Dmitri G. Fedorov

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

Fragmentation Methods: A Route to Accurate Calculations on Large Systems Mark S. Gordon,* Dmitri G. Fedorov, Spencer R. Pruitt, and Lyudmila V. Slipchenko Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States

The importance of three-body terms in the fragment molecular orbital method

A previously proposed two-body fragment molecular orbital method based on the restricted Hartree-Fock (RHF) method was extended to include explicit three-body terms. The accuracy of the method was tested on a set of representative molecules: (H(2)O)(n), n=16, 32, and 64, as well as alpha and beta n-mers of alanine, n=10, 20, and 40, using STO-3G, 3-21G, 6-31G, and 6-31++G(**) basis sets. Two- and three-body results are presented separately for assigning one and two molecules (or residues) per fragment. Total energies are found to differ from the regular RHF method by at most DeltaE(2/1)=0.06, DeltaE(2/2)=0.04, DeltaE(3/1)=0.02, and DeltaE(3/2)=0.003 (a.u.); rms energy gradients differ by at most DeltaG(2/1)=0.0015, DeltaG(2/2)=0.000 75, DeltaG(3/1)=0.000 20, and DeltaG(3/2)=0.000 10 (a.u./bohr), and rms dipole moments are reproduced with at most deltaD(2/1)=3.7, deltaD(2/2)=3.4, deltaD(3/1)=2.6, and deltaD(3/2)=3.1 (%) relative error, where the subscript notation n/m refers to the n-body method based on m molecules (residues) per fragment. A few of the largest three-body calculations were performed with a separated trimer approximation, which presumably somewhat lowered the accuracy of mostly dipole moments which are very sensitive to slight variations in the density distribution. The proposed method is capable of providing sufficient chemical accuracy while providing detailed information on many-body interactions.

Second order Møller-Plesset perturbation theory based upon the fragment molecular orbital method.

The fragment molecular orbital (FMO) method was combined with the second order Møller-Plesset (MP2) perturbation theory. The accuracy of the method using the 6-31G(*) basis set was tested on (H(2)O)(n), n=16,32,64; alpha-helices and beta-strands of alanine n-mers, n=10,20,40; as well as on (H(2)O)(n), n=16,32,64 using the 6-31 + + G(**) basis set. Relative to the regular MP2 results that could be afforded, the FMO2-MP2 error in the correlation energy did not exceed 0.003 a.u., the error in the correlation energy gradient did not exceed 0.000 05 a.u./bohr and the error in the correlation contribution to dipole moment did not exceed 0.03 debye. An approximation reducing computational load based on fragment separation was introduced and tested. The FMO2-MP2 method demonstrated nearly linear scaling and drastically reduced the memory requirements of the regular MP2, making possible calculations with several thousands basis functions using small Pentium clusters. As an example, (H(2)O)(64) with the 6-31 + + G(**) basis set (1920 basis functions) can be run in 1 Gbyte RAM and it took 136 s on a 40-node Pentium4 cluster.

A new hierarchical parallelization scheme: Generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method(FMO)

A two‐level hierarchical scheme, generalized distributed data interface (GDDI), implemented into GAMESS is presented. Parallelization is accomplished first at the upper level by assigning computational tasks to groups. Then each group does parallelization at the lower level, by dividing its task into smaller work loads. The types of computations that can be used with this scheme are limited to those for which nearly independent tasks and subtasks can be assigned. Typical examples implemented, tested, and analyzed in this work are numeric derivatives and the fragment molecular orbital method (FMO) that is used to compute large molecules quantum mechanically by dividing them into fragments. Numeric derivatives can be used for algorithms based on them, such as geometry optimizations, saddle‐point searches, frequency analyses, etc. This new hierarchical scheme is found to be a flexible tool easily utilizing network topology and delivering excellent performance even on slow networks. In one of the typical tests, on 16 nodes the scalability of GDDI is 1.7 times better than that of the standard parallelization scheme DDI and on 128 nodes GDDI is 93 times faster than DDI (on a multihub Fast Ethernet network). FMO delivered scalability of 80–90% on 128 nodes, depending on the molecular system (water clusters and a protein). A numerical gradient calculation for a water cluster achieved a scalability of 70% on 128 nodes. It is expected that GDDI will become a preferred tool on massively parallel computers for appropriate computational tasks.

Spin-orbit coupling in molecules: chemistry beyond the adiabatic approximation

An extensive introduction to spin-orbit coupling (SOC) is presented, starting from a discussion of the phenomenological operators and general chemical importance of SOC to studies of chemical reactions. Quantitative SOC operators are discussed, and the symmetry properties of the SOC Hamiltonian important for understanding the general features of SOC are summarized. Comparison of the one- and two-electron contributions to SOC is given, followed by a discussion of commonly used approximations for the two-electron part. Applications of SOC to studies using effective and model core potentials have been analysed. The theoretical discussion is illustrated with numerous practical examples, including diatomic molecules (with an emphasis on hydrides) and some examples for polyatomic molecules. The fine structure of the SOC interaction (vibrational dependence) for some diatomic molecules has been elucidated.

Pair interaction energy decomposition analysis.

