Molecular dynamics simulations of porphyrin-dendrimer systems: toward modeling electron transfer in solution

We have performed computational simulations of porphyrin-dendrimer systems--a cationic porphyrin electrostatically associated to a negatively charged dendrimer--using the method of classical molecular dynamics (MD) with an atomistic force field. Previous experimental studies have shown a strong quenching effect of the porphyrin fluorescence that was assigned to electron transfer (ET) from the dendrimer's tertiary amines (Paulo, P. M. R.; Costa, S. M. B. J. Phys. Chem. B 2005, 109, 13928). In the present contribution, we evaluate computationally the role of the porphyrin-dendrimer conformation in the development of a statistical distribution of ET rates through its dependence on the donor-acceptor distance. We started from simulations without explicit solvent to obtain trajectories of the donor-acceptor distance and the respective time-averaged distributions for two dendrimer sizes and different initial configurations of the porphyrin-dendrimer pair. By introducing explicit solvent (water) in our simulations, we were able to estimate the reorganization energy of the medium for the systems with the dendrimer of smaller size. The values obtained are in the range 0.6-1.5 eV and show a linear dependence with the inverse of the donor-acceptor distance, which can be explained by a two-phase dielectric continuum model taking into account the medium heterogeneity provided by the dendrimer organic core. Dielectric relaxation accompanying ET was evaluated from the simulations with explicit solvent showing fast decay times of some tens of femtoseconds and slow decay times in the range of hundreds of femtoseconds to a few picoseconds. The variations of the slow relaxation times reflect the heterogeneity of the dendrimer donor sites which add to the complexity of ET kinetics as inferred from the experimental fluorescence decays.     

Photoinduced intramolecular electron transfer reactions within donor-acceptor linked compounds in solution and within donor-acceptor ion-pairs in crystal

Intramolecular electron transfer (ET) processes within donor-acceptor linked compounds in solution and donor-acceptor ion-pairs in crystal have been investigated by means of laser photolysis kinetic spectroscopy. An excited Ru(II)-moiety of donor-acceptor compounds undergoes intramolecular electron-transfer to either ruthenium(III) ion, rhodium(III) ion or a cobalt(III) ion, followed by back ET to regenerate the original reactant. An Arrhenius plot of the ET rate gave a straight line with an intercept (frequency factor) and a slope (activation energy) for the photoinduced ET and the back ET. Mixed-valence isomer states produced via photoinitiated ET rapidly decayed via back ET. A common and large frequency factor observed for Ru(II)-Rh(III) compounds is accounted for in terms of solvent-relaxation dynamics. For the back ET in the Ru(II)-Co(III) compounds, the frequency factors are reduced because of negative entropy change. ET within donor-acceptor ion-pair of Ru(bpy)₂³ and Co(CN)₃⁶ in crystal took place very rapidly compared with in water.     

Isomerization dynamics and thermodynamics of ionic argon clusters

The dynamics and thermodynamics of small Ar(n) (+) clusters, n=3, 6, and 9, are investigated using molecular dynamics (MD) and exchange Monte Carlo (MC) simulations. A diatomic-in-molecule Hamiltonian provides an accurate model for the electronic ground state potential energy surface. The microcanonical caloric curves calculated from MD and MC methods are shown to agree with each other, provided that the rigorous conservation of angular momentum is accounted for in the phase space density of the MC simulations. The previously proposed projective partition of the kinetic energy is used to assist MD simulations in interpreting the cluster dynamics in terms of inertial, internal, and external modes. The thermal behavior is correlated with the nature of the charged core in the cluster by computing a dedicated charge localization order parameter. We also perform systematic quenches to establish a connection with the various isomers. We find that the Ar(3) (+) cluster is very stable in its linear ground state geometry up to about 300 K, and then isomerizes to a T-shaped isomer in which a quasineutral atom lies around a charged dimer. In Ar(6) (+) and Ar(9) (+), the covalent trimer core is solvated by neutral atoms, and the weakly bound solvent shell melts at much lower energies, occasionally leading to a tetramer or pentamer core with weakly charged extremities. At high energies the core itself becomes metastable and the cluster transforms into Ar(2) (+) solvated by a fluid of neutral argon atoms.     

