Biorthogonal projected energies of a Gutzwiller similarity transformed Hamiltonian.

We present a method incorporating biorthogonal orbital-optimization, symmetry projection, and double-occupancy screening with a non-unitary similarity transformation generated by the Gutzwiller factor [Formula: see text], and apply it to the Hubbard model. Energies are calculated with mean-field computational scaling with high-quality results comparable to coupled cluster singles and doubles. This builds on previous work performing similarity transformations with more general, two-body Jastrow-style correlators. The theory is tested on 2D lattices ranging from small systems into the thermodynamic limit and is compared to available reference data.

Van der Waals coefficients beyond the classical shell model.

Van der Waals (vdW) coefficients can be accurately generated and understood by modelling the dynamic multipole polarizability of each interacting object. Accurate static polarizabilities are the key to accurate dynamic polarizabilities and vdW coefficients. In this work, we present and study in detail a hollow-sphere model for the dynamic multipole polarizability proposed recently by two of the present authors (JT and JPP) to simulate the vdW coefficients for inhomogeneous systems that allow for a cavity. The inputs to this model are the accurate static multipole polarizabilities and the electron density. A simplification of the full hollow-sphere model, the single-frequency approximation (SFA), circumvents the need for a detailed electron density and for a double numerical integration over space. We find that the hollow-sphere model in SFA is not only accurate for nanoclusters and cage molecules (e.g., fullerenes) but also yields vdW coefficients among atoms, fullerenes, and small clusters in good agreement with expensive time-dependent density functional calculations. However, the classical shell model (CSM), which inputs the static dipole polarizabilities and estimates the static higher-order multipole polarizabilities therefrom, is accurate for the higher-order vdW coefficients only when the interacting objects are large. For the lowest-order vdW coefficient C6, SFA and CSM are exactly the same. The higher-order (C8 and C10) terms of the vdW expansion can be almost as important as the C6 term in molecular crystals. Application to a variety of clusters shows that there is strong non-additivity of the long-range vdW interactions between nanoclusters.

Composite fermion-boson mapping for fermionic lattice models.

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the 1D and 2D Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.

Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional.

We show that the middle-range exchange-correlation hybrid of Henderson, Izmaylov, Scuseria and Savin (HISS) performs extremely well for elemental and binary semiconductors with narrow or visible spectrum band gaps, as well as some wider gap or more ionic systems used in devices. The lattice parameters are superior to those predicted by the screened hybrid functional of Heyd, Scuseria and Ernzerhof (HSE), and provide a significant improvement over the geometries predicted by typical semilocal functionals, yielding results competitive with PBEsol, which was specially tuned for solids. HISS also yields band gaps superior to those produced by functionals developed specifically for the solid state. Timings indicate that HISS is more computationally efficient than HSE, implying that the high quality lattice constants coupled with improved optical band gap predictions render HISS a useful adjunct to HSE in the modeling of geometry-sensitive semiconductors.

C60 buckminsterfullerene high yields unraveled.

Recently Irle, Morokuma, and collaborators have carried out a series of quantum chemical molecular dynamics simulations of carbon clustering. The results of these computer experiments are that carbon clusters of size greater than 60 atoms are rapidly formed, anneal to giant fullerenes, and then these fullerenes shrink. The simulation could not be carried to long enough times for the shrinking to reach C60, but they propose reasonably that this shrinking process ultimately forms buckminsterfullerene. However, these simulations do not reveal the force driving the shrinking process. Here, this driving force for shrinking is found to be reactions in which C2 is swapped between fullerenes. The key element is that for typical fullerenes the equilibrium constants for such C2 interchanges are near unity, resulting in expansion of the breadth of the fullerene distribution in an annealing process. When fullerenes of 60 or 70 atoms are populated by shrinking, they fall into the local energy minimum of buckminsterfullerene or D5h C70. This simple mechanism accounts for the high yields (>20%) of buckminsterfullerene that can be achieved in pure carbon systems.

Thermochemistry of fluorinated single wall carbon nanotubes.

The gradient corrected Perdew-Burke-Ernzerhof density functional in conjunction with a 3-21G basis set and periodic boundary conditions was employed to investigate the geometries and energies of C(2)F fluorinated armchair single wall carbon nanotubes (F-SWNT's) with diameters ranging from 16.4 to 4.2 A [(12,12) to (3,3)] as well as a C(2)F graphene sheet fluorinated on one side only. Using an isodesmic equation, we find that the thermodynamic stability of F-SWNT's increases with decreasing tube diameter. On the other hand, the mean bond dissociation energies of the C-F bonds increase as the tubes become thinner. The C-F bonds in the (5,5) F-SWNT's are about as strong as those in graphite fluoride (CF)(n)() and are also covalent albeit slightly (<0.04 A) stretched. Whereas a fluorine atom is found not to bind covalently to the concave surface of [60]fullerene, endohedral covalent binding is possible inside a (5,5) SWNT despite a diameter similar to that of the C(60) cage.

