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.

Proton transfer in bulk water using the full adaptive QM/MM method: integration of solute- and solvent-adaptive approaches

The quantum mechanical/molecular mechanical (QM/MM) method is a hybrid molecular simulation technique that increases the accessibility of local electronic structures of large systems. The technique combines the benefit of accuracy found in the QM method and that of cost efficiency found in the MM method. However, it is difficult to directly apply the QM/MM method to the dynamics of solution systems, particularly for proton transfer. As explained in the Grotthuss mechanism, proton transfer is a structural interconversion between hydronium ions and solvent water molecules. Hence, when the QM/MM method is applied, an adaptive treatment, namely on-the-fly revisions on molecular definitions, is required for both the solute and solvent. Although several solvent-adaptive methods have been proposed, a full adaptive framework, which is an approach that also considers adaptation for solutes, remains untapped. In this paper, we propose a new numerical expression for the coordinates of the excess proton and its control algorithm. Furthermore, we confirm that this method can stably and accurately simulate proton transfer dynamics in bulk water.

Development of Divide-and-Conquer Density-Functional Tight-Binding Method for Theoretical Research on Li-Ion Battery

The density-functional tight-binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear-scaling divide-and-conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium-ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC-DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.

Development of Large-Scale Excited-State Calculations Based on the Divide-and-Conquer Time-Dependent Density Functional Tight-Binding Method

In this study, the divide-and-conquer (DC) method was extended to time-dependent density functional tight-binding (TDDFTB) theory to enable excited-state calculations of large systems and is denoted by DC-TDDFTB. The efficient diagonalization algorithms of TDDFTB and DC-TDDFTB methods were implemented into our in-house program. Test calculations of polyethylene aldehyde and p-coumaric acid, a pigment in photoactive yellow protein, in water demonstrate the high accuracy and efficiency of the developed DC-TDDFTB method. Furthermore, the (TD)DFTB metadynamics simulations of acridinium in the ground and excited states give reasonable p K_a values compared with the corresponding experimental values.

Nanoarchitectonic-Based Material Platforms for Environmental and Bioprocessing Applications

The challenges of pollution, environmental science, and energy consumption have become global issues of broad societal importance. In order to address these challenges, novel functional systems and advanced materials are needed to achieve high efficiency, low emission, and environmentally friendly performance. A promising approach involves nanostructure-level controls of functional material design through a novel concept, nanoarchitectonics. In this account article, we summarize nanoarchitectonic approaches to create nanoscale platform structures that are potentially useful for environmentally green and bioprocessing applications. The introduced platforms are roughly classified into (i) membrane platforms and (ii) nanostructured platforms. The examples are discussed together with the relevant chemical processes, environmental sensing, bio-related interaction analyses, materials for environmental remediation, non-precious metal catalysts, and facile separation for biomedical uses.

Catalytic activity of nickel nanoparticles stabilized by adsorbing polymers for enhanced carbon sequestration

This work shows the potential of nickel (Ni) nanoparticles (NPs) stabilized by polymers for accelerating carbon dioxide (CO₂) dissolution into saline aquifers. The catalytic characteristics of Ni NPs were investigated by monitoring changes in diameter of CO₂ microbubbles. An increase in ionic strength considerably reduces an electrostatic repulsive force in pristine Ni NPs, thereby decreasing their catalytic potential. This study shows how cationic dextran (DEX), nonionic poly(vinyl pyrrolidone) (PVP), and anionic carboxy methylcellulose (CMC) polymers, the dispersive behaviors of Ni NPs can be used to overcome the negative impact of salinity on CO₂ dissolution. The cationic polymer, DEX was less adsorbed onto NPs surfaces, thereby limiting the Ni NPs’ catalytic activity. This behavior is due to a competition for Ni NPs’ surface sites between the cation and DEX under high salinity. On the other hand, the non/anionic polymers, PVP and CMC could be relatively easily adsorbed onto anchoring sites of Ni NPs by the monovalent cation, Na⁺. Considerable dispersion of Ni NPs by an optimal concentration of the anionic polymers improved their catalytic capabilities even under unfavorable conditions for CO₂ dissolution. This study has implications for enhancing geologic sequestration into deep saline aquifers for the purposes of mitigating atmospheric CO₂ levels.