6 research outputs found
Robust ab initio calculation of condensed matter: transparent convergence through semicardinal multiresolution analysis
We present the first wavelet-based all-electron density-functional
calculations to include gradient corrections and the first in a solid. Direct
comparison shows this approach to be unique in providing systematic
``transparent'' convergence, convergence with a priori prediction of errors, to
beyond chemical (millihartree) accuracy. The method is ideal for exploration of
materials under novel conditions where there is little experience with how
traditional methods perform and for the development and use of chemically
accurate density functionals, which demand reliable access to such precision.Comment: 4 pages, 3 figures, 4 tables. Submitted to Phys. Rev. Lett. (updated
to include GGA
An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis
An efficient numerical quadrature is proposed for the approximate calculation
of the potential energy in the context of pseudo potential electronic structure
calculations with Daubechies wavelet and scaling function basis sets. Our
quadrature is also applicable in the case of adaptive spatial resolution. Our
theoretical error estimates are confirmed by numerical test calculations of the
ground state energy and wave function of the harmonic oscillator in one
dimension with and without adaptive resolution. As a byproduct we derive a
filter, which, upon application on the scaling function coefficients of a
smooth function, renders the approximate grid values of this function. This
also allows for a fast calculation of the charge density from the wave
function.Comment: 35 pages, 9 figures. Submitted to: Journal of Computational Physic
A physically meaningful method for the comparison of potential energy functions
In the study of the conformational behavior of complex systems, such as
proteins, several related statistical measures are commonly used to compare two
different potential energy functions. Among them, the Pearson's correlation
coefficient r has no units and allows only semi-quantitative statements to be
made. Those that do have units of energy and whose value may be compared to a
physically relevant scale, such as the root mean square deviation (RMSD), the
mean error of the energies (ER), the standard deviation of the error (SDER) or
the mean absolute error (AER), overestimate the distance between potentials.
Moreover, their precise statistical meaning is far from clear. In this article,
a new measure of the distance between potential energy functions is defined
which overcomes the aforementioned difficulties. In addition, its precise
physical meaning is discussed, the important issue of its additivity is
investigated and some possible applications are proposed. Finally, two of these
applications are illustrated with practical examples: the study of the van der
Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y)
and the comparison of different levels of the theory in the ab initio study of
the Ramachandran map of the model peptide HCO-L-Ala-NH2.Comment: 30 pages, 7 figures, LaTeX, BibTeX. v2: A misspelling in the author's
name has been corrected. v3: A new application of the method has been added
at the end of section 9 and minor modifications have also been made in other
sections. v4: Journal reference and minor corrections adde
Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the Alanine dipeptide
If constraints are imposed on a macromolecule, two inequivalent classical
models may be used: the stiff and the rigid one. This work studies the effects
of such constraints on the Conformational Equilibrium Distribution (CED) of the
model dipeptide HCO-L-Ala-NH2 without any simplifying assumption. We use ab
initio Quantum Mechanics calculations including electron correlation at the MP2
level to describe the system, and we measure the conformational dependence of
all the correcting terms to the naive CED based in the Potential Energy Surface
(PES) that appear when the constraints are considered. These terms are related
to mass-metric tensors determinants and also occur in the Fixman's compensating
potential. We show that some of the corrections are non-negligible if one is
interested in the whole Ramachandran space. On the other hand, if only the
energetically lower region, containing the principal secondary structure
elements, is assumed to be relevant, then, all correcting terms may be
neglected up to peptides of considerable length. This is the first time, as far
as we know, that the analysis of the conformational dependence of these
correcting terms is performed in a relevant biomolecule with a realistic
potential energy function.Comment: 37 pages, 4 figures, LaTeX, BibTeX, AMSTe
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment