Michio Katouda

Molecular tailoring approach in conjunction with MP2 and Ri‐MP2 codes: A comparison with fragment molecular orbital method

Many Divide‐and‐Conquer based approaches are being developed to overcome the high scaling problem of the ab initio methods. In this work, one such method, Molecular Tailoring Approach (MTA) has been interfaced with recently developed efficient Møller‐Plesset second order perturbation theory (MP2) codes viz. IMS‐MP2 and RI‐MP2 to reap the advantage of both. An external driver script is developed for implementing MTA at the front‐end and the MP2 codes at the back‐end. The present version of the driver script is written only for a single point energy evaluation of a molecular system at a fixed geometry. The performance of these newly developed MTA‐IMS‐MP2 and MTA‐RI‐MP2 codes is extensively benchmarked for a variety of molecular systems vis‐à‐vis the corresponding actual runs. In addition to this, the performance of these programs is also critically compared with Fragment Molecular Orbital (FMO), another popular fragment‐based method. It is observed that FMO2/2 is superior to FMO3/2 and MTA with respect to time advantage; however, the errors of FMO2 are much beyond chemical accuracy. However, FMO3/2 is a highly accurate method for biological systems but is unsuccessful in case of water clusters. MTA produces estimates with errors within 1 kcal/mol uniformly for all systems with reasonable time advantage. Analysis carried out employing various basis sets shows that FMO gives its optimum performance only for basis sets, which does not include diffuse functions. On the contrary, MTA performance is found to be similar for any basis set used.

MPI/OpenMP Hybrid Parallel Algorithm of Resolution of Identity Second-Order Møller-Plesset Perturbation Calculation for Massively Parallel Multicore Supercomputers.

A new algorithm for massively parallel calculations of electron correlation energy of large molecules based on the resolution of identity second-order Møller-Plesset perturbation (RI-MP2) technique is developed and implemented into the quantum chemistry software NTChem. In this algorithm, a Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) hybrid parallel programming model is applied to attain efficient parallel performance on massively parallel supercomputers. An in-core storage scheme of intermediate data of three-center electron repulsion integrals utilizing the distributed memory is developed to eliminate input/output (I/O) overhead. The parallel performance of the algorithm is tested on massively parallel supercomputers such as the K computer (using up to 45 992 central processing unit (CPU) cores) and a commodity Intel Xeon cluster (using up to 8192 CPU cores). The parallel RI-MP2/cc-pVTZ calculation of two-layer nanographene sheets (C150H30)2 (number of atomic orbitals is 9640) is performed using 8991 node and 71 288 CPU cores of the K computer.

Energy density analysis of cluster size dependence of surface-molecule interactions: H2, C2H2, C2H4, and CO adsorption onto Si(100)-(2×1) surface

Adsorption of H2, C2H2, C2H4, and CO onto a Si(100)-(2x1) surface has been treated theoretically using Si(12n - 3)H(8n + 4) (n = 1-4) clusters. The energy density analysis (EDA) proposed by Nakai has been adopted to examine surface-molecule interactions for different cluster sizes. EDA results for the largest model cluster Si45H36 have shown that the adsorption-induced energy density variation in Si atoms decays with distance from the adsorption site. Analysis of this decay, which can be carried out using the EDA technique, is important because it enables verification of the reliability of the model cluster used. In the cases of H2, C2H2, C2H4, and CO adsorption onto the Si(100)-(2x1) surface, it is found that at least a Si21H20 cluster is necessary to treat the surface-molecule interaction with chemical accuracy.

Application of second-order Møller–Plesset perturbation theory with resolution-of-identity approximation to periodic systems

Efficient periodic boundary condition (PBC) calculations by the second-order Møller-Plesset perturbation (MP2) method based on crystal orbital formalism are developed by introducing the resolution-of-identity (RI) approximation of four-center two-electron repulsion integrals (ERIs). The formulation and implementation of the PBC RI-MP2 method are presented. In this method, the mixed auxiliary basis functions of the combination of Poisson and Gaussian type functions are used to circumvent the slow convergence of the lattice sum of the long-range ERIs. Test calculations of one-dimensional periodic trans-polyacetylene show that the PBC RI-MP2 method greatly reduces the computational times as well as memory and disk sizes, without the loss of accuracy, compared to the conventional PBC MP2 method.

Two‐level hierarchical parallelization of second‐order Møller–plesset perturbation calculations in divide‐and‐conquer method

A two‐level hierarchical parallelization scheme including the second‐order Møller–Plesset perturbation (MP2) theory in the divide‐and‐conquer method is presented. The scheme is a combination of coarse‐grain parallelization assigning each subsystem to a group of processors, with fine‐grain parallelization, where the computational tasks for evaluating MP2 correlation energy of the assigned subsystem are distributed among processors in the group. Test calculations demonstrate that the present scheme shows high parallel efficiency and makes MP2 calculations practical for very large molecules.

Optimization of RI‐MP2 Auxiliary Basis Functions for 6‐31G** and 6‐311G** Basis Sets for First‐, Second‐, and Third‐Row Elements

Auxiliary basis functions for second‐order Møller–Plesset perturbation theory with resolution‐of‐identity approximation (RI‐MP2) are developed for first‐, second‐, and third‐row elements, which are suitable for Pople‐type 6‐31G** and 6‐311G** basis sets. Atomic‐centered Gaussian functions up to the g‐type function are used for auxiliary basis functions to obtain higher accuracy for molecules with the accurate description of bonding properties. The performance of the developed auxiliary basis functions were tested and evaluated for 114 small and 23 large molecules. The developed auxiliary basis functions show much smaller energy differences between MP2 and RI‐MP2 than other auxiliary basis functions used for 6‐31G** and 6‐311G** basis sets with similar computational costs.

