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Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au 20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au 20 beyond the Born-Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au 20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7 ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au 20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ∼10.4 fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process.

Nonadiabatic excited state molecular dynamics underpin many photophysical and photochemical phenomena, such as exciton dynamics, and charge separation and transport. In this work, we present an efficient nonadiabatic molecular dynamics (NAMD) simulation method based on time-dependent density functional tight-binding (TDDFTB) theory. Specifically, the adiabatic electronic structure, an essential NAMD input, is described at the TDDFTB level. The nonadiabatic effects originating from the coupled motions of electrons and nuclei are treated by the trajectory surface hopping algorithm. To improve the computational efficiency, nonadiabatic couplings between excited states within the TDDFTB method are derived and implemented using an analytical approach. Furthermore, the time-dependent nonadiabatic coupling scalars are calculated based on the overlap between molecular orbitals rather than the Slater determinants to speed up the simulations. In addition, the electronic decoherence scheme and a state reassigned unavoided crossings algorithm, which has been implemented in the NEXMD software, are used to improve the accuracy of the simulated dynamics and handle trivial unavoided crossings. Finally, the photoinduced nonadiabatic dynamics of a benzene molecule are simulated to demonstrate our implementation. The results for excited state NAMD simulations of benzene molecule based on TDDFTB method compare well to those obtained with numerically expensive time-dependent density functional theory. The proposed methodology provides an attractive theoretical simulation tool for predicting the photophysical and photochemical properties of complex materials.

The Hückel Hamiltonian is an incredibly simple tight-binding model known for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only two types of empirically fit physics-motivated parameters: the first describes the orbital energies on each atom and the second describes electronic interactions and bonding between atoms. By replacing these empirical parameters with machine-learned dynamic values, we vastly increase the accuracy of the extended Hückel model. The dynamic values are generated with a deep neural network, which is trained to reproduce orbital energies and densities derived from density functional theory. The resulting model retains interpretability, while the deep neural network parameterization is smooth and accurate and reproduces insightful features of the original empirical parameterization. Overall, this work shows the promise of utilizing machine learning to formulate simple, accurate, and dynamically parameterized physics models.

Simulation of electronic dynamics in realistically large molecular systems is a demanding task that has not yet achieved the same level of quantitative prediction already realized for its static counterpart. This is particularly true for processes occurring beyond the Born-Oppenheimer regime. Non-adiabatic molecular dynamics (NAMD) simulations suffer from two convoluted sources of error: numerical algorithms for dynamics and electronic structure calculations. While the former has gained increasing attention, particularly addressing the validity of ad hoc methodologies, the effect of the latter remains relatively unexplored. Indeed, the required accuracy for electronic structure calculations to reach quantitative agreement with experiment in dynamics may be even more strict than that required for static simulations. Here, we address this issue by modeling the electronic energy transfer in a donor-acceptor-donor (D-A-D) molecular light harvesting system using fewest switches surface hopping NAMD simulations. In the studied system, time-resolved experimental measurements deliver complete information on spectra and energy transfer rates. Subsequent modeling shows that the calculated electronic transition energies are "sufficiently good" to reproduce experimental spectra but produce over an order of magnitude error in simulated dynamical rates. We further perform simulations using artificially shifted energy gaps to investigate the complex relationship between transition energies and modeled dynamics to understand factors affecting non-radiative relaxation and energy transfer rates.

We utilize first-principles theory to investigate photo-induced excited-state dynamics of functionalized perylene diimide. This class of materials is highly suitable for solar energy conversion because of the strong optical absorbance, efficient energy transfer, and chemical tunability. We couple time-dependent density functional theory to a recently developed time-resolved non-adiabatic dynamics approach based on a semi-empirical description. By studying the monomer and dimer, we focus on the role stacking plays on the time-scales associated with excited-state non-radiative relaxation from a high excitonic state to the lowest energy exciton. We predict that the time-scale for energy conversion in the dimer is significantly faster than that in the monomer when equivalent excited states are accounted for. Additionally, for the dimer, the decay from the second to the nearly degenerate lowest energy excited-state involves two time-scales: a rapid decay on the order of ∼10 fs followed by a slower decay of ∼100 fs. Analysis of the spatial localization of the electronic transition density during the internal conversion process points out the existence of localized states on individual monomers, indicating that the strength of thermal fluctuations exceeds electronic couplings between the states such that the exciton hops between localized states throughout the simulation.

