644 research outputs found
On the Cholesky Decomposition for electron propagator methods: General aspects and application on C60
To treat the electronic structure of large molecules by electron propagator
methods we developed a parallel computer program called P-RICD. The
program exploits the sparsity of the two-electron integral matrix by using
Cholesky decomposition techniques. The advantage of these techniques is that
the error introduced is controlled only by one parameter which can be chosen as
small as needed. We verify the tolerance of electron propagator methods to the
Cholesky decomposition threshold and demonstrate the power of the
P-RICD program for a representative example (C60). All decomposition
schemes addressed in the literature are investigated. Even with moderate
thresholds the maximal error encountered in the calculated electron affinities
and ionization potentials amount to a few meV only, and the error becomes
negligible for small thresholds.Comment: 30 pages, 6 figures submitted to J.Chem. Phy
On the interactions between molecules in an off-resonant laser beam:Evaluating the response to energy migration and optically induced pair forces
Electronically excited molecules interact with their neighbors differently from their ground-state counterparts. Any migration of the excitation between molecules can modify intermolecular forces, reflecting changes to a local potential energy landscape. It emerges that throughput off-resonant radiation can also produce significant additional effects. The context for the present analysis of the mechanisms is a range of chemical and physical processes that fundamentally depend on intermolecular interactions resulting from second and fourth-order electric-dipole couplings. The most familiar are static dipole-dipole interactions, resonance energy transfer (both second-order interactions), and dispersion forces (fourth order). For neighboring molecules subjected to off-resonant light, additional forms of intermolecular interaction arise in the fourth order, including radiation-induced energy transfer and optical binding. Here, in a quantum electrodynamical formulation, these phenomena are cast in a unified description that establishes their inter-relationship and connectivity at a fundamental level. Theory is then developed for systems in which the interplay of these forms of interaction can be readily identified and analyzed in terms of dynamical behavior. The results are potentially significant in Förster measurements of conformational change and in the operation of microelectromechanical and nanoelectromechanical devices. © 2009 American Institute of Physics
The limitations of Slater's element-dependent exchange functional from analytic density functional theory
Our recent formulation of the analytic and variational Slater-Roothaan (SR)
method, which uses Gaussian basis sets to variationally express the molecular
orbitals, electron density and the one body effective potential of density
functional theory, is reviewed. Variational fitting can be extended to the
resolution of identity method,where variationality then refers to the error in
each two electron integral and not to the total energy. It is proposed that the
appropriate fitting functions be charge neutral and that all ab initio energies
be evaluated using two-center fits of the two-electron integrals. The SR method
has its root in the Slater's Xalpha method and permits an arbitrary scaling of
the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in
the system. Of several ways of choosing the scaling factors (Slater's exchange
parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and
the exact atomic, alpha_EA, values. The performance of this simple analytic
model with both sets for atomization energies of G2 set of 148 molecules is
better than the local density approximation or the HF theory, although the
errors in atomization energy are larger than the target chemical accuracy.
To improve peformance for atomization energies, the SR method is
reparametrized to give atomization energies of 148 molecules to be comparbale
to those obtained by one of the most widely used generalized gradient
approximations. The mean absolute error in ionization potentials of 49 atoms
and molecules is about 0.5 eV and that in bond distances of 27 molecules is
about 0.02 Angstrom. The overall good performance of the computationally
efficient SR method using any reasonable set of alpha values makes it a
promising method for study of large systems.Comment: 33 pages, Uses RevTex, to appear in The Journal of Chemical Physic
Projected Hartree product wavefunctions. VI. Natural orbital CI expansions in nonsinglet cases
The NSO\u27s and NO\u27s have been determined for some wavefunctions for Li, Be1+, B2+, C3+ 2S, and Be 3S wavefunctions containing radial correlation. It is shown how the NO\u27s may be utilized to form rapidly converging CI expansions in general. The role of the NSO\u27s in this problem is discussed. ©1973 The American Institute of Physic
Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory
For closed-shell systems, the local density approximation (LDA) and the LYP,
BLYP, and B3LYP functionals are shown to be compatible with reference-state
one-particle density-matrix theory, where this recently introduced formalism is
based on Brueckner-orbital theory and an energy functional that includes exact
exchange and a non-universal correlation-energy functional. The method is
demonstrated to reduce to a density functional theory when the
exchange-correlation energy-functional has a simplified form, i.e., its
integrand contains only the coordinates of two electron, say r1 and r2, and it
has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner
and Hartree--Fock orbitals are often very similar, any local exchange
functional that works well with Hartree--Fock theory is a reasonable
approximation with reference-state one-particle density-matrix theory. The LDA
approximation is also a reasonable approximation. However, the Colle--Salvetti
correlation-energy functional, and the LYP variant, are not ideal for the
method, since these are universal functionals. Nevertheless, they appear to
provide reasonable approximations. The B3LYP functional is derived using a
linear combination of two functionals: One is the BLYP functional; the other
uses exact exchange and a correlation-energy functional from the LDA.Comment: 26 Pages, 0 figures, RevTeX 4, Submitted to Mol. Phy
Fast hybrid density-functional computations using plane-wave basis sets
A new, very fast, implementation of the exact (Fock) exchange operator for electronic-structure calculations within the plane-wave pseudopotential method is described and carefully validated. Our method combines the recently proposed adaptively compressed exchange approach, to reduce the number of times the exchange is evaluated in the self-consistent loop, with an orbital localization procedure that reduces the number of exchange integrals to be computed at each evaluation. The new implementation, already available in the Quantum ESPRESSO distribution, results in a speedup that is never smaller than 3\u20134 and that increases with the size of the system, according to various realistic benchmark calculations
Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon
Quantum Monte Carlo (QMC) techniques are used to calculate the one-body
density matrix and excitation energies for the valence electrons of bulk
silicon. The one-body density matrix and energies are obtained from a
Slater-Jastrow wave function with a determinant of local density approximation
(LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is
strongly diagonally dominant. The natural orbitals obtained by diagonalizing
the QMC density matrix resemble the LDA orbitals very closely. Replacing the
determinant of LDA orbitals in the wave function by a determinant of natural
orbitals makes no significant difference to the quality of the wave function's
nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended
Koopmans' Theorem for correlated wave functions is used to calculate excitation
energies for silicon, which are in reasonable agreement with the available
experimental data. A diagonal approximation to the theorem, evaluated in the
basis of LDA orbitals, works quite well for both the quasihole and
quasielectron states. We have found that this approximation has an advantageous
scaling with system size, allowing more efficient studies of larger systems.Comment: 13 pages, 4 figures. To appear in Phys. Rev.
Method specific Cholesky decomposition : Coulomb and exchange energies
We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is that the exchange energy and Fock matrix can be evaluated with a linear scaling effort contrary to the RI method or standard Cholesky decomposition of the two-electron integral matrix. The methods presented show the same scaling properties as the so-called local density fitting methods, but with full error [email protected]
Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the
single- and the multireference case to tackle both the many-body problem and
the decay problem encountered, for example, in the study of electronic
resonances in molecules. A complex absorbing potential (CAP) is employed to
facilitate a treatment of resonance states that is similar to the
well-established bound-state techniques. For the perturbative approach, the
full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned
according to the Epstein-Nesbet scheme. The equations we derive in the
framework of the single-reference perturbation theory turn out to be identical
to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The
multireference perturbation theory is studied for a model problem and is shown
to be an efficient and accurate method. Algorithmic aspects of the integration
of the perturbation theories into existing ab initio programs are discussed,
and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review
Wavefunctions and Correlation Energies for Twoâ, Threeâ, and FourâElectron Atoms
- âŠ