The energy decomposition analysis (EDA) by Kitaura and Morokuma was redeveloped in the framework of the fragment molecular orbital method (FMO). The proposed pair interaction energy decomposition analysis (PIEDA) can treat large molecular clusters and the systems in which fragments are connected by covalent bonds, such as proteins. The interaction energy in PIEDA is divided into the same contributions as in EDA: the electrostatic, exchange‐repulsion, and charge transfer energies, to which the correlation (dispersion) term was added. The careful comparison to the ab initio EDA interaction energies for water clusters with 2–16 molecules revealed that PIEDA has the error of at most 1.2 kcal/mol (or about 1%). The analysis was applied to (H2O)1024, the α helix, β turn, and β strand of polyalanine (ALA)10, as well as to the synthetic protein (PDB code 1L2Y) with 20 residues. The comparative aspects of the polypeptide isomer stability are discussed in detail.

The fragment molecular orbital method : practical applications to large molecular systems

Editors Contributors Chapter 1: Introduction Kazuo Kitaura and Dmitri G. Fedorov Chapter 2: Theoretical Background of the Fragment Molecular Orbital (Fmo) Method and Its Implementation in GAMESS Dmitri G. Fedorov and Kazuo Kitaura Chapter 3: Developments of FMO Methodology and Graphical User Interface in ABINIT-MP Tatsuya Nakano, Yuji Mochizuki, Akifumi Kato, Kaori Fukuzawa, Takeshi Ishikawa, Shinji Amari, Ikuo Kurisaki, and Shigenori Tanaka Chapter 4: Excited States of Photoactive Proteins by Configuration Interaction Studies Yuji Mochizuki, Tatsuya Nakano, Naoki Taguchi, and Shigenori Tanaka Chapter 5: The Fragment Molecular Orbital-Based Time-Dependent Density Functional Theory for Excited States in Large Systems Mahito Chiba, Dmitri G. Fedorov, and Kazuo Kitaura Chapter 6: FMO-MD: An Ab Initio-Based Molecular Dynamics of Large Systems Yuto Komeiji Chapter 7: Application of the FMO Method to Specific Molecular Recognition of Biomacromolecules Kaori Fukuzawa, Yuji Mochizuki, Tatsuya Nakano, and Shigenori Tanaka Chapter 8: Detailed Electronic Structure Studies Revealing the Nature of Protein-Ligand Binding Isao Nakanishi, Dmitri G. Fedorov, and Kazuo Kitaura Chapter 9: How Does the FMO Method Help in Studying Viruses and Their Binding to Receptors? Toshihiko Sawada, Tomohiro Hashimoto, Hiroaki Tokiwa, Tohru Suzuki, Hirofumi Nakano, Hideharu Ishida, Makoto Kiso, and Yasuo Suzuki Chapter 10: FMO as a Tool for Structure-Based Drug Design Tomonaga Ozawa, Kosuke Okazaki, and Motohiro Nishio Chapter 11: Modeling a Protein Environment in an Enzymatic Catalysis: A Case Study of the Chorismate Mutase Reaction Toyokazu Ishida Index

Coupled-cluster theory based upon the fragment molecular-orbital method.

The fragment molecular-orbital (FMO) method was combined with the single-reference coupled-cluster (CC) theory. The developed method (FMO-CC) was applied at the CCSD and CCSD(T) levels of theory, for the cc-pVnZ family of basis sets (n=D,T,Q) to water clusters and glycine oligomers (up to 32 molecules/residues using as large basis sets as possible for the given system). The two- and three-body FMO-CC results are discussed at length, with emphasis on the basis-set dependence and three-body effects. Two- and three-body approximations based on interfragment distances were developed and the values appropriate for their accurate application carefully determined. The error in recovering the correlation energy was several millihartree for the two-body FMO-CC method and in the submillihartree range for the three-body FMO-CC method. In the largest calculations, we were able to perform the CCSD(T) calculations of (H2O)32 with the cc-pVQZ basis set (3680 basis functions) and (GLY)32 with the cc-VDZ basis set (712 correlated electrons). FMO-CC was parallelized using the upper level of the two-layer parallelization scheme. The computational scaling of the two-body FMO-CC method was demonstrated to be nearly linear. As an example of timings, CCSD(T) calculations of (H2O)32 with cc-pVDZ took 13 min on an eight node 3.2-GHz Pentium4 cluster.

The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO)

The polarizable continuum model (PCM) for the description of solvent effects is combined with the fragment molecular orbital (FMO) method at several levels of theory, using a many‐body expansion of the electron density and the corresponding electrostatic potential, thereby determining solute (FMO)–solvent (PCM) interactions. The resulting method, denoted FMO/PCM, is applied to a set of model systems, including α‐helices and β‐strands of alanine consisting of 10, 20, and 40 residues and their mutants to charged arginine and glutamate residues. The FMO/PCM error in reproducing the PCM solvation energy for a full system is found to be below 1 kcal/mol in all cases if a two‐body expansion of the electron density is used in the PCM potential calculation and two residues are assigned to each fragment. The scaling of the FMO/PCM method is demonstrated to be nearly linear at all levels for polyalanine systems. A study of the relative stabilities of α‐helices and β‐strands is performed, and the magnitude of the contributing factors is determined. The method is applied to three proteins consisting of 20, 129, and 245 residues, and the solvation energy and computational efficiency are discussed.

Fragment molecular orbital method: application to molecular dynamics simulation, 'ab initio FMO-MD'

Abstract A quantum molecular simulation method applicable to biological molecules is proposed. Ab initio fragment molecular orbital method-based molecular dynamics (FMO-MD) combines molecular dynamics simulation with the ab initio fragment molecular orbital method. Here, FMO computes the force acting on each atom’s nucleus while MD computes the nuclei’s time-dependent evolutions. FMO-MD successfully simulated a small polypeptide, demonstrating the method’s applicability to biological molecules.