667 research outputs found
Ab initio Wannier-function-based many-body approach to Born charge of crystalline insulators
In this paper we present an approach aimed at performing many-body
calculations of Born-effective charges of crystalline insulators, by including
the electron-correlation effects. The scheme is implemented entirely in the
real space, using Wannier-functions as single-particle orbitals. Correlation
effects are computed by including virtual excitations from the Hartree-Fock
mean field, and the excitations are organized as per a Bethe-Goldstone-like
many-body hierarchy. The results of our calculations suggest that the approach
presented here is promising.Comment: 5 pages, to appear in Phys. Rev. B. (Rapid Comm., Dec 15, 2004
Ab initio Wannier-function-based correlated calculations of Born effective charges of crystalline LiO and LiCl
In this paper we have used our recently developed ab initio
Wannier-function-based methodology to perform extensive Hartree-Fock and
correlated calculations on LiO and LiCl to compute their Born effective
charges. Results thus obtained are in very good agreement with the experiments.
In particular, for the case of LiO, we resolve a controversy originating
in the experiment of Osaka and Shindo {[}Solid State Commun. 51 (1984) 421] who
had predicted the effective charge of Li ions to be in the range 0.58--0.61, a
value much smaller compared to its nominal value of unity, thereby, suggesting
that the bonding in the material could be partially covalent. We demonstrate
that effective charge computed by Osaka and Shindo is the Szigeti charge, and
once the Born charge is computed, it is in excellent agreement with our
computed value. Mulliken population analysis of LiO also confirms ionic
nature of the bonding in the substance.Comment: 11 pages, 1 figure. To appear in Phys. Rev. B (Feb 2008
Antiferromagnetic Exchange Interaction between Electrons on Degenerate LUMOs in Benzene Dianion
We discuss the ground state of Benzene dianion (Bz) on the basis of
the numerical diagonalization method of an effective model of orbitals.
It is found that the ground state can be the spin singlet state, and the
exchange coupling between LUMOs can be antiferromagnetic.Comment: Accepted for publication in J. Phys. Soc. Jpn., 2 pages, 3 figure
Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2
Empirically correlated density matrices of N-electron systems are
investigated. Exact closed-form expressions are derived for the one- and
two-electron reduced density matrices from a general pairwise correlated wave
function. Approximate expressions are proposed which reflect dispersive
interactions between closed-shell centro-symmetric subsystems. Said expressions
clearly illustrate the consequences of second-order correlation effects on the
reduced density matrices. Application is made to a simple example: the (He)2
system. Reduced density matrices are explicitly calculated, correct to second
order in correlation, and compared with approximations of independent electrons
and independent electron pairs. The models proposed allow for variational
calculations of interaction energies and equilibrium distance as well as a
clear interpretation of dispersive effects on electron distributions. Both
exchange and second order correlation effects are shown to play a critical role
on the quality of the results.Comment: 22 page
The Bravyi-Kitaev transformation for quantum computation of electronic structure
Quantum simulation is an important application of future quantum computers
with applications in quantum chemistry, condensed matter, and beyond. Quantum
simulation of fermionic systems presents a specific challenge. The
Jordan-Wigner transformation allows for representation of a fermionic operator
by O(n) qubit operations. Here we develop an alternative method of simulating
fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu.
Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation
cost to O(log n) qubit operations for one fermionic operation. We apply this
new Bravyi-Kitaev transformation to the task of simulating quantum chemical
Hamiltonians, and give a detailed example for the simplest possible case of
molecular hydrogen in a minimal basis. We show that the quantum circuit for
simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian
for H2 requires fewer gate applications than the equivalent circuit derived
from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev
method is asymptotically better than the Jordan-Wigner method, this result for
molecular hydrogen in a minimal basis demonstrates the superior efficiency of
the Bravyi-Kitaev method for all quantum computations of electronic structure
A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations
The Hartree-Fock equations are modified to directly yield Wannier functions
following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)].
This approach circumvents the a posteriori application of the Wannier
transformation to Bloch functions. I give a novel and rigorous derivation of
the relevant equations by introducing an orthogonalizing potential to ensure
the orthogonality among the resulting functions. The properties of these,
so-called a priori Wannier functions, are analyzed and the relation of the
modified Hartree-Fock equations to the conventional, Bloch-function-based
equations is elucidated. It is pointed out that the modified equations offer a
different route to maximally localized Wannier functions. Their computational
solution is found to involve an effort that is comparable to the effort for the
solution of the conventional equations. Above all, I show how a priori Wannier
functions can be obtained by a modification of the Kohn-Sham equations of
density-functional theory.Comment: 7 pages, RevTeX4, revise
Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo
Unbiased stochastic sampling of the one- and two-body reduced density
matrices is achieved in full configuration interaction quantum Monte Carlo with
the introduction of a second, "replica" ensemble of walkers, whose population
evolves in imaginary time independently from the first, and which entails only
modest additional computational overheads. The matrices obtained from this
approach are shown to be representative of full configuration-interaction
quality, and hence provide a realistic opportunity to achieve high-quality
results for a range of properties whose operators do not necessarily commute
with the hamiltonian. A density-matrix formulated quasi-variational energy
estimator having been already proposed and investigated, the present work
extends the scope of the theory to take in studies of analytic nuclear forces,
molecular dipole moments and polarisabilities, with extensive comparison to
exact results where possible. These new results confirm the suitability of the
sampling technique and, where sufficiently large basis sets are available,
achieve close agreement with experimental values, expanding the scope of the
method to new areas of investigation.Comment: 11 page
Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications
Using Green-function many-body theory, we present the details of a formally
exact adiabatic-connection fluctuation-dissipation density-functional theory
based on range separation, which was sketched in Toulouse, Gerber, Jansen,
Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated
density-functional theory approaches combining short-range density functional
approximations with long-range random phase approximations (RPA) are then
obtained as well-identified approximations on the long-range Green-function
self-energy. Range-separated RPA-type schemes with or without long-range
Hartree-Fock exchange response kernel are assessed on rare-gas and
alkaline-earth dimers, and compared to range-separated second-order
perturbation theory and range-separated coupled-cluster theory.Comment: 15 pages, 3 figures, 2 table
Order-N Density-Matrix Electronic-Structure Method for General Potentials
A new order-N method for calculating the electronic structure of general
(non-tight-binding) potentials is presented. The method uses a combination of
the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and
Daw, and a representation of the density matrix based on ``travelling basis
orbitals''. The method is applied to several one-dimensional examples,
including the free electron gas, the ``Morse'' bound-state potential, a
discontinuous potential that mimics an interface, and an oscillatory potential
that mimics a semiconductor. The method is found to contain Friedel
oscillations, quantization of charge in bound states, and band gap formation.
Quantitatively accurate agreement with exact results is found in most cases.
Possible advantages with regard to treating electron-electron interactions and
arbitrary boundary conditions are discussed.Comment: 13 pages, REVTEX, 7 postscript figures (not quite perfect
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