10,176 research outputs found
What is a crystal?
Almost 25 years have passed since Shechtman discovered quasicrystals, and 15
years since the Commission on Aperiodic Crystals of the International Union of
Crystallography put forth a provisional definition of the term crystal to mean
``any solid having an essentially discrete diffraction diagram.'' Have we
learned enough about crystallinity in the last 25 years, or do we need more
time to explore additional physical systems? There is much confusion and
contradiction in the literature in using the term crystal. Are we ready now to
propose a permanent definition for crystal to be used by all? I argue that time
has come to put a sense of order in all the confusion.Comment: Submitted to Zeitschrift fuer Kristallographi
The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling
Tensor hypercontraction is a method that allows the representation of a
high-rank tensor as a product of lower-rank tensors. In this paper, we show how
tensor hypercontraction can be applied to both the electron repulsion integral
(ERI) tensor and the two-particle excitation amplitudes used in the parametric
reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions
are needed in both of these approximations, our overall algorithm can be shown
to scale as O(r4), where r is the number of single-particle basis functions. We
apply our algorithm to several small molecules, hydrogen chains, and alkanes to
demonstrate its low formal scaling and practical utility. Provided we use
enough auxiliary functions, we obtain accuracy similar to that of the
traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).Comment: 11 pages, 1 figur
Equivariant pretheories and invariants of torsors
In the present paper we introduce and study the notion of an equivariant
pretheory: basic examples include equivariant Chow groups, equivariant K-theory
and equivariant algebraic cobordism. To extend this set of examples we define
an equivariant (co)homology theory with coefficients in a Rost cycle module and
provide a version of Merkurjev's (equivariant K-theory) spectral sequence for
such a theory. As an application we generalize the theorem of
Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a
G-equivariant pretheory we associate a graded ring which serves as an invariant
of E. In the case of Chow groups this ring encodes the information concerning
the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes
of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous
preprint: the construction of an equivariant cycle (co)homology and the
spectral sequence (generalizing the long exact localization sequence) are
adde
A unified electrostatic and cavitation model for first-principles molecular dynamics in solution
The electrostatic continuum solvent model developed by Fattebert and Gygi is
combined with a first-principles formulation of the cavitation energy based on
a natural quantum-mechanical definition for the surface of a solute. Despite
its simplicity, the cavitation contribution calculated by this approach is
found to be in remarkable agreement with that obtained by more complex
algorithms relying on a large set of parameters. Our model allows for very
efficient Car-Parrinello simulations of finite or extended systems in solution,
and demonstrates a level of accuracy as good as that of established
quantum-chemistry continuum solvent methods. We apply this approach to the
study of tetracyanoethylene dimers in dichloromethane, providing valuable
structural and dynamical insights on the dimerization phenomenon
A note about the ground state of the hydrogen molecular ion
Three simple parametric trial functions for the molecular ion are presented. Each of them provides subsequently the
most accurate approximation for the Born-Oppenheimer ground state energy among
several-parametric trial functions. These trial functions are chosen following
a criterion of physical adequacy and includes the electronic correlation in the
exponential form , where is a variational
parameter. The Born-Oppenheimer energy is found to be \,a.u., respectively, for optimal equilateral triangular
configuration of protons with the equilibrium interproton distance
\,a.u. The variational energy agrees in three significant digits (s.d.)
with most accurate results available at present as well as for major
expectation values.Comment: 12 pages, 1 figure, 3 table
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