961 research outputs found
Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory
Linear-response time-dependent (TD) density-functional theory (DFT) has been
implemented in the pseudopotential wavelet-based electronic structure program
BigDFT and results are compared against those obtained with the all-electron
Gaussian-type orbital program deMon2k for the calculation of electronic
absorption spectra of N2 using the TD local density approximation (LDA). The
two programs give comparable excitation energies and absorption spectra once
suitably extensive basis sets are used. Convergence of LDA density orbitals and
orbital energies to the basis-set limit is significantly faster for BigDFT than
for deMon2k. However the number of virtual orbitals used in TD-DFT calculations
is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT
calculations in deMon2k. As a reality check, we report the x-ray crystal
structure and the measured and calculated absorption spectrum (excitation
energies and oscillator strengths) of the small organic molecule
N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1,2-a]pyridin-3-amine
Calculating energy derivatives for quantum chemistry on a quantum computer
Modeling chemical reactions and complicated molecular systems has been
proposed as the `killer application' of a future quantum computer. Accurate
calculations of derivatives of molecular eigenenergies are essential towards
this end, allowing for geometry optimization, transition state searches,
predictions of the response to an applied electric or magnetic field, and
molecular dynamics simulations. In this work, we survey methods to calculate
energy derivatives, and present two new methods: one based on quantum phase
estimation, the other on a low-order response approximation. We calculate
asymptotic error bounds and approximate computational scalings for the methods
presented. Implementing these methods, we perform the world's first geometry
optimization on an experimental quantum processor, estimating the equilibrium
bond length of the dihydrogen molecule to within 0.014 Angstrom of the full
configuration interaction value. Within the same experiment, we estimate the
polarizability of the H2 molecule, finding agreement at the equilibrium bond
length to within 0.06 a.u. (2% relative error).Comment: 19 pages, 1 page supplemental, 7 figures. v2 - tidied up and added
example to appendice
Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS
Electron correlation effects are studied in ZrSiS using a combination of
first-principles and model approaches. We show that basic electronic properties
of ZrSiS can be described within a two-dimensional lattice model of two nested
square lattices. High degree of electron-hole symmetry characteristic for ZrSiS
is one of the key features of this model. Having determined model parameters
from first-principles calculations, we then explicitly take electron-electron
interactions into account and show that at moderately low temperatures ZrSiS
exhibits excitonic instability, leading to the formation of a pseudogap in the
electronic spectrum. The results can be understood in terms of
Coulomb-interaction-assisted pairing of electrons and holes reminiscent to that
of an excitonic insulator. Our finding allows us to provide a physical
interpretation to the unusual mass enhancement of charge carriers in ZrSiS
recently observed experimentally.Comment: 6 pages, 4 figures. Final versio
Perspective: How good is DFT for water?
Kohn-Sham density functional theory (DFT) has become established as an
indispensable tool for investigating aqueous systems of all kinds, including
those important in chemistry, surface science, biology and the earth sciences.
Nevertheless, many widely used approximations for the exchange-correlation (XC)
functional describe the properties of pure water systems with an accuracy that
is not fully satisfactory. The explicit inclusion of dispersion interactions
generally improves the description, but there remain large disagreements
between the predictions of different dispersion-inclusive methods. We present
here a review of DFT work on water clusters, ice structures and liquid water,
with the aim of elucidating how the strengths and weaknesses of different XC
approximations manifest themselves across this variety of water systems. Our
review highlights the crucial role of dispersion in describing the delicate
balance between compact and extended structures of many different water
systems, including the liquid. By referring to a wide range of published work,
we argue that the correct description of exchange-overlap interactions is also
extremely important, so that the choice of semi-local or hybrid functional
employed in dispersion-inclusive methods is crucial. The origins and
consequences of beyond-2-body errors of approximate XC functionals are noted,
and we also discuss the substantial differences between different
representations of dispersion. We propose a simple numerical scoring system
that rates the performance of different XC functionals in describing water
systems, and we suggest possible future developments
Ionic polaron in a Bose-Einstein condensate
The ground state properties of a degenerate bosonic gas doped with an ion are
investigated by means of quantum Monte Carlo simulations in three dimensions.
The system features competing length and energy scales, which result in vastly
different polaronic properties compared to neutral quantum impurities.
Depending on whether a two-body bound state is supported or not by the atom-ion
potential, we identify a transition between a polaron regime amenable to a
perturbative treatment in the limit of weak atom-ion interactions and a
many-body bound state with vanishing quasi-particle residue composed of
hundreds of atoms. In order to analyze the structure of the corresponding
states we examine the atom-ion and atom-atom correlation functions. Our
findings are directly relevant to experiments using hybrid atom-ion setups that
have recently attained the ultracold regime.Comment: 11 pages, 6 figures, 1 tabl
Real-Space Mesh Techniques in Density Functional Theory
This review discusses progress in efficient solvers which have as their
foundation a representation in real space, either through finite-difference or
finite-element formulations. The relationship of real-space approaches to
linear-scaling electrostatics and electronic structure methods is first
discussed. Then the basic aspects of real-space representations are presented.
Multigrid techniques for solving the discretized problems are covered; these
numerical schemes allow for highly efficient solution of the grid-based
equations. Applications to problems in electrostatics are discussed, in
particular numerical solutions of Poisson and Poisson-Boltzmann equations.
Next, methods for solving self-consistent eigenvalue problems in real space are
presented; these techniques have been extensively applied to solutions of the
Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue
problems arising in semiconductor and polymer physics. Finally, real-space
methods have found recent application in computations of optical response and
excited states in time-dependent density functional theory, and these
computational developments are summarized. Multiscale solvers are competitive
with the most efficient available plane-wave techniques in terms of the number
of self-consistency steps required to reach the ground state, and they require
less work in each self-consistency update on a uniform grid. Besides excellent
efficiencies, the decided advantages of the real-space multiscale approach are
1) the near-locality of each function update, 2) the ability to handle global
eigenfunction constraints and potential updates on coarse levels, and 3) the
ability to incorporate adaptive local mesh refinements without loss of optimal
multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic
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