A new diabatization scheme for direct quantum dynamics : procrustes diabatization

We present a new scheme for diabatizing electronic potential energy surfaces, for use within the recently implemented direct-dynamics grid-based (DD-GB) class of computational nuclear quantum dynamics methods (DD-SM and DD-MCTDH), called Procrustes diabatization. Calculations on the well-studied molecular systems LiF and the butatriene cation, using both Procrustes diabatization and the previously implemented propagation and projection diabatization schemes, have allowed detailed comparisons to be made which indicate that the new method combines the best features of the older approaches; it generates smooth surfaces which cross at the correct molecular geometries, reproduces interstate couplings accurately and hence allows the correct modelling of non-adiabatic dynamics

Sampling reactive pathways with random walks in chemical space : applications to molecular dissociation and catalysis

Automatically generating chemical reaction pathways is a significant computational challenge, particularly in the case where a given chemical system can exhibit multiple reactants and products, as well as multiple pathways connecting these. Here, we outline a computational approach to allow automated sampling of chemical reaction pathways, including sampling of different chemical species at the reaction end-points. The key features of this scheme are (i) introduction of a Hamiltonian which describes a reaction “string” connecting reactant and products, (ii) definition of reactant and product species as chemical connectivity graphs, and (iii) development of a scheme for updating the chemical graphs associated with the reaction end-points. By performing molecular dynamics sampling of the Hamiltonian describing the complete reaction pathway, we are able to sample multiple different paths in configuration space between given chemical products; by periodically modifying the connectivity graphs describing the chemical identities of the end-points we are also able to sample the allowed chemical space of the system. Overall, this scheme therefore provides a route to automated generation of a “roadmap” describing chemical reactivity. This approach is first applied to model dissociation pathways in formaldehyde, H2CO, as described by a parameterised potential energy surface (PES). A second application to the HCo(CO)3 catalyzed hydroformylation of ethene (oxo process), using density functional tight-binding to model the PES, demonstrates that our graph-based approach is capable of sampling the intermediate paths in the commonly accepted catalytic mechanism, as well as several secondary reactions. Further algorithmic improvements are suggested which will pave the way for treating complex multi-step reaction processes in a more efficient manner

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

We present a method for performing non-adiabatic, grid-based nuclear quantum dynamics calculations using diabatic potential energy surfaces (PESs) generated “on-the-fly”. Gaussian process regression is used to interpolate PESs by using electronic structure energies, calculated at points in configuration space determined by the nuclear dynamics, and diabatising the results using the propagation diabatisation method reported recently (Richings and Worth, 2015). Our new method is successfully demonstrated using a grid-based approach to model the non-adiabatic dynamics of the butatriene cation. Overall, our scheme offers a route towards accurate quantum dynamics on diabatic PESs learnt on-the-fly

Direct quantum dynamics using grid-based wavefunction propagation and machine-learned potential energy surfaces

We describe a method for performing nuclear quantum dynamics calculations using standard, grid-based algorithms, including the multi configurational time-dependent Hartree (MCTDH) method, where the potential energy surface (PES) is calculated “on-the-fly”. The method of Gaussian process regression (GPR) is used to construct a global representation of the PES using values of the energy at points distributed in molecular configuration space during the course of the wavepacket propagation. We demonstrate this direct dynamics approach for both an analytical PES function describing 3-dimensional proton transfer dynamics in malonaldehyde, and for 2- and 6-dimensional quantum dynamics simulations of proton transfer in salicylaldimine. In the case of salicylaldimine we also perform calculations in which the PES is constructed using Hartree-Fock calculations through an interface to an ab initio electronic structure code. In all cases, the results of the quantum dynamics simulations are in excellent agreement with previous simulations of both systems, yet do not require prior fitting of a PES at any stage. Our approach (implemented in a development version of the Quantics package) opens a route to performing accurate quantum dynamics simulations via wavefunction propagation of many-dimensional molecular systems in a direct and efficient manner

Improved on-the-fly MCTDH simulations with many-body-potential tensor decomposition and projection diabatisation

