Chapter 8

Computational Molecular ScienceResearch Team

8.1 Members

Takahito Nakajima (Team Leader)

Noriyuki Minezawa (Research Scientist)

Takehiro Yonehara (Research Scientist)

Keisuke Sawada (Postdosctoral Researcher)

William Dawson (Postdosctoral Researcher)

Wataru Uemura (Postdosctoral Researcher)

Kizashi Yamaguchi (Visiting Researcher)

Takashi Kawakami (Visiting Researcher)

Muneaki Kamiya (Visiting Researcher)

8.2 Research Activities

8.2.1 Development of original molecular theory

An atomic- and molecular-level understanding of drug actions and the mechanisms of a variety of chemicalreactions will provide insight for developing new drugs and materials. Although a number of diverse experimentalmethods have been developed, it still remains difficult to investigate the state of complex molecules and tofollow chemical reactions in detail. Therefore, a theoretical molecular science that can predict the propertiesand functions of matter at the atomic and molecular levels by means of molecular theoretical calculations iskeenly awaited as a replacement for experiment. Theoretical molecular science has recently made great stridesdue to progress in molecular theory and computer development. However, it is still unsatisfactory for practicalapplications. Consequently, our main goal is to realize an updated theoretical molecular science by developinga molecular theory and calculation methods to handle large complex molecules with high precision under avariety of conditions. To achieve our aim, we have so far developed several methods of calculation. Examplesinclude a way for resolving a significant problem facing conventional methods of calculation, in which thecalculation volume increases dramatically when dealing with larger molecules; a way for improving the precisionof calculations in molecular simulations; and a way for high-precision calculation of the properties of moleculescontaining heavy atoms such as metal atoms.

77

78 CHAPTER 8. COMPUTATIONAL MOLECULAR SCIENCE RESEARCH TEAM

8.2.2 New molecular science software NTChem

Quantum chemistry software comprises immensely useful tools in material and biological science research.Widely diverse programs have been developed in Western countries as Japan has lagged. In fact, only a fewprograms have been developed in Japan. The mission of our research team is to provide K computer users witha high-performance software for quantum molecular simulation. In the early stage of the K computer project,no quantum chemistry software was available for general purpose and massively parallel computation on the Kcomputer because not every program was designed for use on it. Therefore, we have chosen to develop a newcomprehensive ab initio quantum chemistry software locally: NTChem. NTChem is completely new softwarethat implements not only standard quantum chemistry approaches, but also original and improved theoreticalmethods that we have developed in our research work. The main features of the current version, NTChem2013,are the following:

1). Electronic structure calculation of the ground state of atoms and molecules based on Hartree-Fock (HF)and density functional theory (DFT) methods.

2). Linear-scaling or low-scaling DFT: Gaussian and finite-element Coulomb (GFC) resolution-of-the-identity(RI) DFT, pseudospectral DFT/HF, and dual-level DFT.

3). Low-scaling SCF calculation using diagonalization-free approaches: purification density matrix, pseudo-diagonalization, and quadratic convergence SCF.

4). Excited-state DFT calculation: time-dependent DFT (TDDFT) and transition potential (DFT-TP).

5). Accurate electron correlation methods for ground and excited states: Møller-Plesset perturbation theory,coupled-cluster (CC) theory, and quantum Monte Carlo (QMC) method.

6). Massively parallel computing on the K computer and Intel-based architectures: HF, DFT, resolution-of-the-identity second-order Møller-Plesset (RI-MP2) method, and QMC method.

7). Two-component relativistic electronic structure calculation with spin-orbit (SO) interactions: Douglas-Kroll (DK) (DK1, DK2, and DK3), regular approximation (RA) (zeroth-order RA (ZORA) and infinite-order RA (IORA)), and Relativistic scheme for Eliminating Small Components (RESC).

8). Model calculations for large molecular systems: quantum mechanics/molecular mechanics (QM/MM) andOur own N-layered Integrated molecular Orbital and molecular Mechanics (ONIOM).

