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  1. 020 学位論文
  2. 物理科学研究科
  3. 07 構造分子科学専攻

Development of efficient algorithms for quantum chemistry calculations of large molecules

https://ir.soken.ac.jp/records/249
https://ir.soken.ac.jp/records/249
68bfe1e2-1e63-44d2-9789-334af932d9ea
名前 / ファイル ライセンス アクション
乙178_要旨.pdf 要旨・審査要旨 (489.4 kB)
乙178_本文.pdf 本文 (1.5 MB)
Item type 学位論文 / Thesis or Dissertation(1)
公開日 2010-02-22
タイトル
タイトル Development of efficient algorithms for quantum chemistry calculations of large molecules
タイトル
タイトル Development of efficient algorithms for quantum chemistry calculations of large molecules
言語 en
言語
言語 eng
資源タイプ
資源タイプ識別子 http://purl.org/coar/resource_type/c_46ec
資源タイプ thesis
著者名 石村, 和也

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石村, 和也

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フリガナ イシムラ, カズヤ

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イシムラ, カズヤ

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著者 ISHIMURA, Kazuya

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en ISHIMURA, Kazuya

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学位授与機関
学位授与機関名 総合研究大学院大学
学位名
学位名 博士(理学)
学位記番号
内容記述タイプ Other
内容記述 総研大乙第178号
研究科
値 物理科学研究科
専攻
値 07 構造分子科学専攻
学位授与年月日
学位授与年月日 2007-09-28
学位授与年度
値 2007
要旨
内容記述タイプ Other
内容記述 Quantum chemistry plays an important role in elucidating molecular geometries,<br /> electronic states, and reaction mechanisms, because of the developments of a variety of<br /> theoretical methods, such as Hartree-Fock (HF), M&oslash;ler-Plesset (MP) perturbation,<br /> configuration interaction (CI), coupled-cluster (CC), and density functional theory <br /> (DFT) methods. Electronic structure calculations have been carried out by not only<br /> theoretical chemists but also experimental chemists. DFT is currently most widely used<br />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<br />correctly non-covalent interactions that are important for host-guest molecules,<br /> self-assembly, and molecular recognition, and they tend to underestimate reaction<br /> barriers. Many attempts have been made to develop new functionals and add<br /> semiempirical or empirical correction terms to standard functionals, but no generally<br /> accepted DFT method has emerged yet.<br />  Second-order M&oslash;ler-Plesset perturbation theory (MP2) is the simplest method that<br /> includes electron correlation important for non-covalent interactions and reaction<br /> barriers nonempirically. However, the computational cost of MP2 is considerably<br /> higher than that of DFT. In addition, much larger sizes of fast memory and hard disk<br /> are required in MP2 calculations. These make MP2 calculations increasingly difficult<br /> for larger molecules. Since workstation or personal computer (PC) clusters have<br /> become popular for quantum chemistry calculations, an efficient parallel calculation is<br /> a solution of the problem. Therefore, new parallel algorithms for MP2 energy and<br /> gradient calculations are presented in this thesis. Furthermore, an efficient algorithm<br /> for the generation of two-electron repulsion integrals (ERIs) which is important in <br /> quantum chemistry calculations is also presented.<br />  For the calculations of excited states, different approaches are required: for<br /> example, CI, multi-configuration self-consistent field (MCSCF), time-dependent DFT<br /> (TDDFT), and symmetry adapted cluster (SAC)/SAC-CI methods. One of the most<br /> accurate methods is SAC/SAC-CI, as demonstrated for many molecules. In this thesis,<br /> SAC/SAC-CI calculations of ground, ionized, and excited states are presented.<br />  This thesis consists of five chapters: a new algorithm of two-electron repulsion<br /> integral calculations (Chapter I), a new parallel algorithm of MP2 energy calculations<br /> (Chapter II), a new parallel algorithm of MP2 energy gradient calculations (Chapter<br /> III), applications of MP2 calculations (Chapter IV), and SAC/SAC-CI calculations of <br /> ionized and excited states (Chapter V).<br />  In quantum chemistry calculations, the generation of ERIs is one of the most basic<br /> subjects and is the most time-consuming step especially in direct SCF calculations.<br /> Many algorithms have been developed to reduce the computational cost. In<br /> Pople-Hehre algorithm, Cartesian axes are rotated to make several coordinate<br /> components zero or constant, so that these components are skipped in the generation of ERIs. In McMurchie-Davidson algorithm, ERIs are generated from (<i>ss</i>|<i>ss</i>) type<br /> integrals using a recurrence relation derived from Hermite polynomials. By combining<br /> these two algorithms, a new algorithm is developed in Chapter I. The results show that<br /> the new algorithm reduces the computational cost by 10 - 40%, as compared with the<br /> original algorithms. It is notable that the generation of ERIs including d functions is<br /> considerably fast. The program implemented officially in GAMESS in 2004 has been<br /> used all over the world.<br />  In quantum mechanics, perturbation methods can be used for adding corrections<br /> to reference solutions. In the MP perturbation method, a sum over Fock operators is<br /> used as the reference term, and the exact two-electron repulsion operator minus twice<br /> the average two-electron repulsion operator is used as the perturbation term. It is the<br /> advantage that the MP perturbation method is size consistent and size extensive, unlike<br /> truncated CI methods. The zero-order wave function is the HF Slater determinant, and <br /> the zero-order energy is expressed as a sum of occupied molecular orbital (MO)<br /> energies. The first-order perturbation is the correction for the overcounting of<br /> two-electron repulsions at zero-order, and the first-order energy corresponds to the HF<br /> energy. The MP correlation starts at second-order. In general, second-order (MP2) <br /> accounts for 80 - 90% of electron correlation. Therefore, MP2 is focused in this thesis<br /> since it is applicable to large molecules with considerable reliability and low <br /> computational cost.