The reweighted path ensemble

We introduce a reweighting scheme for the path ensembles in the transition interface sampling framework. The reweighting allows for the analysis of free energy landscapes and committor projections in any collective variable space. We illustrate the reweighting scheme on a two dimensional potential with a nonlinear reaction coordinate and on a more realistic simulation of the Trp-cage folding process. We suggest that the reweighted path ensemble can be used to optimize possible nonlinear reaction coordinates.     

Quantum dynamics study of fulvene double bond photoisomerization: the role of intramolecular vibrational energy redistribution and excitation energy

The double bond photoisomerization of fulvene has been studied with quantum dynamics calculations using the multi-configuration time-dependent Hartree method. Fulvene is a test case to develop optical control strategies based on the knowledge of the excited state decay mechanism. The decay takes place on a time scale of several hundred femtoseconds, and the potential energy surface is centered around a conical intersection seam between the ground and excited state. The competition between unreactive decay and photoisomerization depends on the region of the seam accessed during the decay. The dynamics are carried out on a four-dimensional model surface, parametrized from complete active space self-consistent field calculations, that captures the main features of the seam (energy and locus of the seam and associated branching space vectors). Wave packet propagations initiated by single laser pulses of 5-25 fs duration and 1.85-4 eV excitation energy show the principal characteristics of the first 150 fs of the photodynamics. Initially, the excitation energy is transferred to a bond stretching mode that leads the wave packet to the seam, inducing the regeneration of the reactant. The photoisomerization starts after the vibrational energy has flowed from the bond stretching to the torsional mode. In our propagations, intramolecular energy redistribution (IVR) is accelerated for higher excess energies along the bond stretch mode. Thus, the competition between unreactive decay and isomerization depends on the rate of IVR between the bond stretch and torsion coordinates, which in turn depends on the excitation energy. These results set the ground for the development of future optical control strategies.     

Some formal properties of ensemble density functionals

Formal properties of ensemble density functionals are examined. Expressions for the difference between energy functionals where the particle number differs by one are constructed in terms of their first functional derivatives for the universal energy functional, the electron–electron repulsion energy functional, and the interacting kinetic energy functional. Equations that must be satisfied by second and higher order functional derivatives are derived. It is also shown that the shape of ${\delta V_{ee}[\rho]\over\delta\rho({\bf r})}$ and ${\delta K[\rho]\over\delta\rho({\bf r})}$ , the functional derivatives of the mutual electron–electron repulsion, and kinetic energy, respectively, are separately particle number independent for particle numbers between successive integers. © 2013 Wiley Periodicals, Inc.     

Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C(3))- or four (T(d), tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by F?rster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.     

Energy transfer in polymers and nitroxide decay during photolysis

When polymeric materials doped with nitroxides of the 2,2,6,6-tetramethylpiperidine type are exposed to light, the nitroxide concentration decreases. The two mechanisms for the decrease of the nitroxide are the reaction of nitroxide with free radicals produced during photolysis of the polymer to form amino ethers and the abstraction of hydrogen atoms by excited-state nitroxides to form hydroxyl amines. Excited-state nitroxides can be formed in two ways: by direct absorption and by energy transfer. In this paper, the effect of energy transfer on the rate of decay of the nitroxide signal is studied, and measurements of nitroxide decay are used to probe energy transfer in crosslinked polymeric coatings. A simple kinetic scheme is used to interpret nitroxide decay during photolysis of both solutions and polymers containing benzophenone. These results are used to show that the slope of the line relating nitroxide decay rate to nitroxide concentration is essentially determined by energy transfer from a coating-based chromophore to nitroxide. The nitroxide decay assay is also used to study the effectiveness of a benzotriazole ultraviolet light absorber as a quencher.     

Trapping time statistics and efficiency of transport of optical excitations in dendrimers

We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as a probe of the efficiency of the energy transport across the dendrimer. The transport process is treated as incoherent hopping of excitations between nearest-neighbor dendrimer units and is described using a rate equation. We account for radiative and nonradiative decay of the excitations while diffusing across the dendrimer. We derive exact expressions for the Laplace transform of the trapping time distribution and the efficiency of trapping, and analyze those for various realizations of the energy bias, number of dendrimer generations, and relative rates for decay and hopping. We show that the essential parameter that governs the trapping efficiency is the product of the on-site excitation decay rate and the trapping time (mean first passage time) in the absence of decay.     