9). Calculation of solvation effects: COnductor-like Screening MOdel (COSMO) (interfaced with the HONDOprogram), averaged solvent electrostatic potential/molecular dynamics (ASEP/MD), and QM/MM-MD.

10). Efficient calculation for chemical reaction pathway.

11). Ab initio molecular dynamics calculation.

12). Calculation of magnetic properties: nuclear magnetic resonance (NMR) chemical shifts, magnetizabilities,and electron paramagnetic resonance (EPR) g tensors.

13). Population analysis: Mulliken and natural bond orbital (NBO) analysis (interfaced with NBO 6.0).

14). Orbital interaction analysis: maximally interacting orbital (MIO) and paired interacting orbital (PIO)methods.

8.3 Research Results and Achievements

8.3.1 Massively Parallel Linear Scaling Quantum Chemistry

The goal of this project is to develop techniques for efficiently performing quantum chemistry calculationson systems with thousands of atoms. There are two main operations required in quantum chemistry codes:computing the Fock matrix, and solving for the density matrix. Commonly used computational techniques haveO(N3) or worse scaling behavior, which severely limits the size of systems that can be treated. Additionally,treating systems of this size requires parallel algorithms that reduce both the computational time and thememory footprint. In FY2016, we developed a parallel library for performing the sparse matrix operationswhich are at the heart of low order scaling methods. In this previous fiscal year, we built upon this library toenable calculations on large systems in the NTChem code.

In FY2017, we performed two studies to help understand different linear scaling solvers. Using the sparsematrix library we had developed, we implemented linear scaling methods based on density matrix purification

8.3. RESEARCH RESULTS AND ACHIEVEMENTS 79

and minimization, and analyzed their performance on matrices from several different quantum chemistry codes.We also showed how the same techniques used in quantum chemistry can also be used for network science. Asa part of the RIKEN-CEA collaboration, we helped benchmark and analyze the CheSS library which uses theFermi Operator Expansion technique as a solver.

In Fig. 8.1, we compared the performance of the sparse matrix based solvers with the EigenExa eigen-solver library. The sparse matrix based solver performs significantly better, enabling calculations using tens ofthousands of basis functions.

Figure 8.1: Performance of the density matrix solver.

8.3.1.1 Massively parallel sparse matrix function calculations with NTPoly[1]

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. Thetheory of matrix functions is a well developed framework with a wide range of applications including differentialequations, graph theory, and electronic structure calculations. One particularly important application area isdiagonalization free methods in quantum chemistry. When the input and output of the matrix function aresparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. Wepresent a library based on these methods that can compute a variety of matrix functions. Distributed memoryparallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP taskparallellization is utilized to implement hybrid parallelization. We describe NTPoly’s interface and show how itcan be integrated with programs written in many different programming languages. We demonstrate the meritsof NTPoly by performing large scale calculations on the K computer.

8.3.1.2 Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic StructureCalculations: The CheSS Library[2]

We present CheSS, the “Chebyshev Sparse Solvers” library, which has been designed to solve typical problemsarising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexibleand efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the densitymatrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selectedinterval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the numberof nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted forsetups leading to small spectral widths of the involved matrices and outperforms alternative methods in thisregime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible inpractice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSSexhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

80 CHAPTER 8. COMPUTATIONAL MOLECULAR SCIENCE RESEARCH TEAM

8.3.2 Relativistic Time-Dependent Density Functional Theory for Molecular Prop-erties[3]

In this study, we introduce the two-component relativistic TDDFT with spin窶登 rbit interactions to calculatelinear response properties and excitation energies. The approach is implemented in the NTChem program.Our implementation is based on a noncollinear exchange 窶田 orrelation potential presented by Wang et al.In addition, various DFT functionals including the range-separated hybrid functionals have been derived andimplemented with the aid of a newly developed computerized symbolic algebra system. The two-componentrelativistic TDDFT with spin窶登 rbit interactions was successfully applied to the calculation of the frequency-dependent polarizabilities of SnH4 and PbH4 molecules containing heavy atoms and the excitation spectra of aHI molecule.

