Density functional. Medical search. Frequent questions

In the case of DFT, these are functionals of the spatially dependent electron density. (wikipedia.org)
The first HK theorem demonstrates that the ground-state properties of a many-electron system are uniquely determined by an electron density that depends on only three spatial coordinates. (wikipedia.org)
It set down the groundwork for reducing the many-body problem of N electrons with 3N spatial coordinates to three spatial coordinates, through the use of functionals of the electron density. (wikipedia.org)
The second HK theorem defines an energy functional for the system and proves that the ground-state electron density minimizes this energy functional. (wikipedia.org)
C. Lee, W. Yang and R. G. Parr, "Development of the Colic-Salvetti Correlation-Energy Formula into a Functional of the Electron Density," Physical Review B, Vol. 37, No. 2, 1988, pp. 785-789. (scirp.org)
The current affects the electron-density variation and hence the intermolecular and intramolecular bondings which in turn determine the transport magnitude. (chalmers.se)
With electron density fitting and transfer learning, we build a DFA recommender that selects the DFA with the lowest expected error with respect to gold standard but cost-prohibitive coupled cluster theory in a system-specific manner. (arxiv.org)
First, guess the form of the electron density and approximate the exchange-correlation potential. (stackexchange.com)

To date, however, no single density functional approximation (DFA) with universal accuracy has been identified, leading to uncertainty in the quality of data generated from DFT. (arxiv.org)
An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-$Z$ expansions for the corresponding energies of neutral atoms with atomic number $Z$ and electron number $N=Z$, which are correct to leading order ($-0.221 Z^{5/3}$ and $-0.021 Z \ln Z$ respectively) even in the lowest-rung or local density approximation. (arxiv.org)
Such a functional necessarily compromises between describing fundamentally different types of interactions, making transferability of the density functional approximation a key issue. (dtu.dk)
The approach is applied to designing the Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), a semilocal approximation with an additional nonlocal correlation term. (dtu.dk)
Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. (umsystem.edu)
In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and band structure of rutile titania (TiO$_2$) nanoparticles with particle size. (arxiv.org)
Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals. (cam.ac.uk)
We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). (cam.ac.uk)

Several dissociated and two nondissociated adsorption structures of the phenol molecule on the Si(001)-(2×1) surface are studied using density functional theory with various exchange and correlation functionals. (aalto.fi)
The correct expression for this functional is unknown (except for the case of a uniform electron gas) and there exists a whole zoo of exchange-correlation functionals that have to be used as approximations in place of the unknown correct exchange correlation functional. (stackexchange.com)
Alternative forms and transferability of electron-proton correlation functionals in nuclear-electronic orbital density functional theory. (bvsalud.org)
Both functionals are shown to be transferable for use with a series of diverse electronic exchange-correlation functionals, indicating that any reasonable electronic exchange-correlation functional may be used in tandem with the epc17 and epc18 electron - proton correlation functionals. (bvsalud.org)

Pure DFT calculations will often want to take advantage of density fitting. (gaussian.com)
The addition and abstraction reactions of OH radical with benzoate anion are investigated by density functional theory calculations that include solvent effects using UB3LYP, UCAM-B3LYP, UmPW1PW91 and UM06-2X functionals with the 6-311++G(2d,2p) basis set. (scirp.org)
Spin-polarized van der Waals corrected density functional theory calculations were applied to Sn-Pt alloys with Pt content ≤ 50% (referred to as low Pt alloys) to evaluate their catalytic activity towards the dehydrogenation of methylcyclohexane (MCH), with the formation of toluene as product. (mdpi.com)
The standard approach for efficient characterization of steady-state tunneling combines ground-state density-functional theory (DFT) calculations (of an effective scattering potential) with a Landauer-type formalism and ignores all actual many-body scattering. (chalmers.se)
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. (arxiv.org)
Benchmark calculations of chemical reactions in density functional theory: comparison of the accurate Kohn-Sham solution with generalized gradient approximations for the H2+H and H2+H2 reactions. (vu.nl)
Density functional theory calculations were carried out for three entropic rocksalt oxides, (Mg 0.1 Co 0.1 Ni 0.1 Cu 0.1 Zn 0.1 )O 0.5 , termed J14, and J14 + Li and J14 + Sc, to understand the role of charge neutrality and electronic states on their properties, and to probe whether simple expressions may exist that predict stability. (aip.org)

While most linear scaling DFT assumes a localized density matrix, this assumption is not required for stochastic DFT method which utilizes stochastic orbitals instead of deterministic Kohn-Sham orbitals. (aps.org)
We develop a scheme for building the scalar exchange-correlation (XC) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time- dependent current density functional theory (TDCDFT) and the Kohn-Sham current density response function. (umsystem.edu)

