Full wave function cloning for improving convergence of the multiconfigurational Ehrenfest method: Tests in the zero-temperature spin-boson model regime.

In this paper, we report a new algorithm for creating an adaptive basis set in the Multiconfigurational Ehrenfest (MCE) method, which is termed Full Cloning (FC), and test it together with the existing Multiple Cloning (MC) using the spin-boson model at zero-temperature as a benchmark. The zero-temperature spin-boson regime is a common hurdle in the development of methods that seek to model quantum dynamics. Two versions of MCE exist. We demonstrate that MC is vital for the convergence of MCE version 2 (MCEv2). The first version (MCEv1) converges much better than MCEv2, but FC improves its convergence in a few cases where it is hard to converge it with the help of a reasonably small size of the basis set.

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.

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.

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.

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.

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.

Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics.

We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as "cloning," in analogy to the "spawning" procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, "trains," as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.

Simulation of ultrafast photodynamics of pyrrole with a multiconfigurational Ehrenfest method.

We report the first results of ab initio multiconfigurational Ehrenfest simulations of pyrrole photodynamics. We note that, in addition to the two intersections of 1(1)A2 and 1(1)B1 states with the ground state 1(1)A1, which are known to be responsible for N-H bond fission, another intersection between the 1(2)A2 and 1(2)B1 states of the resulting molecular radical becomes important after the departure of the H atom. This intersection, which is effectively between the two lowest electronic states of the pyrrolyl radical, may play a significant role in explaining the branching ratio between the two states observed experimentally. The exchange of population between the two states of pyrrolyl occurs on a longer scale than that of N-H bond fission.

Numerical implementation and test of the modified variational multiconfigurational Gaussian method for high-dimensional quantum dynamics.

In this paper, a new numerical implementation and a test of the modified variational multiconfigurational Gaussian (vMCG) equations are presented. In vMCG, the wave function is represented as a superposition of trajectory guided Gaussian coherent states, and the time derivatives of the wave function parameters are found from a system of linear equations, which in turn follows from the variational principle applied simultaneously to all wave function parameters. In the original formulation of vMCG, the corresponding matrix was not well-behaved and needed regularization, which required matrix inversion. The new implementation of the modified vMCG equations seems to have improved the method, which now enables straightforward solution of the linear system without matrix inversion, thus achieving greater efficiency, stability and robustness. Here the new version of the vMCG approach is tested against a number of benchmarks, which previously have been studied by split-operator, multiconfigurational time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH) techniques. The accuracy and efficiency of the new implementation of vMCG is directly compared with the method of coupled coherent states (CCS), another technique that uses trajectory guided grids. More generally we demonstrate that trajectory guided Gaussian based methods are capable of simulating quantum systems with tens or even hundreds of degrees of freedom previously accessible only for MCTDH and ML-MCTDH.

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.

On-the-fly ab initio molecular dynamics with multiconfigurational Ehrenfest method.

In this article we report the formalism and first implementation of the ab initio multiconfigurational Ehrenfest (AI-MCE) method for simulation of ultrafast nonadiabatic dynamics, which uses the MOLPRO electronic structure program to calculate the potential energy surfaces on the fly. The approach is tested on the benchmark of the excited ππ∗ state dynamics of ethylene producing the dynamics which agree with previous simulations by ab initio multiple spawning technique. The AI-MCE seems to be robust, stable and efficient.

Peptide kinetics from picoseconds to microseconds using boxed molecular dynamics: power law rate coefficients in cyclisation reactions.

Molecular dynamics (MD) methods are increasingly widespread, but simulation of rare events in complex molecular systems remains a challenge. We recently introduced the boxed molecular dynamics (BXD) method, which accelerates rare events, and simultaneously provides both kinetic and thermodynamic information. We illustrate how the BXD method may be used to obtain high-resolution kinetic data from explicit MD simulations, spanning picoseconds to microseconds. The method is applied to investigate the loop formation dynamics and kinetics of cyclisation for a range of polypeptides, and recovers a power law dependence of the instantaneous rate coefficient over six orders of magnitude in time, in good agreement with experimental observations. Analysis of our BXD results shows that this power law behaviour arises when there is a broad and nearly uniform spectrum of reaction rate coefficients. For the systems investigated in this work, where the free energy surfaces have relatively small barriers, the kinetics is very sensitive to the initial conditions: strongly non-equilibrium conditions give rise to power law kinetics, while equilibrium initial conditions result in a rate coefficient with only a weak dependence on time. These results suggest that BXD may offer us a powerful and general algorithm for describing kinetics and thermodynamics in chemical and biochemical systems.