Predicting the functional properties of many molecular systems relies on understanding how atomistic interactions give rise to macroscale observables. However, current attempts to develop predictive models for the structural and thermodynamic properties of condensed-phase systems often rely on extensive parameter fitting to empirically selected functional forms whose effectiveness is limited to a narrow range of physical conditions. In this article, we illustrate how these traditional fitting paradigms can be superseded using machine learning. Specifically, we use the results of molecular dynamics simulations to train machine learning protocols that are able to produce the radial distribution function, pressure, and internal energy of a Lennard-Jones fluid with increased accuracy in comparison to previous theoretical methods. The radial distribution function is determined using a variant of the segmented linear regression with the multivariate function decomposition approach developed by Craven et al. [J. Phys. Chem. Lett. 11, 4372 (2020)]. The pressure and internal energy are determined using expressions containing the learned radial distribution function and also a kernel ridge regression process that is trained directly on thermodynamic properties measured in simulation. The presented results suggest that the structural and thermodynamic properties of fluids may be determined more accurately through machine learning than through human-guided functional forms.

When the interaction between a molecular system and confined light modes in an optical or plasmonic cavity is strong enough to overcome the dissipative process, hybrid light-matter states (polaritons) become the fundamental excitations in the system. The mixing between the light and matter characters modifies the photophysical and photochemical properties. Notably, it was reported that these polaritons can be employed to control photochemical reactions, charge and energy transfer, and other processes. In addition, according to recent studies, vibrational strong coupling can be employed to resonantly enhance the thermally-activated chemical reactions. In this work, a theoretical model and an efficient numerical method for studying the dynamics of molecules strongly interacting with quantum light are developed based on nonadiabatic excited-state molecular dynamics. The methodology was employed to study the cis-trans photoisomerization of a realistic molecule in a cavity. Numerical simulations demonstrate that the photochemical reactions can be controlled by tuning the properties of the cavity. In the calculated example, the isomerization is suppressed when polaritonic states develop a local minimum on the lower polaritonic state. Moreover, the observed reduction of isomerization is tunable via the photon energy and light-molecule coupling strength. However, the fluctuation in the transition dipole screens the effect of light-matter, which makes it harder to tune the photochemical properties via the coupling strength. These insights suggest quantum control of photochemical reactions is possible by specially designed photonic or plasmonic cavities.

Surface hopping (SH) is a popular mixed quantum-classical method for modeling nonadiabatic excited state processes in molecules and condensed phase materials. The method is simple, efficient, and easy to implement, but the use of classical and independent nuclear trajectories introduces an overcoherence in the electronic density matrix which, if ignored, often leads to spurious results, such as overestimated reaction rates. Several methods have been proposed to incorporate decoherence into SH simulations, but a lack of insightful benchmarks makes their relative accuracy unknown. Herein, we run numerical simulations of common coherence-corrected SH methods including Truhlar's decay-of-mixing (DOM) and Subotnik's augmented SH using a Donor-bridge-Acceptor (DbA) model system. Numerical simulations are carried out in the superexchange regime, where charge transfer proceeds from a donor to an acceptor as a result of donor-bridge and bridge-acceptor couplings. The computed donor-to-acceptor reaction rates are compared to the reference Marcus theory results. For the DbA model under consideration, augmented SH recovers Marcus theory with quantitative accuracy, whereas DOM is only qualitatively accurate depending on whether predefined parameters in the decoherence rate are chosen wisely. We propose a general method for parameterizing the decoherence rate in the DOM method, which improves the method's reaction rates and presumably increases its transferability. Overall, the decoherence method of choice must be chosen with great care and this work provides insight using an exactly solvable model.