This theorem has since been extended to the time-dependent domain to develop time-dependent density functional theory (TDDFT), which can be used to describe excited states. (wikipedia.org)

Further, DFT potentials obtained with adjustable parameters are no longer true DFT potentials, given that they are not functional derivatives of the exchange correlation energy with respect to the charge density. (wikipedia.org)
This step is a numerical integration of the functional (or various derivatives of the functional). (gaussian.com)
To understand why, let me say a bit about functionals and functional derivatives. (stackexchange.com)

A general-purpose density functional for surface science and catalysis studies should accurately describe bond breaking and formation in chemistry, solid state physics, and surface chemistry, and should preferably also include van der Waals dispersion interactions. (dtu.dk)
Generalized van der Waals equations, weighted functional theories, correlation and non-locality approximations. (lu.se)

The isothermal elastic constants for the face‐centered‐cubic (fcc) and body‐centered‐cubic (bcc) hard‐sphere crystal are calculated for a range of densities using the modified weighted‐density functional of Denton and Ashcroft [Phys. (ku.edu)

First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights $\boldsymbol{w}$ in combination with the constrained search would lead to a universal functional of the one-particle reduced density matrix. (harvard.edu)
Quantum-kinetic (Dyson) equations are used for an exact reformulation that expresses the variational noninteracting and interacting many-body scattering T matrices in terms of universal density functionals. (chalmers.se)
The many-body LS variational principle defines an implicit equation for the exact nonequilibrium density. (chalmers.se)
This allows us to get the correct ground state charge density (through the variational theorem). (stackexchange.com)

This paper formulates a Lippmann-Schwinger (LS) collision density-functional theory (LSC DFT) for tunneling transport with full electron-electron interactions. (chalmers.se)
Herein another electron - proton correlation functional, denoted epc18, is derived using a different form for the functional parameter interpreted as representing the correlation length for electron - proton interactions. (bvsalud.org)

Approximate density functional theory (DFT) has become indispensable owing to its cost-accuracy trade-off in comparison to more computationally demanding but accurate correlated wavefunction theory. (arxiv.org)

The analysis of distributional data (probability density functions or histogram data) has recently gained increasing attention in the applications. (iasc-isi.org)
In contrast to the auxiliary particle filter approach, which utilizes the primary weights given by a measurement probability density and a predictive point estimate, the functional approach is based on comparison of the measurement and predictive probability density functions through a suitable metric. (zcu.cz)

Added material discussing the Becke 1988 functional. (arxiv.org)

Comment: on 'Inference for Density Families Using Functional Principal Component Analysis' by Kneip, A. and Utikal, K. J. (bath.ac.uk)
Comment: on 'Inference for Density Families Using Functional Principal Component Analysis' by Kneip, A. and Utikal, K. J. Journal of the American Statistical Association , 96 (454), 537-537. (bath.ac.uk)

A bird's-eye view of density-functional theory , on page 34, equation 73 or Wikipedia . (stackexchange.com)
This is the derivative of the energy functional with respect to the density, and the right side of this equation contains the external potential and Hartree potential terms. (stackexchange.com)

This gene provides instructions for making a protein called a very low density lipoprotein (VLDL) receptor. (medlineplus.gov)
Homozygous deletion of the very low density lipoprotein receptor gene causes autosomal recessive cerebellar hypoplasia with cerebral gyral simplification. (medlineplus.gov)
Results were expressed as mean and Serum high-density lipoprotein (HDL) standard deviation (SD). (who.int)

127, 023001 (2021)] a reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting many-fermion systems. (harvard.edu)

These spaces are mathematical spaces whose points are densities (or, more generally, measures), which generalize to the FDA setting the Aitchison simplex for multivariate compositional data. (iasc-isi.org)