Formation, isolation, spectroscopic properties, and calculated properties of some isomers of C(60)H(36).

Isomers of C(60)H(36) and He@C(60)H(36) have been synthesized by the Birch or dihydroanthracene reduction of C(60) and isolated by preparative high-pressure liquid chromatography. (3)He, (13)C, and (1)H NMR spectroscopic properties were then determined. A comparison of experimental chemical shifts against those computed using density functional theory (B3LYP) with polarized triple- and double-zeta basis sets for He and C,H, respectively, allowed provisional assignment of structure for several isomers to be made. Theoretical calculations have also been carried out to identify low-energy structures. The transfer hydrogenation method using dihydroanthracene gives a major C(60)H(36) isomer and a minor C(60)H(36) isomer with C(3) symmetry as determined by the (13)C NMR spectrum of C(60)H(36) and the (3)He NMR spectrum of the corresponding sample of (3)He@C(60)H(36). In view of the HPLC retention times and the (3)He chemical shifts observed for the Birch and dihydroanthracene reduction products, the two isomers generated by the latter procedure can be only minor isomers of the Birch reduction. A significant energy barrier apparently exists in the dihydroanthracene reduction of C(60) for the conversion of the C(3) and C(1) symmetry isomers of C(60)H(36) to the T symmetry isomer previously predicted by many calculations to be among the most stable C(60)H(36) isomers. Many of the (1)H NMR signals exhibited by C(60)H(36) (and C(60)H(18), previously reported) are unusually deshielded compared to "ordinary" organic compounds, presumably because the unusual structures of C(60)H(36) and C(60)H(18) result in chemical shift tensors with one or more unusual principal values. Calculations clearly show a relationship between exceptionally deshielded protons beta to a benzene ring in C(60)H(18) and C(60)H(36) and relatively long C-C bonds associated with these protons. The additional information obtained from 1D and 2D (1)H NMR spectra obtained at ultrahigh field strengths (up to 900 MHz) will serve as a critical test of chemical shifts to be obtained from future calculations on different C(60)H(36) isomers.

Structure and conformational behavior of biopolymers by density functional calculations employing periodic boundary conditions. I. The case of polyglycine, polyalanine, and poly-alpha-aminoisobutyric acid in vacuo.

Fully quantum mechanical calculations exploiting periodic boundary conditions (PBC) have been applied to the study of four different regular structures (alpha- and 3(10)-helix, fully extended and repeated gamma-turns) of the infinite polypeptides of glycine, alanine, and alpha-aminoisobutyric acid (Aib) in vacuo. alpha-Helix is predicted to be the most stable conformer for polyalanine and polyglycine, being stabilized over the 3(10)-helix mainly by more favorable dipole-dipole interactions. Contrary to previous suggestions, steric effects and hydrogen-bond strengths are comparable for both helix structures. 3(10)-Helix is preferred for poly-Aib, since in this case alpha-helix is strongly distorted due to unfavorable intrachain repulsions. Extended structures and repeated gamma-turns are much less stable than helix structures for all of the polypeptides examined, mainly due to the absence of favorable long-range interactions. The optimized geometries are in good agreement with the available experimental data and reveal a remarkable dependence on the nature of the residue forming the polypeptides; at the same time the electronic and structural parameters of each residue strongly depend on the secondary structure of the polypeptides.

Theoretical evidence for a c60 "window" mechanism.

On the basis of semiempirical and high-level ab initio calculations, theoretical evidence is presented of a "window" mechanism operable on the surface of C(60) and other fullerenes. Through this mechanism, large holes may be formed in fullerenes excited to their triplet state, openings through which atoms and small molecules can pass. This work provides a theoretical foundation for experiments that have prepared endohedral noble gas compounds of C(60) under thermal excitation. A method is proposed that could increase the efficiency of the process of noble gas insertion into C(60) and provide a more general means to create endohedral fullerene compounds.

Uranium stabilization of c28: a tetravalent fullerene.

Laser vaporization experiments with graphite in a supersonic cluster beam apparatus indicate that the smallest fullerene to form in substantial abundance is C(28). Although ab initio quantum chemical calculations predict that this cluster will favor a tetrahedral cage structure, it is electronically open shell. Further calculations reveal that C(28) in this structure should behave as a sort of hollow superatom with an effective valence of 4. This tetravalence should be exhibited toward chemical bonding both on the outside and on the inside of the cage. Thus, stable closed-shell derivatives of C(28) with large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps should be attainable either by reacting at the four tetrahedral vertices on the outside of the C(28) cage to make, for example, C(28)H(4), or by trapping a tetravalent atom inside the cage to make endothedral fullerenes such as Ti@C(28). An example of this second, inside route to C(28) stabilization is reported here: the laser and carbon-arc production of U@C(28).