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 (

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

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

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