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Efficient hybrid DFT simulations of solid state materials would be extremely beneficial for computational chemistry and materials science, but is presently bottlenecked by difficulties in computing Hartree-Fock (HF) exchange with plane wave orbital bases. We present a GPU-accelerated, Gaussian orbital based integral algorithm for systems with periodic boundary conditions, which takes advantage of Ewald summation to efficiently compute electrostatic interactions. We have implemented this approach into the TeraChem software package within the $\Gamma$ point approximation, enabling simulation of unit cells with hundreds or thousands of atoms at the HF or hybrid DFT level on a single GPU card. Our implementation readily parallelizes over multiple GPUs and paves the road to accurate simulation of the properties and dynamics of extended materials in both the ground and excited states.

A coherent vibrational wavepacket is launched and manipulated in the symmetric stretch (a$_1$) mode of CBr$_4$, by impulsive stimulated Raman scattering from non-resonant 400 nm laser pump pulses with various peak intensities on the order of tens of 10$^{12}$ W/cm$^2$. Extreme ultraviolet (XUV) attosecond transient absorption spectroscopy (ATAS) records the wavepacket dynamics as temporal oscillations in XUV absorption energy at the bromine M$_{4,5}$ 3d$_{3/2,5/2}$ edges around 70 eV. The results are augmented by nuclear time-dependent Schr\"odinger equation simulations. Slopes of the (Br-3d$_{3/2,5/2}$)$^{-1}$10a$_1^*$ core-excited state potential energy surface (PES) along the a$_1$ mode are calculated to be -9.4 eV/{\AA} from restricted open-shell Kohn-Sham calculations. Using analytical relations derived for the small-displacement limit with the calculated slopes of the core-excited state PES, a deeper insight into the vibrational dynamics is obtained by retrieving the experimental excursion amplitude of the vibrational wavepacket and the amount of population transferred to the vibrational first-excited state, as a function of pump-pulse peak intensity. Experimentally, the results show that XUV ATAS is capable of easily resolving oscillations in the XUV absorption energy on the order of few to tens of meV and tens of femtosecond time precision, limited only by the averaging times in the experimental scans. This corresponds to oscillations of C-Br bond length on the order of 10$^{-4}$ to 10$^{-3}$ {\AA}. The results and the analytic relationships offer a clear physical picture, on multiple levels of understanding, for how the pump-pulse intensity controls the vibrational dynamics launched by non-resonant ISRS in the small-displacement limit.

The increasing availability of GPUs for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. The complexity of integral kernels for high angular momentum basis functions however often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report implementation of $f$ function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles (CCSD) calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH$_3$) with complete active space self-consistent field (CASSCF) are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules., Comment: Added additional data

The fate of thymine upon excitation by ultraviolet radiation has been the subject of intense debate over the past three decades. Today, it is widely believed that its ultrafast excited state decay stems from a radiationless transition from the bright ${\pi}{\pi}^*$ state to a dark $n{\pi}^*$ state. However, conflicting theoretical predictions have made the experimental data difficult to interpret. Here we simulate the ultrafast dynamics in thymine at the highest level of theory to date, performing wavepacket dynamics with a new coupled cluster method. Our simulation confirms an ultrafast ${\pi}{\pi}^*$ to $n{\pi}^*$ transition (${\tau} = 41 \pm 14$ fs). Furthermore, the predicted oxygen-edge X-ray absorption spectra agree quantitatively with the experimental results. Our simulation also predicts an as-yet uncharacterized photochemical pathway: a ${\pi}{\sigma}^*$ channel that leads to hydrogen dissociation at one of the two N-H bonds in thymine. Similar behavior has been identified in other heteroaromatic compounds, including adenine, and several authors have speculated that a similar pathway may exist in thymine. However, this was never confirmed theoretically or experimentally. This prediction calls for renewed efforts to experimentally identify or exclude the presence of this channel., Comment: 42 pages, 23 figures

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S$_2$). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory and equation-of-motion coupled cluster for the underlying electronic structure theory. We find that the lifetime of the S$_2$ state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted UED spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross-sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time.

