Solvent effects on intramolecular charge transfer dynamics in a fullerene derivative.

We present a real-time time-dependent density functional theory (RT-TDDFT) investigation of exciton dynamics in a C60 derivative, including solvent effects in the real-time time-dependent polarizable continuum model (RT-TDPCM). Dynamical simulations are carried out to gauge the ability of solvents to enhance ligand-to-fullerene charge transfer following photoexcitation. Solvent stabilization of charge transfer states and solute-solvent interactions lead to nonintuitive changes in electron-hole dynamics. An amplification factor of 1.5 in the molecular dipole oscillation, a measure of charge transfer, is achieved by inclusion of a time-dependent solvent environment.

Modeling ultrafast solvated electronic dynamics using time-dependent density functional theory and polarizable continuum model.

A first-principles solvated electronic dynamics method is introduced. Solvent electronic degrees of freedom are coupled to the time-dependent electronic density of a solute molecule by means of the implicit reaction field method, and the entire electronic system is propagated in time. This real-time time-dependent approach, incorporating the polarizable continuum solvation model, is shown to be very effective in describing the dynamical solvation effect in the charge transfer process and yields a consistent absorption spectrum in comparison to the conventional linear response results in solution.

Mechanisms of bridge-mediated electron transfer: a TDDFT electronic dynamics study.

We present a time-dependent density functional theory approach for probing the dynamics of electron transfer on a donor-bridge-acceptor polyene dye scaffold. Two kinds of mechanisms, namely, the superexchange mechanism and the sequential mechanism, may be involved in the electron transfer process. In this work, we have focused on the crossover between these two charge transfer mechanisms on a series of donor-bridge-acceptor polyene dye systems with varying lengths of conjugated bridges. A number of methods and quantities are used to assist in the analysis, including the phase relationship of charge evolution and frequency domain spectra of the time-dependent dipole. Our simulations show that the superexchange mechanism plays a dominant role in the electron transfer from donor to acceptor when the bridge length is small, and the sequential mechanism becomes more important as the polyene bridge is lengthened. Full Ehrenfest dynamics with nuclear motion show that molecular vibrations play a very small role in such ultrafast charge transfer processes.

Open-system electronic dynamics and thermalized electronic structure.

We propose and implement a novel computational method for simulating open-system electronic dynamics and obtaining thermalized electronic structures within an open quantum system framework. The system-bath interaction equation of motion is derived and modeled from the local harmonic oscillator description for electronic density change. The nonequilibrium electronic dynamics in a thermal bath is simulated using first-order kinetics. The resultant electronic densities are temperature-dependent and can take characteristics of the ground and excited states. We present results of calculations performed on H(2) and 1,3-butadiene performed at the Hartree-Fock level of theory using a minimal Slater-type orbital basis set.

Efficient first-principles electronic dynamics.

An efficient first-principles electronic dynamics method is introduced in this article. The approach we put forth relies on incrementally constructing a time-dependent Fock∕Kohn-Sham matrix using active space density screening method that reduces the cost of computing two-electron repulsion integrals. An adaptive stepsize control algorithm is developed to optimize the efficiency of the electronic dynamics while maintaining good energy conservation. A selected set of model dipolar push-pull chromophore molecules are tested and compared with the conventional method of direct formation of the Fock∕Kohn-Sham matrix. While both methods considered herein take on identical dynamical simulation pathways for the molecules tested, the active space density screening algorithm becomes much more computationally efficient. The adaptive stepsize control algorithm, when used in conjunction with the dynamically active space method, yields a factor of ∼3 speed-up in computational cost as observed in electronic dynamics using the time dependent density functional theory. The total computational cost scales nearly linear with increasing size of the molecular system.

On the gauge invariance of nonperturbative electronic dynamics using the time-dependent Hartree-Fock and time-dependent Kohn-Sham.

Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.

Time-dependent density functional theory calculations of Ehrenfest dynamics of laser controlled dissociation of NO+: pulse length and sequential multiple single-photon processes.

Intense laser field controlled dissociation reactions of the nitric oxide cation (NO(+)) are studied by ab initio Ehrenfest dynamics with time-dependent density functional theory. Intense electric fields with five different pulse lengths are compared, combined with potential energy surface and density of state analysis, to reveal the effect of pulse length on the control mechanism. Controllable dissociative charge states are observed, and the correlation between the laser pulse length and the probability of sequential multiple single-photon processes is presented. This work introduces a concept of using laser pulse length to control the sequential multiple single-photon process.

Laser-controlled dissociation of C2H2(2+): Ehrenfest dynamics using time-dependent density functional theory.

Intense laser field dissociations of the acetylene dication C(2)H(2)(2+) are studied by an ab initio Ehrenfest dynamics method with time-dependent density functional theory. Various field frequencies (9.5 to approximately 13.6 eV) and field directions are applied to a Boltzmann ensemble of C(2)H(2)(2+) molecules. With the laser field perpendicular to the molecular axis, four fragmentation channels are observed at high frequency with no dominant pathway. With the field parallel to the molecular axis, fragmentations occur at all frequencies and the amount of C-H bond breakage increases with laser frequency. Selective dissociation patterns are observed with low-frequency fields parallel to the molecular axis. A systematic analysis of excited-state potential energy surfaces is used to rationalize the simulation results.

Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search.

The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the alpha and beta electrons to achieve the two-electron excited states of minimal basis H(2) and HeH(+) [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H(2), HeH(+), lithium hydride, ethylene, and butadiene.

Car-Parrinello density matrix search with a first principles fictitious electron mass method for electronic wave function optimization.

In spite of its success in molecular dynamics and the advantage of being a first order propagation technique, the Car-Parrinello method and its variations have not been successful in self-consistent-field (SCF) wave function optimization due to slow convergence. In this article, we introduce a first principles fictitious mass scheme to weigh each individual density element differently and instantaneously. As an alternative to diagonalization in SCF, the Car-Parrinello scheme is implemented as a density matrix search method. Not only does the fictitious mass scheme developed herein allow a very fast SCF convergence, but also the Car-Parrinello density matrix search (CP-DMS) exhibits linear scaling with respect to the system size for alanine helical chain test molecules. The excellent performance of CP-DMS holds even for very challenging compact three-dimensional quantum particles. While the conventional diagonalization based SCF method has difficulties optimizing electronic wave functions for CdSe quantum dots, CP-DMS shows both smooth and faster convergence.

Using beta binomials to estimate classification uncertainty for ensemble models.

BACKGROUND: Quantitative structure-activity (QSAR) models have enormous potential for reducing drug discovery and development costs as well as the need for animal testing. Great strides have been made in estimating their overall reliability, but to fully realize that potential, researchers and regulators need to know how confident they can be in individual predictions. RESULTS: Submodels in an ensemble model which have been trained on different subsets of a shared training pool represent multiple samples of the model space, and the degree of agreement among them contains information on the reliability of ensemble predictions. For artificial neural network ensembles (ANNEs) using two different methods for determining ensemble classification - one using vote tallies and the other averaging individual network outputs - we have found that the distribution of predictions across positive vote tallies can be reasonably well-modeled as a beta binomial distribution, as can the distribution of errors. Together, these two distributions can be used to estimate the probability that a given predictive classification will be in error. Large data sets comprised of logP, Ames mutagenicity, and CYP2D6 inhibition data are used to illustrate and validate the method. The distributions of predictions and errors for the training pool accurately predicted the distribution of predictions and errors for large external validation sets, even when the number of positive and negative examples in the training pool were not balanced. Moreover, the likelihood of a given compound being prospectively misclassified as a function of the degree of consensus between networks in the ensemble could in most cases be estimated accurately from the fitted beta binomial distributions for the training pool. CONCLUSIONS: Confidence in an individual predictive classification by an ensemble model can be accurately assessed by examining the distributions of predictions and errors as a function of the degree of agreement among the constituent submodels. Further, ensemble uncertainty estimation can often be improved by adjusting the voting or classification threshold based on the parameters of the error distribution. Finally, the profiles for models whose predictive uncertainty estimates are not reliable provide clues to that effect without the need for comparison to an external test set.

The early life of a peptide cation-radical. Ground and excited-state trajectories of electron-based peptide dissociations during the first 330 femtoseconds.

We report a new approach to investigating the mechanisms of fast peptide cation-radical dissociations based on an analysis of time-resolved reaction progress by Ehrenfest dynamics, as applied to an Ala-Arg cation-radical model system. Calculations of stationary points on the ground electronic state that were carried out with effective CCSD(T)/6-311++G(3df,2p) could not explain the experimental branching ratios for loss of a hydrogen atom, ammonia, and N-C(α) bond dissociation in (AR + 2H)(+•). The Ehrenfest dynamics results indicate that the ground and low-lying excited electronic states of (AR + 2H)(+•) follow different reaction courses in the first 330 femtoseconds after electron attachment. The ground (X) state undergoes competing loss of N-terminal ammonia and isomerization to an aminoketyl radical intermediate that depend on the vibrational energy of the charge-reduced ion. The A and B excited states involve electron capture in the Arg guanidine and carboxyl groups and are non-reactive on the short time scale. The C state is dissociative and progresses to a fast loss of an H atom from the Arg guanidine group. Analogous results were obtained by using the B3LYP and CAM-B3LYP density functionals for the excited state dynamics and including the universal M06-2X functional for ground electronic state calculations. The results of this Ehrenfest dynamics study indicate that reaction pathway branching into the various dissociation channels occurs in the early stages of electron attachment and is primarily determined by the electronic states being accessed. This represents a new paradigm for the discussion of peptide dissociations in electron based methods of mass spectrometry.

Ultrafast Coherent Electron-Hole Separation Dynamics in a Fullerene Derivative.

