of the partition coefficient, log P), the analysis of thermodynamic functions of the transfer process provides additional mechanistic information. This may be important for further evaluation of the physiological distribution of drug molecules and may provide a better understanding of biopharmaceutical properties of drugs.     

Probing coherence aspects of adiabatic quantum computation and control

Quantum interference between multiple excitation pathways can be used to cancel the couplings to the unwanted, nonradiative channels resulting in robustly controlling decoherence through adiabatic coherent control approaches. We propose a useful quantification of the two-level character in a multilevel system by considering the evolution of the coherent character in the quantum system as represented by the off-diagonal density matrix elements, which switches from real to imaginary as the excitation process changes from being resonant to completely adiabatic. Such counterintuitive results can be explained in terms of continuous population exchange in comparison to no population exchange under the adiabatic condition.     

The solvation, partitioning, hydrogen bonding, and dimerization of nucleotide bases: a multifaceted challenge for quantum chemistry

We present M06-2X density functional calculations of the chloroform/water partition coefficients of cytosine, thymine, uracil, adenine, and guanine and calculations of the free energies of association of selected unsubstituted and alkylated nucleotide base pairs in chloroform and water. Both hydrogen bonding and π-π stacking interactions are considered. Solvation effects are treated using the continuum solvent models SM8, SM8AD, and SMD, including geometry optimization in solution. Comparison of theoretical results with available experimental data indicates that all three of these solvation models predict the chloroform-water partition coefficients for the studied nucleobases qualitatively well, with mean unsigned errors in the range of 0.4-1.3 log units. All three models correctly predict the preference for hydrogen bonding over stacking for nucleobase pairs solvated in chloroform, and SM8, SM8AD, and SMD show similar accuracy in predicting the corresponding free energies of association. The agreement between theory and experiment for the association free energies of the dimers in water is more difficult to assess, as the relevant experimental data are indirect. Theory predicts that the stacking interaction of nucleobases in water is more favorable than hydrogen bonding for only two out of three tested hetero-dimers.     

Coupled-channels quantum theory of electronic flux density in electronically adiabatic processes: application to the hydrogen molecule ion

This article presents the results of the first quantum simulations of the electronic flux density (j(e)) by the "coupled-channels" (CC) theory, the fundamentals of which are presented in the previous article [Diestler, D. J. J. Phys. Chem. A 2012, DOI: 10.1021/jp207843z]. The principal advantage of the CC scheme is that it employs exclusively standard methods of quantum chemistry and quantum dynamics within the framework of the Born-Oppenheimer approximation (BOA). The CC theory goes beyond the BOA in that it yields a nonzero j(e) for electronically adiabatic processes, in contradistinction to the BOA itself, which always gives j(e) = 0. The CC is applied to oriented H(2)(+) vibrating in the electronic ground state ((2)Σ(g)(+)), for which the nuclear and electronic flux densities evolve on a common time scale of about 22 fs per vibrational period. The system is chosen as a touchstone for the CC theory, because it is the only one for which highly accurate flux densities have been calculated numerically without invoking the BOA [Barth et al, Chem. Phys. Lett. 2009, 481, 118]. Good agreement between CC and accurate results supports the CC approach, another advantage of which is that it allows a transparent interpretation of the temporal and spatial properties of j(e).     

Comparison of electron-transfer rates for metal- versus ring-centered redox processes of porphyrins in monolayers on Au(111)

