RESEARCH

Scalable MO Theory

The computational cost of molecular orbital (MO) theory exhibits a steep scaling of N4-N6 or higher, with respect to number of atoms N. Consequently, the development of scalable approaches that reduce the computational scaling is of crucial importance for large-scale MO calculations. We investigate fast algorithms and approximate decomposition schemes for electron repulsion integrals. Furthermore, minimax quadrature is incorporated into Laplace-transformed Møller-Plesset perturbation theory. Those methodologies have been successfully applied to various hybrid approaches integrating many-body perturbation and coupled-cluster theories.

Explicitly Correlated F12 Electronic Structure Theory

The slow convergence of configuration interaction (CI) expansion continues to pose a major obstacle to high-accuracy electronic structure calculations, as standard orbital-based methods require large basis sets. We have developed F12 electronic structure theory using a rational generator that enforces the electron-electron cusp conditions in combination with the Slater-type (exponential) correlation factor. F12 methods have been successfully applied to perturbation, CI, and coupled-cluster theories and are now standard tools for acheiving high accuracy. In addition, the projective transcorrelated Hamiltonian including F12 effects has been applied to stronlgy correlatted systems and to the construction of accurate qubit Hamiltonian for quantum computation.

Model Space Quantum Monte Carlo Method

We advocate the model space quantum Monte Carlo (MSQMC) that stochastically samples the transfer matrix in the effective Hamiltonian of energy dependent partitioning (EDP). By combining deterministic and stochastic techniques to address the exponential scaling CI problem, MSQMC enables accurate calculations of quasi-degenerate states and arbitrary excited states while avoiding the sign problem. We are implementing efficient MSQMC implementations to acheive accurate descriptions of strongly correlated electrons, where conventional electronic structure methods often fail even qualitatively. In addition, we apply MSQMC to highly excited electronic states and transition metal complexes in oxgen evolution.

Full coupled-cluster expansion for strong electron correlation

The theoretical development of methods for treating strong electron correlation is expected to open a wide range of research fields that transcend the traditional framework of electronic structure calculations. To this end, selected CI methods employing both stochastic and deterministic algorithms have been developed in recent years. Nevertheless, the exponentially increasing complexity of the CI expansion with system size severely limits the applicability of these approaches. As an alternative, we have developed full coupled-cluster reduction (FCCR), which exploits the sparsity of cluster operators and their products. FCCR treats dynamic and nondynamic correlation effects on an equal footing to enable accurate modeling of multi-nuclear transition metal catalysis.

Development of Massively Parallel Computation Algorithms

The advanced use of massively parallel environments is rapidly progressing in high-performance computing, and it is forecast that the number of CPU cores employed in applications will increase by two to five orders of magnitude. This trend enables a new computational-science paradigm capable of delivering results that differ substantially in achievable accuracy as well as spatial and temporal scales. Using the Message Passing Interface (MPI) and Open Multi-Processing (OpenMP), we develop methods and algorithms designed to scale to several hundred-thousand CPU cores. In parallel, general-purpose software in molecular science has become increasingly complex, motivating recent advances in technologies for automatically generating source code from fundamental equations. We investigate optimization and automatic tuning techniques based on by sorting and restructuring operators using symbolic representations of mathematical formulas.

Electronic Structure Theory in Solution

Because most industrially important chemical reactions occur in solution, understanding solvation effects is essential in chemistry. We were the first to couple extended reference interaction site model (RISM) theory with ab initio electronic structure methods, leading to the development of a fast and fully atomistic solvation model (RISM-SCF). We subsequently developed a novel integral-equation theory based on the partial-wave expansion of the molecular Ornstein–Zernike equation. By introducing the full intramolecular correlation function with explicit angular dependence, this framework provides a rigorous theoretical basis for describing interactions involving chiral molecules—an effect that cannot be captured using atomic distances alone. The solvation free energy expression derived from the partial-wave formulation has been successfully applied to the calculation of partition coefficients for a wide range of organic molecules.

Development of Novel QM/MM Methods

Hybrid quantum mechanics/molecular mechanics (QM/MM) methods are powerful tools for describing chemical reactions in enzymatic and solvated environments. We have extended the generalized hybrid orbital (GHO) QM/MM approach by incorporating charge equalization and orthogonalization schemes with respect to auxiliary orbitals. This method has been applied to cAMP-dependent protein kinase (PKA) and to a variety of enzymatic reactions. In addition, the restrained hybrid matrix method accurately reproduces molecular geometries at the QM/MM boundary. Molecular dynamics simulations based on GHO–MP2 energy gradients have further been employed to compute circular dichroism (CD) spectra of enzymes.

Development of the GELLAN Quantum Chemistry Program

We are developing the GELLAN quantum chemistry program as a collaborative platform to enhance the research activities of our group. Researchers from both domestic and international institutions are actively involved in its development.