WEKO3
アイテム
Development of efficient algorithms for quantum chemistry calculations of large molecules
https://ir.soken.ac.jp/records/249
https://ir.soken.ac.jp/records/24968bfe1e21e6344d29789334af932d9ea
名前 / ファイル  ライセンス  アクション 

要旨・審査要旨 (489.4 kB)


本文 (1.5 MB)

Item type  学位論文 / Thesis or Dissertation(1)  

公開日  20100222  
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
× 石村, 和也 

フリガナ 
イシムラ, カズヤ
× イシムラ, カズヤ 

著者 
ISHIMURA, Kazuya
× ISHIMURA, Kazuya 

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  20070928  
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 HartreeFock (HF), MølerPlesset (MP) perturbation,<br /> configuration interaction (CI), coupledcluster (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 noncovalent interactions that are important for hostguest molecules,<br /> selfassembly, 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 /> Secondorder MølerPlesset perturbation theory (MP2) is the simplest method that<br /> includes electron correlation important for noncovalent 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 twoelectron 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, multiconfiguration selfconsistent field (MCSCF), timedependent DFT<br /> (TDDFT), and symmetry adapted cluster (SAC)/SACCI methods. One of the most<br /> accurate methods is SAC/SACCI, as demonstrated for many molecules. In this thesis,<br /> SAC/SACCI calculations of ground, ionized, and excited states are presented.<br /> This thesis consists of five chapters: a new algorithm of twoelectron 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/SACCI 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 timeconsuming step especially in direct SCF calculations.<br /> Many algorithms have been developed to reduce the computational cost. In<br /> PopleHehre 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 McMurchieDavidson 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 twoelectron repulsion operator minus twice<br /> the average twoelectron 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 zeroorder wave function is the HF Slater determinant, and <br /> the zeroorder energy is expressed as a sum of occupied molecular orbital (MO)<br /> energies. The firstorder perturbation is the correction for the overcounting of<br /> twoelectron repulsions at zeroorder, and the firstorder energy corresponds to the HF<br /> energy. The MP correlation starts at secondorder. In general, secondorder (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 cutoffs 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 SaebøAlmlöf 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 halftransformed integrals. A new parallel algorithm for MP2 energy<br /> calculations based on the twostep 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 singleprocessor.<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 coupledperturbed 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 631G(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 /> spincomponent 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 /> SCSMP2 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 /> higherorder 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. SACCI is developed to treat excited states. SAC and SACCI wave <br /> functions are orthogonal and Hamiltonianorthogonal to each other. These<br /> orthogonalities are especially important for the calculations of transitions<br /> and relaxations. In general, the SACCI operators <i>R</i> are restricted to single and double<br /> excitations. This is called the SACCI SDR method. For the calculations of highspin<br /> states and multiple excitation processes, triple, quadruple, and higher excitation<br /> operators are included. This is called the SACCI generalR 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/SACCI SDR method. The calculated<br /> results are in good agreement with experimental values. It is found that shakeup<br /> processes (one electron ionization and one electron excitation) contribute to the first<br /> two ionization peaks.  
所蔵  
値  有 