The standard electron-transfer rate constants ( k ( 0 )) are measured for redox processes of Fe versus Zn porphyrins in monolayers on Au(111); the former undergoes a metal-centered redox process (conversion between Fe (III) and Fe (II) oxidation states) whereas the latter undergoes a ring-centered redox process (conversion between the neutral porphyrin and the pi-cation radical). Each porphyrin contains three meso-mesityl groups and a benzyl thiol for surface attachment. Under identical solvent (propylene carbonate)/electrolyte (1.0 M Bu 4NCl) conditions, the Zn (II) center has a coordinated Cl (-) ion when the porphyrin is in either the neutral or oxidized state. In the case of the Fe porphyrin, two species are observed a low-potential form ( E l (0) approximately -0.6 V) wherein the metal center has a coordinated Cl (-) ion when it is in either the Fe (II) or Fe (III) state and a high-potential form ( E h (0) approximately +0.2 V) wherein the metal center undergoes ligand exchange upon conversion from the Fe (III) to Fe (II) states. The k ( 0 ) values observed for all of the porphyrins depend on surface concentration, with higher concentrations resulting in slower rates, consistent with previous studies on porphyrin monolayers. The k ( 0 ) values for the ring-centered redox process (Zn chelate) are 10-40 times larger than those for the metal-centered process (Fe chelate); the k ( 0 ) values for the two forms of the Fe porphyrin differ by a factor of 2-4 (depending on surface concentration), the Cl (-) exchanging form generally exhibiting a faster rate. The faster rates for the ring- versus metal-centered redox process are attributed to the participating molecular orbitals and their proximity to the surface (given that the porphyrins are relatively upright on the surface): a pi molecular orbital that has significant electron density at the meso-carbon atoms (one of which is the site of attachment of the linker to the surface anchoring thiol) versus a d-orbital that is relatively well localized on the metal center.     

Photochemical reactivity of 2-vinylbiphenyl and 2-vinyl-1,3-terphenyl: the balance between nonadiabatic and adiabatic photocyclization

A mechanism for the photochemical conversion of 2-vinyl-1,3-terphenyl to 8,9a-dihydrophenanthrene (Lewis, F. D.; Zuo, X.; Gevorgyan, V.; Rubin, M. J. Am. Chem. Soc. 2002, 124, 13664-13665) is presented in this study, based on ab initio restricted active space self-consistent field calculations and a molecular mechanics-valence bond dynamics simulation of a model system: the syn isomer of 2-vinylbiphenyl. An extended crossing seam between the ground and first excited electronic states was found to be largely responsible for the efficient photocyclization of the photochemically active syn isomer. This mechanism is nonadiabatic in nature, with an excited-state reaction pathway approaching the crossing region during the initial stage of cyclization. Dynamics simulation shows that this seam is easily accessible by vibrational motion in the branching space, once a small barrier is passed on the S1 excited-state potential energy surface. Ultrafast radiationless decay to the ground state then follows, and the cyclization is completed on this surface. A second possible mechanism was identified, which involves complete adiabatic cyclization on the S1 surface, with decay to the ground state (at a different conical intersection) only taking place once the product is formed. Thus, there is a competition between these two mechanisms-nonadiabatic and adiabatic-governed by the dynamics of the system. A large quantum yield is predicted for the photocyclization of the syn isomer of 2-vinylbiphenyl and 2-vinyl-1,3-terphenyl, in agreement with experimental observations.     

Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations.     

An anthracene-appended beta-cyclodextrin-based dyad: study of self-assembly and photoinduced electron-transfer processes

The self-assembly of a beta-cyclodextrin (beta-CD)-based supramolecular dyad is reported, in which the donor anthracene moiety is covalently linked to the smaller rim of the beta-CD and the acceptor pyromellitic diimide (PMDI) is encapsulated within the beta-CD cavity. Encapsulation of the PMDI into the beta-CD cavity was studied by a variety of techniques, which suggested that PMDI is encapsulated so as to position the aromatic part at the centre of the cavity with the 2-propyl end at the narrower rim among the overhanging primary OH groups and the N-ethylpyridinium end situated at the wider rim exposed to water. Photoinduced electron transfer (PET) in the system was studied by fluorescence quenching and laser flash photolysis techniques. At [PMDI]<10(-4) M, the equilibrium is in favour of the free molecules, and under these conditions fluorescence quenching is negligible and diffusion-mediated electron transfer involving the triplet excited state of anthracene predominates. At higher concentrations of PMDI, the equilibrium is largely in favour of the supramolecular dyad and intra-ensemble PET processes predominate. The experimentally determined electron-transfer rate constant agrees very well with that calculated by using the Marcus equation. It was observed that a fraction of the ion pairs survived for more than 200 micros.     