The efficiency of the intramolecular energy transfer in light harvesting dendrimers is determined by their well-defined architecture with high degree of order. After photoexcitation, through-space and through-bond energy transfer mechanisms can take place, involving vectorial exciton migration among different chromophores within dendrimer highly branched structures. Their inherent intramolecular energy gradient depends on how the multiple chromophoric units have been assembled, subject to their inter-connects, spatial distances, and orientations. Herein, we compare the photoinduced nonadiabatic molecular dynamics simulations performed on a set of different combinations of a chain of linked dendrimer building blocks composed of two-, three-, and four-ring linear polyphenylene chromophoric units. The calculations are performed with the recently developed ab initio multiple cloning-time dependent diabatic basis implementation of the Multiconfigurational Ehrenfest (MCE) approach. Despite differences in short time relaxation pathways and different initial exciton localization, at longer time scales, electronic relaxation rates and exciton final redistributions are very similar for all combinations. Unlike the systems composed of two building blocks, considered previously, for the larger 3 block systems here we observe that bifurcation of the wave function accounted by cloning is important. In all the systems considered in this work, at the time scale of few hundreds of femtoseconds, cloning enhances the electronic energy relaxation by ∼13% compared to that of the MCE method without cloning. Thus, accurate description of quantum effects is essential for understanding of the energy exchange in dendrimers both at short and long time scales.

Conjugated energetic molecules (CEMs) are a class of explosives with high nitrogen content that posses both enhanced safety and energetic performance properties and are ideal for direct optical initiation. As isolated molecules, they absorb within the range of conventional lasers. Crystalline CEMs are used in practice, however, and their properties can differ due to intermolecular interaction. Herein, time-dependent density functional theory was used to investigate one-photon absorption (OPA) and two-photon absorption (TPA) of monomers and dimers obtained from experimentally determined crystal structures of CEMs. OPA scales linearly with the number of chromophore units, while TPA scales nonlinearly, where a more than 3-fold enhancement in peak intensity, per chromophore unit, is calculated. Cooperative enhancement depends on electronic delocalization spanning both chromophore units. An increase in sensitivity to nonlinear laser initiation makes these materials suitable for practical use. This is the first study predicting a cooperative enhancement of the nonlinear optical response in energetic materials composed of relatively small molecules. The proposed model quantum chemistry is validated by comparison to crystal structure geometries and the optical absorption of these materials dissolved in solution.

The effects of solvent on molecular processes such as excited state relaxation and photochemical reaction often occurs in a nonequilibrium regime. Dynamic processes such as these can be simulated using excited statemolecular dynamics. In this work, we describe methods of simulating nonequilibrium solvent effects in excited statemolecular dynamics using linear-response time-dependent density functional theory and apparent surface charge methods. These developments include a propagation method for solvent degrees of freedom and analytical energy gradients for the calculation of forces. Molecular dynamics of acetaldehyde in water or acetonitrile are demonstrated where the solute-solvent system is out of equilibrium due to photoexcitation and emission.

This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solvent models are examined. Enforcing a variational ground state energy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempirical model chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Analytical gradients are further tested by performing microcanonical excited state molecular dynamics with p-nitroaniline.

Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.

Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system.

We implement and examine three excited state solvent models in time-dependent self-consistent field methods using a consistent formalism which unambiguously shows their relationship. These are the linear response, state specific, and vertical excitation solvent models. Their effects on energies calculated with the equivalent of COSMO/CIS/AM1 are given for a set of test molecules with varying excited state charge transfer character. The resulting solvent effects are explained qualitatively using a dipole approximation. It is shown that the fundamental differences between these solvent models are reflected by the character of the calculated excitations.

Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.

