Spencer R. Pruitt

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

Accurate methods for large molecular systems.

Three exciting new methods that address the accurate prediction of processes and properties of large molecular systems are discussed. The systematic fragmentation method (SFM) and the fragment molecular orbital (FMO) method both decompose a large molecular system (e.g., protein, liquid, zeolite) into small subunits (fragments) in very different ways that are designed to both retain the high accuracy of the chosen quantum mechanical level of theory while greatly reducing the demands on computational time and resources. Each of these methods is inherently scalable and is therefore eminently capable of taking advantage of massively parallel computer hardware while retaining the accuracy of the corresponding electronic structure method from which it is derived. The effective fragment potential (EFP) method is a sophisticated approach for the prediction of nonbonded and intermolecular interactions. Therefore, the EFP method provides a way to further reduce the computational effort while retaining accuracy by treating the far-field interactions in place of the full electronic structure method. The performance of the methods is demonstrated using applications to several systems, including benzene dimer, small organic species, pieces of the alpha helix, water, and ionic liquids.

Systematic Fragmentation Method and the Effective Fragment Potential: An Efficient Method for Capturing Molecular Energies

The systematic fragmentation method fragments a large molecular system into smaller pieces, in such a way as to greatly reduce the computational cost while retaining nearly the accuracy of the parent ab initio electronic structure method. In order to attain the desired (sub-kcal/mol) accuracy, one must properly account for the nonbonded interactions between the separated fragments. Since, for a large molecular species, there can be a great many fragments and therefore a great many nonbonded interactions, computations of the nonbonded interactions can be very time-consuming. The present work explores the efficacy of employing the effective fragment potential (EFP) method to obtain the nonbonded interactions since the EFP method has been shown previously to capture nonbonded interactions with an accuracy that is often comparable to that of second-order perturbation theory. It is demonstrated that for nonbonded interactions that are not high on the repulsive wall (generally >2.7 A), the EFP method appears to be a viable approach for evaluating the nonbonded interactions. The efficacy of the EFP method for this purpose is illustrated by comparing the method to ab initio methods for small water clusters, the ZOVGAS molecule, retinal, and the alpha-helix. Using SFM with EFP for nonbonded interactions yields an error of 0.2 kcal/mol for the retinal cis-trans isomerization and a mean error of 1.0 kcal/mol for the isomerization energies of five small (120-170 atoms) alpha-helices.

The fragment molecular orbital and systematic molecular fragmentation methods applied to water clusters

Two electronic structure methods, the fragment molecular orbital (FMO) and systematic molecular fragmentation (SMF) methods, that are based on fragmenting a large molecular system into smaller, more computationally tractable components (fragments), are presented and compared with fully ab initio results for the predicted binding energies of water clusters. It is demonstrated that, even when explicit three-body effects are included (especially necessary for water clusters due to their complex hydrogen-bonded networks) both methods present viable, computationally efficient alternatives to fully ab initio quantum chemistry.

Open-Shell Formulation of the Fragment Molecular Orbital Method.

Performing accurate calculations on large molecular systems is desirable for closed- and open-shell systems. In this work, the fragment molecular orbital method is extended to open-shell systems and implemented in the GAMESS (General Atomic and Molecular Electronic Structure System) program package. The accuracy of the method is tested, and the ability to reproduce reaction enthalpies is demonstrated. These tests also demonstrate its utility in providing an efficient means to model large open-shell systems.

Efficient and accurate fragmentation methods.

