4,097 research outputs found
Progress in Time-Dependent Density-Functional Theory
The classic density-functional theory (DFT) formalism introduced by
Hohenberg, Kohn, and Sham in the mid-1960s, is based upon the idea that the
complicated N-electron wavefunction can be replaced with the mathematically
simpler 1-electron charge density in electronic struc- ture calculations of the
ground stationary state. As such, ordinary DFT is neither able to treat
time-dependent (TD) problems nor describe excited electronic states. In 1984,
Runge and Gross proved a theorem making TD-DFT formally exact. Information
about electronic excited states may be obtained from this theory through the
linear response (LR) theory formalism. Begin- ning in the mid-1990s, LR-TD-DFT
became increasingly popular for calculating absorption and other spectra of
medium- and large-sized molecules. Its ease of use and relatively good accuracy
has now brought LR-TD-DFT to the forefront for this type of application. As the
number and the diversity of applications of TD-DFT has grown, so too has grown
our understanding of the strengths and weaknesses of the approximate
functionals commonly used for TD-DFT. The objective of this article is to
continue where a previous review of TD-DFT in this series [Annu. Rev. Phys.
Chem. 55: 427 (2004)] left off and highlight some of the problems and solutions
from the point of view of applied physical chemistry. Since doubly-excited
states have a particularly important role to play in bond dissociation and
formation in both thermal and photochemistry, particular emphasis will be
placed upon the problem of going beyond or around the TD-DFT adiabatic
approximation which limits TD-DFT calculations to nominally singly-excited
states. Posted with permission from the Annual Review of Physical Chemistry,
Volume 63 \c{opyright} 2012 by Annual Reviews, http://www.annualreviews.org
Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What is Missing in, and Corrections to, the TD-DFT Adiabatic Approximation
In their famous paper Kohn and Sham formulated a formally exact
density-functional theory (DFT) for the ground-state energy and density of a
system of interacting electrons, albeit limited at the time by certain
troubling representability questions. As no practical exact form of the
exchange-correlation (xc) energy functional was known, the xc-functional had to
be approximated, ideally by a local or semilocal functional. Nowadays however
the realization that Nature is not always so nearsighted has driven us up
Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction
hybrid functionals. Time-dependent (TD-) DFT is a younger development which
allows DFT concepts to be used to describe the temporal evolution of the
density in the presence of a perturbing field. Linear response (LR) theory then
allows spectra and other information about excited states to be extracted from
TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in
practical calculations and this has historically been done using the TD-DFT
adiabatic approximation (AA) which is to TD-DFT very much like what the local
density approximation (LDA) is to conventional ground-state DFT. While some of
the recent advances in TD-DFT focus on what can be done within the AA, others
explore ways around the AA. After giving an overview of DFT, TD-DFT, and
LR-TD-DFT, this article will focus on many-body corrections to LR-TD-DFT as one
way to building hybrid density-functional/wavefunction methodology for
incorporating aspects of nonlocality in time not present in the AA.Comment: 56 pages, 17 figure
Alloying effects on the optical properties of GeSi nanocrystals from TDDFT and comparison with effective-medium theory
We present the optical spectra of GeSi alloy nanocrystals
calculated with time-dependent density-functional theory in the adiabatic
local-density ap proximation (TDLDA). The spectra change smoothly as a function
of the compositio n . On the Ge side of the composition range, the lowest
excitations at the ab sorption edge are almost pure Kohn-Sham
independent-particle HOMO-LUMO transitio ns, while for higher Si contents
strong mixing of transitions is found. Within T DLDA the first peak is slightly
higher in energy than in earlier independent-par ticle calculations. However,
the absorption onset and in particular its composit ion dependence is similar
to independent-particle results. Moreover, classical depolarization effects are
responsible for a very strong suppression of the abs orption intensity. We show
that they can be taken into account in a simpler way using Maxwell-Garnett
classical effective-medium theory. Emission spectra are in vestigated by
calculating the absorption of excited nanocrystals at their relaxe d geometry.
The structural contribution to the Stokes shift is about 0.5 eV. Th e
decomposition of the emission spectra in terms of independent-particle transit
ions is similar to what is found for absorption. For the emission, very weak
tra nsitions are found in Ge-rich clusters well below the strong absorption
onset.Comment: submitted to Phys. Rev.