Effective tight-binding models have been introduced to describe vertical electronic excitations in branched conjugated molecules. The excited-state electronic structure is characterized by quantum particles (excitons) that reside on an irregular lattice (graph) that reflects the molecular structure. The methodology allows for the exciton spectra and energy-dependent exciton scattering matrices to be described in terms of a small number of lattice parameters which can be obtained from quantum-chemical computations using the exciton scattering approach as a tool. We illustrate the tight-binding model approach using the time-dependent Hartree-Fock computations in phenylacetylene oligomers. The on-site energies and hopping constants have been identified from the exciton dispersion and scattering matrices. In particular, resonant, as well as bound states, are reproduced for a symmetric quadruple branching center. The capability of the tight-binding model approach to describe the exciton-phonon coupling and energetic disorder in large branched conjugated molecules is briefly discussed.

Within the fewest switches surface hopping (FSSH) formulation, a swarm of independent trajectories is propagated and the equations of motion for the quantum coefficients are evolved coherently along each independent nuclear trajectory. That is, the phase factors, or quantum amplitudes, are retained. At a region of strong coupling, a trajectory can branch into multiple wavepackets. Directly following a hop, the two wavepackets remain in a region of nonadiabatic coupling and continue exchanging population. After these wavepackets have sufficiently separated in phase space, they should begin to evolve independently from one another, the process known as decoherence. Decoherence is not accounted for in the standard surface hopping algorithm and leads to internal inconsistency. FSSH is designed to ensure that at any time, the fraction of classical trajectories evolving on each quantum state is equal to the average quantum probability for that state. However, in many systems this internal consistency requirement is violated. Treating decoherence is an inherent problem that can be addressed by implementing some form of decoherence correction to the standard FSSH algorithm. In this study, we have implemented two forms of the instantaneous decoherence procedure where coefficients are reinitialized following hops. We also test the energy-based decoherence correction (EDC) scheme proposed by Granucci et al. and a related version where the form of the decoherence time is taken from Truhlar's Coherent Switching with Decay of Mixing method. The sensitivity of the EDC results to changes in parameters is also evaluated. The application of these computationally inexpensive ad hoc methods is demonstrated in the simulation of nonradiative relaxation in two conjugated oligomer systems, specifically poly-phenylene vinylene and poly-phenylene ethynylene. We find that methods that have been used successfully for treating small systems do not necessarily translate to large polyatomic systems and their success depends on the particular system under study.

Non-adiabatic excited-state molecular dynamics is used to study the ultrafast intramolecular energy transfer between two-, three-, and four-ring linear polyphenylene ethynylene chromophore units linked through meta-substitutions. Twenty excited-state electronic energies, with their corresponding gradients and nonadiabatic coupling vectors were included in the simulations. The initial laser excitation creates an exciton delocalized between the different absorbing two-ring linear PPE units. Thereafter, we observe an ultrafast directional change in the spatial localization of the transient electronic transition density. The analysis of the intramolecular flux of the transition density shows a sequential through-bond two-ring→three-ring→four-ring transfer as well as an effective through-space direct two-to-four ring transfer. The vibrational excitations of C≡C stretching motions change according to that. Finally, a mechanism of unidirectional energy transfer is presented based on the variation of the energy gaps between consecutive electronic excited states in response to the intramolecular flux of the transition density. The mechanism resembles a Shishiodoshi Japanese bamboo water fountain where, once the electronic population has been transferred to the state directly below in energy, the two states decouple thereby preventing energy transfer in the opposite direction.

Radiationless transitions between electronic excited states in polyatomic molecules take place through unavoided crossings of the potential energy surfaces with substantial non-adiabatic coupling between the respective adiabatic states. While the extent in time of these couplings are large enough, these transitions can be reasonably well simulated through quantum transitions using trajectory surface hopping-like methods. In addition, complex molecular systems may have multiple "trivial" unavoided crossings between noninteracting states. In these cases, the non-adiabatic couplings are described as sharp peaks strongly localized in time. Therefore, their modeling is commonly subjected to the identification of regions close to the particular instantaneous nuclear configurations for which the energy surfaces actually cross each other. Here, we present a novel procedure to identify and treat these regions of unavoided crossings between non-interacting states using the so-called Min-Cost algorithm. The method differentiates between unavoided crossings between interacting states (simulated by quantum hops), and trivial unavoided crossings between non-interacting states (detected by tracking the states in time with Min-Cost procedure). We discuss its implementation within our recently developed non-adiabatic excited state molecular dynamics framework. Fragments of two- and four-ring linear polyphenylene ethynylene chromophore units at various separations have been used as a representative molecular system to test the algorithm. Our results enable us to distinguish and analyze the main features of these different types of radiationless transitions the molecular system undertakes during internal conversion.

