Development of efficient algorithms for quantum chemistry calculations of large molecules

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), Møler-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 Møler-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 (ss|ss) 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 ...

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