arXiv subjects

A. Grassi

Publications and source records attributed to A. Grassi.

27 records · Page 2Linked to original sources

arXiv2005

Electronic structure of clusters (LiBC)_n: n=1, 2, 4

A crystalline form of LiBC is known which has been predicted to be superconducting, with a Tc comparable to that of MgB_2. In both compounds, superconductivity is enhanced by the presence of two electronic bands, one of which is close to a dimensional crossover. Here, we take a quantum chemical approach, and investigate the structural and electronic properties of small clusters (LiBC)_n (n=1-4). With increasing cluster size, we find that several properties of crystalline LiBC evolve naturally from the corresponding properties of the clusters. In particular, one may recognize the origin of the solid bilayered structure, typical of magnesium diboride, and the character of the electronic sigma-band, arising from the overlap of the atomic orbitals in the in-plane BC rings. Two aspects especially emphasized are (a) the HOMO-LUMO gap as function of n and (b) the role of different spin multiplicity.

physics.atm-clus↗

arXiv2004

Bond-order correlation energies for small Si-containing molecules compared with ab initio results from low-order Moller-Plesset perturbation theory

The present study of small molecules containing silicon has been motivated by (a) the considerable interest being shown currently in the kinetics and reactivity of such molecules, and (b) the biotechnological potential of silicon-derivate surfaces as substrates in the adsorption of, for instance, amino acids and proteins. Therefore, we have studied by (i) a semi-empirical approach and (ii) an ab initio procedure employing low-order Moller-Plesset perturbation theory, the molecular correlation energies of some neutral closed and open shell silicon-containing molecules in the series SiXnYm. Procedure (i) is shown to have particular merit for the correlation of the ionic members studied in the above series, while the ab initio procedures employed come into their own for neutral species.

physics.chem-ph↗

arXiv2004

Stretched chemical bonds in Si6H6: A transition from ring currents to localized pi-electrons?

Motivated by solid-state studies on the cleavage force in Si, and the consequent stretching of chemical bonds, we here study bond stretching in the, as yet unsynthesized, free space molecule Si6H6. We address the question as to whether substantial bond stretching (but constrained to uniform scaling on all bonds) can result in a transition from ring current behaviour, characteristic say of benzene at its equilibrium geometry, to localized pi-electrons on Si atoms. Some calculations are also recorded on dissociation into 6 SiH radicals. While the main studies have been carried out by unrestricted Hartree-Fock (HF) theory, the influence of electron correlation has been examined using two forms of density functional theory. Planar Si6H6 treated by HF is bound to be unstable, not all vibrational frequencies being real. Some buckling is then allowed, which results in real frequencies and stability. Evidence is then provided that the non-planar structure, as the Si-Si distance is increased, exhibits pi-electron localization in the range 1.2-1.5 times the equilibrium distance.

physics.chem-ph↗

arXiv2004

Equilibrium geometries of low-lying isomers of some Li clusters, within Hartree-Fock theory plus bond order or MP2 correlation corrections

In a recent study by Kornath et al. [J. Chem. Phys. 118 (2003) 6957], the Li_n clusters with n=2, 4 and 8 have been isolated in argon matrices at 15 K and characterized by Raman spectroscopy. This has prompted us to carry out a theoretical study on such clusters up to n=10, using Hartree-Fock theory, plus low-order Moeller-Plesset perturbation corrections. To check against the above study of Kornath et al., as a by-product we have made the same approximations for n=6 and 8 as we have for n=10. This has led us to emphasize trends with n through the Li_n clusters for (i) ground-state energy, (ii) HOMO-LUMO energy gap, (iii) dissociation energy, and (iv) Hartree-Fock eigenvalue sum. The role of electron correlation in distinguishing between low-lying isomers is plainly crucial, and will need a combination of experiment and theory to obtain decisive results such as that of Kornath et al. for Li_8. In particular, it is shown that Hartree-Fock theory plus bond order correlations does account for the experimentally observed symmetry T_d symmetry for Li_8.

physics.chem-ph↗

arXiv2000

Toric Calabi-Yau Fourfolds, Duality Between N=1 Theories and Divisors that Contribute to the Superpotential

We study issues related to F-theory on Calabi-Yau fourfolds and its duality to heterotic theory for Calabi-Yau threefolds. We discuss principally fourfolds that are described by reflexive polyhedra and show how to read off some of the data for the heterotic theory from the polyhedron. We give a procedure for constructing examples with given gauge groups and describe some of these examples in detail. Interesting features arise when the local pieces are fitted into a global manifold. An important issue is how to compute the superpotential explicitly. Witten has shown that the condition for a divisor to contribute to the superpotential is that it have arithmetic genus 1. Divisors associated with the short roots of non-simply laced gauge groups do not always satisfy this condition while the divisors associated to all other roots do. For such a `dissident' divisor we distinguish cases for which the arithmetic genus is greater than unity corresponding to an X that is not general in moduli (in the toric case this corresponds to the existence of non-toric parameters). In these cases the `dissident' divisor D does not remain an effective divisor for general complex structure. If however the arithmetic genus is less than or equal to 0, then the divisor is general in moduli and there is a genuine instability.

hep-th↗

arXiv1998

Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory, I

Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of ``M-theory'') and a four-dimensional physical theory (using the ``F-theory'' construction). A key issue in both theories is the calculation of the ``superpotential''of the theory. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold. When B is Fano, we show how divisors contributing to the superpotential are always "exceptional" (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, that is birational transformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. If a smoothing exists, then the Hodge numbers change. We speculate that divisors contributing to the superpotential are always "exceptional" (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which toric varieties.

alg-geom↗

arXiv1996

A Non-Perturbative Superpotential With $E_8$ Symmetry

We compute the non-perturbative superpotential in $F$-theory compactification to four dimensions on a complex three-fold $¶^1\times S$, where $S$ is a rational elliptic surface. In contrast to examples considered previously, the superpotential in this case has interesting modular properties; it is essentially an $E_8$ theta function.

hep-th↗

arXiv1993

Log contractions and equidimensional models of elliptic threefolds

This work was initially motivated by Miranda's work on elliptic Weierstrass threefolds. Miranda [Mi] describes a smooth equidimensional (flat) model for any elliptic Weierstrass threefold; such models occur naturally in the study of moduli spaces. In this paper we use minimal model theory to link birational maps of log surfaces (log contractions) to equidimensional fibrations of elliptic threefolds. As a corollary we show that an elliptic fibration of positive Kodaira dimension has a minimal model with an equidimensional birationally equivalent elliptic fibration satisfying certain good properties that naturally generalize the case of elliptic fibrations of surfaces. We apply the results to the case of Weierstrass models and give a global explanation of Miranda's algorithm.

alg-geom↗

arXiv1992

The Singularities of the parameter surface of a minimal elliptic threefold

Let f : X -> S be any elliptic fibration. If X has dimension 3 and is not uniruled, then X has a minimal model (with terminal singularities) [Mori]. In earlier work we have shown that there exists a birationally equivalent elliptic fibration p: Y -> T such that Y is minimal and a multiple of K_Y can be expressed as the pullback of a divisor from T. Moreover T has at worst quotient singularities; it is not difficult to find examples where T is actually singular. In this paper we describe the singularities of this parameter surface T in the case of no multiple fibers. Although T is not uniquely determined by the birational equivalence class of the fibration, any two such T are related by a particular kind of birational map.

alg-geom↗