The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures.

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

The Back Door to the Surface Hydrated Electron.

We use a Mg+ metal to extend the size regime of aqueous clusters to extrapolate to the bulk limit of the vertical detachment energy (VDE) of the solvated electron to >3,200, a value between 1 to over 2 orders of magnitude larger than the one previously measured experimentally or computed theoretically. We relate the VDE to the energy difference between the Mg+(H2O)n and Mg2+(H2O)n systems and the metal's second ionization potential. The extrapolated bulk VDEs of the localized surface electron, which moves away from the metal as n increases, are 1.89 ± 0.01 eV for semiempirical (n ∼ 3,200; PM6-D3H4) and 1.73 ± 0.03 eV (n ∼ 150; HF) and 1.83 ± 0.02 eV (n ∼ 150; MP2) for ab initio, in excellent agreement with the 1.6-1.8 eV range of experimental results. The VDEs converge from above (larger values) to the bulk limit, in a manner that is qualitatively opposite from previous studies and experiments lacking a charged metal, a fact justifying the "back door" approach to the solvated electron.

The many-body expansion for metals. I. The alkaline earth metals Be, Mg, and Ca.

We examine the many-body expansion (MBE) for alkaline earth metal clusters, Ben, Mgn, Can (n = 4, 5, 6), at the Møller-Plesset second order perturbation theory, coupled-cluster singles and doubles with perturbative triples, multi-reference perturbation theory, and multi-reference configuration interaction levels of theory. The magnitude of each term in the MBE is evaluated for several geometrical configurations. We find that the behavior of the MBE for these clusters depends strongly on the geometrical arrangement and, to a lesser extent, on the level of theory used. Another factor that affects the MBE is the in situ (ground or excited) electronic state of the individual atoms in the cluster. For most geometries, the three-body term is the largest, followed by a steady decrease in absolute energy for subsequent terms. Though these systems exhibit non-negligible multi-reference effects, there was little qualitative difference in the MBE when employing single vs multi-reference methods. Useful insights into the connectivity and stability of these clusters have been drawn from the respective potential energy surfaces and quasi-atomic orbitals for the various dimers, trimers, and tetramers. Through these analyses, we investigate the similarities and differences in the binding energies of different-sized clusters for these metals.

Adaptive-Partitioning Multilayer Dynamics Simulations: 1. On-the-Fly Switch between Two Quantum Levels of Theory.

We propose to generalize the previously developed two-layer permuted adaptive-partitioning quantum-mechanics/molecular-mechanics (QM/MM), which reclassifies atoms as QM or MM on-the-fly in dynamics simulations, to multilayer adaptive-partitioning algorithms that enable multiple levels of theory. In this work, we formulate two new algorithms that smoothly interpolate the energy between two QM (Q1 and Q2) levels of theory. The first "permuted adaptive-partitioning" scheme is based on the weighted many-body expansion of the potential, as in the adaptive-partitioning QM/MM. Unconventional and potentially more efficient, the second "interpolated adaptive-partitioning" method employs alchemical QM calculations with Q1/Q2-mixed basis sets, Fock matrices, and overlap matrices. To our knowledge, this is the first time that such alchemical calculations are performed in QM, although they are routinely done in MM. Test calculations on water-cluster models show that both new algorithms indeed yield smooth energy curves when water molecules shift between Q1 and Q2.

Stability and Dissociation of Ethylenedione (OCCO).

This work examines the electronic structure and apparent instability of ethylenedione (OCCO), including an analysis of the singlet and triplet potential energy surfaces along the bending vibrations. While the singlet state is inherently unstable due to the Renner-Teller effect, theory predicts the triplet state to have a stable minimum on the potential energy surface. The stability of the triplet state is examined in detail, taking into account spin-orbit interactions. Using multireference quantum chemical methods, the lifetime of the triplet state is estimated to be in the picosecond range, significantly lower than previously computed. A quasi-atomic molecular orbital (QUAO) analysis is also used to elucidate the nature of bonding along the potential energy surface in both the singlet and triplet states. These calculations confirm the transient nature of the OCCO molecule, although they do not fully explain the lack of experimental detection via spectroscopy, which is known have the capability to probe even shorter lifetimes.

