Hierarchical parallelization of divide‐and‐conquer density functional tight‐binding molecular dynamics and metadynamics simulations

Species-selective nanoreactor molecular dynamics simulations based on linear-scaling tight-binding quantum chemical calculations

Here, extensions to quantum chemical nanoreactor molecular dynamics simulations for discovering complex reactive events are presented. The species-selective algorithm, where the nanoreactor effectively works for the selected desired reactants, was introduced to the original scheme. Moreover, for efficient simulations of large model systems with the modified approach, the divide-and-conquer linear-scaling density functional tight-binding method was exploited. Two illustrative applications of the polymerization of propylene and cyclopropane mixtures and the aggregation of sodium chloride from aqueous solutions indicate that species-selective quantum chemical nanoreactor molecular dynamics is a promising method to accelerate the sampling of multicomponent chemical processes proceeding under relatively mild conditions.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver

The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.

Scalable Ehrenfest Molecular Dynamics Exploiting the Locality of Density-Functional Tight-Binding Hamiltonian

To explore the science behind excited-state dynamics in high-complexity chemical systems, a scalable nonadiabatic molecular dynamics (MD) technique is indispensable. In this study, by treating the electronic degrees of freedom at the density-functional tight-binding level, we developed and implemented a reduced scaling and multinode-parallelizable Ehrenfest MD method. To achieve this goal, we introduced a concept called patchwork approximation (PA), where the effective Hamiltonian for real-time propagation of the electronic density matrix is partitioned into a set of local parts. Numerical results for giant icosahedral fullerenes, which comprise up to 6000 atoms, suggest that the scaling of the present PA-based method is less than quadratic, which yields a significant advantage over the conventional cubic scaling method in terms of computational time. The acceleration by the parallelization on multiple nodes was also assessed. Furthermore, the electronic and structural dynamics resulting from the perturbation by the external electric field were accurately reproduced with the PA, even when the electronic excitation was spatially delocalized.

Quantum-Mechanical Molecular Dynamics Simulations on Secondary Proton Transfer in Bacteriorhodopsin Using Realistic Models

Bacteriorhodopsin (BR) transports a proton from intracellular to extracellular (EC) sites through five proton transfers. The second proton transfer is the release of an excess proton stored in BR into the EC medium, and an atomistic understanding of this whole process has remained unexplored due to its ubiquitous environment. Here, fully quantum mechanical (QM) molecular dynamics (MD) and metadynamics (MTD) simulations for this process were performed at the divide-and-conquer density-functional tight-binding level using realistic models (∼50000 and ∼20000 atoms) based on the time-resolved photointermediate structures from an X-ray free electron laser. Regarding the proton storage process, the QM-MD/MTD simulations confirmed the Glu-shared mechanism, in which an excess proton is stored between Glu194 and Glu204, and clarified that the activation occurs by localizing the proton at Glu204 in the photocycle. Furthermore, the QM-MD/MTD simulations elucidated a release pathway from Glu204 through Ser193 to the EC water molecules and clarified that the proton release starts at ∼250 μs. In the ubiquitous proton diffusion in the EC medium, the transient proton receptors predicted experimentally were assigned to carboxylates in Glu9 and Glu74. Large-scale QM-MD/MTD simulations beyond the conventional sizes, which provided the above findings and confirmations, were possible by adopting our Dcdftbmd program.

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

Tunneling matrix element and tunneling pathways of protein electron transfer calculated with a fragment molecular orbital method

Practical ways to calculate the tunneling matrix elements and analyze the tunneling pathways for protein electron-transfer (ET) reactions with a fragment molecular orbital (FMO) method are presented. The straightforward use of minimal basis sets only for the atoms involved in the covalent bond detachment in FMO can properly describe the ETs through the protein main-chains with the cost-effective two-body corrections (FMO2) without losing the quality of double-zeta basis sets. The current FMO codes have been interfaced with density functional theory, polarizable continuum model, and model core potentials, with which the FMO-based protein ET calculations can consider the effects of electron correlation, solvation, and transition-metal redox centers. The reasonable performance of the FMO-based ET calculations is demonstrated for three different sets of protein-ET model molecules: (1) hole transfer between two tryptophans covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, (2) ET between two plastoquinones covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, and (3) hole transfer between ruthenium (Ru) and copper (Cu) complexes covalently bridged by a stretch of a polyglycine linker as a model for Ru-modified derivatives of azurin.