Electrocyclic reactions are characterized by the concerted formation and cleavage of both {\sigma} and {\pi} bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule {\alpha}-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated {\pi} bonds. The {\sigma} bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general., Comment: Combined manuscript and supplementary information

We develop a quartic-scaling implementation of coupled-cluster singles and doubles based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units (GPUs) and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Further, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

We present the first investigation of excited state dynamics by resonant Auger-Meitner spectroscopy (also known as resonant Auger spectroscopy) using the nucleobase thymine as an example. Thymine is photoexcited in the UV and probed with X-ray photon energies at and below the oxygen K-edge. After initial photoexcitation to a {\pi}{\pi}* excited state, thymine is known to undergo internal conversion to an n{\pi}* excited state with a strong resonance at the oxygen K-edge, red-shifted from the ground state {\pi}* resonances of thymine (see our previous study Wolf et al., Nat. Commun., 2017, 8, 29). We resolve and compare the Auger-Meitner electron spectra associated both with the excited state and ground state resonances, and distinguish participator and spectator decay contributions. Furthermore, we observe simultaneously with the decay of the n{\pi}* state signatures the appearance of additional resonant Auger-Meitner contributions at photon energies between the n{\pi}* state and the ground state resonances. We assign these contributions to population transfer from the n{\pi}* state to a {\pi}{\pi}* triplet state via intersystem crossing on the picosecond timescale based on simulations of the X-ray absorption spectra in the vibrationally hot triplet state. Moreover, we identify signatures from the initially excited {\pi}{\pi}* singlet state which we have not observed in our previous study.

The de Broglie wave nature of matter is a paradigmatic example of fundamental quantum physics and enables precise measurements of forces, fundamental constants and even material properties. However, even though matter-wave interferometry is nowadays routinely realized in many laboratories, this feat has remained an outstanding challenge for the vast class of native polypeptides, the building blocks of life, which are ubiquitous in biology but fragile and difficult to handle. Here, we demonstrate the quantum wave nature of gramicidin, a natural antibiotic composed of 15 amino acids. Femtosecond laser desorption of a thin biomolecular film with intensities up to 1~TW/cm$^2$ transfers these molecules into a cold noble gas jet. Even though the peptide's de Broglie wavelength is as tiny as 350~fm, the molecular coherence is delocalized over more than 20 times the molecular size in our all-optical time-domain Talbot-Lau interferometer. We compare the observed interference fringes for two different interference orders with a model that includes both a rigorous treatment of the peptide's quantum wave nature as well as a quantum chemical assessment of its optical properties to distinguish our result from classical predictions. The successful realization of quantum optics with this polypeptide as a prototypical biomolecule paves the way for quantum-assisted molecule metrology and in particular the optical spectroscopy of a large class of biologically relevant molecules.

Singlet fission is a spin-allowed exciton multiplication process in organic semiconductors that converts one spin-singlet exciton to two triplet excitons. It offers the potential to enhance solar energy conversion by circumventing the Shockley-Queisser limit on efficiency. Recently, the mechanism of the primary singlet fission process in pentacene and its derivatives have been extensively investigated, however, the nature of the primary ultrafast process in singlet fission is still a matter of debate. Here, we study the singlet fission process in a pentacene film by employing a combination of transient-grating (TG) and two-dimensional (2D) electronic spectroscopy complemented by quantum chemical and nonadiabatic dynamics calculations. The high sensitivity of heterodyne detected TG spectroscopy enabled us to capture the vibrational coherence and to show that it mediates the transition from the singlet excited electronic state to the triplet-pair state. This coherent process is further examined by 2D electronic spectroscopy. Detailed analysis of the experimental data reveals that significant vibronic couplings of a few key modes in the low- and high-frequency region connect the excited singlet and triplet-pair states. Based on quantum chemical calculations, we identify these key intermolecular rocking modes along the longitudinal molecular axis between the pentacene molecules. They play the essential role of an electronic bridge between the singlet and triplet-pair states. Along with high-frequency local vibrations acting as tuning modes, these rocking motions drive the ultrafast dynamics at the multidimensional conical intersection in the singlet fission process.

The maturation of analytical derivative theory over the past few decades has enabled classical electronic structure theory to provide accurate and efficient predictions of a wide variety of observable properties. However, classical implementations of analytical derivative theory take advantage of explicit computational access to the approximate electronic wavefunctions in question, which is not possible for the emerging case of hybrid quantum/classical methods. Here, we develop an efficient Lagrangian-based approach for analytical first derivatives of hybrid quantum/classical methods using only observable quantities from the quantum portion of the algorithm. Specifically, we construct the key first-derivative property of the nuclear energy gradient for the recently-developed multistate, contracted variant of the variational quantum eigensolver (MC-VQE) within the context of the ab initio exciton model (AIEM). We show that a clean separation between the quantum and classical parts of the problem is enabled by the definition of an appropriate set of relaxed density matrices, and show how the wavefunction response equations in the quantum part of the algorithm (coupled-perturbed MC-VQE or CP-MC-VQE equations) are decoupled from the wavefunction response equations and and gradient perturbations in the classical part of the algorithm. We explore the magnitudes of the Hellmann-Feynman and response contributions to the gradients in quantum circuit simulations of MC-VQE+AIEM and demonstrate a quantum circuit simulator implementation of adiabatic excited state dynamics with MC-VQE+AIEM., Comment: 26 pages, 3 figures, 4 tables

