{"_buckets": {"deposit": "327b45ea-95f5-441d-ae07-76bdd14039e4"}, "_deposit": {"created_by": 1, "id": "249", "owners": [1], "pid": {"revision_id": 0, "type": "depid", "value": "249"}, "status": "published"}, "_oai": {"id": "oai:ir.soken.ac.jp:00000249", "sets": ["9"]}, "author_link": ["0", "0", "0"], "item_1_biblio_info_21": {"attribute_name": "書誌情報（ソート用）", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2007-09-28", "bibliographicIssueDateType": "Issued"}, "bibliographic_titles": [{}]}]}, "item_1_creator_2": {"attribute_name": "著者名", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "石村, 和也"}], "nameIdentifiers": [{"nameIdentifier": "0", "nameIdentifierScheme": "WEKO"}]}]}, "item_1_creator_3": {"attribute_name": "フリガナ", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "イシムラ, カズヤ"}], "nameIdentifiers": [{"nameIdentifier": "0", "nameIdentifierScheme": "WEKO"}]}]}, "item_1_date_granted_11": {"attribute_name": "学位授与年月日", "attribute_value_mlt": [{"subitem_dategranted": "2007-09-28"}]}, "item_1_degree_grantor_5": {"attribute_name": "学位授与機関", "attribute_value_mlt": [{"subitem_degreegrantor": [{"subitem_degreegrantor_name": "総合研究大学院大学"}]}]}, "item_1_degree_name_6": {"attribute_name": "学位名", "attribute_value_mlt": [{"subitem_degreename": "博士（理学）"}]}, "item_1_description_1": {"attribute_name": "ID", "attribute_value_mlt": [{"subitem_description": "2007808", "subitem_description_type": "Other"}]}, "item_1_description_12": {"attribute_name": "要旨", "attribute_value_mlt": [{"subitem_description": "　　Quantum chemistry plays an important role in elucidating molecular geometries,\u003cbr /\u003e electronic states, and reaction mechanisms, because of the developments of a variety of\u003cbr /\u003e theoretical methods, such as Hartree-Fock (HF), M\u0026oslash;ler-Plesset (MP) perturbation,\u003cbr /\u003e  configuration interaction (CI), coupled-cluster (CC), and density functional theory \u003cbr /\u003e (DFT) methods. Electronic structure calculations have been carried out by not only\u003cbr /\u003e theoretical chemists but also experimental chemists. DFT is currently most widely used\u003cbr /\u003eto investigate large molecules in the ground state as well as small molecules because of the low computational cost. However, the generally used functionals fail to describe\u003cbr /\u003ecorrectly non-covalent interactions that are important for host-guest molecules,\u003cbr /\u003e self-assembly, and molecular recognition, and they tend to underestimate reaction\u003cbr /\u003e barriers. Many attempts have been made to develop new functionals and add\u003cbr /\u003e semiempirical or empirical correction terms to standard functionals, but no generally\u003cbr /\u003e accepted DFT method has emerged yet.\u003cbr /\u003e　　Second-order M\u0026oslash;ler-Plesset perturbation theory (MP2) is the simplest method that\u003cbr /\u003e includes electron correlation important for non-covalent interactions and reaction\u003cbr /\u003e  barriers nonempirically. However, the computational cost of MP2 is considerably\u003cbr /\u003e  higher than that of DFT. In addition, much larger sizes of fast memory and hard disk\u003cbr /\u003e  are required in MP2 calculations. These make MP2 calculations increasingly difficult\u003cbr /\u003e  for larger molecules. Since workstation or personal computer (PC) clusters have\u003cbr /\u003e  become popular for quantum chemistry calculations, an efficient parallel calculation is\u003cbr /\u003e  a solution of the problem. Therefore, new parallel algorithms for MP2 energy and\u003cbr /\u003e gradient calculations are presented in this thesis. Furthermore, an efficient algorithm\u003cbr /\u003e for the generation of two-electron repulsion integrals (ERIs) which is important in \u003cbr /\u003e quantum chemistry calculations is also presented.\u003cbr /\u003e　　For the calculations of excited states, different approaches are required: for\u003cbr /\u003e example, CI, multi-configuration self-consistent field (MCSCF), time-dependent DFT\u003cbr /\u003e (TDDFT), and symmetry adapted cluster (SAC)/SAC-CI methods. One of the most\u003cbr /\u003e accurate methods is SAC/SAC-CI, as demonstrated for many molecules. In this thesis,\u003cbr /\u003e SAC/SAC-CI calculations of ground, ionized, and excited states are presented.