Nonadiabatic molecular dynamics simulations, involving multiple Born-Oppenheimer potential energy surfaces, often require a large number of independent trajectories in order to achieve the desired convergence of the results, and simulation relies on different parameters that should be tested and compared. In addition to influencing the speed of the simulation, the chosen parameters combined with the frequently reduced number of trajectories can sometimes lead to unanticipated changes in the accuracy of the simulated dynamics. We have previously developed a nonadiabatic excited state molecular dynamics methodology employing Tully's fewest switches surface hopping algorithm. In this study, we seek to investigate the impact of the number of trajectories and the various parameters on the simulation of the photoinduced dynamics of distyrylbenzene (a small oligomer of polyphenylene vinylene) within our developed framework. Various user-defined parameters are analyzed: classical and quantum integration time steps, the value of the friction coefficient for Langevin dynamics, and the initial seed used for stochastic thermostat and hopping algorithms. Common approximations such as reduced number of nonadiabatic coupling terms and the classical path approximation are also investigated. Our analysis shows that, at least for the considered molecular system, a minimum of ~400 independent trajectories should be calculated in order to achieve statistical averaging necessary for convergence of the calculated relaxation timescales.

The electronic excitation energies and transition dipole moments are the essential ingredients to compute an optical spectrum of any molecular system. Here we extend the exciton scattering (ES) approach, originally developed for computing excitation energies in branched conjugated molecules, to the calculation of the transition dipole moments. The ES parameters that characterize contributions of molecular building blocks to the total transition dipole can be extracted from the quantum-chemical calculations of the excited states in simple molecular fragments. Using these extracted parameters, one can then effortlessly calculate the oscillator strengths and optical spectra of various large molecular structures. We illustrate application of this extended ES approach using an example of phenylacetylene-based molecules. Absorption spectra predicted by the ES approach show close agreement with the results of the reference quantum-chemical calculations.

Perylene bisimide and triphenyl diamine are prototypical organic dyes frequently used in organic solar cells and light emitting devices. Recent Forster-resonant-energy-transfer experiments on a bridged organic dyad consisting of triphenyl diamine as an energy-donor and perylene bisimide as an energy-acceptor revealed a strong fluorescence quenching on the perylene bisimide. This quenching is absent in a solution of free donors and acceptors and thus attributed to the presence of the saturated CH(2)O(CH(2))(12)-bridge. We investigate the cause of the fluorescence quenching as well as the special role of the covalently bound bridge by means of time dependent density functional theory and molecular dynamics. The conformational dynamics of the bridged system leads to a charge transfer process between donor and acceptor that causes the acceptor fluorescence quenching.

The electronic coupling values and approximate energy transfer rates between semiconductor single-wall carbon nanotubes are calculated using two different approximations, the point dipole approximation and the distributed transition monopole approximation, and the results are compared. It is shown that the point dipole approximation fails dramatically at tube separations typically found in nanotube bundles ( approximately 12-16 A) and that the disagreement persists at large tube separations (>100 A, over ten nanotube diameters). When used in Forster resonance energy transfer theory, the coupling between two point transition dipoles is found to overestimate energy transfer rates. It is concluded that the point dipole approximation is inappropriate for use with elongated systems such as carbon nanotubes and that methods which can account for the shape of the particle are more suitable.