<br />  The formal computational scaling of MP2 energy calculations with respect to<br /> molecular size is fifth order, much higher than that of DFT energy calculations.<br /> Therefore, less expensive methods, such as Local MP2, density fitting (resolution of<br /> identity, RI) MP2, and Laplace Transform MP2, have been developed. However, all of<br /> these methods include approximations or cut-offs that need to be checked against full<br /> MP2 energies. An alternative approach to reduce the computational cost is to<br /> parallelize MP2 energy calculations. A number of papers on parallel MP2 energy<br /> calculations have been published. Almost all of them are based on simple <br /> parallelization methods that distribute only atomic orbital (AO) or MO indices to each <br /> processor. These methods have a disadvantage since intermediate integrals are <br /> broadcasted to all CPUs or the same AO ERIs are generated in all processors. Baker <br /> and Pulay developed a new parallel algorithm using Saeb&oslash;Alml&ouml;f integral<br /> transformation method. This algorithm parallelizes the first half transformation by AO<br /> indices and the second half transformation by MO indices. The advantages are that the<br /> total amount of network communication is independent of the number of processors <br /> and the AO integrals are generated only once. The disadvantage is the I/O overhead for<br /> the sorting of half-transformed integrals. A new parallel algorithm for MP2 energy<br /> calculations based on the two-step parallelization idea is presented in Chapter II. In<br /> this algorithm, AO indices are distributed in the AO integral generation and the first<br /> three quarter transformation, and MO indices are distributed in the last quarter<br /> transformation and MP2 energy calculation. Because the algorithm makes the sorting<br /> of intermediate integrals very simple, the parallel efficiency is highly improved and <br /> the I/O overhead is removed. Furthermore, the algorithm reduces highly the floating<br /> point operation (FLOP) count as well as the required memory and hard disk space, in <br /> comparison with other algorithms. Test calculations of taxol (C<small>47</small>H<small>51</small>NO<small>14</small>) and <br /> luciferin (C<small>11</small>H<small>8</small>N<small>2</small>O<small>3</small>S<small>2</small>) were performed on a cluster of Pentium 4 computers<br /> connected by gigabit Ethernet. The parallel scaling of the developed code is excellent<br /> up to the largest number of processors we have tested. For instance, the elapsed time<br /> for the MP2 energy calculations on 16 processors is on average 15.4 times faster than<br /> that on the single-processor.<br />  Determination of molecular geometries and reaction paths is a fundamental task in<br /> quantum chemistry and requires energy gradients with respect to nuclear coordinates. <br /> In Chapter III, a new parallel algorithm for MP2 energy gradient calculations is <br /> presented. The algorithm consists of 5 steps, the integral transformation, the MP2<br /> amplitude calculation, the MP2 Lagrangian calculation, the coupled-perturbed HF <br /> calculation, and the integral derivative calculation. All steps are parallelized by <br /> distributing AO or MO indices. The algorithm also reduces the FLOP count, the<br /> required memory, and hard disk space. Test calculations of MP2 energy gradients were <br /> performed for taxol and luciferin on a cluster of Pentium 4 computers. The speedups <br /> are very good up to 80 CPU cores we have tested. For instance, the speedup ratios are <br /> 28.2 - 33.0 on 32 processors, corresponding to 88% - 103% of linear speedup. This <br /> indicates the high parallel efficiency of the present algorithm. The calculation of taxol<br /> with 6-31G(d) (1032 contracted basis functions) finishes within 2 hours on 32<br /> processors, which requires only 1.8GB memory and 13.4GB hard disk per processor.<br /> Therefore, geometry optimization of molecules with 1000 basis functions can be easily<br /> performed using standard PC clusters.<br />  In Chapter IV, several applications of MP2 are performed using the program<br /> developed in Chapters II and III. Some molecules that DFT cannot treat well are <br /> optimized at the MP2 level. Geometry optimization is also carried out using the<br /> spin-component scaled (SCS) MP2 method. In this method, a different scaling is<br /> employed for the same and opposite spin components of the MP2 energy, so that<br /> SCS-MP2 performs as well as the much more costly CCSD(T) method at a high level<br /> of theory.<br />SAC theory is developed for ground states and based on CC theory that describes<br /> higher-order electron correlation. The main factor of electron correlation is collisions<br /> of two electrons. In CC theory, most collisions of four electrons can be taken in as the<br /> product of collisions of two electrons. Only a symmetry adapted excitation operator is <br /> used for the SAC expansion. Since the operator of the SAC expansion is totally<br /> symmetric, the unlinked terms (the products of the operators) are also totally <br /> symmetric. SAC-CI is developed to treat excited states. SAC and SAC-CI wave <br /> functions are orthogonal and Hamiltonian-orthogonal to each other. These<br /> orthogonalities are especially important for the calculations of transitions<br /> and relaxations. In general, the SAC-CI operators <i>R</i> are restricted to single and double<br /> excitations. This is called the SAC-CI SD-R method. For the calculations of high-spin<br /> states and multiple excitation processes, triple, quadruple, and higher excitation<br /> operators are included. This is called the SAC-CI general-R method. In Chapter V, the<br /> ground, singlet and triplet excited, ionized and electron attached states of ferrocene <br /> (Fe(C<small>5</small>H<small>5</small>)<small>2</small>) were calculated using the SAC/SAC-CI SD-R method. The calculated<br /> results are in good agreement with experimental values. It is found that shake-up<br /> processes (one electron ionization and one electron excitation) contribute to the first<br /> two ionization peaks.
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