The effect of ionic strength on the electron-transfer rate of surface immobilized cytochrome C

Horse heart cytochrome c was immobilized on four different self-assembled monolayer (SAM) films. The electron tunneling kinetics were studied in the different assemblies as a function of the ionic strength of the buffer solution using cyclic voltammetry. When cytochrome c is electrostatically immobilized, the standard electron exchange rate constant k0 decreases with the increase of the solution's ionic strength. In contrast, the protein covalently attached or ligated has a rate constant independent of the ionic strength. The inhomogeneity of electrostatically immobilized cytochrome c increases with the increase of the solution's ionic strength whereas that of the covalently attached protein is independent of the ionic strength. A comparison of these different electron-transfer behaviors suggests that the thermodynamically stable geometry of cytochrome c in the electrostatic assemblies is also an electron transfer favorable one. It suggests that the surface charges of cytochrome c are capable of guiding it into geometries in which its front surface faces the electron-transfer partner. The inhomogeneity observed in this study indicates that a distribution of cytochrome c orientations and thus a distribution of electron transfer rate constants exists.     

Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies

Our previously developed approaches for integrating quantum mechanical molecular orbital methods with microscopic solvent models are refined and examined. These approaches consider the nonlinear solute–solvent coupling in a self-consistent way by incorporating the potential from the solvent dipoles in the solute Hamiltonian, while considering the polarization of the solvent by the potential from the solute charges. The solvent models used include the simplified Langevin Dipoles (LD) model and the much more expensive surface constrained All Atom Solvent (SCAAS) model, which is combined with a free energy pertubation (FEP) approach. Both methods are effectively integrated with the quantum mechanical AMPAC package and can be easily combined with other quantum mechanical programs. The advantages of the present approaches and their earlier versions over macroscopic reaction field models and supermolecular approaches are considered. A LD/MNDO study of solvated organic ions demonstrates that this model can yield reliable solvation energies, provided the quantum mechanical charges are scaled to have similar magnitudes to those obtained by high level ab initio methods. The incorporation of a field-dependent hydrophobic term in the LD free energy makes the present approach capable of evaluating the free energy of transfer of polar molecules from non polar solvents to aqueous solutions. The reliability of the LD approach is examined not only by evaluating a rather standard set of solvation energies of organic ions and polar molecules, but also by considering the stringent test case of sterically hindered hydrophobic ions. In this case, we compare the LD/MNDO solvation energies to the more rigorous FEP/SCAAS/MNDO solvation energies. Both methods are found to give similar results even in this challenging test case. The FEP/SCAAS/AMPAC method is incorporated into the current version of the program ENZYMIX. This option allows one to study chemical reactions in enzymes and in solutions using the MNDO and AM1 approximations. A special procedure that uses the EVB method as a reference potential for SCF MO calculations should help in improving the reliability of such studies.     

Probing mechanistic photochemistry of glyoxal in the gas phase by ab initio calculations of potential-energy surfaces and adiabatic and nonadiabatic rates

In the present work, the wavelength-dependent mechanistic photochemistry of glyoxal in the gas phase has been explored by ab initio calculations of potential-energy surfaces, surface crossing points, and adiabatic and nonadiabatic rates. The CHOCHO molecules in S1 by photoexcitation at 393-440 nm mainly decay to the ground state via internal conversion, which is followed by molecular eliminations to form CO, H2CO,H2, and HCOH. Upon photodissociation of CHOCHO at 350-390 nm, intersystem crossing to T1 followed by the C-C bond cleavage is the dominant process in this wavelength range, which is responsible for the formation of the CHO radicals. The C-C and C-H bond cleavages along the S1 pathway are energetically accessible upon photodissociation of CHOCHO at 290-310 nm, which can compete with the S1-->T1 intersystem crossing process. The present study predicts that the C-H bond cleavage on the S1 surface is probably a new photolysis pathway at high excitation energy, which has not been observed experimentally. In addition, the trans-cis isomerization is predicted to occur more easily in the ground state than in the excited states.