Practical performance assessment of accompanying coordinate expansion recurrence relation algorithm for computation of electron repulsion integrals

We have developed a computer program for evaluation of electron repulsion integrals (ERIs) based on the accompanying coordinate expansion recurrence relation (ACE-RR) algorithm, which has been recently developed as an efficient algorithm for computation of ERIs using Pople-type basis sets (STO-3G and 6-31G, for example) and derivatives of ERIs [Kobayashi and Nakai, J Chem Phys121:4050 2004]. The computer program can be linked to GAMESS ab initio quantum chemistry program. The practical performance of the ACE-RR method is assessed by means of the central processing unit (CPU) time for the first direct self-consistent field cycle on a model system (4 × 4 × 4 cubic hydrogen lattice), taxol (C47H51NO14), and valinomycin (C54H90N6O18) using Pople-type basis sets. The considerable efficiency of the present ACE-RR method is demonstrated by measuring the CPU time. The present ACE-RR method is comparable to or at most 30% faster than the Pople–Hehre method which is also designed for efficient computation of ERIs using Pople-type basis sets. Furthermore, the ACE-RR method is drastically faster than the Dupuis–Rys–King method in the case where the degree of contraction of Pople-type basis sets is high: 7.5 times faster in the case of valinomycin using STO-6G basis set, for example.

Massively parallel algorithm and implementation of RI‐MP2 energy calculation for peta‐scale many‐core supercomputers

A new parallel algorithm and its implementation for the RI‐MP2 energy calculation utilizing peta‐flop‐class many‐core supercomputers are presented. Some improvements from the previous algorithm (J. Chem. Theory Comput. 2013, 9, 5373) have been performed: (1) a dual‐level hierarchical parallelization scheme that enables the use of more than 10,000 Message Passing Interface (MPI) processes and (2) a new data communication scheme that reduces network communication overhead. A multi‐node and multi‐GPU implementation of the present algorithm is presented for calculations on a central processing unit (CPU)/graphics processing unit (GPU) hybrid supercomputer. Benchmark results of the new algorithm and its implementation using the K computer (CPU clustering system) and TSUBAME 2.5 (CPU/GPU hybrid system) demonstrate high efficiency. The peak performance of 3.1 PFLOPS is attained using 80,199 nodes of the K computer. The peak performance of the multi‐node and multi‐GPU implementation is 514 TFLOPS using 1349 nodes and 4047 GPUs of TSUBAME 2.5.

From Linear to Foldamer and Assembly: Hierarchical Transformation of a Coplanar Conjugated Polymer into a Microsphere

Despite the coplanar structure, a conjugated alternating copolymer forms amorphous, well-defined microspheres without π-stacked crystalline domains. Here, we gain insights into the mechanism of how the coplanar conjugated polymer forms amorphous microspheres by means of spectroscopic studies on the assembly/disassembly processes. The difference of the spectral profiles of photoabsorption and photoluminescence with varying solvent/nonsolvent composition clarifies that stepwise assembly takes place through the microsphere formation; [1] intrapolymer linear-to-folding transformation upon diffusion of polar nonsolvent and [2] interpolymer assembly of the foldamers upon further addition of the nonsolvent to form microspheres. As shown in various biopolymers such as proteins and DNA, such stepwise folding and assembly behaviors of conjugated polymers from primary to secondary and tertiary structure open a new way to create transformable functional materials.

Theory of chemical bonds in metalloenzymes XXI. Possible mechanisms of water oxidation in oxygen evolving complex of photosystem II

ABSTRACT Possible mechanisms for water cleavage in oxygen evolving complex (OEC) of photosystem II (PSII) have been investigated based on broken-symmetry (BS) hybrid DFT (HDFT)/def2 TZVP calculations in combination with available XRD, XFEL, EXAFS, XES and EPR results. The BS HDFT and the experimental results have provided basic concepts for understanding of chemical bonds of the CaMn4O5 cluster in the catalytic site of OEC of PSII for elucidation of the mechanism of photosynthetic water cleavage. Scope and applicability of the hybrid DFT (HDFT) methods have been examined in relation to relative stabilities of possible nine intermediates 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 these intermediates are variable, depending on the weight of the Hartree–Fock exchange term of HDFT. The Mn-hydroxide, Mn-oxo and Mn-superoxo intermediates are found to be preferable in the weak, intermediate and strong electron correlation regimes, respectively. Recent different serial femtosecond X-ray (SFX) results in the S3 state are investigated based on the proposed basic concepts under the assumption of different water-insertion steps for water cleavage in the Kok cycle. The observation of water insertion in the S3 state is compatible with previous large-scale QM/MM results and previous theoretical proposal for the chemical equilibrium mechanism in the S3 state . On the other hand, the no detection of water insertion in the S3 state based on other SFX results is consistent with previous proposal of the O–OH (or O–O) bond formation in the S4 state . Radical coupling and non-adiabatic one-electron transfer (NA-OET) mechanisms for the OO-bond formation are examined using the energy diagrams by QM calculations and by QM(UB3LYP)/MM calculations . Possible reaction pathways for the O–O and O–OH bond formations are also investigated based on two water-inlet pathways for oxygen evolution in OEC of PSII. Future perspectives are discussed in relation to post HDFT calculations of the energy diagrams for elucidation of the mechanism of water oxidation in OEC of PSII.