The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds

We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 {\AA} for RHF and MP2, respectively.Comment: Revised manuscrip

Catalytic Mechanism of Amyloid-β Peptide Degradation by Insulin Degrading Enzyme: Insights from QM/MM MP2 Calculation

Insulin degrading enzyme (IDE), a metalloprotease that degrades amyloid-β (Aβ) peptides and insulin, is associated with Alzheimer’s disease and diabetes. The mechanism of IDE catalyzed degrading of Aβ peptides, which is of fundamental importance in the design of therapeutic methods for Alzheimer’s disease, has not been fully understood. In this work, combined quantum mechanics and molecular mechanics (QM/MM) style Møller-Plesset second order perturbation theory (MP2) geometry optimization calculations are performed to investigate the catalytic mechanism of the Aβ40 Phe19-Phe20 peptide bond cleavage by human IDE. The analyses using QM/MM MP2 optimization suggest that a neutral water molecule is at the active site of the enzyme-substrate (ES) complex. The water molecule is in hydrogen bonding with the nearby anionic Glu111 of IDE, but not directly bound to the catalytic Zn ion. This is confirmed by QM/MM DFTB3 molecular dynamics simulation. Our studies also reveal that the hydrolysis of the Aβ40 Phe19-Phe20 peptide bond by IDE consists of four key steps. The neutral water is first activated by moving toward and binding to the Zn ion. A gem-diol intermediate is then formed by the activated neutral water molecule attacking the C atom of the Phe19-Phe20 peptide bond. The next is the protonation of the N atom of Phe19-Phe20 peptide bond to form an intermediate with an elongated C-N bond. The final step is the breaking of the Phe19-Phe20 C-N bond. The final step is the rate-determining step with a calculated Gibbs free energy of activation of 17.34 kcal/mol, in good agreement with the experimental value 16.7 kcal/mol. This mechanism provides the basis for the design of biochemical methods to modulate the activity of IDE in humans

Modernizing the core quantum chemistry algorithms

This document covers the basics of computational chemistry and how using the modern programming techniques the theory can be efficiently implemented on digital computers. The computer implementations are developed from the core two-electron integrals to many-body and coupled cluster algorithms. A particular attention is paid to the physical constraints of he computer resources and the emergence of the novel architectures

Development of efficient algorithms for quantum chemistry calculations of large molecules

　　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 usedto 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 describecorrectly 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