\u003cbr /\u003e　　This thesis consists of five chapters: a new algorithm of two-electron repulsion\u003cbr /\u003e  integral calculations (Chapter I), a new parallel algorithm of MP2 energy calculations\u003cbr /\u003e  (Chapter II), a new parallel algorithm of MP2 energy gradient calculations (Chapter\u003cbr /\u003e III), applications of MP2 calculations (Chapter IV), and SAC/SAC-CI calculations of \u003cbr /\u003e ionized and excited states (Chapter V).\u003cbr /\u003e　　In quantum chemistry calculations, the generation of ERIs is one of the most basic\u003cbr /\u003e subjects and is the most time-consuming step especially in direct SCF calculations.\u003cbr /\u003e Many algorithms have been developed to reduce the computational cost. In\u003cbr /\u003e Pople-Hehre algorithm, Cartesian axes are rotated to make several coordinate\u003cbr /\u003e components zero or constant, so that these components are skipped in the generation of ERIs. In McMurchie-Davidson algorithm, ERIs are generated from (\u003ci\u003ess\u003c/i\u003e|\u003ci\u003ess\u003c/i\u003e) type\u003cbr /\u003e integrals using a recurrence relation derived from Hermite polynomials. By combining\u003cbr /\u003e these two algorithms, a new algorithm is developed in Chapter I. The results show that\u003cbr /\u003e the new algorithm reduces the computational cost by 10 - 40%, as compared with the\u003cbr /\u003e original algorithms. It is notable that the generation of ERIs including d functions is\u003cbr /\u003e considerably fast. The program implemented officially in GAMESS in 2004 has been\u003cbr /\u003e  used all over the world.\u003cbr /\u003e　　In quantum mechanics, perturbation methods can be used for adding corrections\u003cbr /\u003e to reference solutions. In the MP perturbation method, a sum over Fock operators is\u003cbr /\u003e used as the reference term, and the exact two-electron repulsion operator minus twice\u003cbr /\u003e the average two-electron repulsion operator is used as the perturbation term. It is the\u003cbr /\u003e advantage that the MP perturbation method is size consistent and size extensive, unlike\u003cbr /\u003e truncated CI methods. The zero-order wave function is the HF Slater determinant, and \u003cbr /\u003e the zero-order energy is expressed as a sum of occupied molecular orbital (MO)\u003cbr /\u003e  energies. The first-order perturbation is the correction for the overcounting of\u003cbr /\u003e two-electron repulsions at zero-order, and the first-order energy corresponds to the HF\u003cbr /\u003e energy. The MP correlation starts at second-order. In general, second-order (MP2) \u003cbr /\u003e accounts for 80 - 90% of electron correlation. Therefore, MP2 is focused in this thesis\u003cbr /\u003e since it is applicable to large molecules with considerable reliability and low \u003cbr /\u003e computational cost.\u003cbr /\u003e　　The formal computational scaling of MP2 energy calculations with respect to\u003cbr /\u003e molecular size is fifth order, much higher than that of DFT energy calculations.\u003cbr /\u003e Therefore, less expensive methods, such as Local MP2, density fitting (resolution of\u003cbr /\u003e identity, RI) MP2, and Laplace Transform MP2, have been developed. However, all of\u003cbr /\u003e these methods include approximations or cut-offs that need to be checked against full\u003cbr /\u003e MP2 energies. An alternative approach to reduce the computational cost is to\u003cbr /\u003e parallelize MP2 energy calculations. A number of papers on parallel MP2 energy\u003cbr /\u003e calculations have been published. Almost all of them are based on simple \u003cbr /\u003e parallelization methods that distribute only atomic orbital (AO) or MO indices to each \u003cbr /\u003e processor. These methods have a disadvantage since intermediate integrals are \u003cbr /\u003e broadcasted to all CPUs or the same AO ERIs are generated in all processors. Baker \u003cbr /\u003e and Pulay developed a new parallel algorithm using Saeb\u0026oslash;Alml\u0026ouml;f integral\u003cbr /\u003e transformation method. This algorithm parallelizes the first half transformation by AO\u003cbr /\u003e indices and the second