8.3.3 A coupled cluster theory with iterative inclusion of triple excitations and as-sociated equation of motion formulation for excitation energy and ionizationpotential[4]

A single reference coupled cluster theory that is capable of including the effect of connected triple excitationshas been developed and implemented. This is achieved by regrouping the terms appearing in perturbationtheory and parametrizing through two different sets of exponential operators: while one of the exponentials,involving general substitution operators, annihilates the ground state but has a non-vanishing effect when itacts on the excited determinant, the other is the regular single and double excitation operator in the sense ofconventional coupled cluster theory, which acts on the HF ground state. The two sets of operators are solved ascoupled non-linear equations in an iterative manner without significant increase in computational cost than theconventional coupled cluster theory with singles and doubles excitations. A number of physically motivated andcomputationally advantageous sufficiency conditions are invoked to arrive at the working equations and havebeen applied to determine the ground state energies of a number of small prototypical systems having weakmulti-reference character. With the knowledge of the correlated ground state, we have reconstructed the tripleexcitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples toobtain the ionization potential and excitation energies of these molecules as well. Our results suggest that thisis quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground stateremains weakly multi-reference.

8.3.4 Correlation effects beyond coupled cluster singles and doubles approxima-tion through Fock matrix dressing[5]

We present an accurate single reference coupled cluster theory in which the conventional Fock operator matrixis suitably dressed to simulate the effect of triple and higher excitations within a singles and doubles framework.The dressing thus invoked originates from a second-order perturbative approximation of a similarity transformedHamiltonian and induces higher rank excitations through local renormalization of individual occupied andunoccupied orbital lines. Such a dressing is able to recover a significant amount of correlation effects beyondsingles and doubles approximation, but only with an economic n5 additional cost. Due to the inclusion ofhigher rank excitations via the Fock matrix dressing, this method is a natural improvement over conventional

8.3. RESEARCH RESULTS AND ACHIEVEMENTS 81

coupled cluster theory with singles and doubles approximation, and this method would be demonstrated viaapplications on some challenging systems. This highly promising scheme has a conceptually simple structurewhich is also easily generalizable to a multi-reference coupled cluster scheme for treating strong degeneracy.We shall demonstrate that this method is a natural lowest order perturbative approximation to the recentlydeveloped iterative n-body excitation inclusive coupled cluster singles and doubles scheme.

8.3.5 Solving the problem of many electronic system with the Antisymmetrizedgeminal powers

The problem of the many electronic system can be described by the diagonalization of the large matrix of thehamiltonian. When the size of the system is getting larger the dimension of the matrix grows exponentially sothe true ground state becomes more and more difficult to obtain. To solve this problem there are proposed avariety of electronic wavefunctions including the matrix product states or the Jastrow Slater states. We proposemore sophisticated way that is the superpostion of several antisymmetrized geminal states. We named thismethod as extended symmetric tensor decompositon (ESTD).

We obtained the method to obtain the second order reduced density matrix of the above mentioned state.This density matrix is a more extended version of the so called one electron density and containing moreinformation. Since the electronic problem is a problem of two body interaction the density matrix could withno approximation describe the behavior of the electronic wavefunction.

By using the gradient based variational method for the parameters we obtained numerical results very closeto the exact ground states(Fig. 8.2, Fig. 8.3). The calculation could be done with the time scaling of the fifthpower of the system size so this method is likely to be extended to larger systems.

There are several way to develop this formalism on the quantum states. We could extend the variationalmethod to the excited states by using the orthogonalization of each state. Also we could do the large scalecalculation with the parralelization of the method. When using the tensor decomposition of the two electronmatrix element further acceleration of the geminal states could be expected.

