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

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

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

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 quantum dynamics of indistinguishable bosons with the method of coupled coherent states

Computer simulations of many-body quantum dynamics of indistinguishable particles is a challenging task for computational physics. In this paper we demonstrate that the method of coupled coherent states (CCS) developed previously for multidimensional quantum dynamics of distinguishable particles can be used to study indistinguishable bosons in the second-quantization formalism. To prove its validity, the technique termed here coupled coherent states for indistinguishable bosons (CCSB) is tested on two model problems. The first is a system-bath problem consisting of a tunneling mode coupled to a harmonic bath, previously studied by CCS and other methods in distinguishable representation in 20 dimensions. The harmonic bath is comprised of identical oscillators, and may be second quantized for use with CCSB, so that this problem may be thought of as a bosonic bath with an impurity. The cross-correlation function for the dynamics of the system and Fourier transform spectrum compare extremely well with a benchmark calculation, which none of the prior methods of studying the problem achieved. The second model problem involves 100 bosons in a shifted harmonic trap. Breathing oscillations in the one-body density are calculated and shown to compare favorably to a multiconfigurational time-dependent Hartree for bosons calculation, demonstrating the applicability of the method as a new formally exact way to study the quantum dynamics of Bose-Einstein condensates

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

Simulation of the dynamics of vibrationally mediated photodissociation for deuterated pyrrole

The dynamics of photodissociation for vibrationally pre-excited deuterated pyrrole molecules is simulated using ab initio multiple cloning (AIMC) approach. Total kinetic energy release (TKER) spectra and dissociation times are calculated. The results for pyrrole and deuterated pyrrole molecules with and without vibrational pre-excitation are compared. Calculations show that, as expected, the kinetic energy of additional dissociation fragments is lower in deuterated pyrrole and mostly located in the upper-middle part of the TKER spectrum. However, despite lower energy of dissociative bond vibrations, pre-excitation of deuterated pyrrole leads to higher dissociation yield increase than in pyrrole and significantly shortens dissociation time

Quantum system-bath dynamics with quantum superposition sampling and coupled generalized coherent states

Previously, we introduced two versions of the Multiconfigurational Ehrenfest (MCE) approach to high dimensional quantum dynamics. It has been shown that the first version, MCEv1, converges well to the existing benchmarks for high dimensional model systems. At the same time, it was found that the second version, MCEv2, had more difficulty converging in some regimes. As MCEv2 is particularly suited for direct dynamics, it is important to facilitate its convergence. This paper investigates an efficient method of basis set sampling, called Quantum Superposition Sampling (QSS), which dramatically improves the performance of the MCEv2 approach. QSS is tested on the spin-boson model, often used for modeling of open quantum systems. It is also shown that the quantum subsystem in the spin-boson model can be conveniently treated with the help of two level system coherent states. Generalized coherent states, which combine two level system coherent states for the description of the system and Gaussian coherent states for description of the bath, are introduced. Various forms of quantum equations of motion in the basis of generalized coherent states can be developed by analogy with known quantum dynamics equations in the basis of Gaussian coherent states; in particular, the multiconfigurational Ehrenfest method becomes a version of coupled generalized coherent states, and QSS can then be viewed as a generalization of a sampling method known for the existing coupled coherent states method which uses Gaussian coherent states

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

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