Paul C. Redfern

Gaussian-3 (G3) theory for molecules containing first and second-row atoms

Gaussian-3 theory (G3 theory) for the calculation of molecular energies of compounds containing first (Li–F) and second row (Na–Cl) atoms is presented. This new theoretical procedure, which is based on ab initio molecular-orbital theory, modifies G2 theory [J. Chem. Phys. 94, 7221 (1991)] in several ways including a new sequence of single point energy calculations using different basis sets, a new formulation of the higher level correction, a spin–orbit correction for atoms, and a correction for core correlation. G3 theory is assessed using 299 energies from the G2/97 test set including enthalpies of formation, ionization potentials, electron affinities, and proton affinities. This new procedure corrects many of the deficiencies of G2 theory. There is a large improvement for nonhydrogen systems such as SiF4 and CF4, substituted hydrocarbons, and unsaturated cyclic species. Core-related correlation is found to be a significant factor, especially for species with unsaturated rings. The average absolute devi...

Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation

A set of 148 molecules having well-established enthalpies of formation at 298 K is presented. This set, referred to as the G2 neutral test set, includes the 55 molecules whose atomization energies were used to test Gaussian-2 ~G2! theory @J. Chem. Phys. 94, 7221 ~1991!# and 93 new molecules. The G2 test set includes 29 radicals, 35 nonhydrogen systems, 22 hydrocarbons, 47 substituted hydrocarbons, and 15 inorganic hydrides. It is hoped that this new test set will provide a means for assessing and improving new theoretical models. From an assessment of G2 and density functional theories ~DFT! on this test set it is found that G2 theory is the most reliable method both in terms of average absolute deviation ~1.58 kcal/mol! and maximum deviation ~8.2 kcal/mol!. The largest deviations between experiment and G2 theory occur for molecules having multiple halogens. Inclusion of spin‐orbit effects reduces the average absolute deviation to 1.47 kcal/mol and significantly improves the results for the chlorine substituted molecules, but little overall improvement is seen for the fluorine substituted molecules. Of the two modified versions of G2 theory examined in this study, G2~MP2,SVP! theory ~average absolute deviation51.93 kcal/mol! performs better than G2~MP2! theory ~2.04 kcal/mol!. The G2~MP2,SVP! theory is found to perform very well for hydrocarbons, radicals, and inorganic hydrides. Of the seven DFT methods investigated, the B3LYP method has the smallest average absolute deviation ~3.11 kcal/mol!. It also has a significantly larger distribution of error than the G2 methods with a maximum deviation of 20.1 kcal/mol.

Gaussian-3 theory using density functional geometries and zero-point energies

A variation of Gaussian-3 (G3) theory is presented in which the geometries and zero-point energies are obtained from B3LYP density functional theory [B3LYP/6-31G(d)] instead of geometries from second-order perturbation theory [MP2(FU)/6-31G(d)] and zero-point energies from Hartree–Fock theory [HF/6-31G(d)]. This variation, referred to as G3//B3LYP, is assessed on 299 energies (enthalpies of formation, ionization potentials, electron affinities, proton affinities) from the G2/97 test set [J. Chem. Phys. 109, 42 (1998)]. The G3//B3LYP average absolute deviation from experiment for the 299 energies is 0.99 kcal/mol compared to 1.01 kcal/mol for G3 theory. Generally, the results from the two methods are similar, with some exceptions. G3//B3LYP theory gives significantly improved results for several cases for which MP2 theory is deficient for optimized geometries, such as CN and O2+. However, G3//B3LYP does poorly for ionization potentials that involve a Jahn–Teller distortion in the cation (CH4+, BF3+, BCl3+)...

6‐31G* basis set for third‐row atoms

Medium basis sets based upon contractions of Gaussian primitives are developed for the third‐row elements Ga through Kr. The basis functions generalize the 6‐31G and 6‐31G* sets commonly used for atoms up to Ar. A reexamination of the 6‐31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6‐31G basis for the whole third‐row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split‐valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third‐row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d‐type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor‐phase metal complexes.

Gaussian-4 theory

The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li-F), second- (Na-Cl), and third-row main group (K, Ca, and Ga-Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is assessed on the 454 experimental energies in the G305 test set [L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005)], and the average absolute deviation from experiment shows significant improvement from 1.13 kcal/mol (G3 theory) to 0.83 kcal/mol (G4 theory). The largest improvement is found for 79 nonhydrogen systems (2.10 kcal/mol for G3 versus 1.13 kcal/mol for G4). The contributions of the new features to this improvement are analyzed and the performance on different types of energies is discussed.