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.

Accuracy of the PM6 and PM7 Methods on Bare and Thiolate-Protected Gold Nanoclusters.

Semiempirical quantum mechanical (SEQM) methods offer an attractive middle ground between fully ab initio quantum chemistry and force-field simulations, allowing for a quantum mechanical treatment of the system at a relatively low computational cost. However, SEQM methods have not been frequently utilized in the study of transition metal systems, mostly due to the difficulty in obtaining reliable parameters. This paper examines the accuracy of the PM6 and PM7 semiempirical methods to predict geometries, ionization potentials, and HOMO-LUMO energy gaps of several bare gold clusters (Aun) and thiolate-protected gold nanoclusters (AuSNCs). Contrary to PM6, the PM7 method can predict qualitatively correct geometries and ionization potentials when compared to DFT. PM6 fails to predict the characteristic gold core and gold-sulfur ligand shell (staple motifs) of the AuSNC structures. Both the PM6 and PM7 methods overestimate the HOMO-LUMO gaps. Overall, PM7 provides a more accurate description of bare gold and gold-thiolate nanoclusters than PM6. Nevertheless, refining the gold parameters could help achieve better quantitative accuracy.

Analytic non-adiabatic couplings for the spin-flip ORMAS method.

Analytic non-adiabatic coupling matrix elements (NACME) are derived and implemented for the spin-flip occupation restricted multiple active space configuration interaction (SF-ORMAS-CI) method. SF-ORMAS is a general spin correct implementation of the SF-CI method and has been shown to correctly describe various stationary geometries, including regions of conical intersections. The availability of non-adiabatic coupling allows a fuller examination of non-adiabatic phenomena with the SF-ORMAS method. In this study, the implementation of the NACME is tested using two model systems, MgFH and ethylene. In both cases, the SF-ORMAS method exhibits good qualitative agreement with established multi-reference methods, suggesting that SF-ORMAS is a suitable method for the study of non-adiabatic chemical phenomena.

Analytic Gradients for the Spin-Flip ORMAS-CI Method: Optimizing Minima, Saddle Points, and Conical Intersections.

Analytic nuclear gradients are derived and implemented for the recently introduced SF-ORMAS-CI (spin-flip occupation restricted multiple active space CI) method. Like most SF methods, SF-ORMAS-CI successfully describes bond breaking, diradical systems, transition states, and low-lying excited states, without suffering from spin contamination. The availability of analytic gradients now enables the efficient optimization of equilibrium structures in both ground and excited electronic states, as well as the computation of seminumerical Hessians. Therefore, it is now possible to determine minima, transition states, and conical intersections using the SF-ORMAS-CI method without the need for numerical differentiation. In the present study the SF-ORMAS method and gradient are applied to optimize structures for several organic molecules, such as ethylene, azomethane, and trimethylmethylene. In most cases, structures optimized with SF-ORMAS are almost identical to those obtained using other multireference methods, despite the lack of dynamic correlation in SF-ORMAS.

A general spin-complete spin-flip configuration interaction method.

A new, general spin-correct spin-flip configuration interaction (SF-CI) method is introduced by extending the occupation restricted multiple active spaces (ORMAS) CI method in GAMESS. SF-ORMAS is a single reference CI method that utilizes a high-spin restricted open shell determinant on which an arbitrary amount of spin-flipped excitations are carried out to generate a wave function of desired multiplicity. Furthermore, the SF-ORMAS method allows for a flexible design of the active space(s) to fit the chemical problem at hand. Therefore, a variety of spin-flip schemes can be implemented within this one formalism. As SF-ORMAS mostly accounts for static correlation, dynamic correlation is included through perturbation theory. The new method is demonstrated for single and multiple bond breaking, diradical systems, vertical excitations of linear alkenes, and the singlet-triplet energy gap of silicon trimer.