We have investigated the structural dynamics in photoexcited 1,2-diiodotetrafluoroethane molecules (C2F4I2) in the gas phase experimentally using ultrafast electron diffraction and theoretically using FOMO-CASCI excited state dynamics simulations. The molecules are excited by an ultra-violet femtosecond laser pulse to a state characterized by a transition from the iodine 5p orbital to a mixed 5p|| hole and CF2 antibonding orbital, which results in the cleavage of one of the carbon-iodine bonds. We have observed, with sub-Angstrom resolution, the motion of the nuclear wavepacket of the dissociating iodine atom followed by coherent vibrations in the electronic ground state of the C2F4I radical. The radical reaches a stable classical (non-bridged) structure in less than 200 fs., Comment: 13 pages, 11 figures

We develop an extension of the variational quantum eigensolver (VQE) algorithm - multistate, contracted VQE (MC-VQE) - that allows for the efficient computation of the transition energies between the ground state and several low-lying excited states of a molecule, as well as the oscillator strengths associated with these transitions. We numerically simulate MC-VQE by computing the absorption spectrum of an ab initio exciton model of an 18-chromophore light-harvesting complex from purple photosynthetic bacteria., Comment: Updated with addl references and SI case study of H-aggregate BChl-a stack

We studied the reaction dynamics of a proposed prebiotic reaction theoretically. The chemical process involves acetone cyanohydrin or formalcyanohydrin reacting with hydrosulfide in an aqueous environment. Rate constants and populations of reactant and product bimolecular geometric orientations for the reactions were obtained by using density functional theory for the energies, transition state theory for the rates and matrix exponentiation as well as the hybrid tau-leaping algorithm for the population dynamics. The role of including the solvent explicitly versus implicitly was also investigated. We found that adding water or hydrogen sulfide molecules explicitly lowers the activation energy barrier and leads to a more efficient reaction pathway. In particular, hydrogen sulfide was a better proton donor. Further, when adding the solvent explicitly a synchronous reaction mechanism was observed while a concerted reaction mechanism was seen when using an implicit solvent model. Finally, we studied the role of including more than one reactant and product bimolecular orientation geometry in the dynamics. Including all pathways, reactant to reactant, product to product, reactant to product and product to reactant reduced the reaction half-time by two orders of magnitude and was therefore determined to be fundamental for an accurate description of the dynamics. Overall, we found that most reactions which involve formalcyanohydrin occur more rapidly or at the same speed as reactions which involve acetone cyanohydrin at room temperature.

We derive the crossing conditions at conical intersections between electronic states in coupled cluster theory, and show that if the coupled cluster Jacobian matrix is nondefective, two (three) independent conditions are correctly placed on the nuclear degrees of freedom for an inherently real (complex) Hamiltonian. Calculations using coupled cluster theory on an $2 {^{1}}A' / 3 {^{1}}A'$ conical intersection in hypofluorous acid illustrate the nonphysical artifacts associated with defects at accidental same-symmetry intersections. In particular, the observed intersection seam is folded about a space of the correct dimensionality, indicating that minor modifications to the theory are required for it to provide a correct description of conical intersections in general. We find that an accidental symmetry allowed $1 {^{1}}A" / 2 {^{1}}A"$ intersection in hydrogen sulfide is properly described, showing no artifacts as well as linearity of the energy gap to first order in the branching plane., Comment: 9 pages and 4 figures

The conductor-like polarization model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in chemical simulations. However, its application in quantum mechanical calculations of large-scale biomolecular systems can be limited by computational expense of both the gas phase electronic structure and the solvation interaction. We have previously used graphical processing units (GPUs) to accelerate the first of these steps. Here, we extend the use of GPUs to accelerate electronic structure calculations including C-PCM solvation. Implementation on the GPU leads to significant acceleration of the generation of the required integrals for C-PCM. We further propose two strategies to improve the solution of the required linear equations: a dynamic convergence threshold and a randomized block-Jacobi preconditioner. These strategies are not specific to GPUs and are expected to be beneficial for both CPU and GPU implementations. We benchmark the performance of the new implementation using over 20 small proteins in solvent environment. Using a single GPU, our method evaluates the C-PCM related integrals and their derivatives more than 10X faster than a conventional CPU based implementation. Our improvements to the linear solver provide a further 3X acceleration. The overall calculations including C-PCM solvation require typically 20-40% more effort than their gas phase counterparts for moderate basis set and molecule surface discretization level. The relative cost of the C-PCM solvation correction decreases as the basis sets and/or cavity radii increase. Therefore description of solvation with this model should be routine. We also discuss applications to the study of the conformational landscape of an amyloid fibril., Comment: 36 pages, 12 figures