Gaussian-3 theory using reduced Mo/ller-Plesset order

A variation of Gaussian-3 (G3) theory is presented in which the basis set extensions are obtained at the second-order Mo/ller–Plesset level. This method, referred to as G3(MP2) theory, is assessed on 299 energies from the G2/97 test set [J. Chem. Phys. 109, 42 (1998)]. The average absolute deviation from experiment of G3(MP2) theory for the 299 energies is 1.30 kcal/mol and for the subset of 148 neutral enthalpies it is 1.18 kcal/mol. This is a significant improvement over the related G2(MP2) theory [J. Chem. Phys. 98, 1293 (1993)], which has an average absolute deviation of 1.89 kcal/mol for all 299 energies and 2.03 kcal/mol for the 148 neutral enthalpies. The corresponding average absolute deviations for full G3 theory are 1.01 and 0.94 kcal/mol, respectively. The new method provides significant savings in computational time compared to G3 theory and, also, G2(MP2) theory.

Assessment of Gaussian-3 and density functional theories for a larger experimental test set

The G2/97 test set [J. Chem. Phys. 106, 1063 (1997)] for assessing quantum chemical methods used to predict thermochemical data is expanded to include 75 additional enthalpies of formation of larger molecules. This new set, referred to as the G3/99 test set, includes enthalpies of formation, ionization potentials, electron affinities, and proton affinities in the G2/97 set and 75 new enthalpies of formation. The total number of energies in the G3/99 set is 376. Overall, G3 theory has a mean absolute deviation of 1.07 kcal/mol for the G3/99 test set and does about as well for the new hydrocarbons and substituted hydrocarbons as it does for those in the G2/97 test. However, G3 theory has large deviations for several of the new nonhydrogen systems in the G3/99 test set such as SF6 and PF5. Part of the source of error is traced to the inadequate geometries used in G3 theory for these molecules. Other variations of G3 theory are also assessed such as G3(MP2), G3(MP3), and the versions of G3 theory using scaled...

Increased Silver Activity for Direct Propylene Epoxidation via Subnanometer Size Effects

Silver Cluster Catalysts for Propylene Oxide The formation of ethylene oxide—in which an oxygen atom bridges the double bond of ethylene—can be made directly and efficiently from ethylene and oxygen with the aid of silver catalysts (typically comprising a small silver cluster on aluminum oxide). Similar approaches are not so successful for making propylene oxide—an important starting material for polyurethane plastics, which are made from chlorinated intermediates. Lei et al. (p. 224) report that silver trimers, Ag3, deposited on alumina are active for direct propylene oxide formation at low temperatures with only a low level of formation of CO2 by-product, unlike larger particles that form from these clusters at higher temperatures. Density functional calculations suggest that the open-shell nature of the clusters accounts for the improved reactivity. Clusters of three silver atoms deposited on alumina are active for the low-temperature direct formation of propylene oxide. Production of the industrial chemical propylene oxide is energy-intensive and environmentally unfriendly. Catalysts based on bulk silver surfaces with direct propylene epoxidation by molecular oxygen have not resolved these problems because of substantial formation of carbon dioxide. We found that unpromoted, size-selected Ag3 clusters and ~3.5-nanometer Ag nanoparticles on alumina supports can catalyze this reaction with only a negligible amount of carbon dioxide formation and with high activity at low temperatures. Density functional calculations show that, relative to extended silver surfaces, oxidized silver trimers are more active and selective for epoxidation because of the open-shell nature of their electronic structure. The results suggest that new architectures based on ultrasmall silver particles may provide highly efficient catalysts for propylene epoxidation.

Subnanometre platinum clusters as highly active|[nbsp]|and selective catalysts for the oxidative dehydrogenation of propane

Small clusters are known to possess reactivity not observed in their bulk analogues, which can make them attractive for catalysis. Their distinct catalytic properties are often hypothesized to result from the large fraction of under-coordinated surface atoms. Here, we show that size-preselected Pt(8-10) clusters stabilized on high-surface-area supports are 40-100 times more active for the oxidative dehydrogenation of propane than previously studied platinum and vanadia catalysts, while at the same time maintaining high selectivity towards formation of propylene over by-products. Quantum chemical calculations indicate that under-coordination of the Pt atoms in the clusters is responsible for the surprisingly high reactivity compared with extended surfaces. We anticipate that these results will form the basis for development of a new class of catalysts by providing a route to bond-specific chemistry, ranging from energy-efficient and environmentally friendly synthesis strategies to the replacement of petrochemical feedstocks by abundant small alkanes.

Assessment of Gaussian-2 and density functional theories for the computation of ionization potentials and electron affinities

A set of 146 well-established ionization potentials and electron affinities is presented. This set, referred to as the G2 ion test set, includes the 63 atoms and molecules whose ionization potentials and electron affinities were used to test Gaussian-2 (G2) theory [J. Chem. Phys. 94, 7221 (1991)] and 83 new atoms and molecules. It is hoped that this new test set combined with the recently published test set of enthalpies of neutral molecules [J. Chem. Phys. 106, 1063 (1997)] will provide a means for assessing and improving theoretical models. From an assessment of G2 and density functional theories on this test set, it is found that G2 theory is the most reliable method. It has an average absolute deviation of 0.06 eV for both ionization potentials and electron affinities. The two modified versions of G2 theory, G2(MP2,SVP) and G2(MP2) theory, have average absolute deviations of 0.08–0.09 eV for both ionization potentials and electron affinities. The hybrid B3LYP density functional method has the smallest...