Nathan E. Schultz

Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions

We present a new hybrid meta exchange-correlation functional, called M05-2X, for thermochemistry, thermochemical kinetics, and noncovalent interactions. We also provide a full discussion of the new M05 functional, previously presented in a short communication. The M05 functional was parametrized including both metals and nonmetals, whereas M05-2X is a high-nonlocality functional with double the amount of nonlocal exchange (2X) that is parametrized only for nonmetals. In particular, M05 was parametrized against 35 data values, and M05-2X is parametrized against 34 data values. Both functionals, along with 28 other functionals, have been comparatively assessed against 234 data values:  the MGAE109/3 main-group atomization energy database, the IP13/3 ionization potential database, the EA13/3 electron affinity database, the HTBH38/4 database of barrier height for hydrogen-transfer reactions, five noncovalent databases, two databases involving metal-metal and metal-ligand bond energies, a dipole moment database, a database of four alkyl bond dissociation energies of alkanes and ethers, and three total energies of one-electron systems. We also tested the new functionals and 12 others for eight hydrogen-bonding and stacking interaction energies in nucleobase pairs, and we tested M05 and M05-2X and 19 other functionals for the geometry, dipole moment, and binding energy of HCN-BF3, which has recently been shown to be a very difficult case for density functional theory. We tested eight functionals for four more alkyl bond dissociation energies, and we tested 12 functionals for several additional bond energies with varying amounts of multireference character. On the basis of all the results for 256 data values in 18 databases in the present study, we recommend M05-2X, M05, PW6B95, PWB6K, and MPWB1K for general-purpose applications in thermochemistry, kinetics, and noncovalent interactions involving nonmetals and we recommend M05 for studies involving both metallic and nonmetallic elements. The M05 functional, essentially uniquely among the functionals with broad applicability to chemistry, also performs well not only for main-group thermochemistry and radical reaction barrier heights but also for transition-metal-transition-metal interactions. The M05-2X functional has the best performance for thermochemical kinetics, noncovalent interactions (especially weak interaction, hydrogen bonding, π···π stacking, and interactions energies of nucleobases), and alkyl bond dissociation energies and the best composite results for energetics, excluding metals.

Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions

By incorporating kinetic-energy density in a balanced way in the exchange and correlational functionals and removing self-correlation effects, we have designed a density functional that is broadly applicable to organometallic, inorganometallic, and nonmetallic bonding, thermochemistry, thermochemical kinetics, and noncovalent interactions as well as satisfying the uniform electron gas limit. The average error is reduced by a factor of 1.3 compared with the best previously available functionals, but even more significantly, we find a functional that has a high accuracy for all four categories of interaction.

Benchmarking approximate density functional theory for s/d excitation energies in 3d transition metal cations

Holthausen has recently provided a comprehensive study of density functional theory for calculating the s/d excitation energies of the 3d transition metal cations. This study did not include the effects of scalar relativistic effects, and we show here that the inclusion of scalar relativistic effects significantly alters the conclusions of the study. We find, contrary to the previous study, that local functionals are more accurate for the excitation energies of 3d transition method cations than hybrid functionals. The most accurate functionals, of the 38 tested, are SLYP, PBE, BP86, PBELYP, and PW91.

TraPPE-UA force field for acrylates and Monte Carlo simulations for their mixtures with Alkanes and alcohols

An extension of the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field to acrylate and methacrylate monomers is presented. New parameters were fit to the liquid density, normal boiling point, saturated vapor pressure, and (where experimentally available) critical constants of 1,3-butadiene, isoprene, methyl acrylate, and methyl methacrylate using Gibbs ensemble Monte Carlo simulations. Excellent agreement with experiment was obtained for the parametrization compounds and seven additional acrylate and methacrylate compounds, with average errors in liquid density and normal boiling point of approximately 1%. The TraPPE-UA force field also predicts accurate heats of vaporization at 298 K. In addition, Gibbs ensemble Monte Carlo simulations of binary vapor-liquid equilibria for the mixtures methyl acrylate/1-butanol and methyl acrylate/n-decane show that the TraPPE-UA acrylate force field performs well in mixtures with both polar and nonpolar molecules. These simulations also indicate structural microheterogeneity in the liquid phase of these mixtures.

New Effective Core Method (Effective Core Potential and Valence Basis Set) for Al Clusters and Nanoparticles and Heteronuclear Al-Containing Molecules.

