## RESEARCH

### Scalable MO Theory

The computational cost of molecular orbital (MO) theory is on the orders of N^{4}-N^{6} or even greater with respect to number of atoms N. The development of scalable methods to minimize the required orders is vitally important for large-scale MO calculations. We have studied fast algorithms and approximate decomposition schemes for electron repulsion integrals. The minimax quadrature was also introduced in Laplace-transformed Møller-Plesset perturbation theory. Those techniques have been applied to various hybrid methods consisting of many-body perturbation and coupled-cluster theories.

### Explicitly Correlated F12 Electronic Structure Theory

The slow convergence of configuration interaction (CI) expansion has presented a formidable barrier to high-accuracy calculations. The standard orbital-based methods require sizable basis sets for accurate results. We have developed F12 electronic structure theory based on the rational generator for the electron-electron cusp conditions along with the Slater-type (exponential) correlation factor that is dependent on the inter-electronic distance explicitly. F12 theory has been applied to various perturbation, CI, and coupled-cluster methods as standard means in highly accurate electronic structure calculations.

### 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 crossing deterministic and stochastic techniques on the exponential scaling full CI problem, MSQMC enables us to calculate quasi-degenerate and arbitrary excited states accurately avoiding the sign problem. We are implementing efficient MSQMC methods to realize accurate calculations of strongly correlated electrons where the usual electronic structure methods cannot be applied even qualitatively. We employ MSQMC for highly excited electronic states and transition metal complexes in oxgen evolution.

### Full coupled-cluster expansion for strong electron correlation

Theoretical development of strong electron correlation will open a wide variety of fields transcending the traditional framework of electronic structure calculations. For this purpose, selected CI methods using stochastic and deterministic algorithms have been developed in recent years. Nevertheless, the exponentially increasing complexity of the CI expansion with the system size prevents the applicability of such approaches. We alternatively have developed a full coupled-cluster reduction (FCCR) exploiting the sparsity of the cluster operators and their products. FCCR features the treatment of dynamic and nondynamic correlation effects on the same footing realizing precise design of multi-nuclear transition metal catalysis and high-temperature superconducting materials.

### Development of Massively Parallel Computation Algorithms

The advanced use of massively parallel environments is progressing rapidly in high-performance computing, and it is forecast that the number of CPU cores employed in applications has increased by 2-5 orders of magnitude. We can therefore envision a new computational-science paradigm that brings forth results substantially different in terms of accuracy and spatial/time scales. Using the Message Passing Interface (MPI) and Open Multi-Processing (OpenMP), methods and algorithms are developed targeting up to several hundred-thousand CPU cores. Moreover, general-purpose programs in molecular science are getting extremely complex, and technology for automatically generating source code from basic equations has been progressing in recent years. We study optimization and automatic tuning by sorting operators based on the symbolic representations of formulas.

### Electronic Structure Theory in Solution

Since most of industrially important chemical reactions proceed in solution, studying the solvation effects is essential in chemistry. We applied the extended RISM theory to ab initio theory for the first time to develop a fast and atomistic solvation model (RISM-SCF). We have further developed a novel integral-equation theory based on the partial wave expansion of the molecular Ornstein-Zernike equation. By introducing the full intra-molecular correlation function with angular dependence, we have introduced a rigorous theoretical framework that is eligible to explain the interactions of chiral molecules. This feature could not be obtained only by the use of atomic distances. The solvation free energy expression from PW has been applied successfully to the calculation of partition coefficients of various organic molecules.

### Development of Novel QM/MM Methods

Hybrid methods combining quantum and molecular mechanics (QM/MM methods) are powerful tools for describing chemical reactions in the presence of enzymes or solvents. We have extended the generalized hybrid orbital (GHO) QM/MM method using charge equalization and orthogonalization methods with respect to the auxiliary orbitals. The method has been applied to PKA (c-AMP dependent protein kinase) and various enzymatic reactions. The restrained hybrid matrix method accurately reproduces the geometric structure about the QM/MM boundary. The molecular dynamics simulation based on the GHO-MP2 energy gradient has been utilized to calculate CD spectra in enzyme.

### Development of the GELLAN Quantum Chemistry Program

We are developing the GELLAN quantum chemistry program as a platform to increase the activity of the research group. Various domestic and foreign researchers are involved in the development of GELLAN.