Theoretical chemists have always strived to perform quantum mechanics (QM) calculations on larger and larger molecules and molecular systems, as well as condensed phase species, that are frequently much larger than the current state-of-the-art would suggest is possible. The desire to study species (with acceptable accuracy) that are larger than appears to be feasible has naturally led to the development of novel methods, including semiempirical approaches, reduced scaling methods, and fragmentation methods. The focus of the present review is on fragmentation methods, in which a large molecule or molecular system is made more computationally tractable by explicitly considering only one part (fragment) of the whole in any particular calculation. If one can divide a species of interest into fragments, employ some level of ab initio QM to calculate the wave function, energy, and properties of each fragment, and then combine the results from the fragment calculations to predict the same properties for the whole, the possibility exists that the accuracy of the outcome can approach that which would be obtained from a full (nonfragmented) calculation. It is this goal that drives the development of fragmentation methods. Disciplines Chemistry CommentsReprinted (adapted) with permission from Chemical Reviews 112 (2012): 632,

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree–Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Following the brief review of the modern fragment-based methods and other approaches to perform quantum-mechanical calculations of large systems, the theoretical development of the fragment molecular orbital method (FMO) is covered in detail, with the emphasis on the physical properties, which can be computed with FMO. The FMO-based polarizable continuum model (PCM) for treating the solvent effects in large systems and the pair interaction energy decomposition analysis (PIEDA) are described in some detail, and a range of applications of FMO to biological studies is introduced. The factors determining the relative stability of polypeptide conformers (alpha-helix, beta-turn, and extended form) are elucidated using FMO/PCM and PIEDA, and the interactions in the Trp-cage miniprotein construct (PDB: 1L2Y) are analyzed using PIEDA.

Abstract: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 (H 2 O) 1024 , the helix, turn, and 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.

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.