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SymmetryAdapted Phonon Analysis of Nanotubes (to
, 2014
"... The characteristics of phonons, i.e. linearized normal modes of vibration, provide important insights into many aspects of crystals, e.g. stability and thermodynamics. In this paper, we use the Objective Structures framework to make concrete analogies between crystalline phonons and normal modes of ..."
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The characteristics of phonons, i.e. linearized normal modes of vibration, provide important insights into many aspects of crystals, e.g. stability and thermodynamics. In this paper, we use the Objective Structures framework to make concrete analogies between crystalline phonons and normal modes of vibration in noncrystalline but highly symmetric nanostructures. Our strategy is to use an intermediate linear transformation from realspace to an intermediate space in which the Hessian matrix of second derivatives is blockcirculant. The blockcirculant nature of the Hessian enables us to then follow the procedure to obtain phonons in crystals: namely, we use the Discrete Fourier Transform from this intermediate space to obtain a blockdiagonal matrix that is readily diagonalizable. We formulate this for general Objective Structures and then apply it to study carbon nanotubes of various chiralities that are subjected to axial elongation and torsional deformation. We compare the phonon spectra computed in the Objective Framework with spectra computed for armchair and zigzag nanotubes. We also demonstrate the approach by computing the Density of States. In addition to the computational efficiency afforded by Objective Structures in providing the transformations to almostdiagonalize the Hessian, the framework provides an important conceptual simplification to interpret
SymmetryAdapted Wavelet Analysis
, 1996
"... We review the construction of continuous wavelet transforms adapted to a given symmetry. Then we discuss in detail successively spatial wavelets, wavelets on the sphere and spacetime wavelets. 1. HOW TO DEFINE AN ADAPTED WAVELET TRANSFORM? As it is wellknown [1], wavelet analysis comes in two ve ..."
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transform (WT) itself, and this clearly requires the use of the continuous approach. The aim of this talk is to show how a WT adapted to a given symmetry may be derived systematically from the symmetry group itself. Consider the class of finite energy signals living on a manifold Y , i.e. s 2 L 2 (Y; d
The SymmetryAdapted Configurational Ensemble Approach to the Computer Simulation of SiteDisordered Solids
"... Abstract: Siteoccupancy disorder, defined as the nonperiodic occupation of lattice sites in a crystal structure, is a ubiquitous phenomenon in solidstate physics and chemistry. Examples are mineral solid solutions, synthetic nonstoichiometric compounds and metal alloys. The experimental investig ..."
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. Thermodynamics and nonthermodynamic properties are then defined from the statistics in the symmetryadapted configurational ensemble. I will briefly summarize and discuss some recent applications of this methodology to problems in materials science.
Rapid computation of intermolecular interactions in molecular and ionic clusters: selfconsistent polarization plus symmetryadapted perturbation theory
, 2011
"... A method that we have recently introduced for rapid computation of intermolecular interaction energies is reformulated and subjected to further tests. The method employs monomerbased selfconsistent field calculations with an electrostatic embedding designed to capture manybody polarization (the ‘ ..."
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‘‘XPol’ ’ procedure), augmented by pairwise symmetryadapted perturbation theory (SAPT) to capture dispersion and exchange interactions along with any remaining induction effects. A rigorous derivation of the XPol+SAPT methodology is presented here, which demonstrates that the method is systematically
A Fast Algorithm for the Construction of Integrity Bases Associated to Symmetry–Adapted Polynomial Representations. Application to Tetrahedral XY4 Molecules
, 2014
"... Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry–adapted polynomials in the symmetry coordinates of a molecular system, because it is based on a finer ..."
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Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry–adapted polynomials in the symmetry coordinates of a molecular system, because it is based on a
SAPT: A Program for ManyBody SymmetryAdapted Perturbation Theory Calculations of Intermolecular Interaction Energies
"... this paper (the Einstein convention). We shall also always assume that ff; fi; fl; ffi (ae; oe; ; !) label occupied (virtual) spinorbitals while ; ; ; ..."
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Cited by 1 (0 self)
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this paper (the Einstein convention). We shall also always assume that ff; fi; fl; ffi (ae; oe; ; !) label occupied (virtual) spinorbitals while ; ; ;
Article SymmetryAdapted Rotator Functions for Molecules in Cylindrical Confinement
, 2011
"... Abstract: We present a general description of the formalism of symmetryadapted rotator functions (SARFs) for molecules in cylindrical confinement. Molecules are considered as clusters of interaction centers (ICs), can have any symmetry, and can display different types of ICs. Cylindrical confinemen ..."
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Abstract: We present a general description of the formalism of symmetryadapted rotator functions (SARFs) for molecules in cylindrical confinement. Molecules are considered as clusters of interaction centers (ICs), can have any symmetry, and can display different types of ICs. Cylindrical
Breakdown of the SingleExchange Approximation in ThirdOrder SymmetryAdapted Perturbation Theory
 J. Phys. Chem. A
"... ABSTRACT: We report thirdorder symmetryadapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the singleexchange approximation (SEA) employed to derive the thirdorder exchange−induction correction (Ee ..."
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ABSTRACT: We report thirdorder symmetryadapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the singleexchange approximation (SEA) employed to derive the thirdorder exchange−induction correc
Results 1  10
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