Ultrafast electron diffraction of photoexcited gas-phase cyclobutanone predicted by ab initio multiple cloning simulations.

We present the result of our calculations of ultrafast electron diffraction (UED) for cyclobutanone excited into the S2 electronic state, which is based on the non-adiabatic dynamics simulations with the Ab Initio Multiple Cloning (AIMC) method with the electronic structure calculated at the SA(3)-CASSCF(12,12)/aug-cc-pVDZ level of theory. The key features in the UED pattern were identified, which can be used to distinguish between the reaction pathways observed in the AIMC dynamics, although there is a significant overlap between representative signals due to the structural similarity of the products. The calculated UED pattern can be compared with the experiment.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Electronic energies from coupled fermionic "Zombie" states' imaginary time evolution.

Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution [D. V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work, we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie states and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie states, that allows much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" that removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure. The proposed algorithm of imaginary time propagation on biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods.

ChemDyME: Kinetically Steered, Automated Mechanism Generation through Combined Molecular Dynamics and Master Equation Calculations.

In many scientific fields, there is an interest in understanding the way in which chemical networks evolve. The chemical networks which researchers focus upon have become increasingly complex, and this has motivated the development of automated methods for exploring chemical reactivity or conformational change in a "black-box" manner, harnessing modern computing resources to automate mechanism discovery. In this work, we present a new approach to automated mechanism generation which couples molecular dynamics and statistical rate theory to automatically find kinetically important reactions and then solve the time evolution of the species in the evolving network. The key to this chemical network mapping through combined dynamics and ME simulation approach is the concept of "kinetic convergence", whereby the search for new reactions is constrained to those species which are kinetically favorable at the conditions of interest. We demonstrate the capability of the new approach for two systems, a well-studied combustion system and a multiple oxygen addition system relevant to atmospheric aerosol formation.

Simulation of Time- and Frequency-Resolved Four-Wave-Mixing Signals at Finite Temperatures: A Thermo-Field Dynamics Approach.

We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal. It is shown that a detailed dynamical picture of the singlet fission process can be extracted from the three spectroscopic signals. An increasing temperature leads to lower intensities of the signals and broadened vibrational peaks, which can be attributed to faster singlet-triplet population transfer and stronger bath-induced electronic dephasing at higher temperatures.

Simulation of the effect of vibrational pre-excitation on the dynamics of pyrrole photo-dissociation.

Photo-dissociation dynamics is simulated for vibrationally pre-excited pyrrole molecules using an ab initio multiple cloning approach. Total kinetic energy release (TKER) spectra and dissociation times are calculated. It is found that pre-excitation of N-H bond vibrations facilitates fast direct dissociation, which results in a significant increase in the high-energy wing of TKER spectra. The results are in very good agreement with the recent vibrationally mediated photo-dissociation experiment, where the TKER spectrum was measured for pyrrole molecules excited by a combination of IR and UV laser pulses. Calculations for other vibrational modes show that this effect is specific for N-H bond vibrations: Pre-excitation of other modes does not result in any significant changes in TKER spectra.

Efficient simulation of time- and frequency-resolved four-wave-mixing signals with a multiconfigurational Ehrenfest approach.

We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules.

Mechanical Unfolding of Proteins-A Comparative Nonequilibrium Molecular Dynamics Study.

Mechanical signals regulate functions of mechanosensitive proteins by inducing structural changes that are determinant for force-dependent interactions. Talin is a focal adhesion protein that is known to extend under mechanical load, and it has been shown to unfold via intermediate states. Here, we compared different nonequilibrium molecular dynamics (MD) simulations to study unfolding of the talin rod. We combined boxed MD (BXD), steered MD, and umbrella sampling (US) techniques and provide free energy profiles for unfolding of talin rod subdomains. We conducted BXD, steered MD, and US simulations at different detail levels and demonstrate how these different techniques can be used to study protein unfolding under tension. Unfolding free energy profiles determined by BXD suggest that the intermediate states in talin rod subdomains are stabilized by force during unfolding, and US confirmed these results.