In previous work we have shown that the PBE0 hybrid density functional method with the MG3 all-electron basis set is an accurate method for calculating the atomization energies of small aluminum clusters (Al2-Al7). However, the MG3 basis set is very expensive for molecules much larger than Al13; therefore, we have developed a new effective core potential (ECP) method for aluminum to reduce the cost of obtaining accurate results for nanoparticles. Our method involves a hybrid of the Stuttgart semiempirical effective core potential and the compact effective potential (CEP) potential, and it uses a newly optimized polarized valence triple-ζ basis set. The combination of the new ECP and the new polarized valence triple-ζ basis set for Al is called the Minnesota effective core (MEC) method for Al. The method was optimized with a training set of atomization energies and geometries for AlH, AlC, AlO, AlCCH, Al2H, Al2C, Al2O, and Al3 and atomization energies of three Al13 structures, and we tested it on six test sets composed of 20 atomization energies for systems as large as Al13. We also present an improved all-electron polarized triple split basis set for oxygen, called 6-311+G(d*,p). For the test sets, the mean unsigned error (MUE) of the new method with respect to PBE0/MG3 is 0.06 eV for atomization energies and 0.007 Å for bond lengths, which constitutes a very significant improvement over the quality of the results that can be obtained with effective core potentials and valence basis sets in the literature (of the eight methods in the literature, the best previous method had average errors of 0.63 eV and 0.036 Å). We have also tested the MEC method with a variety of hybrid density functional theory, hybrid meta density functional theory, and pure GGA and meta GGA functionals and found that the average MUE, relative to each functional with all-electron basis sets, is 0.04 eV for atomization energies and 0.009 Å for bond lengths for the new effective core method and 0.16-0.20 eV and 0.013-0.033 Å for effective core potential and valence basis sets in the literature.

Valence–Bond Order (VBO): A New Approach to Modeling Reactive Potential Energy Surfaces for Complex Systems, Materials, and Nanoparticles

The extension of molecular mechanics to reactive systems, metals, and covalently bonded clusters with variable coordination numbers requires new functional forms beyond those popular for organic chemistry and biomolecules. Here we present a new scheme for reactive molecular mechanics, which is denoted as the valence-bond order model, for approximating reactive potential energy surfaces in large molecules, clusters, nanoparticles, solids, and other condensed-phase materials, especially those containing metals. The model is motivated by a moment approximation to tight binding molecular orbital theory, and we test how well one can approximate potential energy surfaces with a very simple functional form involving only interatomic distances with no explicit dependence on bond angles or dihedral angles. For large systems the computational requirements scale linearly with system size, and no diagonalizations or iterations are required; thus the method is well suited to large-scale simulations. The method is illustrated here by developing a force field for particles and solids composed of aluminum and hydrogen. The parameters were optimized against both interaction energies and relative interaction energies. The method performs well for pure aluminum clusters, nanoparticles, and bulk lattices and reasonably well for pure hydrogen clusters; the mean unsigned error per atom for the aluminum-hydrogen clusters is 0.1 eV/atom.

Transferability of orthogonal and nonorthogonal tight-binding models for aluminum clusters and nanoparticles

Several semiempirical tight-binding models are parametrized and tested for aluminum clusters and nanoparticles using a data set of 808 accurate AlN (N = 2-177) energies and geometries. The effects of including overlap when solving the secular equation and of incorporating many-body (i.e., nonpairwise) terms in the repulsion and electronic matrix elements are studied. Pairwise orthogonal tight-binding (TB) models are found to be more accurate and their parametrizations more transferable (for particles of different sizes) than both pairwise and many-body nonorthogonal tight-binding models. Many-body terms do not significantly improve the accuracy or transferability of orthogonal TB, whereas some improvement in the nonorthogonal models is observed when many-body terms are included in the electronic Hamiltonian matrix elements.

Adsorption, X-ray Diffraction, Photoelectron, and Atomic Emission Spectroscopy Benchmark Studies for the Eighth Industrial Fluid Properties Simulation Challenge

The primary goal of the eighth industrial fluid properties simulation challenge was to test the ability of molecular simulation methods to predict the adsorption of organic adsorbates in activated carbon materials. The challenge focused on the adsorption of perfluorohexane in the activated carbon standard BAM-P109. Entrants were challenged to predict the adsorption of perfluorohexane in the activated carbon at a temperature of 273 K and at relative pressures of 0.1, 0.3, and 0.6. The relative pressure (P/Po) is defined as that relative to the bulk saturation pressure predicted by the fluid model at a given temperature (273 K in this case). The predictions were judged by comparison to a set of experimentally determined values, which are published here for the first time and were not disclosed to the entrants prior to the challenge. Benchmark experimental studies, described herein, were also carried out and provided to entrants in order to aid in the development of new force fields and simulation methods to be employed in the challenge. These studies included argon, carbon dioxide, and water adsorption in the BAM-P109 activated carbon as well as X-ray diffraction, X-ray microtomography, photoelectron spectroscopy, and atomic emission spectroscopy studies of BAM-P109. Several concurrent studies were carried out for the BAM-P108 activated carbon. These are included in the current manuscript for comparison.

The Eighth Industrial Fluids Properties Simulation Challenge

The goal of the eighth industrial fluid properties simulation challenge was to test the ability of molecular simulation methods to predict the adsorption of organic adsorbates in activated carbon materials. In particular, the eighth challenge focused on the adsorption of perfluorohexane in the activated carbon BAM-P109. Entrants were challenged to predict the adsorption in the carbon at 273 K and relative pressures of 0.1, 0.3, and 0.6. The predictions were judged by comparison with a benchmark set of experimentally determined values. Overall, good agreement and consistency were found between the predictions of most entrants.