We have recently demonstrated how potential energy surface (PES) interpola- tion methods such as kernel ridge regression (KRR), can be combined with accu- rate wavefunction time-propagation methods, specifically the multi-configuration time- dependent Hartree (MCTDH) method, to generate a new “on-the-fly” MCTDH scheme (DD-MCTDH) which does not require the pre-fitting of the PES which is normally re- quired by MCTDH. Specifically, we have shown how our DD-MCTDH strategy can be used to model non-adiabatic dynamics in a 4-mode/2-state model of pyrazine, with ab initio electronic structure calculations performed directly during propagation, requir- ing around 100 hours of computer wall-time. In this Article, we show how the efficiency and accuracy of DD-MCTDH can be dramatically improved further still by: (i) using systematic tensor decompositions of the KRR PES, and (ii) using a novel scheme for di- abatisation within the framework of configuration interaction (CI) methods which only requires local adiabatic electronic states, rather than non-adiabatic coupling matrix el- ements. The result of these improvements is that our latest version of DD-MCTDH can perform a 12-mode/2-state simulation of pyrazine, with PES evaluations at CAS level, in just 29-90 hours on a standard desktop computer; this work therefore represents an enormous step towards direct quantum dynamics with MCTDH

Quantum dynamics with short-time trajectories and minimal adaptive basis sets

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation

Solving the Schrödinger equation using program synthesis

We demonstrate that a program synthesis approach based on a linear code representation can be used to generate algorithms which approximate the ground-state solutions of one- dimensional time-independent Schrödinger equations constructed with bound polynomial potential energy surfaces (PESs). Here, an algorithm is constructed as a linear series of instructions operating on a set of input vectors, matrices and constants which define the problem characteristics, such as the PES. Discrete optimization is performed using sim- ulated annealing in order to identify sequences of code-lines, operating on the program inputs, which can reproduce the expected ground-state wavefunctions ψ(x) for a set of target PESs. The outcome of this optimization is not simply a mathematical function ap- proximating ψ(x), but is instead a complete algorithm which converts the input vectors describing the system into a ground-state solution of the Schrödinger equation. These ini- tial results point the way towards an alternative route for developing novel algorithms for quantum chemistry applications

Assessing mixed quantum-classical molecular dynamics methods for nonadiabatic dynamics of molecules on metal surfaces

Mixed-quantum classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule-metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, Independent Electron Surface Hopping, and the Broadened Classical Master Equation approach. In the case of Independent Electron Surface Hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally-inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence, but return different vibrational energy distributions. Finally, by varying the molecule-metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable.Comment: 15 pages, 13 figure

Robustness, efficiency, and optimality in the Fenna-Matthews-Olson photosynthetic pigment-protein complex

Pigment-protein complexes (PPCs) play a central role in facilitating excitation energy transfer (EET) from light-harvesting antenna complexes to reaction centres in photosynthetic systems; understanding molecular organisation in these biological networks is key to developing better artificial light-harvesting systems. In this article, we combine quantum-mechanical simulations and a network-based picture of transport to investigate how chromophore organization and protein environment in PPCs impacts on EET efficiency and robustness. In a prototypical PPC model, the Fenna-Matthews-Olson (FMO) complex, we consider the impact on EET efficiency of both disrupting the chromophore network and changing the influence of (local and global) environmental dephasing. Surprisingly, we find a large degree of resilience to changes in both chromophore network and protein environmental dephasing, the extent of which is greater than previously observed; for example, FMO maintains EET when 50% of the constituent chromophores are removed, or when environmental dephasing fluctuations vary over two orders-of-magnitude relative to the in vivo system. We also highlight the fact that the influence of local dephasing can be strongly dependent on the characteristics of the EET network and the initial excitation; for example, initial excitations resulting in rapid coherent decay are generally insensitive to the environment, whereas the incoherent population decay observed following excitation at weakly coupled chromophores demonstrates a more pronounced dependence on dephasing rate as a result of the greater possibility of local exciton trapping. Finally, we show that the FMO electronic Hamiltonian is not particularly optimised for EET; instead, it is just one of many possible chromophore organisations which demonstrate a good level of EET transport efficiency following excitation at different chromophores. Overall, these robustness and efficiency characteristics are attributed to the highly connected nature of the chromophore network and the presence of multiple EET pathways, features which might easily be built into artificial photosynthetic systems