Ogb-lsc: A large-scale challenge for machine learning on graphs W Hu, M Fey, H Ren, M Nakata, Y Dong, J Leskovec arXiv preprint arXiv:2103.09430, 2021 | 358 | 2021 |

Reduced-density-matrix mechanics: with application to many-electron atoms and molecules AJ Coleman, M Rosina, DA Mazziotti, RM Erdahl, BJ Braams, JK Percus, ... John Wiley & Sons, Inc. 134, 1-9, 2007 | 344 | 2007 |

Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm M Nakata, H Nakatsuji, M Ehara, M Fukuda, K Nakata, K Fujisawa The Journal of Chemical Physics 114 (19), 8282-8292, 2001 | 313 | 2001 |

PubChemQC project: a large-scale first-principles electronic structure database for data-driven chemistry M Nakata, T Shimazaki Journal of chemical information and modeling 57 (6), 1300-1308, 2017 | 256 | 2017 |

A high-performance software package for semidefinite programs: SDPA 7 M Yamashita, K Fujisawa, K Nakata, M Nakata, M Fukuda, K Kobayashi, ... Tokyo, Japan, 2010 | 132 | 2010 |

Latest developments in the SDPA family for solving large-scale SDPs M Yamashita, K Fujisawa, M Fukuda, K Kobayashi, K Nakata, M Nakata Handbook on semidefinite, conic and polynomial optimization, 687-713, 2012 | 110 | 2012 |

A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP,-QD and-DD. M Nakata 2010 IEEE International Symposium on Computer-Aided Control System Design, 29-34, 2010 | 104 | 2010 |

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver M Nakata, BJ Braams, K Fujisawa, M Fukuda, JK Percus, M Yamashita, ... The Journal of chemical physics 128 (16), 2008 | 104 | 2008 |

Large-scale semidefinite programs in electronic structure calculation M Fukuda, BJ Braams, M Nakata, ML Overton, JK Percus, M Yamashita, ... Mathematical programming 109, 553-580, 2007 | 96 | 2007 |

Density matrix variational theory: Application to the potential energy surfaces and strongly correlated systems M Nakata, M Ehara, H Nakatsuji The Journal of chemical physics 116 (13), 5432-5439, 2002 | 96 | 2002 |

Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization H Waki, M Nakata, M Muramatsu Computational Optimization and Applications 53, 823-844, 2012 | 58 | 2012 |

PubChemQC PM6: Data sets of 221 million molecules with optimized molecular geometries and electronic properties M Nakata, T Shimazaki, M Hashimoto, T Maeda Journal of Chemical Information and Modeling 60 (12), 5891-5899, 2020 | 55 | 2020 |

Direct determination of the density matrix using the density equation: Potential energy curves of HF, CH4, BH3, NH3, and H2O M Ehara, M Nakata, H Kou, K Yasuda, H Nakatsuji Chemical physics letters 305 (5-6), 483-488, 1999 | 43 | 1999 |

The MPACK (MBLAS/MLAPACK); multiple-precision arithmetic version of BLAS and LAPACK M Nakata http://mplapack. sourceforge. net/, 2010 | 36 | 2010 |

Direct determination of second-order density matrix using density equation: Open-shell system and excited state M Nakata, M Ehara, K Yasuda, H Nakatsuji The Journal of Chemical Physics 112 (20), 8772-8778, 2000 | 36 | 2000 |

Molecule3d: A benchmark for predicting 3d geometries from molecular graphs Z Xu, Y Luo, X Zhang, X Xu, Y Xie, M Liu, K Dickerson, C Deng, M Nakata, ... arXiv preprint arXiv:2110.01717, 2021 | 26 | 2021 |

The PubChemQC project: A large chemical database from the first principle calculations N Maho AIP conference proceedings 1702 (1), 2015 | 25 | 2015 |

Algorithm 925: Parallel solver for semidefinite programming problem having sparse schur complement matrix M Yamashita, K Fujisawa, M Fukuda, K Nakata, M Nakata ACM Transactions on Mathematical Software (TOMS) 39 (1), 1-22, 2012 | 24 | 2012 |

High-performance general solver for extremely large-scale semidefinite programming problems K Fujisawa, H Sato, S Matsuoka, T Endo, M Yamashita, M Nakata SC'12: Proceedings of the International Conference on High Performance …, 2012 | 23 | 2012 |

Size extensivity of the variational reduced-density-matrix method M Nakata, K Yasuda Physical Review A—Atomic, Molecular, and Optical Physics 80 (4), 042109, 2009 | 22 | 2009 |