Recent developments in the general atomic and molecular electronic structure system.

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.

Proton Transfer in 1,2,4-Triazolium Dinitramide: Effect of Aqueous Microsolvation.

The gas phase proton transfer process in 1,2,4-triazolium dinitramide (TD) was studied using second-order perturbation theory to determine how the presence of one and two water molecules modifies the potential energy surface that connects the ion pair to the neutral pair. The presence of one water molecule can introduce small proton transfer energy barriers that separate the ion pair from the lower-energy neutral pair. These energy barriers are easily surmounted. Reaction paths were determined for single proton transfers and double proton transfers via one water molecule. In the presence of two water molecules, the global minimum is an ion pair, as are most of the lower-energy local minima. Energy barriers for single, double, and triple proton transfers were also found for TD in the presence of two water molecules. One TD ion pair structure with two water molecules has no corresponding neutral pair energy minimum. A quasi-atomic orbital analysis is used to understand the nature of the bonding in the various species studied in this work.

Mapping Interaction Energies in Chorismate Mutase with the Fragment Molecular Orbital Method.

The Claisen rearrangement of chorismate to prephenate is mapped across the entire reaction pathway using the fragment molecular orbital (FMO) method. Three basis sets (6-31G(d), cc-pVDZ, and pcseg-1) are studied to provide guidance toward obtaining high accuracy with the FMO method on such systems. Using a fragmentation scheme of one residue per fragment, the FMO method using the 6-31G(d) basis set and second-order Møller-Plesset perturbation theory (MP2) with the hybrid orbital projection fragmentation scheme provides the most reliable results across the entire reaction pathway. Calculations using the multilayer FMO method are performed and shown to be in agreement with single-layer calculations in all cases with differences of less than one kilocalorie per mole for all tested basis set combinations along the entire reaction path. The use of restricted Hartree-Fock for the lower-level layer and MP2 for the higher-level layer gives the most consistent results when using the same basis set for both layers. Pair interaction energy decomposition analysis calculations confirm that electrostatic interactions are the predominant force between three key arginine residues and chorismate and that dispersion and charge transfer interactions in the binding pocket also play a role in the local chemistry of the reaction.

Ab Initio Multiple Spawning Method for Intersystem Crossing Dynamics: Spin-Forbidden Transitions between (3)B1 and (1)A1 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.

Importance of Three-Body Interactions in Molecular Dynamics Simulations of Water Demonstrated with the Fragment Molecular Orbital Method.

The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted second-order Møller-Plesset perturbation theory, as well as for both restricted and unrestricted Hartree-Fock and density functional theory. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores are also discussed.

Ab initio investigation of the aqueous solvation of the nitrate ion.

The surface affinity of the nitrate ion in aqueous clusters is investigated with a variety of theoretical methods. A sampling of structures in which the nitrate ion is solvated by 32 water molecules is optimized using second order Møller-Plesset perturbation theory (MP2). Four of these MP2 optimized structures are used as starting points for fully ab initio molecular dynamics simulations at the dispersion corrected restricted Hartree-Fock (RHF-D) level of theory. The nitrate ion solvated by 16, 32, and 64 water molecules is also investigated with umbrella sampling molecular dynamics simulations using QM/MM methodology, where the nitrate ion is modeled with MP2 and the water molecules are described using either the non-empirical effective fragment potential (EFP) or the empirical TIP5P potential. The turning point between surface and interior solvation of the nitrate ion is predicted to lie around a cluster size of 64 water molecules.

Surface affinity of the hydronium ion: the effective fragment potential and umbrella sampling.

The surface affinity of the hydronium ion in water is investigated with umbrella sampling and classical molecular dynamics simulations, in which the system is described with the effective fragment potential (EFP). The solvated hydronium ion is also explored using second order perturbation theory for the hydronium ion and the empirical TIP5P potential for the waters. Umbrella sampling is used to analyze the surface affinity of the hydronium ion, varying the number of solvent water molecules from 32 to 256. Umbrella sampling with the EFP method predicts the hydronium ion to most probably lie about halfway between the center and edge of the water cluster, independent of the cluster size. Umbrella sampling using MP2 for the hydronium ion and TIP5P for the solvating waters predicts that the solvated proton most probably lies about 0.5-2.0 Å from the edge of the water cluster independent of the cluster size.

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.

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%.

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.

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.

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.

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.

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.

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.