Ultrafast photodissociation dynamics of pyrazole, imidazole and their deuterated derivatives using ab initio multiple cloning.

We present results obtained using the ab initio multiple cloning (AIMC) method to simulate fully quantum dynamics for imidazole and its structural isomer pyrazole along with their selectively deuterated species. We simulate the ultrafast dissociation of the N-H/D bond for these molecules along the repulsive 1πσ* state which agrees well with previous experimental results. Our results give evidence for a two-stage dissociation of the N-H/D bond on the sub-50 fs regime for imidazole, pyrazole and their selectively deuterated species, and give evidence for the importance of the repulsive 1πσ* state along the N-H/D bond coordinate for the relaxation of both imidazole and pyrazole. The ability of these calculations to reproduce experimental results lends confidence that larger complex systems could be explored with predictive capabilities with the AIMC method. These results also confirm the ability of the AIMC method to add detailed insights into which experiments are blind.

Ultrafast photodissociation dynamics of 2-ethylpyrrole: adding insight to experiment with ab initio multiple cloning.

The ultrafast photodissociation dynamics of 2-ethylpyrrole (2-EP) is simulated in a fully quantum manner on the S1 and S2 πσ* states by the ab initio multiple cloning (AIMC) method. AIMC treats electrons with accurate electronic structure methods "on the fly", and nuclear dynamics with wavefunction propagation via a basis set of Ehrenfest trajectory guided Gaussian wavepackets. Total kinetic energy release (TKER) spectra are produced, as well as velocity map images and N-H dissociation times. These are compared to results from time-resolved velocity map imaging studies, and the AIMC method is able to provide quantitative reproduction of experimental data, including dissociation times of 50-80 fs. Novel insight into the dissociation mechanism is then obtained, with the experimentally obtained time constant shown to be composed of two components. Firstly, there is a contribution in <50 fs from 2-EP molecules that have sufficient energy in the N-H stretch coordinate to dissociate almost immediately over the barrier, and this is followed by a second slower contribution from 2-EP molecules that must sample the potential energy surface before finding a way around the barrier to dissociate. This two component mechanism is not observed experimentally due to the temporal widths of the laser pulses obscuring the dynamics in the <50 fs window, and is shown for the first time via theory. Calculations are also performed on selectively deuterated 2-EP, demonstrating that AIMC is able to produce a kinetic isotope effect for the dissociation time constant, and correctly predict a shift to lower energy in the TKER spectrum. The S2 πσ* state is also shown to be unstable with respect to the S1 πσ* state, with the N-H dissociation proceeding along S1 when initially excited to S2. This work demonstrates that the combination of state of the art theory and experiments can provide unprecedented novel insight into the N-H dissociation mechanism, with the tantalising prospect of providing insight into more general heteroatom hydride bond dissociation.

Dynamics of a one-dimensional Holstein polaron: The multiconfigurational Ehrenfest method.

We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integrals and exciton-phonon couplings are carefully examined by a detailed comparison with the fully variational multiple Davydov D2 ansatz. It is found that while the MCE approach and the multi-D2 ansatz produce almost exactly the same results for a small transfer integral, the results obtained by the multi-D2 ansatz start to deviate from those by the MCE approach at longer times for a large transfer integral. A large number of coherent state basis functions are required to characterize the delocalized features of the phonon wavefunction in the case of large transfer integral, which becomes computationally too demanding for the multi-D2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate and efficient simulations of polaron dynamics.

Zombie states for description of structure and dynamics of multi-electron systems.

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.

A Blind Test of Computational Technique for Predicting the Likelihood of Peptide Sequences to Cyclize.

