Assessment of the accuracy of density functionals for prediction of relative energies and geometries of low-lying isomers of water hexamers.

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order Møller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.

Optimization of the Coupled Cluster Implementation in NWChem on Petascale Parallel Architectures.

The coupled cluster singles and doubles (CCSD) algorithm in the NWChem software package has been optimized to alleviate the communication bottleneck. This optimization provided a 2-fold to 5-fold speedup in the CCSD iteration time depending on the problem size and available memory, and improved the CCSD scaling to 20 000 nodes of the NCSA Blue Waters supercomputer. On 20 000 XE6 nodes of Blue Waters, a complete conventional CCSD(T) calculation of a system encountering 1042 basis functions and 103 occupied correlated orbitals obtained a performance of 0.32 petaflop/s and took 5 h and 24 min to complete. The reported time and performance included all stages of the calculation from initialization to termination for iterative single and double excitations as well as perturbative triples correction. In perturbative triples alone, the computation sustained a rate of 1.18 petaflop/s. The CCSD and (T) phases took approximately (3)/4 and (1)/4 of the total time to solution, respectively, showing that CCSD is the most time-consuming part at the large scale. The MP2, CCSD, and CCSD(T) computations in 6-311++G** basis set performed on guanine-cytosine deoxydinucleotide monophosphate probed the conformational energy difference between the A- and B-conformations of single stranded DNA. Good agreement between MP2 and coupled cluster methods has been obtained, suggesting the utility of MP2 for conformational analysis in these systems. The study revealed a significant discrepancy between the quantum mechanical and classical force field predictions, suggesting a need to improve the dihedral parameters.

Isomers of Au8.

Using newly developed correlation consistent basis sets for gold, the relative energies for the neutral Au8 geometric isomers have been re-evaluated and the vertical ionization potentials calculated. The results using the correlation consistent basis sets show that second-order Moller-Plesset perturbation theory calculations strongly favor nonplanar Au8 structures for all basis sets that were employed. However, the general trend at the coupled cluster singles and doubles with perturbative triples level of theory is to increasingly favor planar structures as the basis set is improved. The effects of basis set and the effects of core-valence correlation are discussed.

Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges.

A new universal continuum solvation model (where "universal" denotes applicable to all solvents), called SM8, is presented. It is an implicit solvation model, also called a continuum solvation model, and it improves on earlier SMx universal solvation models by including free energies of solvation of ions in nonaqueous media in the parametrization. SM8 is applicable to any charged or uncharged solute composed of H, C, N, O, F, Si, P, S, Cl, and/or Br in any solvent or liquid medium for which a few key descriptors are known, in particular dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters. It does not require the user to assign molecular-mechanics types to an atom or group; all parameters are unique and continuous functions of geometry. It may be used with any level of electronic structure theory as long as accurate partial charges can be computed for that level of theory; we recommend using it with self-consistently polarized Charge Model 4 or other self-consistently polarized class IV charges, in which case analytic gradients are available. The model separates the observable solvation free energy into two components: the long-range bulk electrostatic contribution arising from a self-consistent reaction field treatment using the generalized Born approximation for electrostatics is augmented by the non-bulk-electrostatic contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. The cavities for the bulk electrostatics calculation are defined by superpositions of nuclear-centered spheres whose sizes are determined by intrinsic atomic Coulomb radii. The radii used for aqueous solution are the same as parametrized previously for the SM6 aqueous solvation model, and the radii for nonaqueous solution are parametrized by a training set of 220 bare ions and 21 clustered ions in acetonitrile, methanol, and dimethyl sulfoxide. The non-bulk-electrostatic terms are proportional to the solvent-accessible surface areas of the atoms of the solute and have been parametrized using solvation free energies for a training set of 2346 solvation free energies for 318 neutral solutes in 90 nonaqueous solvents and water and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The model is tested with three density functionals and with four basis sets: 6-31+G(d,p), 6-31+G(d), 6-31G(d), and MIDI!6D. The SM8 model achieves mean unsigned errors of 0.5-0.8 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 2.2-7.0 kcal/mol for ions. The model outperforms the earlier SM5.43R and SM7 universal solvation models as well as the default Polarizable Continuum Model (PCM) implemented in Gaussian 98/03, the Conductor-like PCM as implemented in GAMESS, Jaguar's continuum model based on numerical solution of the Poisson equation, and the GCOSMO model implemented in NWChem.

Charge Model 4 and Intramolecular Charge Polarization.

Partial atomic charges provide the most widely used model for molecular charge polarization, and Charge Model 4 (CM4) is designed to provide partial atomic charges that correspond to an accurate charge distribution, even though they may be calculated with polarized double-ζ basis sets with any density functional. Here we extend CM4 to six additional basis sets, and we present a model (CM4M) that is individually optimized for the M06 suite of density functionals for ten basis sets. These charge models yield class IV partial atomic charges by mapping from those obtained with Löwdin or redistributed Löwdin population analyses of density functional electronic charge distributions. CM4M/M06-2X/6-31G(d)//M06-2X/6-31+G(d,p) partial atomic charges are calculated for ethylene, CHnCl4-n (n = 0-4), benzene, nitrobenzene, phenol, and fluoromethanol and used to discuss gas-phase polarization effects.

Polarization Effects in Aqueous and Nonaqueous Solutions.