The use of fullerene derivatives as electron donors in bulk heterojunctions is a promising development in the search for efficient energy conversion in hybrid solar cells. A long-lived photoexcited electron-hole pair will give rise to increased efficiency in photoenergy conversion. One way to prevent fast electron-hole recombination is to engineer fullerene derivatives that exhibit intrinsic electron-hole separation through accessible charge-transfer excited states. In this letter, the dynamics of photoexcited electron-hole pairs in a C60 derivative is studied using the real-time time-dependent density functional theory. Although the charge-transfer excited state is not directly accessible from the ground state, intrinsic coherent electron-hole separation is observed following photoexcition as a result of direct coupling between excited states. Ultrafast charge-transfer dynamics is the dominant phenomenon in <60 fs after visible photoexcitation. This work provides insights into the characteristics of ultrafast dynamics in photoexcited fullerene derivatives, and aids in the rational design of efficient solar cells.

Solvents level dipole moments.

The dipole moments of highly polar molecules measured in solution are usually smaller than the molecular dipole moments that are calculated with reaction field methods, whereas vacuum values are routinely calculated in good agreement with available vapor phase data. Whether from Onsager's theory (or variations thereof) or from quantum mechanical methods, the calculated molecular dipoles in solution are found to be larger than those measured. The reason, of course, is that experiments measure the net dipole moment of solute together with the polarized (perturbed) solvent "cloud" surrounding it. Here we show that the reaction field charges that are generated in the quantum mechanical self-consistent reaction field (SCRF) method give a good estimate of the net dipole moment of the solute molecule together with the moment arising from the reaction field charges. This net dipole is a better description of experimental data than the vacuum dipole moment and certainly better than the bare dipole moment of the polarized solute molecule.

Energy-Specific Linear Response TDHF/TDDFT for Calculating High-Energy Excited States.

An energy-specific TDHF/TDDFT method is introduced in this article for excited state calculations. This approach extends the conventional TDHF/TDDFT implementation to obtain excited states above a predefined energy threshold. The method introduced and developed in this work enables computationally efficient yet rigorous calculations of energy-specific spectra, e.g., X-ray absorption involving extremely high-energy transitions. All transitions are solved in the full molecular orbital space, and orthogonality to the ground state and lower-lying excited states is preserved for each high-energy excited state. Encouraging computational savings are observed in calculating the targeted energy spectrum, while the transition energies, as well as oscillator strengths, remain identical to the results from the standard implementation.

Dielectric dependence of the first molecular hyperpolarizability for electro-optic chromophores.

Experimental and computational studies of the solvent dependence of the first molecular hyperpolarizability (ß) for two donor-bridge-acceptor chromophores (CLD-1 and YLD156) are presented. Hyper-Rayleigh scattering (HRS) measurements are performed with 1907 nm excitation in a series of solvents with dielectric constants ranging from ~2 (toluene) to ~36 (acetonitrile). For both chromophores an approximately 2-fold increase in ß is observed by HRS over this range of dielectric constants. Computational studies employing a polarized continuum model to represent the solvent are capable of reproducing this experimental result. The experimental and computational results are compared to the predictions of the widely employed two-state model (TSM) for ß. Surprisingly, for the chromophores studied here the TSM predicts that ß should decrease with increasing dielectric constant over the range investigated. The results presented here demonstrate that the TSM provides neither a quantitative nor qualitative description of the solvent dependence of ß for CLD-1 and YLD156. The enhancement of ß with increased dielectric constant suggests that modification of the dielectric surrounding the chromophore is one path by which the performance of nonlinear optical devices employing these chromophores may be significantly enhanced.

Eigenspace Update for Molecular Geometry Optimization in Nonredundant Internal Coordinate.

An eigenspace update method is introduced in this article for molecular geometry optimization. This approach is used to obtain the nonredundant internal coordinate space and diagonalize the Hessian matrix. A select set of large molecules is tested and compared with the conventional method of direct diagonalization in redundant space. While all methods considered herein take on similar optimization pathways for most molecules tested, the eigenspace update algorithm becomes much more computationally efficient with increasing size of the molecular system. A factor of 3 speed-up in overall computational cost is observed in geometry optimization of the 25-alanine chain molecule. The contributing factors to the computational savings are the reduction to the much smaller nonredundant coordinate space and the O(N(2)) scaling of the algorithm.

Geometry Optimization with Multilayer Methods Using Least-Squares Minimization.

In this article, we introduce a least-squares minimization scheme for optimizing molecular structures with mixed quantum mechanics (QM) and molecular mechanics (MM) multilayer models. A mixed-coordinate optimization framework was developed. The QM and MM regions are modeled with redundant internal coordinates and Cartesian coordinates, respectively. Within this mixed-coordinate system, a least-squares minimization method using the quasi-Newton step as the evaluation of error is constructed. The couplings between layers are treated rigidly in accordance with the mechanical embedding approach, and the MM Hessian is approximated as a scalar constant of the root-mean-square QM Hessian eigenvalues. Both two-layer and three-layer models were tested. The performance of the method developed herein shows consistently stable and fast convergence.