The fcc elastic constants are shown to be in excellent agreement with the computer simulation data and to represent a significant improvement over the predictions of other density‐functional methods. (ku.edu)
Master's students Rajeev Kalloe, Priya Jogie, Damian den Ouden, Priyanka Singh and Fajar Fathurrahman were commissioned by the municipality of Amsterdam to analyse the GVB data of the three busiest public transport stations in Amsterdam - Central Station, Station Zuid and Station Bijlmer ArenA - and investigate how they could use machine learning to make accurate predictions about traffic density. (uva.nl)
The online Materials Modelling using Density Functional Theory: Properties and Predictions 2014 of Years your bank became for at least 15 mutations, or for n't its close canard if it has shorter than 15 sets. (lexcaliburs.com)
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Real-space/plane-wave based density function theory (DFT) is an important approach to understand electronic, optical, and magnetic properties of semiconductor and metallic materials. (aps.org)
The course will provide an introduction to the analysis of these data using a Functional Data Analysis (FDA) approach, grounded on the perspective of Bayes spaces. (iasc-isi.org)
A new functional approach is proposed and discussed. (zcu.cz)
The approach follows the idea of the auxiliary particle filter which introduces the concept of primary weights into sampling density design. (zcu.cz)
The particle filter with the sampling density given by the functional approach provides estimates that are closer to exact filtering probability density function in terms of point estimates. (zcu.cz)
An alternative approach for estimating E region density profiles using radio occultation total electron content (ROTEC) measurements is presented. (sri.com)
In this approach, the F region contribution to the measured ROTEC is removed using the estimated F region from an assimilative model of ionospheric density. (sri.com)
The results indicate that accurate estimates of the E region peak height and density can be obtained with this approach. (sri.com)
It is time for a positive approach to dietary guidance using nutrient density as a basic principle. (nfpt.com)
The approach is based on calculating conditional probabilities from data densities. (lu.se)

An ultra-high energy density (35 J cm −3 ) with a high efficiency (74%) is achieved in a pressed-and-folded poly(vinylidene fluoride) (670-700 kg mol −1 ), which is higher than that of other reported polymer-based dielectric capacitors to the best of our knowledge. (nature.com)
Therefore, achieving high energy density in dielectric capacitors is a major bottleneck in extending their practical applications. (nature.com)
Polymeric nitrogen, stabilized by compressing pure molecular nitrogen, has yet to be recovered to ambient conditions, precluding its application as a high-energy density material. (osti.gov)
The nitrogen framework persists to ambient pressure on decompression after removal of helium, forming pure polymeric nitrogen, t-N. t-N is dynamically and mechanically stable at ambient pressure with an estimated energy density of ~11.31 kJ/g, marking it out as a remarkable high-energy density material. (osti.gov)

Energy density of C. helgolandicus exhibited a spatial pattern with the highest values in the plume of the Gironde estuary. (ifremer.fr)
In contrast, no spatial pattern of energy density has been detected considering size-classes. (ifremer.fr)
Finally, we discussed how interspecific and spatial variability of energy density among the mesozooplankton community can have important implications on fish population dynamics. (ifremer.fr)

Proposed functionals lead to integrals which cannot be evaluated in closed form and are solved by numerical quadrature. (gaussian.com)
E region density profiles are then obtained from a numerical inversion of the residual ROTEC, which is assumed to be the E region contribution to the ROTEC. (sri.com)

Thus, to avoid biased assumptions, this study assessed the relationship between masticatory muscles hypofunction, induced by a prolonged powdered diet, and mandibular morphological measurements (i.e. assessment of bone curvatures, sagittal and vertical dimensions), estimation of mineral bone density and quantification of basal area. (bvsalud.org)

Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. (wikipedia.org)

The development of new DFT methods designed to overcome this problem, by alterations to the functional or by the inclusion of additive terms, is a current research topic. (wikipedia.org)
where the methods differ in which function f is used for E X and which (if any) f is used for E C . In addition to pure DFT methods, Gaussian supports hybrid methods in which the exchange functional is a linear combination of the Hartree-Fock exchange and a functional integral of the above form. (gaussian.com)
C. Adamo and V. Barone, "Exchange Functionals with Improved Long-Range Behavior and Adiabatic Connection Methods without Adjustable Parameters: The mPW and mPW1PW Models," The Journal of Chemical Physics, Vol. 108, No. 2, 1998, pp. 664-675. (scirp.org)
Her research interests focus on the study of innovative statistical models and methods for the analysis of complex and large data (such as functional data, distributional data and images), with particular emphasis on the applications to Earth and Environmental Sciences. (iasc-isi.org)
A methodology for semiempirical density functional optimization, using regularization and cross-validation methods from machine learning, is developed. (dtu.dk)
Hartree-Fock theory, Density Functional Theory, multiconfigurational methods. (lu.se)

Stereological quantification of degenerative myofibers and interstitial space changes were associated with functional defects 48-72 h after SSC-induced injury, thus demonstrating stereology is an accurate measure of SSC-induced skeletal muscle injury. (cdc.gov)

Classical density functional theory uses a similar formalism to calculate the properties of non-uniform classical fluids. (wikipedia.org)
Recently the epc17 electron - proton correlation functional was derived using a multicomponent extension of the Colle-Salvetti formalism and was implemented within the nuclear- electronic orbital (NEO) framework for treating electrons and specified protons quantum mechanically. (bvsalud.org)