half transformation by MO indices. The advantages are that the\u003cbr /\u003e total amount of network communication is independent of the number of processors \u003cbr /\u003e and the AO integrals are generated only once. The disadvantage is the I/O overhead for\u003cbr /\u003e the sorting of half-transformed integrals. A new parallel algorithm for MP2 energy\u003cbr /\u003e calculations based on the two-step parallelization idea is presented in Chapter II. In\u003cbr /\u003e this algorithm, AO indices are distributed in the AO integral generation and the first\u003cbr /\u003e three quarter transformation, and MO indices are distributed in the last quarter\u003cbr /\u003e transformation and MP2 energy calculation. Because the algorithm makes the sorting\u003cbr /\u003e of intermediate integrals very simple, the parallel efficiency is highly improved and \u003cbr /\u003e the I/O overhead is removed. Furthermore, the algorithm reduces highly the floating\u003cbr /\u003e point operation (FLOP) count as well as the required memory and hard disk space, in \u003cbr /\u003e comparison with other algorithms. Test calculations of taxol (C\u003csmall\u003e47\u003c/small\u003eH\u003csmall\u003e51\u003c/small\u003eNO\u003csmall\u003e14\u003c/small\u003e) and \u003cbr /\u003e luciferin (C\u003csmall\u003e11\u003c/small\u003eH\u003csmall\u003e8\u003c/small\u003eN\u003csmall\u003e2\u003c/small\u003eO\u003csmall\u003e3\u003c/small\u003eS\u003csmall\u003e2\u003c/small\u003e) were performed on a cluster of Pentium 4 computers\u003cbr /\u003e connected by gigabit Ethernet. The parallel scaling of the developed code is excellent\u003cbr /\u003e up to the largest number of processors we have tested. For instance, the elapsed time\u003cbr /\u003e for the MP2 energy calculations on 16 processors is on average 15.4 times faster than\u003cbr /\u003e that on the single-processor.\u003cbr /\u003e　　Determination of molecular geometries and reaction paths is a fundamental task in\u003cbr /\u003e quantum chemistry and requires energy gradients with respect to nuclear coordinates. \u003cbr /\u003e In Chapter III, a new parallel algorithm for MP2 energy gradient calculations is \u003cbr /\u003e presented. The algorithm consists of 5 steps, the integral transformation, the MP2\u003cbr /\u003e amplitude calculation, the MP2 Lagrangian calculation, the coupled-perturbed HF \u003cbr /\u003e calculation, and the integral derivative calculation. All steps are parallelized by \u003cbr /\u003e distributing AO or MO indices. The algorithm also reduces the FLOP count, the\u003cbr /\u003e required memory, and hard disk space. Test calculations of MP2 energy gradients were \u003cbr /\u003e performed for taxol and luciferin on a cluster of Pentium 4 computers. The speedups \u003cbr /\u003e are very good up to 80 CPU cores we have tested. For instance, the speedup ratios are \u003cbr /\u003e 28.2 - 33.0 on 32 processors, corresponding to 88% - 103% of linear speedup. This \u003cbr /\u003e indicates the high parallel efficiency of the present algorithm. The calculation of taxol\u003cbr /\u003e with 6-31G(d) (1032 contracted basis functions) finishes within 2 hours on 32\u003cbr /\u003e processors, which requires only 1.8GB memory and 13.4GB hard disk per processor.\u003cbr /\u003e Therefore, geometry optimization of molecules with 1000 basis functions can be easily\u003cbr /\u003e performed using standard PC clusters.\u003cbr /\u003e　　In Chapter IV, several applications of MP2 are performed using the program\u003cbr /\u003e developed in Chapters II and III. Some molecules that DFT cannot treat well are \u003cbr /\u003e optimized at the MP2 level. Geometry optimization is also carried out using the\u003cbr /\u003e spin-component scaled (SCS) MP2 method. In this method, a different scaling is\u003cbr /\u003e employed for the same and opposite spin components of the MP2 energy, so that\u003cbr /\u003e SCS-MP2 performs as well as the much more costly CCSD(T) method at a high level\u003cbr /\u003e of theory.