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in studies of enzymatic catalysis. Until recently, it has been cost prohibitive to determine the asymptotic limit of key energetic and structural properties with respect to increasingly large QM regions. Leveraging recent advances in electronic structure efficiency and accuracy, we investigate catalytic properties in catechol O-methyltransferase, a representative example of a methyltransferase critical to human health. Using QM regions ranging in size from reactants-only (64 atoms) to nearly one-third of the entire protein (940 atoms), we show that properties such as the activation energy approach within chemical accuracy of the large-QM asymptotic limits rather slowly, requiring approximately 500-600 atoms if the QM residues are chosen simply by distance from the substrate. This slow approach to asymptotic limit is due to charge transfer from protein residues to the reacting substrates. Our large QM/MM calculations enable identification of charge separation for fragments in the transition state as a key component of enzymatic methyl transfer rate enhancement. We introduce charge shift analysis that reveals the minimum number of protein residues (ca. 11-16 residues or 200-300 atoms for COMT) needed for quantitative agreement with large-QM simulations. The identified residues are not those that would be typically selected using criteria such as chemical intuition or proximity. These results provide a recipe for a more careful determination of QM region sizes in future QM/MM studies of enzymes., Comment: 27 pages, 10 figures

Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions are described by empirical potentials is now well established, their application to ab initio molecular dynamics calculations has been limited by difficulties associated with splitting the ab initio potential into fast and slowly varying components. Here we show that such a timescale separation is possible using two different schemes: one based on fragment decomposition and the other on range separation of the Coulomb operator in the electronic Hamiltonian. We demonstrate for both water clusters and a solvated hydroxide ion that multiple time-scale molecular dynamics allows for outer time steps of 2.5 fs, which are as large as those obtained when such schemes are applied to empirical potentials, while still allowing for bonds to be broken and reformed throughout the dynamics. This permits computational speedups of up to 4.4x, compared to standard Born-Oppenheimer ab initio molecular dynamics with a 0.5 fs time step, while maintaining the same energy conservation and accuracy., Comment: 28 pages, 7 Figures

We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. \v{S}ulc and J. Van\'i\v{c}ek, Mol. Phys. 110, 945 (2012)]. Here we focus on increasing the accuracy of this approximation by first implementing an exact Gaussian basis method, which benefits from the accuracy of quantum dynamics and efficiency of classical dynamics. Starting from this exact method, the DR is derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These methods include the Gaussian DR, an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. The newly obtained methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0/S1 model, and quartic oscillator. Numerical results confirm that both the Gaussian basis method and the Gaussian DR increase the accuracy of the DR. Surprisingly, in chaotic systems the Gaussian DR can outperform the presumably more accurate Gaussian basis method, in which the two bases are evolved separately., Comment: 15 pages, 7 figures

Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the eXact Tensor HyperContraction (X-THC) method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchange-like" contractions., Comment: Third version of the manuscript after referee's comments. In press in PRL. Main text: 4 pages, 2 figures, 1 table; Supplemental material (also included): 14 pages, 2 figures, 2 tables

We have studied the photo-induced isomerization from 1,3-cyclohexadiene to 1,3,5-hexatriene in the presence of an intense ultrafast laser pulse. We find that the laser field maximally suppresses isomerization if it is both polarized parallel to the excitation dipole and present 50 fs after the initial photoabsorption, at the time when the system is expected to be in the vicinity of a conical intersection that mediates this structural transition. A modified ab initio multiple spawning (AIMS) method shows that the laser induces a resonant coupling between the excited state and the ground state, i.e., a light-induced conical intersection. The theory accounts for the timing and direction of the effect.