In contrast, our previous density functional theory disagreement for the fast-exchanging substrate. (lu.se)

However, obtaining a polar phase with relaxor-like behavior in poly(vinylidene fluoride), as required for high energy storage density, is a major challenge. (nature.com)
Electrochemical capacitors have at least an order of magnitude higher energy density compared to dielectric capacitors, but suffer from lower power density and lower output voltage. (nature.com)
However, the application of dielectric capacitors is currently limited by their low energy density, especially in applications requiring large capacitances and small packaging size. (nature.com)
We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on band structure and density of states (DOS). (arxiv.org)
Most vegetables can be said to have a high nutrient density with a low energy density since water and non-digestible fiber account for much of their mass. (nfpt.com)
Returning to the sugar cookie example, for all its wealth of energy from sugar, fat, and starch, it has few vitamins and minerals and therefore can be said to have a low nutrient density. (nfpt.com)
Here again, energy density comes into play: fat represents more food energy, gram per gram, than either protein or carbohydrates. (nfpt.com)
In addition to weight gain, a sustained diet high in energy dense foods that are low in nutrient density can lead to nutrient deficiencies. (nfpt.com)
For health reasons, active women may self-select diets lower in energy density (ED, kcal/g), which can inadvertently contribute to inadequate EI. (mdpi.com)
I have read the paper of ' A bird's-eye view of density-functional theory [PDF] ' and I have a question about the functional derivative of the energy by the density. (stackexchange.com)
If the functional derivative results in its derivative being zero at each positions (all positions), does this mean that the energy does not change with the density, i.e., is this a constant function and does this mean the ground-state? (stackexchange.com)
Now consider what it really means for the functional derivative of the energy with respect to the density, to be 0. (stackexchange.com)
To explore some aspects of mesozooplankton functional diversity, this study quantified energy density during the springtime in the Bay of Biscay both between different species and between different size-classes. (ifremer.fr)
Energy densities of copepod species (Centropages typicus, Anomalocera patersoni, Calanus helgolandicus, and Labidocera wollastoni), as well as anchovy eggs (Engraulis encrasicolus) ranged from 0.5 to 6.7 kJ/g wet weight (ww). (ifremer.fr)
Considering size-classes, energy densities varied from 0.74 to 1.26 kJ/g ww. (ifremer.fr)
We argued that the energy density is a key functional trait of mesozooplankton species. (ifremer.fr)

Despite the current popularity of these alterations or of the inclusion of additional terms, they are reported to stray away from the search for the exact functional. (wikipedia.org)
To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. (harvard.edu)

Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. (wikipedia.org)
The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. (cam.ac.uk)

In this lesson, students will determine the mass and volume and use the data to calculate density. (ti.com)

Disease-related inflammation in RA is associated with low Bone Mineral Density (BMD). (lu.se)
A calibrated examiner performed linear and angular measurements (mandibular body length and height, mandibular lengths, ramus depth and height, mandibular base depth, mandibular head and gonial angle) on photographs, estimated bone density in the mandibular ramus region on digital radiographs and assessed the area of cortical and trabecular bone tissue in the second molar region, in 5-μm-thick serial cuts stained with Cason's Trichrome. (bvsalud.org)

By anticipating their future pivotal role in functional theories and to keep our work self-contained, several required concepts from convex analysis are introduced and discussed. (harvard.edu)

Multicomponent density functional theory (DFT) allows the consistent quantum mechanical treatment of both electrons and nuclei. (bvsalud.org)

Human Resources for Health (HRH) have been a priority on the regional and global health development agenda, as a critical component of functional health systems that can ensure universal access to quality health care.1 Successively in 1998, 2002 and 2009, the WHO Regional Committee for Africa adopted resolutions calling for the expansion of the health workforce through their optimal production and utilization. (who.int)

The density matrix. (gaussian.com)

T. Yanai, D. P. Tew and N. C. Handy, "A New Hybrid Exchange-Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP)," Chemical Physics Letters, Vol. 393, No. 1-3, 2004, pp. 51-57. (scirp.org)
The Department of Nanophotonics, Integration, and Neural Technology at the MPI of Microstructure Physics is developing wafer-scale photonic circuit technologies to miniaturize and increase the integration density of optical systems. (mpg.de)

In this paper we show that the set of points where the density of a Wiener functional is strictly positive is an open connected set, assuming some regularity conditions. (projecteuclid.org)

Anatomy8

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