{"created":"2023-06-20T13:20:14.353711+00:00","id":249,"links":{},"metadata":{"_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":["2:427:9"]},"author_link":["0","0","0"],"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_12":{"attribute_name":"要旨","attribute_value_mlt":[{"subitem_description":" Quantum chemistry plays an important role in elucidating molecular geometries,
electronic states, and reaction mechanisms, because of the developments of a variety of
theoretical methods, such as Hartree-Fock (HF), Møler-Plesset (MP) perturbation,
configuration interaction (CI), coupled-cluster (CC), and density functional theory
(DFT) methods. Electronic structure calculations have been carried out by not only
theoretical chemists but also experimental chemists. DFT is currently most widely used
to 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
correctly non-covalent interactions that are important for host-guest molecules,
self-assembly, and molecular recognition, and they tend to underestimate reaction
barriers. Many attempts have been made to develop new functionals and add
semiempirical or empirical correction terms to standard functionals, but no generally
accepted DFT method has emerged yet.
Second-order Møler-Plesset perturbation theory (MP2) is the simplest method that
includes electron correlation important for non-covalent interactions and reaction
barriers nonempirically. However, the computational cost of MP2 is considerably
higher than that of DFT. In addition, much larger sizes of fast memory and hard disk
are required in MP2 calculations. These make MP2 calculations increasingly difficult
for larger molecules. Since workstation or personal computer (PC) clusters have
become popular for quantum chemistry calculations, an efficient parallel calculation is
a solution of the problem. Therefore, new parallel algorithms for MP2 energy and
gradient calculations are presented in this thesis. Furthermore, an efficient algorithm
for the generation of two-electron repulsion integrals (ERIs) which is important in
quantum chemistry calculations is also presented.
For the calculations of excited states, different approaches are required: for
example, CI, multi-configuration self-consistent field (MCSCF), time-dependent DFT
(TDDFT), and symmetry adapted cluster (SAC)/SAC-CI methods. One of the most
accurate methods is SAC/SAC-CI, as demonstrated for many molecules. In this thesis,
SAC/SAC-CI calculations of ground, ionized, and excited states are presented.
This thesis consists of five chapters: a new algorithm of two-electron repulsion
integral calculations (Chapter I), a new parallel algorithm of MP2 energy calculations
(Chapter II), a new parallel algorithm of MP2 energy gradient calculations (Chapter
III), applications of MP2 calculations (Chapter IV), and SAC/SAC-CI calculations of
ionized and excited states (Chapter V).
In quantum chemistry calculations, the generation of ERIs is one of the most basic
subjects and is the most time-consuming step especially in direct SCF calculations.
Many algorithms have been developed to reduce the computational cost. In
Pople-Hehre algorithm, Cartesian axes are rotated to make several coordinate
components zero or constant, so that these components are skipped in the generation of ERIs. In McMurchie-Davidson algorithm, ERIs are generated from (ss|ss) type
integrals using a recurrence relation derived from Hermite polynomials. By combining
these two algorithms, a new algorithm is developed in Chapter I. The results show that
the new algorithm reduces the computational cost by 10 - 40%, as compared with the
original algorithms. It is notable that the generation of ERIs including d functions is
considerably fast. The program implemented officially in GAMESS in 2004 has been
used all over the world.
In quantum mechanics, perturbation methods can be used for adding corrections
to reference solutions. In the MP perturbation method, a sum over Fock operators is
used as the reference term, and the exact two-electron repulsion operator minus twice
the average two-electron repulsion operator is used as the perturbation term. It is the
advantage that the MP perturbation method is size consistent and size extensive, unlike
truncated CI methods. The zero-order wave function is the HF Slater determinant, and
the zero-order energy is expressed as a sum of occupied molecular orbital (MO)
energies. The first-order perturbation is the correction for the overcounting of
two-electron repulsions at zero-order, and the first-order energy corresponds to the HF
energy. The MP correlation starts at second-order. In general, second-order (MP2)
accounts for 80 - 90% of electron correlation. Therefore, MP2 is focused in this thesis
since it is applicable to large molecules with considerable reliability and low
computational cost.
The formal computational scaling of MP2 energy calculations with respect to
molecular size is fifth order, much higher than that of DFT energy calculations.