An in silico computational technique for predicting peptide sequences that can be cyclized by cyanobactin macrocyclases, e.g., PatGmac, is reported. We demonstrate that the propensity for PatGmac-mediated cyclization correlates strongly with the free energy of the so-called pre-cyclization conformation (PCC), which is a fold where the cyclizing sequence C and N termini are in close proximity. This conclusion is driven by comparison of the predictions of boxed molecular dynamics (BXD) with experimental data, which have achieved an accuracy of 84%. A true blind test rather than training of the model is reported here as the in silico tool was developed before any experimental data was given, and no parameters of computations were adjusted to fit the data. The success of the blind test provides fundamental understanding of the molecular mechanism of cyclization by cyanobactin macrocyclases, suggesting that formation of PCC is the rate-determining step. PCC formation might also play a part in other processes of cyclic peptides production and on the practical side the suggested tool might become useful for finding cyclizable peptide sequences in general.

Toward fully quantum modelling of ultrafast photodissociation imaging experiments. Treating tunnelling in the ab initio multiple cloning approach.

We present an account of our recent effort to improve simulation of the photodissociation of small heteroaromatic molecules using the Ab Initio Multiple Cloning (AIMC) algorithm. The ultimate goal is to create a quantitative and converged technique for fully quantum simulations which treats both electrons and nuclei on a fully quantum level. We calculate and analyse the total kinetic energy release (TKER) spectra and Velocity Map Images (VMI), and compare the results directly with experimental measurements. In this work, we perform new extensive calculations using an improved AIMC algorithm that now takes into account the tunnelling of hydrogen atoms. This can play an extremely important role in photodissociation dynamics.

Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach.

Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method, a new variant of the MCE approach developed by us for dynamics involving multiple electronic states with numerous abrupt crossings. Excited-state energies, gradients and non-adiabatic coupling terms needed for dynamics simulation are calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. A comparative analysis of our results obtained using MCE-TDDB, the conventional Ehrenfest method and the surface-hopping approach with and without decoherence corrections is presented.

A two-layer approach to the coupled coherent states method.

In this paper, a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, matching-pursuit/split-operator Fourier transform, and configuration interaction expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations.

Fully Atomistic Simulations of Protein Unfolding in Low Speed Atomic Force Microscope and Force Clamp Experiments with the Help of Boxed Molecular Dynamics.

The results of boxed dynamics (BXD) fully atomistic simulations of protein unfolding by atomic force microscopy (AFM) in both force clamp (FC) and velocity clamp (VC) modes are reported. In AFM experiments the unfolding occurs on a time scale which is too long for standard atomistic molecular dynamics (MD) simulations, which are usually performed with the addition of forces which exceed those of experiment by many orders of magnitude. BXD can reach the time scale of slow unfolding and sample the very high free energy unfolding pathway, reproducing the experimental dependence of pulling force against extension and extension against time. Calculations show the presence of the pulling force "humps" previously observed in the VC AFM experiments and allow the identification of intermediate protein conformations responsible for them. Fully atomistic BXD simulations can estimate the rate of unfolding in the FC experiments up to the time scale of seconds.

Ultrafast X-ray Scattering from Molecules.

We present a theoretical framework for the analysis of ultrafast X-ray scattering experiments using nonadiabatic quantum molecular dynamics simulations of photochemical dynamics. A detailed simulation of a pump-probe experiment in ethylene is used to examine the sensitivity of the scattering signal to simulation parameters. The results are robust with respect to the number of wavepackets included in the total expansion of the molecular wave function. Overall, the calculated scattering signals correlate closely with the dynamics of the molecule.

Ab initio multiple cloning simulations of pyrrole photodissociation: TKER spectra and velocity map imaging.

We report a detailed computational simulation of the photodissociation of pyrrole using the ab initio Multiple Cloning (AIMC) method implemented within MOLPRO. The efficiency of the AIMC implementation, employing train basis sets, linear approximation for matrix elements, and Ehrenfest configuration cloning, allows us to accumulate significant statistics. We calculate and analyze the total kinetic energy release (TKER) spectrum and Velocity Map Imaging (VMI) of pyrrole and compare the results directly with experimental measurements. Both the TKER spectrum and the structure of the velocity map image (VMI) are well reproduced. Previously, it has been assumed that the isotropic component of the VMI arises from long time statistical dissociation. Instead, our simulations suggest that ultrafast dynamics contributes significantly to both low and high energy portions of the TKER spectrum.