Molecular dynamics simulation in the grand canonical ensemble

An extended system Hamiltonian is proposed to perform molecular dynamics (MD) simulation in the grand canonical ensemble. The Hamiltonian is similar to the one proposed by Lynch and Pettitt (Lynch and Pettitt, J Chem Phys 1997, 107, 8594), which consists of the kinetic and potential energies for real and fractional particles as well as the kinetic and potential energy terms for material and heat reservoirs interacting with the system. We perform a nonlinear scaling of the potential energy parameters of the fractional particle, as well as its mass to vary the number of particles dynamically. On the basis of the equations of motion derived from this Hamiltonian, an algorithm has been proposed for MD simulation at constant chemical potential. The algorithm has been tested for the ideal gas, for the Lennard-Jones fluid over a wide range of temperatures and densities, and for water. The results for the low-density Lennard-Jones fluid are compared with the predictions from a truncated virial equation of state. In the case of the dense Lennard-Jones fluid and water our predicted results are compared with the results reported using other available methods for the calculation of the chemical potential. The method is also applied to the case of vapor-liquid coexistence point predictions.     

On the origin of the ultrafast internal conversion of electronically excited pyrimidine bases

The ultrafast radiationless decay of photoexcited uracil and cytosine has been investigated by ab initio quantum chemical methods based on CIS and CR-EOM-CCSD(T) electronic energy calculations at optimized CIS geometries. The calculated potential energy profiles indicate that the S(1) --> S(0) internal conversion of the pyrimidine bases occurs through a barrierless state switch from the initially excited (1)pipi state to the out-of-plane deformed excited state of biradical character, which intersects the ground state at a lower energy. This three-state nonradiative decay mechanism predicts that replacement of the C5 hydrogen by fluorine introduces an energy barrier for the initial state switch, whereas replacement of the C6 hydrogen by fluorine does not. These predictions are borne out by the very different fluorescence yields of 5-fluorinated bases relative to the corresponding 6-fluorinated bases. It is concluded from these results that the origin of the ultrafast radiationless decay is the same for the two pyrimidine bases.     

Pressure derivatives in the classical molecular-dynamics ensemble

The calculation of thermodynamic state variables, particularly derivatives of the pressure with respect to density and temperature, in conventional molecular-dynamics simulations is considered in the frame of the comprehensive treatment of the molecular-dynamics ensemble by Lustig [J. Chem. Phys. 100, 3048 (1994)]. This paper improves the work of Lustig in two aspects. In the first place, a general expression for the basic phase-space functions in the molecular-dynamics ensemble is derived, which takes into account that a mechanical quantity G is, in addition to the number of particles, the volume, the energy, and the total momentum of the system, a constant of motion. G is related to the initial position of the center of mass of the system. Secondly, the correct general expression for volume derivatives of the potential energy is derived. This latter result solves a problem reported by Lustig [J. Chem. Phys. 109, 8816 (1998)] and Meier [Computer Simulation and Interpretation of the Transport Coefficients of the Lennard-Jones Model Fluid (Shaker, Aachen, 2002)] and enables the correct calculation of the isentropic and isothermal compressibilities, the speed of sound, and, in principle, all higher pressure derivatives. The derived equations are verified by calculations of several state variables and pressure derivatives up to second order by molecular-dynamics simulations with 256 particles at two state points of the Lennard-Jones fluid in the gas and liquid regions. It is also found that it is impossible for systems of this size to calculate third- and higher-order pressure derivatives due to the limited accuracy of the algorithm employed to integrate the equations of motion.     

Production of 35S for a liquid semiconductor betavoltaic

The specific energy density from radioactive decay is five to six orders of magnitude greater than the specific energy density in conventional chemical battery and fuel cell technologies. We are currently investigating the use of liquid semiconductor based betavoltaics as a way to directly convert the energy of radioactive decay into electrical power and potentially avoid the radiation damage that occurs in solid state semiconductor devices due to non-ionizing energy loss. Sulfur-35 was selected as the isotope for the liquid semiconductor demonstrations because it can be produced in high specific activity and is chemically compatible with known liquid semiconductor media.     

The energy gap law for triplet states in Pt-containing conjugated polymers and monomers

The energy gap law established for aromatic hydrocarbons and rare earth ions relates the nonradiative decay rate to the energy gap of a transition through a multiphonon emission process. We show that this energy gap law can be applied to the phosphoresce of a series of conjugated polymers and monomers for which the radiative decay rate has been enhanced through incorporation of a heavy metal. We find that the nonradiative decay rate from the triplet state T(1) increases exponentially with decreasing T(1)-S(0) gap for the polymers and monomers at 300 and 20 K. Comparison of the nonradiative decay of polymers with that of their corresponding monomers highlights the role of electron-lattice coupling.     