Combining a polarizable force-field and a coarse-grained polarizable solvent model. II. Accounting for hydrophobic effects

A revised and improved version of our efficient polarizable force-field/coarse grained solvent combined approach (Masella, Borgis, and Cuniasse, J. Comput. Chem. 2008, 29, 1707) is described. The polarizable pseudo-particle solvent model represents the macroscopic solvent polarization by induced dipoles placed on mobile pseudo-particles. In this study, we propose a new formulation of the energy term handling the nonelectrostatic interactions among the pseudo-particles. This term is now able to reproduce the energetic and structural response of liquid water due to the presence of a hydrophobic spherical cavity. Accordingly, the parameters of the energy term handling the nonpolar solute/solvent interactions have been refined to reproduce the free-solvation energy of small solutes, based on a standard thermodynamic integration scheme. The reliability of this new approach has been checked for the properties of solvated methane and of the solvated methane dimer, as well as by performing 10 × 20 ns molecular dynamics (MD) trajectories for three solvated proteins. A long-time stability of the protein structures along the trajectories is observed. Moreover, our method still provides a measure of the protein solvation thermodynamic at the same accuracy as standard Poisson-Boltzman continuum methods. These results show the relevance of our approach and its applicability to massively coupled MD schemes to accurately and intensively explore solvated macromolecule potential energy surfaces.     

Determination of the structural features of a long-lived electron-transfer state of 9-mesityl-10-methylacridinium ion

Extensive efforts have been devoted to developing electron donor-acceptor systems that mimic the utilization of solar energy that occurs in photosynthesis. X-ray crystallographic analysis shows how absorbed photon energy is stabilized in those compounds by structural changes upon photoinduced electron transfer (ET). In this study, structural changes of a simple electron donor-acceptor dyad, 9-mesityl-10-methylacridinium cation (Acr(+)-Mes), upon photoinduced ET were directly observed by laser pump and X-ray probe crystallographic analysis. The N-methyl group in Acr(+) was bent, and a weak electrostatic interaction between Mes and a counteranion in the crystal (ClO(4)) was generated by photoinduced ET. These structural changes correspond to reduction and oxidation due to photoinduced ET and directly elucidate the mechanism in Acr(+)-Mes for mimicking photosynthesis efficiently.     

Ab initio calculation for inner reorganization energy of gas-phase electron transfer in organic molecule–ion systems

A series of electron transfer (ET) reactions between some organic molecules have been investigated through ab initio calculations. Biphenyl (Bp) and 9,9^′-dimethylfluorene anion radicals are chosen as the donor, whereas several organic molecules with different redox abilities are chosen as the acceptor. The inner reorganization energy and the endothermicity of the ET reactions in those molecule–ion systems have been estimated through the HFSCF and complete active space multiconfiguration SCF calculations. Double-well potentials for the gas-phase ET reactions have been constructed using the linear reaction coordinate, and the results show that the quinone-containing ET reactions are in Marcus' inverted region. It has been found that the inner reorganization energies are different for various donor-acceptor couples, unlike the experimentally fitted ones. The contribution from the inter-ring torsional motion in Bp to the inner reorganization energy has been evaluated from the energy difference of the biphenyl-acceptor and the dimethylfluorine-acceptor systems. Comparisons with the experimentally observed results have been made.     