10-1410-1210-1010-810-610-410-2100102

1 2 3 4 5

Ener

gy e

rror

K (number of terms)

Hubbard U=1.0 ESTD-CIHubbard U=1.0 STD-CI

Figure 8.2: Energy error of 4 sites U=1.0 Hubbardmodel for ESTD (solid line with circle) and STD-CI(broken line with circle).

10-1610-1410-1210-1010-810-610-410-2100102

1 2 3 4 5

Ener

gy e

rror

K (number of terms)

Hubbard U=100.0 ESTD-CIHubbard U=100.0 STD-CI

Figure 8.3: Energy error of 4 sites U=100.0 Hubbardmodel for ESTD (solid line with circle) and STD-CI(broken line with circle).

8.3.6 Development of a quantum dynamics method for excited electrons in molec-ular aggregate system using a group diabatic Fock matrix[6]

Our main research subject is to understand a photochemical quantum process in excited states associated witha light–energy conversion. Beyond a possible experimental mesurement for the ultrafast photochemistry, weadvance a theoretical research on an excited electron dynamics in molecules coupled with light-matter, non-adiabatic, and SO interactions.

In FY2017, we developed a practical calculation scheme for a description of excited electron dynamics inmolecular aggregates within a local group diabatic Fock representation. This scheme makes it easy to analyzethe interacting time-dependent excitation of local sites in complex systems. We demonstrated the usability ofthe present method. NTChem was used for ab initio electronic structure calculation.

8.3. RESEARCH RESULTS AND ACHIEVEMENTS 83

Born–Oppenheimer MD. We interfaced the code with the electronic structure program package NTChem andperformed a preliminary simulation. In the present study, we applied the program to the ring-opening reactionof unsubstituted coumarin on the excited state. The coumarin is usually a good fluorophore, and many coumarinmolecules with functional groups have been synthesized industrially. Interestingly, coumarin with no functionalgroup has a low quantum yield of fluorescence. Previous theoretical studies suggest that unsubstituted coumarinhas nonradiative decay paths to the ground state via direct (ππ∗/S0) or indirect (ππ

∗ → nπ∗ → nπ∗/S0) way.We examine the photochemical processes of this molecule after the excitation to the S3 (ππ

∗) by TDDFT/FSSH-MD.

Fig. 8.5(a) shows the summary of the time-dependent population for each state (S0–S3) by averaging over75 trajectories. The initial S3 state halves its population in 100 fs, and the S1 state increases at the samerate. The S1 state is dominant through the maximum simulation time of 500 fs. The ground state begins torecover at the 300 fs, but 60 percent of trajectories still stay on the S1 state. The fast relation to the S1 stateis consistent with Kasha’s rule. Fig. 8.5(b) gives a typical trajectory that reaches the S0/S1 crossing. Themolecular structure distorts significantly. The bond between the ether oxygen and the carbonyl carbon breaksand the six-membered ring loses the planarity. It is interesting that one could enhance nonradiative decay ofother coumarin molecules with large fluorescence quantum yields by exciting the stretch motion selectively.

At present, the algorithm does not account for spin-forbidden processes. The thiophene molecule, which isone of the building blocks for solar cells, has an efficient intersystem crossing to the triplet state. Therefore, it isnecessary to treat both the spin-allowed and spin-forbidden processes on an equal footing to understand the lossof PCE. The development of the TDDFT with SO-TDDFT is in progress, and the combination of SO-TDDFTand FSSH-MD is straightforward.

Figure 8.5: (a) Time-dependent population of state S0–S3. (b) Typical trajectory of coumarin leading to S0/S1crossing.