Therefore, less expensive methods, such as Local MP2, density fitting (resolution of
identity, RI) MP2, and Laplace Transform MP2, have been developed. However, all of
these methods include approximations or cut-offs that need to be checked against full
MP2 energies. An alternative approach to reduce the computational cost is to
parallelize MP2 energy calculations. A number of papers on parallel MP2 energy
calculations have been published. Almost all of them are based on simple
parallelization methods that distribute only atomic orbital (AO) or MO indices to each
processor. These methods have a disadvantage since intermediate integrals are
broadcasted to all CPUs or the same AO ERIs are generated in all processors. Baker
and Pulay developed a new parallel algorithm using SaebøAlmlöf integral
transformation method. This algorithm parallelizes the first half transformation by AO
indices and the second half transformation by MO indices. The advantages are that the
total amount of network communication is independent of the number of processors
and the AO integrals are generated only once. The disadvantage is the I/O overhead for
the sorting of half-transformed integrals. A new parallel algorithm for MP2 energy
calculations based on the two-step parallelization idea is presented in Chapter II. In
this algorithm, AO indices are distributed in the AO integral generation and the first
three quarter transformation, and MO indices are distributed in the last quarter
transformation and MP2 energy calculation. Because the algorithm makes the sorting
of intermediate integrals very simple, the parallel efficiency is highly improved and
the I/O overhead is removed. Furthermore, the algorithm reduces highly the floating
point operation (FLOP) count as well as the required memory and hard disk space, in
comparison with other algorithms. Test calculations of taxol (C47H51NO14) and
luciferin (C11H8N2O3S2) were performed on a cluster of Pentium 4 computers
connected by gigabit Ethernet. The parallel scaling of the developed code is excellent
up to the largest number of processors we have tested. For instance, the elapsed time
for the MP2 energy calculations on 16 processors is on average 15.4 times faster than
that on the single-processor.
Determination of molecular geometries and reaction paths is a fundamental task in
quantum chemistry and requires energy gradients with respect to nuclear coordinates.
In Chapter III, a new parallel algorithm for MP2 energy gradient calculations is
presented. The algorithm consists of 5 steps, the integral transformation, the MP2
amplitude calculation, the MP2 Lagrangian calculation, the coupled-perturbed HF
calculation, and the integral derivative calculation. All steps are parallelized by
distributing AO or MO indices. The algorithm also reduces the FLOP count, the
required memory, and hard disk space. Test calculations of MP2 energy gradients were
performed for taxol and luciferin on a cluster of Pentium 4 computers. The speedups
are very good up to 80 CPU cores we have tested. For instance, the speedup ratios are
28.2 - 33.0 on 32 processors, corresponding to 88% - 103% of linear speedup. This
indicates the high parallel efficiency of the present algorithm. The calculation of taxol
with 6-31G(d) (1032 contracted basis functions) finishes within 2 hours on 32
processors, which requires only 1.8GB memory and 13.4GB hard disk per processor.
Therefore, geometry optimization of molecules with 1000 basis functions can be easily
performed using standard PC clusters.
In Chapter IV, several applications of MP2 are performed using the program
developed in Chapters II and III. Some molecules that DFT cannot treat well are
optimized at the MP2 level. Geometry optimization is also carried out using the
spin-component scaled (SCS) MP2 method. In this method, a different scaling is
employed for the same and opposite spin components of the MP2 energy, so that
SCS-MP2 performs as well as the much more costly CCSD(T) method at a high level
of theory.
SAC theory is developed for ground states and based on CC theory that describes
higher-order electron correlation. The main factor of electron correlation is collisions
of two electrons. In CC theory, most collisions of four electrons can be taken in as the
product of collisions of two electrons. Only a symmetry adapted excitation operator is
used for the SAC expansion. Since the operator of the SAC expansion is totally
symmetric, the unlinked terms (the products of the operators) are also totally
symmetric. SAC-CI is developed to treat excited states. SAC and SAC-CI wave
functions are orthogonal and Hamiltonian-orthogonal to each other. These
orthogonalities are especially important for the calculations of transitions
and relaxations. In general, the SAC-CI operators R are restricted to single and double
excitations. This is called the SAC-CI SD-R method. For the calculations of high-spin
states and multiple excitation processes, triple, quadruple, and higher excitation
operators are included. This is called the SAC-CI general-R method. In Chapter V, the
ground, singlet and triplet excited, ionized and electron attached states of ferrocene
(Fe(C5H5)2) were calculated using the SAC/SAC-CI SD-R method. The calculated
results are in good agreement with experimental values. It is found that shake-up
processes (one electron ionization and one electron excitation) contribute to the first
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","filename":"乙178_要旨.pdf","filesize":[{"value":"489.4 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","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","filename":"乙178_本文.pdf","filesize":[{"value":"1.5 MB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","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"],"pubdate":{"attribute_name":"公開日","attribute_value":"2010-02-22"},"publish_date":"2010-02-22","publish_status":"0","recid":"249","relation_version_is_last":true,"title":["Development of efficient algorithms for quantum chemistry calculations of large molecules"],"weko_creator_id":"1","weko_shared_id":1},"updated":"2023-06-20T16:02:51.764519+00:00"}