NO2^-/NO2体系电子转移的外电场效应和温度效应

用半经典模型研究NO2^-/NO2体系自交换电子转移的反应机理和速率常数, 探讨了外电场对反应过程势能面, 反应能垒及电子转移速率常数的影响, 确定了能垒崩溃的阈值; 讨论了低能垒条件下电子转移反应的速率常数随温度变化的特征。研究表明, 一定方向的外电场能显著降低电子转移反应的活化能垒并提高反应速率常数k, 而对非绝热电子转移反应, 当温度T和活能能垒Ec满足T=2Ec/R时, k取得极大值。     

Rotational dynamics of solvated carbon dioxide studied by infrared, Raman, and time-resolved infrared spectroscopies and a molecular dynamics simulation

Rotational dynamics of solvated carbon dioxide (CO(2)) has been studied. The infrared absorption band of the antisymmetric stretch mode in acetonitrile is found to show a non-Lorentzian band shape, suggesting a non-exponential decay of the vibrational and/or rotational correlation functions. A combined method of a molecular dynamics (MD) simulation and a quantum chemical calculation well reproduces the observed band shape. The analysis suggests that the band broadening is almost purely rotational, while the contribution from the vibrational dephasing is negligibly small. The non-exponential rotational correlation decay can be explained by a simple rotor model simulation, which can treat large angle rotations of a relatively small molecule. A polarized Raman study of the symmetric stretch mode in acetonitrile gives a rotational bandwidth consistent with that obtained from the infrared analysis. A sub-picosecond time-resolved infrared absorption anisotropy measurement of the antisymmetric stretch mode in ethanol also gives a decay rate that is consistent with the observed rotational bandwidths.     

Size resolved infrared spectroscopy of Na(CH3OH)n (n = 4-7) clusters in the OH stretching region: unravelling the interaction of methanol clusters with a sodium atom and the emergence of the solvated electron

Size resolved IR action spectra of neutral sodium doped methanol clusters have been measured using IR excitation modulated photoionisation mass spectroscopy. The Na(CH(3)OH)(n) clusters were generated in a supersonic He seeded expansion of methanol by subsequent Na doping in a pick-up cell. A combined analysis of IR action spectra, IP evolutions and harmonic predictions of IR spectra (using density functional theory) of the most stable structures revealed that for n = 4, 5 structures with an exterior Na atom showing high ionisation potentials (IPs) of ~4 eV dominate, while for n = 6, 7 clusters with lower IPs (~3.2 eV) featuring fully solvated Na atoms and solvated electrons emerge and dominate the IR action spectra. For n = 4 simulations of photoionisation spectra using an ab initio MD approach confirm the dominance of exterior structures and explain the previously reported appearance IP of 3.48 eV by small fractions of clusters with partly solvated Na atoms. Only for this cluster size a shift in the isomer composition with cluster temperature has been observed, which may be related to kinetic stabilisation of less Na solvated clusters at low temperatures. Features of slow fragmentation dynamics of cationic Na(+)(CH(3)OH)(6) clusters have been observed for the photoionisation near the adiabatic limit. This finding points to the relevance of previously proposed non-vertical photoionisation dynamics of this system.     

Ultrafast bimolecular electron transfer dynamics in micellar media

Ultrafast photoinduced bimolecular electron transfer (ET) dynamics between 7-aminocoumarin derivatives and N,N-dimethylaniline (DMAN) has been studied in neutral (TX100), cationic (DTAB) and anionic (SDS) micellar media. A very fast decay time constant (tau(fast)) shorter than approximately 10 ps has been observed for the coumarins in the presence of DMAN in all of the three micellar media. In this time scale, reactants in the micellar phase undergo ET interactions without involving diffusion or reorientation of the reactants and thus can be envisaged as equivalent to nondiffusive bimolecular ET reaction. The fastest ET rates estimated as the inverse of the shortest lifetime components of the fluorescence decay (k(et) congruent with tau(fast)(-1)) nicely follow the predicted Marcus inversion behavior with reaction exergonicity (-DeltaG degrees), irrespective of the nature of micelles considered. Onset of inversion in ET rates occur at approximately 0.61 eV lower exergonicity in SDS and TX100 micelles compared with that in DTAB micelle and are rationalized following two-dimensional ET (2DET) theory. These differences suggest the possibility of tuning Marcus inversion by proper selection of micelles. Interestingly, ET rates (k'(et)) obtained from the conventional Stern-Volmer analysis of the relatively longer time constants of the fluorescence decays also exhibit similar Marcus correlation with DeltaG degrees, showing clear inversion behavior. Fitting of Marcus correlation curves for k(et) and k'(et) indicate two largely different values for the electronic coupling parameters. In micellar media, as the interacting donor-acceptor molecules are on an average expected to be separated by an intervening surfactant chain and the reorientation rate of the reactants is quite slow, it is predicted that the ultrafast ET (k(et)) component arises because of the surfactant separated donor-acceptor pairs that are orientated perfectly to give the maximum electronic coupling. The slower ET (k'(et)) is predicted to arise because of those pairs where the donor-acceptor orientations are not very suitable but good enough to give a sizable electronic coupling.     