8.3.8 Discovery of Pb-free Perovskite solar cells via high-throughput simulationon the K computer[7]

We performed a systematic high-throughput simulation with DFT for 11025 compositions of hybrid organic-inorganic halide compounds in ABX3 and A2BB’X6 forms, where A is an organic or inorganic component, B/B’is a metal atom, and X is a halogen atom. The computational results were compiled as a materials database. Weperformed massive computational simulation by using the K computer, which is a massively parallel many-coresupercomputer in Japan. By applying the screening procedure to all the compounds in the materials database,we discovered novel candidates for environmentally friendly lead-free perovskite solar cells and propose 51 low-toxic halide single and double perovskites, most of which are newly proposed in this study. The proposedlow-toxic halide double perovskites are classified under six families: group-14-group-14, group-13-group-15,group-11-group-11, group-9-group-13, group-11-group-13, and group-11-group-15 double perovskites.

84 CHAPTER 8. COMPUTATIONAL MOLECULAR SCIENCE RESEARCH TEAM

8.3.9 Can electron-rich oxygen (O2−) withdraw electrons from metal centers? ADFT study on oxoanion-caged polyoxometalates[8]

The answer to the question “Can electron-rich oxygen (O2−) withdraw electrons from metal centers?” is seem-ingly simple, but how the electron population on the M atom behaves when the O-M distance changes is amatter of controversy. A case study has been conducted for Keggin-type polyoxometalate (POM) complexes,and the first-principles electronic structure calculations were carried out not only for real POM species butalso for “hypothetical” ones whose heteroatom was replaced with a point charge. From the results of naturalpopulation analysis, it was proven that even an electron-rich O2−, owing to its larger electronegativity as aneutral atom, withdraws electrons when electron redistribution occurs by the change of the bond length. In thecase where O2− coexists with a cation having a large positive charge (e.g., P5+(O2−)4 = [PO4]

3−), the grosselectron population (GEP) on the M atom seemingly increases as the O atom comes closer, but this incrementin GEP is not due to the role of the O atom but due to a Coulombic effect of the positive charge located on thecation. Furthermore, it was suggested that not GEP but net electron population (NEP) should be responsiblefor the redox properties.

8.3.10 Quantum Chemical Study on the Multi-Electron Transfer of Keggin-TypePolyoxotungstate Anions: The Relation of Redox Potentials to the BondValence of µ4-O-W[9]

By selectively investigating the effect of the bond valence using the hypothetical [(PO4)W12O36]3− species

having various bond valences, we could clearly reveal the origin of the linear dependence of the LUMO energy

8.3. RESEARCH RESULTS AND ACHIEVEMENTS 85

(or the redox potential) on the bond valence. The LUMO of the Keggin-type polyoxotungstates mainly consistsof W 5d. The energy of W 5d as well as of the LUMO goes down as the bond valence becomes large (i.e., asthe net electron population on W decreases due to the electron-withdrawing effect of the µ4-O atoms). This isthe origin of the linear dependence of LUMO energy on the bond valence.

8.3.11 Full-valence density matrix renormalisation group calculations on meta-benzyne based on unrestricted natural orbitals. Revisit of seamless con-tinuation from broken-symmetry to symmetry-adapted models for diradi-cals[10]

In this work, we show that the natural orbitals of unrestricted hybrid DFT (UHDFT) can be used as the activespace orbitals to perform multireference (MR) calculations, for example, the density matrix renormalisationgroup (DMRG) and Mukherjee-type (Mk) MR coupled-cluster (CC) method. By including a sufficiently largenumber of these natural orbitals, full-valence (FV) active space can be identified without recourse of the ex-pensive self-consistent procedures for DMRG-SCF. Several useful chemical indices are derived based on theoccupation numbers of the natural orbitals for seamless continuation from broken-symmetry (BS) to symmetry-adapted (SA) methods. These procedures are used on 1,3-didehydrobenzene (meta-benzyne) to calculate itssinglet (S)-triplet (T) gap. We compare our results to available experiments and computational results obtainedby several other groups. We see our procedures as a seamless bridge between single-reference BS methods, suchas UHDFT, and the SA MR methods, such as FV DMRG and MkMRCC.