An analytical solution of fluctuating-charge models using Gaussian elimination allows us to isolate the contribution of charge conservation effects in determining the charge distribution. We use this analytical solution to calculate dipole moments and polarizabilities and show that charge conservation plays a critical role in maintaining the correct translational properties of the electrostatic properties predicted by these models., Comment: 9 pages, submitted to J. Chem. Phys

We have recently developed the QTPIE (charge transfer with polarization current equilibration) fluctuating-charge model, a new model with correct dissociation behavior for nonequilibrium geometries. The correct asymptotics originally came at the price of representing the solution in terms of charge-transfer variables instead of atomic charges. However, we have found an exact reformulation of fluctuating-charge models in terms of atomic charges again, which is made possible by the symmetries of classical electrostatics. We show how this leads to the distinguishing between two types of atomic electronegativities in our model. While one is a intrinsic property of individual atoms, the other takes into account the local electrical surroundings. This suggests that this distinction could resolve some confusion surrounding the concept of electronegativity as to whether it is an intrinsic property of elements, or otherwise., Comment: 17 pages, prepared for "Proceedings of QSCP-XIII" in Prog. Theor. Chem. Phys

Fluctuating-charge models have been used to model polarization effects in molecular mechanics methods. However, they overestimate polarizabilities in large systems. Previous attempts to remedy this have been at the expense of forbidding intermolecular charge-transfer. Here, we investigate this lack of size-extensivity and show that the neglect of terms arising from charge conservation is partly responsible; these terms are also vital for maintaining the correct translational symmetries of the dipole moment and polarizability that classical electrostatic theory requires. Also, QTPIE demonstrates linear-scaling polarizabilities when coupling the external electric field in a manner that treats its potential as a perturbation of the atomic electronegativities. Thus for the first time, we have a fluctuating-charge model that predicts size-extensive dipole polarizabilities, yet allows intermolecular charge-transfer., Comment: 16 pages, 4 figures

A two-electron one-dimensional model of a heteroatomic molecule composed of two open-shell atoms is considered. Including only two electrons isolates and examines the effect that the highest occupied molecular orbital has on the Kohn-Sham potential as the molecule dissociates. We reproduce the characteristic step and peak that previous high-level wavefunction methods have shown to exist for real molecules in the low-density internuclear region. The simplicity of our model enables us to investigate in detail their development as a function of bond-length, with little computational effort, and derive properties of their features in the dissociation limit. We show that the onset of the step is coincident with the internuclear separation at which an avoided crossing between the ground-state and lowest charge-transfer excited state is approached. Although the step and peak features have little effect on the ground-state energetics, we discuss their important consequences for dynamics and response., Comment: 12 pages

The Full Multiple Spawning (FMS) method is designed to simulate quantum dynamics in the multi-state electronic problem. The FMS nuclear wavefunction is represented in a basis of coupled, frozen Gaussians, and the spawning procedure prescribes a means of adaptively increasing the size of the basis in order to capture population transfer between electronic states. Parent trajectories create children when passing through regions of significant nonadiabatic coupling. In order to converge branching ratios without allowing the basis to reach an impractical size, population transfer at individual spawning events should be made as effective as possible. Herein we detail a new algorithm for specifying the initial conditions of freshly spawned basis functions, one that minimizes the number of spawns needed for convergence by maximizing the efficiency of individual spawning events. Optimization is achieved by maximizing the coupling between parent and child trajectories, as a function of child position and momentum, at the point of spawning. The method is tested with a two-state, one-mode avoided crossing model and a two-state, two-mode conical intersection model., Comment: 35 pages, 8 figures, for submission to JCP

Our previously introduced QTPIE (charge transfer with polarization current equilibration) model (J. Chen and T. J. Martinez, Chem. Phys. Lett. 438, 315 (2007)) is a fluctuating-charge model with correct asymptotic behavior. Unlike most other fluctuating-charge models, QTPIE is formulated in terms of charge-transfer variables and pairwise electronegativities, not atomic charge variables and electronegativities. The pairwise character of the electronegativities in QTPIE avoids spurious charge transfer when bonds are broken. However, the increased number of variables leads to considerable computational expense and a rank-deficient set of working equations, which is numerically inconvenient. Here, we show that QTPIE can be exactly reformulated in terms of atomic charge variables, leading to a considerable reduction in computational complexity. The transformation between atomic and bond variables is generally applicable to arbitrary fluctuating charge models, and uncovers an underlying topological framework that can be used to understand the relation between fluctuating-charge models and the classical theory of electrical circuits., Comment: 36 pages, 7 figures; submitted to J. Chem. Phys

Polarization and charge transfer are important effects which are difficult to describe using conventional force fields. Charge equilibration models can include both of these effects in large-scale molecular simulations. However, these models behave incorrectly when bonds are broken, making it difficult to use them in the context of reactive force fields. We develop a new method for describing charge flow in molecules -- QTPIE. The QTPIE method is based on charge transfer variables (as opposed to atomic charges) and correctly treats asymptotic behavior near dissociation. It is also able to provide a realistic description of in-plane polarizabilities., Comment: 22 pages, 5 figures