Four different numerical algorithms suitable for a linear scaling implementation of time-dependent Hartree-Fock and Kohn-Sham self-consistent field theories are examined. We compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures to solve the random-phase approximation (RPA) (non-Hermitian) and Tamm-Dancoff approximation (TDA) (Hermitian) eigenvalue equations in the molecular orbital-free framework. Semiempirical Hamiltonian models are used to numerically benchmark algorithms for the computation of excited states of realistic molecular systems (conjugated polymers and carbon nanotubes). Convergence behavior and stability are tested with respect to a numerical noise imposed to simulate linear scaling conditions. The results single out the most suitable procedures for linear scaling large-scale time-dependent perturbation theory calculations of electronic excitations.

We develop a formalism for the exciton scattering (ES) approach to calculation of the excited state electronic structure of branched conjugated polymers with insignificant numerical expense. The ES approach attributes electronic excitations in quasi-one-dimensional molecules to standing waves formed by the scattering of quantum quasiparticles. We derive the phenomenology from the microscopic description in terms of many-electron excitations. The presented model can be used to compute both excited state frequencies and transition dipoles in large molecules after the ES ingredients are extracted from smaller molecular fragments.

We obtain the parameters of the exciton scattering (ES) model from the quantum-chemical calculations of the electronic excitations in simple phenylacetylene-based molecules. We determine the exciton dispersion and the frequency-dependent scattering matrices which describe scattering properties of the molecular ends as well as of meta- and orthoconjugated links. The extracted functions are smooth, which confirms the validity of the ES picture. We find a good agreement between the ES and quantum-chemical results for the excitation energies in simple test molecules.

The exciton scattering (ES) approach is an efficient tool to calculate the excited states electronic structure in large branched polymeric molecules. Using the previously extracted parameters, we apply the ES approach to a number of phenylacetylene-based test molecules. Comparison of ES predictions with direct quantum chemistry results for the excitation energies shows an agreement within several meV. The ES framework provides powerful insights into photophysics of macromolecules by revealing the connections between the molecular structure and the properties of the collective electronic states, including spatial localization of excitations controlled by the energy.

Colloidal quantum dots are semiconductor nanocrystals (NCs) which have stimulated a great deal of research and have attracted technical interest in recent years due to their chemical stability and the tunability of photophysical properties. While internal structure of large quantum dots is similar to bulk, their surface structure and passivating role of capping ligands (surfactants) are not fully understood to date. We apply ab initio wavefunction methods, density functional theory, and semiempirical approaches to study the passivation effects of substituted phosphine and amine ligands on the minimal cluster Cd(2)Se(2), which is also used to benchmark different computational methods versus high level ab initio techniques. Full geometry optimization of Cd(2)Se(2) at different theory levels and ligand coverage is used to understand the affinities of various ligands and the impact of ligands on cluster structure. Most possible bonding patterns between ligands and surface CdSe atoms are considered, including a ligand coordinated to Se atoms. The degree of passivation of Cd and Se atoms (one or two ligands attached to one atom) is also studied. The results suggest that B3LYP/LANL2DZ level of theory is appropriate for the system modeling, whereas frequently used semiempirical methods (such as AM1 and PM3) produce unphysical results. The use of hydrogen atom for modeling of the cluster passivating ligands is found to yield unphysical results as well. Hence, the surface termination of II-VI semiconductor NCs with hydrogen atoms often used in computational models should probably be avoided. Basis set superposition error, zero-point energy, and thermal corrections, as well as solvent effects simulated with polarized continuum model are found to produce minor variations on the ligand binding energies. The effects of Cd-Se complex structure on both the electronic band gap (highest occupied molecular orbital-lowest unoccupied molecular orbital energy difference) and ligand binding energies are systematically examined. The role played by positive charges on ligand binding is also explored. The calculated binding energies for various ligands L are found to decrease in the order OPMe(3)>OPH(3)>NH(2)Me>/=NH(3)>/=NMe(3)>PMe(3)>PH(3) for neutral clusters and OPMe(3)>OPH(3)>PMe(3)>/=NMe(3)>/=NH(2)Me>/=NH(3)>PH(3) and OPMe(3)>OPH(3)>NH(2)Me>/=NMe(3)>/=PMe(3)>/=NH(3)>PH(3) for single and double ligations of positively charged Cd(2)Se(2) (2+) cluster, respectively.