Polarization effects in aqueous and nonaqueous solutions were analyzed for nine neutral and three charged organic solutes by the SM8 universal implicit solvation model and class IV partial atomic charges based on Charge Model 4M (CM4M) with the M06-2X density functional. The CM4M partial atomic charges in neutral and ionic solutes and in the corresponding clustered solutes (supersolutes), which included one solute molecule and one or two solvent molecules, were modeled in three solvents (benzene, methylene chloride, and water) and compared to those in the gas phase. The use of the supersolute approach (microsolvation) allows one to account for charge transfer from the solute to the solvent, and we find charge transfers as large as 0.06 atomic units for neutral solutes (pyridine in water) and 0.32 atomic units for ions (methoxide anion in water). Relaxation of the electronic structure of the solute in the presence of solvent increases the polarization free energy of the neutral solutes studied here, on average, by 16% in benzene, 30% in methylene chloride, and 43% in water. The increase for the ions in water averaged 43%.

The structure of the Si9H12 cluster: A coupled cluster and multi-reference perturbation theory study.

Full geometry optimizations using both singles and doubles coupled cluster theory with perturbative triple excitations, CCSD(T), and second order multi-reference perturbation theory, MRMP2, have been employed to predict the structure of Si9H12, a cluster commonly used in calculations to represent the Si(100) surface. Both levels of theory predict the structure of this cluster to be symmetric (not buckled), and no evidence for a buckled (asymmetric) structure is found at either level of theory.

Parallel coupled perturbed CASSCF equations and analytic CASSCF second derivatives.

A parallel algorithm for solving the coupled-perturbed MCSCF (CPMCSCF) equations and analytic nuclear second derivatives of CASSCF wave functions is presented. A parallel scheme for evaluating derivative integrals and their subsequent use in constructing other derivative quantities is described. The task of solving the CPMCSCF equations is approached using a parallelization scheme that partitions the electronic hessian matrix over all processors as opposed to simple partitioning of the 3 N solution vectors among the processors. The scalability of the current algorithm, up to 128 processors, is demonstrated. Using three test cases, results indicate that the parallelization of derivative integral evaluation through a simple scheme is highly effective regardless of the size of the basis set employed in the CASSCF energy calculation. Parallelization of the construction of the MCSCF electronic hessian during solution of the CPMCSCF equations varies quantitatively depending on the nature of the hessian itself, but is highly scalable in all cases.

Where does the planar-to-nonplanar turnover occur in small gold clusters?

Several levels of theory, including both Gaussian-based and plane wave density functional theory (DFT), second-order perturbation theory (MP2), and coupled cluster methods (CCSD(T)), are employed to study Au6 and Au8 clusters. All methods predict that the lowest energy isomer of Au6 is planar. For Au8, both DFT methods predict that the two lowest isomers are planar. In contrast, both MP2 and CCSD(T) predict the lowest Au8 isomers to be nonplanar.

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.

A study of the reactions of molecular hydrogen with small gold clusters.

This work presents a study of reactions between neutral and negatively charged Au(n) clusters (n=2,3) and molecular hydrogen. The binding energies of the first and second hydrogen molecule to the gold clusters were determined using density functional theory (DFT), second order perturbation theory (MP2) and coupled cluster (CCSD(T)) methods. It is found that molecular hydrogen easily binds to neutral Au(2) and Au(3) clusters with binding energies of 0.55 eV and 0.71 eV, respectively. The barriers to H(2) dissociation on these clusters with respect to Au(n)H(2) complexes are 1.10 eV and 0.59 eV for n=2 and 3. Although negatively charged Au(n) (-) clusters do not bind molecular hydrogen, H(2) dissociation can occur with energy barriers of 0.93 eV for Au(2) (-) and 1.39 eV for Au(3) (-). The energies of the Au(2)H(2) (-) and Au(3)H(2) (-) complexes with dissociated hydrogen molecules are lower than the energies of Au(2) (-)+H(2) and Au(3) (-)+H(2) by 0.49 eV and 0.96 eV, respectively. There is satisfactory agreement between the DFT and CCSD(T) results for binding energies, but the agreement is not as good for barrier heights.

Enthalpies of formation of gas-phase N3, N3-, N5+, and N5- from Ab initio molecular orbital theory, stability predictions for N5(+)N3(-) and N5(+)N5(-), and experimental evidence for the instability of N5(+)N3(-).

Ab initio molecular orbital theory has been used to calculate accurate enthalpies of formation and adiabatic electron affinities or ionization potentials for N3, N3-, N5+, and N5- from total atomization energies. The calculated heats of formation of the gas-phase molecules/ions at 0 K are DeltaHf(N3(2Pi)) = 109.2, DeltaHf(N3-(1sigma+)) = 47.4, DeltaHf(N5-(1A1')) = 62.3, and DeltaHf(N5+(1A1)) = 353.3 kcal/mol with an estimated error bar of +/-1 kcal/mol. For comparison purposes, the error in the calculated bond energy for N2 is 0.72 kcal/mol. Born-Haber cycle calculations, using estimated lattice energies and the adiabatic ionization potentials of the anions and electron affinities of the cations, enable reliable stability predictions for the hypothetical N5(+)N3(-) and N5(+)N5(-) salts. The calculations show that neither salt can be stabilized and that both should decompose spontaneously into N3 radicals and N2. This conclusion was experimentally confirmed for the N5(+)N3(-) salt by low-temperature metathetical reactions between N5SbF6 and alkali metal azides in different solvents, resulting in violent reactions with spontaneous nitrogen evolution. It is emphasized that one needs to use adiabatic ionization potentials and electron affinities instead of vertical potentials and affinities for salt stability predictions when the formed radicals are not vibrationally stable. This is the case for the N5 radicals where the energy difference between vertical and adiabatic potentials amounts to about 100 kcal/mol per N5.