\u003cbr /\u003eSAC theory is developed for ground states and based on CC theory that describes\u003cbr /\u003e  higher-order electron correlation. The main factor of electron correlation is collisions\u003cbr /\u003e of two electrons. In CC theory, most collisions of four electrons can be taken in as the\u003cbr /\u003e product of collisions of two electrons. Only a symmetry adapted excitation operator is \u003cbr /\u003e used for the SAC expansion. Since the operator of the SAC expansion is totally\u003cbr /\u003e symmetric, the unlinked terms (the products of the operators) are also totally \u003cbr /\u003e symmetric. SAC-CI is developed to treat excited states. SAC and SAC-CI wave \u003cbr /\u003e functions are orthogonal and Hamiltonian-orthogonal to each other. These\u003cbr /\u003e  orthogonalities are especially important for the calculations of transitions\u003cbr /\u003e and relaxations. In general, the SAC-CI operators \u003ci\u003eR\u003c/i\u003e are restricted to single and double\u003cbr /\u003e excitations. This is called the SAC-CI SD-R method. For the calculations of high-spin\u003cbr /\u003e states and multiple excitation processes, triple, quadruple, and higher excitation\u003cbr /\u003e  operators are included. This is called the SAC-CI general-R method. In Chapter V, the\u003cbr /\u003e ground, singlet and triplet excited, ionized and electron attached states of ferrocene \u003cbr /\u003e (Fe(C\u003csmall\u003e5\u003c/small\u003eH\u003csmall\u003e5\u003c/small\u003e)\u003csmall\u003e2\u003c/small\u003e) were calculated using the SAC/SAC-CI SD-R method. The calculated\u003cbr /\u003e  results are in good agreement with experimental values. It is found that shake-up\u003cbr /\u003e processes (one electron ionization and one electron excitation) contribute to the first\u003cbr /\u003e two ionization peaks.", "subitem_description_type": "Other"}]}, "item_1_description_7": {"attribute_name": "学位記番号", "attribute_value_mlt": [{"subitem_description": "総研大乙第178号", "subitem_description_type": "Other"}]}, "item_1_select_14": {"attribute_name": "所蔵", "attribute_value_mlt": [{"subitem_select_item": "有"}]}, "item_1_select_8": {"attribute_name": "研究科", "attribute_value_mlt": [{"subitem_select_item": "物理科学研究科"}]}, "item_1_select_9": {"attribute_name": "専攻", "attribute_value_mlt": [{"subitem_select_item": "07 構造分子科学専攻"}]}, "item_1_text_10": {"attribute_name": "学位授与年度", "attribute_value_mlt": [{"subitem_text_value": "2007"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "ISHIMURA, Kazuya", "creatorNameLang": "en"}], "nameIdentifiers": [{"nameIdentifier": "0", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2016-02-17"}], "displaytype": "simple", "download_preview_message": "", "file_order": 0, "filename": "乙178_要旨.pdf", "filesize": [{"value": "489.4 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_11", "mimetype": "application/pdf", "size": 489400.0, "url": {"label": "要旨・審査要旨", "url": "https://ir.soken.ac.jp/record/249/files/乙178_要旨.pdf"}, "version_id": "6c8f40c3-bb28-47b9-9e74-71426e5c34e2"}, {"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2016-02-17"}], "displaytype": "simple", "download_preview_message": "", "file_order": 1, "filename": "乙178_本文.pdf", "filesize": [{"value": "1.5 MB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_11", "mimetype": "application/pdf", "size": 1500000.0, "url": {"label": "本文", "url": "https://ir.soken.ac.jp/record/249/files/乙178_本文.pdf"}, "version_id": "9c182790-a8ae-492b-829f-e0e55bd73257"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "thesis", "resourceuri": "http://purl.org/coar/resource_type/c_46ec"}]}, "item_title": "Development of efficient algorithms for quantum chemistry calculations of large molecules", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "Development of efficient algorithms for quantum chemistry calculations of large molecules"}, {"subitem_title": "Development of efficient algorithms for quantum chemistry calculations of large molecules", "subitem_title_language": "en"}]}, "item_type_id": "1", "owner": "1", "path": ["9"], "permalink_uri": "https://ir.soken.ac.jp/records/249", "pubdate": {"attribute_name": "公開日", "attribute_value": "2010-02-22"}, "publish_date": "2010-02-22", "publish_status": "0", "recid": "249", "relation": {}, "relation_version_is_last": true, "title": ["Development of efficient algorithms for quantum chemistry calculations of large molecules"], "weko_shared_id": 1}