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
Time-dependent Kohn-Sham theory with memory
In time-dependent density-functional theory, exchange and correlation (xc)
beyond the adiabatic local density approximation can be described in terms of
viscoelastic stresses in the electron liquid. In the time domain, this leads to
a velocity-dependent xc vector potential with a memory containing short- and
long-range components. The resulting time-dependent Kohn-Sham formalism
describes the dynamics of electronic systems including decoherence and
relaxation. For the example of collective charge-density oscillations in a
quantum well, we illustrate the xc memory effects, clarify the dissipation
mechanism, and extract intersubband relaxation rates for weak and strong
excitations.Comment: 4 pages, 4 figure
Advancing the Science of Self‐Management in Adults With Long‐Term Left Ventricular Assist Devices
This study tested the applicability of the individual and family self‐management theory (IFSMT) to self‐management (SM) in patients with left ventricular assist devices (LVADs). From an existing data set, we extracted the following variables that correspond to IFSMT’s conceptual dimensions: anxiety, depression, and cognition (context dimension); self‐efficacy (SM process dimension); adherence and quality of life (QOL; outcome dimensions). Descriptive statistics and partial least squares path modeling procedures were used for data analyses. A total of 100 patients (mean age 52 ± 13.4 years) with continuous flow LVAD designs comprised the present study. Most patients were White (78%), married (69%), college‐educated (72%), and on disability (53%). Their mean anxiety and depression scores were slightly above normal, while their cognitive function scores were slightly lower than normal. LVAD care self‐efficacy, adherence, and QOL were within normal ranges. Factor loadings ranged from 0.50 to 1.0, and there were significant forward path relationships among the context, process, and outcome dimensions (β ranges from 0.02 to 0.60, all P values < 0.05). In conclusion, the IFSMT provides a good fit for SM in LVAD. Further research is needed to clarify how best to improve LVAD SM practice and treatment outcomes.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146581/1/aor13113_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146581/2/aor13113.pd
The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges
In principle, the Luttinger-Ward Green's function formalism allows one to
compute simultaneously the total energy and the quasiparticle band structure of
a many-body electronic system from first principles. We present approximate and
exact expressions for the correlation energy within the GW-RPA approximation
that are more amenable to computation and allow for developing efficient
approximations to the self-energy operator and correlation energy. The exact
form is a sum over differences between plasmon and interband energies. The
approximate forms are based on summing over screened interband transitions. We
also demonstrate that blind extremization of such functionals leads to
unphysical results: imposing physical constraints on the allowed solutions
(Green's functions) is necessary. Finally, we present some relevant numerical
results for atomic systems.Comment: 3 figures and 3 tables, under review at Physical Review
Partial Density of States Ligand Field Theory (PDOS-LFT): Recovering a LFT-Like Picture and Application to Photoproperties of Ruthenium(II) Polypyridine Complexes
Gas phase density-functional theory (DFT) and time-dependent DFT (TD-DFT)
calculations are reported for a data base of 98 ruthenium(II) polypyridine
complexes. Comparison with X-ray crystal geometries and with experimental
absorption spectra measured in solution show an excellent linear correlation
with the results of the gas phase calculations. Comparing this with the usual
chemical understanding based upon ligand field theory (LFT) is complicated by
the large number of molecular orbitals present and especially by the heavy
mixing of the antibonding metal e* orbitals with ligand orbitals.
Nevertheless, we show that a deeper understanding can be obtained by a partial
density-of-states (PDOS) analysis which allows us to extract approximate metal
t and e* and ligand \pi* orbital energies in a well-defined way,
thus providing a PDOS analogue of LFT (PDOS-LFT). Not only do PDOS-LFT energies
generate a spectrochemical series for the ligands, but orbital energy
differences provide good estimates of TD-DFT absorption energies. Encouraged by
this success, we use frontier-molecular-orbital-theory-like reasoning to
construct a model which allows us in most, but not all, of the cases studied to
use PDOS-LFT energies to provide a semiquantitative relationship between
luminescence lifetimes at room temperature and liquid nitrogen temperature
Undoing static correlation: Long-range charge transfer in time-dependent density functional theory
Long-range charge transfer excited states are notoriously badly
underestimated in time-dependent density functional theory (TDDFT). We resolve
how {\it exact} TDDFT captures charge transfer between open-shell species: in
particular the role of the step in the ground-state potential, and the severe
frequency-dependence of the exchange-correlation kernel. An expression for the
latter is derived, that becomes exact in the limit that the charge-transfer
excitations are well-separated from other excitations. The exchange-correlation
kernel has the task of undoing the static correlation in the ground state
introduced by the step, in order to accurately recover the physical
charge-transfer states.Comment: 2 figure
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