86 CHAPTER 8. COMPUTATIONAL MOLECULAR SCIENCE RESEARCH TEAM

8.3.12 Ab initio computations of zero-field splitting parameters and effective ex-change integrals for single-molecule magnets (Mn12− and Mn11Cr-acetateclusters)[11]

In this study, the zero-field splitting parameters (D, E) and effective exchange integrals (J) for a Mn12/Mn11Crmixed crystal were evaluated using ab initio molecular orbital (MO) computations based on the hybrid DFTmethods for Mn11Cr

∗-acetate cluster (Mn12 and Mn11Cr mixing). In this study, Mn12-acetate, Mn11Cr-acetate,and Mn12−nCrn-acetate clusters were focused on. The zero-field splitting (ZFS) parameters are obtained byUB3LYP methods, i.e. −0.339 cm−1 (Mn12-acetate) and −0.351 cm−1 (Mn11Cr-acetate). The energy barrierswere estimated to be 53.7 K and 50.4 K, which showed good agreement with previously reported experimentalvalues of 68.8 K and 56.8 K, respectively. The origin of such anisotropy is assumed to be the eight MnIII ionswith d4-electrons in their outer ring subunits, where elongated conformation along the axial direction becomesvery important and leads to negative D values. The spin networks in these clusters were discussed by using theeffective exchange integral sets. The Js value, as estimated by the UB3LYP method revealed that the J2, J3,and J3’ interactions played important roles in describing the parallel spin ordering in cubane and ring subunitsas well as the antiferromagnetic coupling between two subunits. The other interactions, i.e. J1, J1’, J4, and J4’somewhat disturbed the spin ordering in the Mn12-acetate cluster. The substitution of MnIV by CrIII did notchange the spin network. However, the total S value changed after the substitution.

8.3.13 Theory of chemical bonds in metalloenzymes XXI. Possible mechanisms ofwater oxidation in oxygen evolving complex of photosystem II[12]

Possible mechanisms for water cleavage in oxygen evolving complex (OEC) of photosystem II (PSII) have beeninvestigated based on broken-symmetry (BS) hybrid DFT (HDFT)/def2 TZVP calculations in combinationwith available XRD, XFEL, EXAFS, XES and EPR results. The BS HDFT and the experimental resultshave provided basic concepts for understanding of chemical bonds of the CaMn4O5 cluster in the catalytic siteof OEC of PSII for elucidation of the mechanism of photosynthetic water cleavage. Scope and applicabilityof the hybrid DFT (HDFT) methods have been examined in relation to relative stabilities of possible nineintermediates such as Mn-hydroxide, Mn-oxo, Mn-peroxo, Mn-superoxo, etc., in order to understand the O-O (O-OH) bond formation in the S3 and/or S4 states of OEC of PSII. The relative stabilities among theseintermediates are variable, depending on the weight of the HF exchange term of HDFT. The Mn-hydroxide,Mn-oxo and Mn-superoxo intermediates are found to be preferable in the weak, intermediate and strong electroncorrelation regimes, respectively. Recent different serial femtosecond X-ray (SFX) results in the S3 state areinvestigated based on the proposed basic concepts under the assumption of different water-insertion steps forwater cleavage in the Kok cycle. The observation of water insertion in the S3 state is compatible with previouslarge-scale QM/MM results and previous theoretical proposal for the chemical equilibrium mechanism in theS3 state. On the other hand, the no detection of water insertion in the S3 state based on other SFX resultsis consistent with previous proposal of the O-OH (or O-O) bond formation in the S4 state. Radical couplingand non-adiabatic one-electron transfer (NA-OET) mechanisms for the OO-bond formation are examined usingthe energy diagrams by QM calculations and by QM(UB3LYP)/MM calculations. Possible reaction pathwaysfor the O-O and O-OH bond formations are also investigated based on two water-inlet pathways for oxygenevolution in OEC of PSII. Future perspectives are discussed in relation to post HDFT calculations of the energydiagrams for elucidation of the mechanism of water oxidation in OEC of PSII.