Lithium ion-ketocyanine dye interactions in the ground and excited states

Electronic absorption and emission spectral characteristics of a ketocyanine dye have been studied in solution in the presence of lithium perchlorate. Absorption spectral studies indicate complex formation between lithium ion and the dye in the ground state. The value of the equilibrium constant along with the molar absorbance of the absorbing species has been determined for the dye-cation interaction. The energy of maximum fluorescence shifts toward the red with the addition of LiClO(4). Steady-state emission studies point to the existence of two emitting species, viz., the solvated and the complexed dye in equilibrium. The values of the equilibrium constant for the process have been determined in acetone and acetonitrile. Time-resolved studies in the picosecond domain in pure solvents reveal that the lifetime (tau) value increases as the solvation interaction increases. Time-resolved studies also indicate the presence of two emitting species in equilibrium.     

The mechanism of fluorescence quenching of aromatic compounds by acids: ZDO calculations

The fluorescence quenching of cyano, hydroxy, methoxy, and amino derivatives of naphthalene, anthracene and pyrene by acids in polar solvents has been studied by quantum-chemistry methods in semi-empirical approximation. Quenching mechanisms, including protonation of the aromatic nucleus and electron transfer have been considered. It is shown that the mechanism of radiationless deactivation in encounter complexes of reagents consists in the specific interaction of the solvated proton with certain carbon atoms of the aromatic nucleus, not in the electron transfer. It is found that the rate constant of radiationless deactivation correlates with the charge at the corresponding carbon atom of the excited molecule. It is shown that the fluorescence quenching is determined mainly by the nature of the fluorescent state and electron donor-acceptor properties of the aromatic nucleus and the substituent. The present model makes it possible to predict the fluorescent properties of some aromatic compounds in the presence of acids.     

Dipole–reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone–benzoquinone anion radical system

 Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 10⁷M⁻¹s⁻¹ was obtained for the second-order rate constant, and it agrees quite well with the experimental one. Received: 19 October 2001 / Accepted: 17 January 2002 / Published online: 3 May 2002     

Charge recombination versus charge separation in donor-bridge-acceptor systems

Optimizing the ratio of the rates for charge separation (CS) over charge recombination (CR) is crucial to create long-lived charge-separated states. Mastering the factors that govern the electron transfer (ET) rates is essential when trying to achieve molecular-scale electronics, artificial photosynthesis, and also for the further development of solar cells. Much work has been put into the question of how the donor-acceptor distances and donor-bridge energy gaps affect the electronic coupling, V(DA), and thus the rates of ET. We present here a unique comparison on how these factors differently influence the rates for CS and CR in a porphyrin-based donor-bridge-acceptor model system. Our system contains three series, each of which focuses on a separate charge-transfer rate-determining factor, the donor-acceptor distance, the donor-bridge energy gap, and last, the influence of the electron acceptor on the rate for charge transfer. In these three series both CS and CR are governed by superexchange interactions which make a CR/CS comparative study ideal. We show here that the exponential distance dependence increases slightly for CR compared to that for CS as a result of the increased tunneling barrier height for this reaction, in accordance with the McConnell superexchange model. We also show that the dependence on the tunneling barrier height is different for CS and CR. This difference is highly dependent on the electron acceptor and thus cannot solely be explained by the differences in the frontier orbitals of the electron donor in these porphyrin systems.     