Conspectus Three novel fragmentation methods that are available in the electronic structure program GAMESS (general atomic and molecular electronic structure system) are discussed in this Account. The fragment molecular orbital (FMO) method can be combined with any electronic structure method to perform accurate calculations on large molecular species with no reliance on capping atoms or empirical parameters. The FMO method is highly scalable and can take advantage of massively parallel computer systems. For example, the method has been shown to scale nearly linearly on up to 131 000 processor cores for calculations on large water clusters. There have been many applications of the FMO method to large molecular clusters, to biomolecules (e.g., proteins), and to materials that are used as heterogeneous catalysts. The effective fragment potential (EFP) method is a model potential approach that is fully derived from first principles and has no empirically fitted parameters. Consequently, an EFP can be generated for any molecule by a simple preparatory GAMESS calculation. The EFP method provides accurate descriptions of all types of intermolecular interactions, including Coulombic interactions, polarization/induction, exchange repulsion, dispersion, and charge transfer. The EFP method has been applied successfully to the study of liquid water, π-stacking in substituted benzenes and in DNA base pairs, solvent effects on positive and negative ions, electronic spectra and dynamics, non-adiabatic phenomena in electronic excited states, and nonlinear excited state properties. The effective fragment molecular orbital (EFMO) method is a merger of the FMO and EFP methods, in which interfragment interactions are described by the EFP potential, rather than the less accurate electrostatic potential. The use of EFP in this manner facilitates the use of a smaller value for the distance cut-off (Rcut). Rcut determines the distance at which EFP interactions replace fully quantum mechanical calculations on fragment-fragment (dimer) interactions. The EFMO method is both more accurate and more computationally efficient than the most commonly used FMO implementation (FMO2), in which all dimers are explicitly included in the calculation. While the FMO2 method itself does not incorporate three-body interactions, such interactions are included in the EFMO method via the EFP self-consistent induction term. Several applications (ranging from clusters to proteins) of the three methods are discussed to demonstrate their efficacy. The EFMO method will be especially exciting once the analytic gradients have been completed, because this will allow geometry optimizations, the prediction of vibrational spectra, reaction path following, and molecular dynamics simulations using the method.

Large-Scale MP2 Calculations on the Blue Gene Architecture Using the Fragment Molecular Orbital Method

Benchmark timings are presented for the fragment molecular orbital method on a Blue Gene/P computer. Algorithmic modifications that lead to enhanced performance on the Blue Gene/P architecture include strategies for the storage of fragment density matrices by process subgroups in the global address space. The computation of the atomic forces for a system with more than 3000 atoms and 44 000 basis functions, using second order perturbation theory and an augmented and polarized double-ζ basis set, takes ∼7 min on 131 072 cores.

Fully Integrated Effective Fragment Molecular Orbital Method.

In this work, the effective fragment potential (EFP) method is fully integrated (FI) into the fragment molecular orbital (FMO) method to produce an effective fragment molecular orbital (EFMO) method that is able to account for all of the fundamental types of both bonded and intermolecular interactions, including many-body effects, in an accurate and efficient manner. The accuracy of the method is tested and compared to both the standard FMO method as well as to fully ab initio methods. It is shown that the FIEFMO method provides significant reductions in error while at the same time reducing the computational cost associated with standard FMO calculations by up to 96%.

Geometry Optimizations of Open-Shell Systems with the Fragment Molecular Orbital Method

The ability to perform geometry optimizations on large molecular systems is desirable for both closed- and open-shell species. In this work, the restricted open-shell Hartree-Fock (ROHF) gradients for the fragment molecular orbital (FMO) method are presented. The accuracy of the gradients is tested, and the ability of the method to reproduce adiabatic excitation energies is also investigated. Timing comparisons between the FMO method and full ab initio calculations are also performed, demonstrating the efficiency of the FMO method in modeling large open-shell systems.

Ab Initio Multiple Spawning Method for Intersystem Crossing Dynamics: Spin-Forbidden Transitions between 3B1 and 1A1 States of GeH2

Dynamics at intersystem crossings are fundamental to many processes in chemistry, physics, and biology. The ab initio multiple spawning (AIMS) method was originally developed to describe internal conversion dynamics at conical intersections where derivative coupling is responsible for nonadiabatic transitions between electronic states with the same spin multiplicity. Here, the applicability of the AIMS method is extended to intersystem crossing dynamics in which transitions between electronic states with different spin multiplicities are mediated by relativistic spin-orbit coupling. In the direct AIMS dynamics, the nuclear wave function is expanded in the basis of frozen multidimensional Gaussians propagating on the coupled electronic potential energy surfaces calculated on the fly. The AIMS method for intersystem crossing is used to describe the nonadiabatic transitions between the (3)B1 and (1)A1 states of GeH2. The potential energies and gradients were obtained at the CASSCF(6,6)/6-31G(d) level of theory. The spin-orbit coupling matrix elements were calculated with the configuration interaction method using the two-electron Breit-Pauli Hamiltonian. The excited (3)B1 state lifetime and intersystem crossing rate constants were estimated by fitting the AIMS state population with the first-order kinetics equation for a reversible unimolecular reaction. The obtained rate constants are compared with the values predicted by the statistical nonadiabatic transition state theory with transition probabilities calculated using the Landau-Zener and weak coupling formulas.