8.4. SCHEDULE AND FUTURE PLAN 87

8.4 Schedule and Future Plan

In the next fiscal year, we will continue to develop new algorithms and improve the parallel efficiency of theNTChem suit of program. We will work to develop a new version of NTChem which can perform quantumchemistry calculations on systems with thousands of atoms. The NTPoly library will be utilized to developa memory parallelization scheme, removing a significant cause of system size limitations from NTChem. Wewill replace the basic solver routines with linear scaling methods based on density matrix minimization andpurification. We will also work to implement TDDFT with the same memory parallelization scheme. Moreover,we will continue to develop the SO-TDDFT, related methods for excited-state dynamics, and high-accuracyquantum chemical methods.

8.5 Publications

8.5.1 Articles

[1]W. Dawson and T. Nakajima, “Massively parallel sparse matrix function calculations with NTPoly”, Comput.Phys. Commun. 225, 154 (2018).[2]S. Mohr, W. Dawson, M. Wagner, D. Caliste, T. Nakajima, and L. Genovese, “Efficient Computation ofSparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library”, J. Chem.Theory Comput. 13, 4684 (2017).[3]M. Kamiya and T. Nakajima, “Relativistic Time-Dependent Density Functional Theory for Molecular Prop-erties”, Frontiers of Quantum Chemistry, 223 (2018).[4]R. Maitra, Y. Akinaga, and T. Nakajima, “A coupled cluster theory with iterative inclusion of triple excita-tions and associated equation of motion formulation for excitation energy and ionization potential”, J. Chem.Phys. 147, 074103 (2017).[5]R. Maitra and T. Nakajima, “Correlation effects beyond coupled cluster singles and doubles approximationthrough Fock matrix dressing”, J. Chem. Phys. 147, 204108 (2017).[6]T. Yonehara and T. Nakajima, “A quantum dynamics method for excited electrons in molecular aggregatesystem using a group diabatic Fock matrix”, J. Chem. Phys. 147, 074110 (2017).[7]T. Nakajima and K. Sawada, “Discovery of Pb-free Perovskite solar cells via high-throughput simulation onthe K computer”, J. Phys. Chem. Lett. 8, 4826 (2017).[8]A. Takazaki, K. Eda, T. Osakai, and T. Nakajima, “Can electron-rich oxygen (O2−) withdraw electrons frommetal centers? A DFT study on oxoanion-caged polyoxometalates”, J. Phys. Chem. A 121, 7684 (2017).[9]A. Takazaki, K. Eda, T. Osakai, and T. Nakajima, “Quantum Chemical Study on the Multi-Electron Transferof Keggin-Type Polyoxotungstate Anions: The Relation of Redox Potentials to the Bond Valence of µ4-O-W”,J. Comput. Chem. Jpn. 16, 93 (2017).[10]T. Kawakami, T. Saito, S. Sharma, S. Yamanaka, S. Yamada, T. Nakajima, M. Okumura, and K. Yamaguchi,“Full-valence density matrix renormalisation group calculations on meta-benzyne based on unrestricted naturalorbitals. Revisit of seamless continuation from broken-symmetry to symmetry-adapted models for diradicals”,Mol. Phys. 115, 2267 (2017).

88 CHAPTER 8. COMPUTATIONAL MOLECULAR SCIENCE RESEARCH TEAM

[11]S. Sano, T. Kawakami, S. Yoshimura, M. Shoji, S. Yamanaka, M. Okumura, T. Nakajima, and K. Yamaguchi,“Ab initio computations of zero-field splitting parameters and effective exchange integrals for single-moleculemagnets (Mn12− and Mn11Cr-acetate clusters)”, Polyhedron 136, 159 (2017).[12]K. Yamaguchi, M. Shoji, H. Isobe, S. Yamanaka, T. Kawakami, S. Yamada, M. Katouda, and T. Nakajima,“Theory of chemical bonds in metalloenzymes XXI. Possible mechanisms of water oxidation in oxygen evolvingcomplex of photosystem II”, Mol. Phys. 116, 717 (2018).