Solvent effects in active-site molecular dynamics simulations on the binding of 8-methyl-N5-deazapterin and 8-methylpterin to dihydrofolate reductase

Molecular dynamics (MD) simulation methods have been used to study the active site of the ternary complex formed between avian dihydrofolate reductase (DHFR), NADPH cofactor, and the inhibitor 8-methyl-N5-deazapterin in aqueous solution. Spherical shells of water molecules (initially at the bulk-solvent density) are used to solvate the active site and the surrounding protein surface. Two models for treating the effects of the neglected bulk solvent are then considered. The tethered water (TW) model is characterized by the use of harmonic restraining potentials to tether the water molecules to their initial (bulk solvent) positions; whereas, in the capped water (CW) model, water molecules are prevented from escaping from the solvent shell by the use of half-harmonic potentials, but otherwise their motions within the solvation shell are unrestrained. As measured by overall rms differences between coordinates, the distribution of solvent molecules in the active-site region, and the numbers of hydrogen bonds, the TW model compares favorably with the CW model but requires far fewer water molecules, i.e., relatively small solvent shells. The smaller shells of unrestrained water (CW model) gave rise to a distortion in the orientation of the side chain of the active-site residue Tyr-31, whereas no such distortion was apparent in the TW model or for the larger solvent shells in the CW model. A value for the force constant of 0.005 kcal/mol/Å2 for the tethering potential [Solmajer and Mehler, Int. J. Quant. Chem., 44, 291 (1992)] gave satisfactory results for DHFR, although we found that distance-dependent dielectric functions were unable to reproduce accurately the effects of the explicit water models. The free-energy change for the mutation of 8-methyl-N5-deazapterin to 8-methylpterin was computed using both nonsolvated and solvated models. The solvated models gave free energy differences about 1 kcal/mol lower than for nonsolvated models, but the differences between solvated models was much less than 1 kcal/mol. Overall, the calculated differences in thermodynamic stability of the deazapterin and pterin complexes are in fair agreement with experiment, i.e., a small binding differential is predicted. © 1996 by John Wiley & Sons, Inc.     

The implementation of a fast and accurate QM/MM potential method in Amber

Version 9 of the Amber simulation programs includes a new semi-empirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run constant energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semi-empirical Hamiltonians as well as the self-consistent charge density functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.     

Photoinduced intramolecular charge transfer reaction in (E)-3-(4-Methylamino-phenyl)-acrylic acid methyl ester: A fluorescence study in combination with TDDFT calculation

A donor-acceptor substituted aromatic system (E)-3-(4-Methylamino-phenyl)-acrylic acid methyl ester (MAPAME) has been synthesized, and its photophysical behavior obtained spectroscopically has been compared with the theoretical results. The observed dual fluorescence from MAPAME has been assigned to emission from locally excited and twisted intramolecular charge transfer states. The donor and acceptor angular dependency on the ground and excited states potential energy surfaces have been calculated both in vacuo and in acetonitrile solvent using time dependent density functional theory (TDDFT) and TDDFT polarized continuum model (TDDFT-PCM), respectively. Calculation predicts that a stabilized twisted excited state is responsible for red shifted charge transfer emission.     

QM/MM investigation of the degradation mechanism of the electron-transporting layer

The mechanism of charge transfer among tris(8-hydroxyquinolinate)aluminum (Alq₃) molecules in the electron-transporting layer (ETL) under amorphous conditions was theoretically investigated using both quantum mechanical/molecular mechanical (QM/MM) calculations and molecular dynamics (MD) simulations. The rate constant of the electron transfer was estimated for the equilibrated structure taken from the QM/MM MD simulations, based on the hopping model and Marcus theory. It was found that the coordination of a (LiF)₄ cluster in ETL drastically lowers the energy of the lowest unoccupied molecular orbital in the Alq₃ molecule. The small rate constant, namely the slow charge mobility, in ETL is believed to be causally related to the low-lying delocalized unoccupied molecular orbital of Alq₃ coordinated by the (LiF)₄ cluster. The results suggest that their interaction has a considerable influence on efficiency and is attributed in part to ETL degradation in organic light-emitting diodes.