A complete description of tunnelling using direct quantum dynamics simulation: Salicylaldimine proton transfer

Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction

We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the time-dependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single- and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.

Propagating multi-dimensional density operators using the multi-layer-ρ multi-configurational time-dependent Hartree method

Solving the Liouville-von-Neumann equation using a density operator provides a more complete picture of dynamical quantum phenomena than by using a wavepacket and solving the Schrödinger equation. As density operators are not restricted to the description of pure states, they can treat both thermalized and open systems. In practice, however, they are rarely used to study molecular systems as the computational resources required are even more prohibitive than those needed for wavepacket dynamics. In this paper, we demonstrate the potential utility of a scheme based on the powerful multi-layer multi-configurational time-dependent Hartree algorithm for propagating multi-dimensional density operators. Studies of two systems using this method are presented at a range of temperatures and including up to 13 degrees of freedom. The first case is single proton transfer in salicylaldimine, while the second is double proton transfer in porphycene. A comparison is also made with the approach of using stochastic wavepackets.

Variational Approach for Linearly Dependent Moving Bases in Quantum Dynamics: Application to Gaussian Functions

In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schrödinger equation. The method is based on (i) the definition of a linearly independent working space and (ii) a variational construction of the propagator over finite time steps. The second point allows the method to properly account for changes in the dimensionality of the working space along the time evolution. In particular, the time evolution is represented by a semi-unitary transformation. Tests are carried out on a quartic double-well potential with Gaussian basis functions whose centers evolve according to classical equations of motion. We show that the resulting dynamics converges to the exact one and is unitary by construction.

Analyzing Grid-Based Direct Quantum Molecular Dynamics Using Non-Linear Dimensionality Reduction

Grid-based schemes for simulating quantum dynamics, such as the multi-configuration time-dependent Hartree (MCTDH) method, provide highly accurate predictions of the coupled nuclear and electronic dynamics in molecular systems. Such approaches provide a multi-dimensional, time-dependent view of the system wavefunction represented on a coordinate grid; in the case of non-adiabatic simulations, additional information about the state populations adds a further layer of complexity. As such, wavepacket motion on potential energy surfaces which couple many nuclear and electronic degrees-of-freedom can be extremely challenging to analyse in order to extract physical insight beyond the usual expectation-value picture. Here, we show that non-linear dimensionality reduction (NLDR) methods, notably diffusion maps, can be adapted to extract information from grid-based wavefunction dynamics simulations, providing insight into key nuclear motions which explain the observed dynamics. This approach is demonstrated for 2-D and 9-D models of proton transfer in salicylaldimine, as well as 8-D and full 12-D simulations of cis-trans isomerization in ethene; these simulations demonstrate how NLDR can provide alternative views of wavefunction dynamics, and also highlight future developments.

Nonadiabatic quantum dynamics of the coherent excited state intramolecular proton transfer of 10-hydroxybenzo[h]quinoline

The photoinduced nonadiabatic dynamics of the enol-keto isomerization of 10-hydroxybenzo[h]quinoline (HBQ) are studied computationally using high-dimensional quantum dynamics. The simulations are based on a diabatic vibronic coupling Hamiltonian, which includes the two lowest [Formula: see text] excited states and a [Formula: see text] state, which has high energy in the Franck-Condon zone, but significantly stabilizes upon excited state intramolecular proton transfer. A procedure, applicable to large classes of excited state proton transfer reactions, is presented to parametrize this model using potential energies, forces and force constants, which, in this case, are obtained by time-dependent density functional theory. The wave packet calculations predict a time scale of 10-15 fs for the photoreaction, and reproduce the time constants and the coherent oscillations observed in time-resolved spectroscopic studies performed on HBQ. In contrast to the interpretation given to the most recent experiments, it is found that the reaction initiated by [Formula: see text] photoexcitation proceeds essentially on a single potential energy surface, and the observed coherences bear signatures of Duschinsky mode-mixing along the reaction path. The dynamics after the [Formula: see text] excitation are instead nonadiabatic, and the [Formula: see text] state plays a major role in the relaxation process. The simulations suggest a mainly active role of the proton in the isomerization, rather than a passive migration assisted by the vibrations of the benzoquinoline backbone.

Improved algorithm for the direct dynamics variational multi-configurational Gaussian method

The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations.

