Douglas L. Strout

A quantitative study of the scaling properties of the Hartree–Fock method

Although it is usually stated that the Hartree–Fock method formally scales as N4, where N is the number of basis functions employed in the calculation, it is also well known that mathematical bounds computed with the Schwarz inequality can be used to screen and eliminate four‐center two‐electron integrals smaller than a certain threshold. In this work, quantitative data is presented to illustrate the effects of this integral screening on the scaling properties of the Hartree–Fock (HF) method. Calculations are performed on a range of carbon–hydrogen model systems, two‐dimensional graphitic sheets, and three‐dimensional diamond pieces, to determine the effective scaling exponent α of the computational expense. The data obtained in this paper for calculations including over 250 carbon atoms and 1500 basis functions shows two significant trends: (1) in the asymptotic limit of large molecules, α is found to be approximately 2.2–2.3, and (2) for molecules of modest size, α is still very much less than 4. Theref...

A theoretical study of buckminsterfullerene reaction products: C60+C60

Abstract Several possible structures for reaction products of two buckminsterfullerene (C60) molecules are presented and discussed. Geometries are optimized with the MNDO and tight-binding methods, followed by single-point energy calculations using the Hartree—Fock self-consistent field procedure and a recently proposed hybrid of Hartree—Fock and density functional theory. Our results are discussed in the context of recent experimental evidence of the solid-state polymerization of C60 and the coalescence of buckminsterfullerene by laser desorption of a film. The theoretical predictions are consistent with a polymerization process that proceeds through 2 + 2 cycloaddition of fullerene double bonds.

Isomers of C20. Dramatic effect of gradient corrections in density functional theory

Abstract Density functional techniques including gradient corrections are used to investigate the relative energies of the ring, bowl (corannulene-like), and cage (fullerche-like) isomers of C20. In agreement with previous studies, the local density approximation yields the cage to be the most stable isomer with the bowl and ring forms being significantly higher in energy. However, the inclusion of gradient corrections completely reverses the energy ordering of the isomers. The gradient correction alters the relative energy between the cage and ring isomers by more than 7 eV and yields the ring as the most stable form.

Theoretical studies of fullerene annealing and fragmentation

Abstract We have examined the processes of fullerene annealing and fragmentation using semiempirical and high level ab initio theoretical methods. In this paper we discuss the energy barriers of a wide range of reactions that may occur on the fullerenes as they anneal and fragment, and we present a variety of novel mechanisms based on these calculations. These results reveal a chemistry of the fullerene surface that is much richer than previously thought, for at high energies the cage is a dynamic network of shifting polygons, seven-membered rings, sp 3 and sp carbons, and other odd-looking structures. In addition to rationalizing many experiments probing fullerene annealing and fragmentation, our predictions suggest new experiments and will hopefully aid in the design of processes to control fullerene shape, size, and structure.

A coupled-cluster study of the electron affinity of the oxygen atom

Despite quantum chemists’ best efforts, a highly accurate ab initio prediction of the electron affinity of atomic oxygen has remained elusive. In this study the coupled cluster method including all single, double, and perturbative triple excitations [CCSD(T)] is employed in conjunction with very large uncontracted Gaussian basis sets. A systematic shell‐by‐shell optimization at this level of theory leads to an optimal 23s26p10d5f3g basis set. Second‐order configuration interaction (SOCI) calculations are also carried out and the coupled cluster results are found to be in good agreement with them. Our best theoretical prediction (1.415 eV) is 0.047 eV smaller than the experimental result but still marks a substantial improvement over previous high‐quality calculations. The potential sources of error in our predictions are discussed.

N22C2 versus N24: Role of Molecular Curvature in Determining Isomer Stability

Three-dimensional N(22)C(2) cages are examined by theoretical calculations to determine relative stability among various isomers. Stability as a function of cage shape and stability as a function of carbon location are calculated and discussed. The results are compared to isomers of N(24) to determine the effects of carbon substitution into the cage structure. Further, since the various cage shapes in this study vary by degree of curvature, model calculations are carried out to determine the energetic consequences of curving the local structure around nitrogen and carbon. The model calculations are compared to the actual results on the larger cages to determine how well curvature effects explain the relative stability of N(22)C(2) isomer as compared to the corresponding N(24).

Stability and Dissociation Energies of Open-Chain N4C2.

Complex forms of nitrogen are of interest due to their potential as high-energy materials. Many forms of nitrogen, including open-chain and cage molecules, have been studied previously. While many all-nitrogen molecules Nx have been shown to be too unstable for high-energy applications, it has been shown that certain heteroatoms (including carbon) can stabilize a nitrogen structure. A molecule that is not 100% nitrogen will be less energetic, but that energy loss is a tradeoff for the improved stability. In this study, open-chain N4C2 (70% nitrogen by mass) isomers are studied by theoretical calculations to determine isomer stability and dissociation energies. Calculations are carried out with density functional theory (PBE1PBE), perturbation theory (MP2), and coupled-cluster theory (CCSD(T)). Trends in stability of the molecules are calculated and discussed.

Structure and Decomposition Energies of High-Energy Open-Chain Carbon-Nitrogen Compounds NxC2

Molecules and ions consisting entirely or predominantly of nitrogen are of interest because of their energy release properties. Such molecules can decompose into N(2), a process that is very exothermic. Following a study predicting the stability properties of isomers of open-chain N(4)C(2), the current study involves calculations on a series of open-chain carbon-nitrogen molecules. Molecules with the general formulas N(x)C(2) are studied to determine their structure and bonding, as well as their energy release capabilities. Theoretical calculations are carried out on this series of molecules to determine geometries and heats of formation. The MP2 method is used for geometry optimizations and vibrational frequencies, with single energies calculated with coupled-cluster theory (CCSD(T)). Energetic and structural trends are calculated and discussed.

Stability of N10C10H10 and N12C12H12 Cages and the Effects of Endohedral Atoms and Ions.

Cages of carbon and nitrogen have been studied by theoretical calculations to determine the potential of these molecules as high-energy density materials. Following previous theoretical studies of high-energy N6C6H6 and N8C8H8 cages, a series of calculations on several isomers of the larger N10C10H10 and N12C12H12 is carried out to determine relative stability among a variety of three-coordinate cage isomers with four-membered, five-membered, and/or six-membered rings. Additionally, calculations are carried out on the same molecules with atoms or ions inside the cage. Calculations are carried out with the B3LYP and PBE1PBE density functional (DFT) methods, with MP2 and MP4 calculations carried out to evaluate the accuracy of the DFT results. Trends in stability with respect to cage geometry and arrangements of atoms are calculated and discussed. Stability effects caused by the endohedral atoms and ions are also calculated and discussed.

Metal-ion binding to high-energy N12C4.

Carbon-nitrogen compounds are of interest for their potential as high-energy materials. One major issue in determining the structures of high-energy materials is molecular stability; a more stable energetic compound is more likely to be useful in a wider variety of applications. In this study, binding energies are calculated for a high-energy N(12)C(4) structure with a series of metal ions to determine preferred binding sites. A metal ion bound to the molecule at a preferred site may stabilize the molecule and render it more potentially useful. The results are calculated on using the PBE1PBE density functional method with the cc-pVDZ basis set of Dunning. Trends in binding energies are calculated and discussed with respect to both the identity of the ion and the various binding sites on the N(12)C(4) molecule.