Inhomogeneous dephasing masks coherence lifetimes in ensemble measurements

An open question at the forefront of modern physical sciences is what role, if any, quantum effects may play in biological sensing and energy transport mechanisms. One area of such research concerns the possibility of coherent energy transport in photosynthetic systems. Spectroscopic evidence of long-lived quantum coherence in photosynthetic light-harvesting pigment protein complexes (PPCs), along with theoretical modeling of PPCs, has indicated that coherent energy transport might boost efficiency of energy transport in photosynthesis. Accurate assessment of coherence lifetimes is crucial for modeling the extent to which quantum effects participate in this energy transfer, because such quantum effects can only contribute to mechanisms proceeding on timescales over which the coherences persist. While spectroscopy is a useful way to measure coherence lifetimes, inhomogeneity in the transition energies across the measured ensemble may lead to underestimation of coherence lifetimes from spectroscopic experiments. Theoretical models of antenna complexes generally model a single system, and direct comparison of single system models to ensemble averaged experimental data may lead to systematic underestimation of coherence lifetimes, distorting much of the current discussion. In this study, we use simulations of the Fenna-Matthews-Olson complex to model single complexes as well as averaged ensembles to demonstrate and roughly quantify the effect of averaging over an inhomogeneous ensemble on measured coherence lifetimes. We choose to model the Fenna-Matthews-Olson complex because that system has been a focus for much of the recent discussion of quantum effects in biology, and use an early version of the well known environment-assisted quantum transport model to facilitate straightforward comparison between the current model and past work. Although ensemble inhomogeneity is known to lead to shorter lifetimes of observed oscillations (simply inhomogeneous spectral broadening in the time domain), this important fact has been left out of recent discussions of spectroscopic measurements of energy transport in photosynthesis. In general, these discussions have compared single-system theoretical models to whole-ensemble laboratory measurements without addressing the effect of inhomogeneous dephasing. Our work addresses this distinction between single system and ensemble averaged observations, and shows that the ensemble averaging inherent in many experiments leads to an underestimation of coherence lifetimes in individual systems.     

Molecular-dynamics simulation of argon nucleation from supersaturated vapor in the NVE ensemble

The possibility to conduct simulations of homogeneous nucleation of argon from a supersaturated vapor phase using a microcanonical or NVE ensemble is evaluated (NVE: number of particles N, volume V, and energy E are constant). In order to initiate a phase separation kinetic energy is removed from the system in one step which transfers the system into a supersaturated state. After this temperature jump the simulation is continued in a NVE ensemble. The simulations are performed for different initial-state points and different temperature jumps. The cluster formation and growth over the course of the adiabatic simulations are analyzed. The progression of the temperature being related to the cluster size in NVE systems is traced. Also the influence of the size of the simulation system is investigated. For a certain range of low supersaturation a dynamic coexistence between two states has been found. Furthermore, the obtained nucleation rates are correlated with two simple functions. By applying the nucleation theorems to these functions the size and excess energy of the critical cluster are estimated. The results are consistent with other theoretical data and experimental data available in the literature.     

Photophysics of soret-excited tetrapyrroles in solution. II. Effects of perdeuteration, substituent nature and position, and macrocycle structure and conformation in zinc(II) porphyrins

The steady-state absorption, fluorescence, and excitation spectra and upper excited-state temporal fluorescence decay profiles of 11 tetrapyrroles in several fluid solvents are presented and analyzed to ascertain the factors that control their S2 population decay times. The S2 lifetimes, which vary by more than 2 orders of magnitude, are controlled exclusively by their rates of radiationless decay. The only important electronic relaxation path is S2-S1 internal conversion, the efficiency of which is near 1.0 in all compounds studied (except CdTPP where it is 0.69). The rate of S1 population rise equals the rate of S2 population decay in all cases. Among the compounds studied, only MgTPP exhibits S2-S1 decay behavior that corresponds to the weak coupling limit of radiationless transition theory; all zinc metalloporphyrins exhibit intermediate to strong coupling. Perdeuteration of ZnTPP produces no significant change in the rate of S2 decay or in the quantum yield of S2-S0 fluorescence, indicating that in-plane C-C and C-N vibrations are the accepting modes in S1 with the largest Franck-Condon factors. The initial vibrational energy content of the S2 states (0 < E(vib) < 3500 cm(-1) over the range of compounds) plays no significant role in determining their overall population decay rates in solution. The S2 population decay rates of these tetrapyrroles are controlled by two factors: the Franck-Condon factor, which is inversely proportional to the exponent of the S2-S1 electronic energy spacing and the S2-S1 coupling energy. The S2-S1 electronic energy spacing is determined in solution by the difference in the polarizabilities of the S2 and S1 states and can be controlled by varying the polarizability of the solvent. The S2-S1 coupling energy is influenced by the nature, location, and effect of the substituents, with beta-alkyl substitution and reduction of symmetry in the tetrapyrrole--for example by loss of planarity--increasing the interstate coupling energy.     