Photooxidation of water with heptazine-based molecular photocatalysts: Insights from spectroscopy and computational chemistry

We present a conspectus of recent joint spectroscopic and computational studies that provided novel insight into the photochemistry of hydrogen-bonded complexes of the heptazine (Hz) chromophore with hydroxylic substrate molecules (water and phenol). It was found that a functionalized derivative of Hz, tri-anisole-heptazine (TAHz), can photooxidize water and phenol in a homogeneous photochemical reaction. This allows the exploration of the basic mechanisms of the proton-coupled electron-transfer (PCET) process involved in the water photooxidation reaction in well-defined complexes of chemically tunable molecular chromophores with chemically tunable substrate molecules. The unique properties of the excited electronic states of the Hz molecule and derivatives thereof are highlighted. The potential energy landscape relevant for the PCET reaction has been characterized by judicious computational studies. These data provided the basis for the demonstration of rational laser control of PCET reactions in TAHz-phenol complexes by pump-push-probe spectroscopy, which sheds light on the branching mechanisms occurring by the interaction of nonreactive locally excited states of the chromophore with reactive intermolecular charge-transfer states. Extrapolating from these results, we propose a general scenario that unravels the complex photoinduced water-splitting reaction into simple sequential light-driven one-electron redox reactions followed by simple dark radical-radical recombination reactions.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy

Quantum dynamics simulations are used to simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom.

Computational Approach to Molecular Catalysis by 3d Transition Metals: Challenges and Opportunities

Computational chemistry provides a versatile toolbox for studying mechanistic details of catalytic reactions and holds promise to deliver practical strategies to enable the rational in silico catalyst design. The versatile reactivity and nontrivial electronic structure effects, common for systems based on 3d transition metals, introduce additional complexity that may represent a particular challenge to the standard computational strategies. In this review, we discuss the challenges and capabilities of modern electronic structure methods for studying the reaction mechanisms promoted by 3d transition metal molecular catalysts. Particular focus will be placed on the ways of addressing the multiconfigurational problem in electronic structure calculations and the role of expert bias in the practical utilization of the available methods. The development of density functionals designed to address transition metals is also discussed. Special emphasis is placed on the methods that account for solvation effects and the multicomponent nature of practical catalytic systems. This is followed by an overview of recent computational studies addressing the mechanistic complexity of catalytic processes by molecular catalysts based on 3d metals. Cases that involve noninnocent ligands, multicomponent reaction systems, metal-ligand and metal-metal cooperativity, as well as modeling complex catalytic systems such as metal-organic frameworks are presented. Conventionally, computational studies on catalytic mechanisms are heavily dependent on the chemical intuition and expert input of the researcher. Recent developments in advanced automated methods for reaction path analysis hold promise for eliminating such human-bias from computational catalysis studies. A brief overview of these approaches is presented in the final section of the review. The paper is closed with general concluding remarks.

Direct quantum dynamics using variational Gaussian wavepackets and Gaussian process regression

The method of direct variational quantum nuclear dynamics in a basis of Gaussian wavepackets, combined with the potential energy surfaces fitted on-the-fly using Gaussian process regression, is described together with its implementation. Enabling exact and efficient analytic evaluation of Hamiltonian matrix elements, this approach allows for black-box quantum dynamics of multidimensional anharmonic molecular systems. Example calculations of intra-molecular proton transfer on the electronic ground state of salicylaldimine are provided, and future algorithmic improvements as well as the potential for multiple-state non-adiabatic dynamics are discussed.

Modified Gaussian Wave Packet Method for Calculating Initial State Wave Functions in Photodissociation

A modified Gaussian wave packet relaxation method is proposed to calculate the ground state wave function using an expansion of frozen Gaussian wave packets. This new procedure consists of two steps. In the first step, a multidimensional Gaussian product placed at the ground state equilibrium geometry is propagated in imaginary time. The relaxation optimizes the widths of the one-dimensional Gaussians. In the second step, additional Gaussian wave packets with the same widths are placed near the equilibrium geometry, and the corresponding expansion coefficients are optimized using the same relaxation method. This new algorithm is tested in photodissociation of NOCl and NH₃, and the results show good agreement with the exact results in the energy, wave function, and absorption spectrum. In particular, the highly structured absorption spectrum of NH₃ is reproduced, underscoring the accuracy of both the initial wave packet and the excited state propagation.

Mixed Quantum/Classical Method for Nonadiabatic Quantum Dynamics in Explicit Solvent Models: The ππ*/nπ* Decay of Thymine in Water as a Test Case

We present a novel mixed quantum classical dynamical method to include solvent effects on internal conversion (IC) processes. All the solute degrees of freedom are represented by a wavepacket moving according to nonadiabatic quantum dynamics, while the motion of an explicit solvent model is described by an ensemble of classical trajectories. The mutual coupling of the solute and solvent dynamics is included within a mean-field framework and the quantum and classical equations of motions are solved simultaneously. As a test case we apply our method to the ultrafast ππ* → nπ* decay of thymine in water. Solvent dynamical response modifies IC yield already on the 50 fs time scale. This effect is due to water librational motions that stabilize the most populated state. Pure static disorder, that is, the existence of different solvent configurations when photoexcitation takes place, also has a remarkable impact on the dynamics.

Accelerating direct quantum dynamics using graphical processing units

The direct dynamics variational multi-configurational Gaussian (DD-vMCG) method is combined with electronic structure calculations accelerated by Graphical Processing Units (GPUs). This is used to identify GPU acceleration will have a significant effect for both ground and excited state simulations.