A nonlinear conjugate gradient optimization scheme is used to obtain excitation energies within the random phase approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size N is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular-orbital-free algorithm is found to be robust and computationally efficient, providing a first step toward large-scale, reduced complexity calculations of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent density functional theory.

We propose a scheme for calculation of linear optical response of current-carrying molecular junctions for the case when electronic tunneling through the junction is much faster than characteristic time of external laser field. We discuss relationships between nonequilibrium Green's function (NEGF) and time-dependent density functional theory (TDDFT) approaches and derive expressions for optical response and linear polarizability within NEGF-TDDFT scheme. Corresponding results for isolated molecule, derived within TDDFT approach previously, are reproduced when coupling to contacts is neglected.

It is known that the adiabatic approximation in time-dependent density functional theory usually provides a good description of low-lying excitations of molecules. In the present work, the capability of the adiabatic nonempirical meta-generalized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) to describe atomic and molecular excitations is tested. The adiabatic (one-parameter) hybrid version of the TPSS meta-GGA and the adiabatic GGA of Perdew, Burke, and Ernzerhof (PBE) are also included in the test. The results are compared to experiments and to those obtained with two well-established hybrid functionals PBE0 and B3LYP. Calculations show that both adiabatic TPSS and TPSSh functionals produce excitation energies in fairly good agreement with experiments, and improve upon the adiabatic local spin density approximation and, in particular, the adiabatic PBE GGA. This further confirms that TPSS is indeed a reliable nonhybrid universal functional which can serve as the starting point from which higher-level approximations can be constructed. The systematic underestimate of the low-lying vertical excitation energies of molecules with time-dependent density functionals within the adiabatic approximation suggests that further improvement can be made with nonadiabatic corrections.

Excited state properties of one-dimensional molecular materials are dominated by many-body interactions resulting in strongly bound confined excitons. These effects cannot be neglected or treated as a small perturbation and should be appropriately accounted for by electronic structure methodologies. We use adiabatic time-dependent density functional theory to investigate the electronic structure of one-dimensional organic semiconductors, conjugated polymers. Various commonly used functionals are applied to calculate the lowest singlet and triplet state energies and oscillator strengths of the poly(phenylenevinylene) and ladder-type (poly)(para-phenylene) oligomers. Local density approximations and gradient-corrected functionals cannot describe bound excitonic states due to lack of an effective attractive Coulomb interaction between photoexcited electrons and holes. In contrast, hybrid density functionals, which include long-range nonlocal and nonadiabatic corrections in a form of a fraction of Hartree-Fock exchange, are able to reproduce the excitonic effects. The resulting finite exciton sizes are strongly dependent on the amount of the orbital exchange included in the functional.

We use first-principles quantum-chemical approaches to study absorption and emission properties of recently synthesized distyrylbenzene (DSB) derivative chromophores and their dimers (two DSB molecules linked through a [2.2]paracyclophane moiety). Several solvent models are applied to model experimentally observed shifts and radiative lifetimes in Stokes nonpolar organic solvents (toluene) and water. The molecular environment is simulated using the implicit solvation models, as well as explicit water molecules and counterions. Calculations show that neither implicit nor explicit solvent models are sufficient to reproduce experimental observations. The contact pair between the chromophore and counterion, on the other hand, is able to reproduce the experimental data when a partial screening effect of the solvent is taken into account. Based on our simulations we suggest two mechanisms for the excited-state lifetime increase in aqueous solutions. These findings may have a number of implications for organic light-emitting devices, electronic functionalities of soluble polymers and molecular fluorescent labels, and their possible applications as biosensors and charge/energy conduits in nanoassemblies.