Molecular dynamics calculation of half-lives for thermal decay of Lennard-Jones clusters

Molecular dynamics has been used with a Lennard-Jones (6–12) potential in order to study the decay behavior of neutral Argon clusters containing between 12 and 14 atoms. The clusters were heated to temperatures well above their melting points and then tracked in time via molecular dynamics until evaporation of one or more atoms was observed. In each simulation, the mode of evaporation, energy released during evaporation, and cluster lifetime were recorded. Results from roughly 2000 simulation histories were combined in order to compute statistically significant values of cluster half-lives and decay energies. It was found that cluster half-life decreases with increasing energy and that for a given value of excess energy (defined asE=(E _tot ?E _gnd)/n), the 13 atom cluster is more stable against decay than clusters containing either 12 or 14 atoms. The dominant decay mechanism for all clusters was determined to be single atom emission.     

Competitive partitioning of rotational energy in gas ensemble equilibration

A wide-ranging computational study of equilibration in binary mixtures of diatomic gases reveals the existence of competition between the constituent species for the orbital angular momentum and energy available on collision with the bath gas. The ensembles consist of a bath gas AB(v;j), and a highly excited minor component CD(v';j'), present in the ratio AB:CD = 10:1. Each ensemble contains 8000 molecules. Rotational temperatures (T(r)) are found to differ widely at equilibration with T(r)(AB)/T(r)(CD) varying from 2.74 to 0.92, indicating unequal partitioning of rotational energy and angular momentum between the two species. Unusually, low values of T(r) are found generally to be associated with diatomics of low reduced mass. To test effects of the equi-partition theorem on low T(r) we undertook calculations on HF(6;4) in N(2)(0;10) over the range 100-2000 K. No significant change in T(r)(N2)/T(r)(HF) was found. Two potential sources of rotational inequality are examined in detail. The first is possible asymmetry of -Δj and +Δj probabilities for molecules in mid- to high j states resulting from the quadratic dependence of rotational energy on j. The second is the efficiency of conversion of orbital angular momentum, generated on collision with bath gas molecules, into molecular rotation. Comparison of these two possible effects with computed T(r)(AB)/T(r)(CD) shows the efficiency factor to be an excellent predictor of partitioning between the two species. Our finding that T(r) values for molecules such as HF and OH are considerably lower than other modal temperatures suggests that the determination of gas ensemble temperatures from Boltzmann fits to rotational distributions of diatomics of low reduced mass may require a degree of caution.     

Influence of pressure of free radical decay in irradiated polyethylene

Information is given on the effect of high pressure on the decay of free radicals in irradiated polyethylene. The dependence of the rate constant for decay on pressure (1–13,000 atm) was determined at 80, 90, 100 and 110°. The mechanism of the effect of pressure on the rate constant and activation energy for free radical decay is discussed.     

Algorithms for sampling a quantum microcanonical ensemble of harmonic oscillators at potential minima and conical intersections

Algorithms are presented for sampling quantum microcanonical ensembles for a potential energy minimum and for the conical intersection at the minimum energy crossing point of two coupled electronic states. These ensembles may be used to initialize trajectories for chemical dynamics simulations. The unimolecular dynamics of a microcanonical ensemble about a potential energy minimum may be compared with the dynamics predicted by quantum Rice-Ramsperger-Kassel-Marcus (RRKM) theory. If the dynamics is non-RRKM, it will be of particular interest to determine which states have particularly long lifetimes. Initializing a microcanonical ensemble for the electronically excited state at a conical intersection is a model for electronic nonadiabatic dynamics. The trajectory surface-hopping approach may be used to study the ensuing chemical dynamics. A strength of the model is that zero-point energy conditions are included for the initial nonadiabatic dynamics at the conical intersection.     

Effect of High Order Coulombic Interaction on Radiationless Resonance Transfer of Electronic Excitation

The decay of sensitizer phosphorescence in a rigid solution modified by the electronic energy transfer by the mechanism of dipole-dipole interaction mixing with the dipole-quadrupole interaction is proposed. The rate constant for the transfer process transfer process as (equation).where (equation). Calculations are made of the yield and the decay time of the sensitizer phosphorescence as functions of the activator concentration and the mixing coefficient of dipole-dipole interaction with dipole-quadrupole interaction. It is hoped that the proposed mechanism will provide a sound, quantitative basis for analyzing experimental data in a triplet-singlet energy transfer process. As a demonstration, results indicate that about 9% of the electronic energy radiationlessly transferred from triplet triphenylene-d₁₂ to singlet Rhodamine B is induced by the electric dipole-quadrupole coulombic interaction.