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5. Radial electronic density of the argon and mercury atoms versus the distance to the nucleus. Both the solid and dashed curves were obtained using the GGA to approximate the xc potential. For comparison the density resulting from a relativistic GGA calculation for mercury is also shown. The density is normalized so that the area under each curve is 1
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The success of density functional theory (DFT) is clearly demonstrated by the overwhelming amount of research articles describing
results obtained within DFT that were published in the last decades. There is also a fair number of books reviewing the basics
of the theory and its extensions (e.g., the present volume, [1] and [2]). These works fall ma...
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We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yiel...
Citations
... In general, the v nadd contribution can be applied to an average atom model of any element with the use of pseudopotentials [46]. In fact, this model may prove to be more accurate for helium and beyond since the approximations used in DFT lead to some peculiarities for hydrogen that deviate from the true ground-state behavior for instance as discussed in Table 6.1 of Ref. [47]. Extreme pressures in the WDM regime can result in core orbital overlaps between adjacent atoms, especially in the stagnation pressures present in laboratory fusion studies [48,49]. ...
Accurate modeling in the warm dense matter regime is a persistent challenge with the most detailed models such as quantum molecular dynamics and path integral Monte Carlo being immensely computationally expensive. Density functional theory (DFT)-based average atom models (AAM) offer significant speed-ups in calculation times while still retaining fair accuracy in evaluating equations of state, mean ionizations, and more. Despite their success, AAMs struggle to precisely account for electronic interactions -- in particular, they do not account for effects on the kinetic energy arising from overlaps in neighboring atom densities. We aim to enhance these models by including such interactions via the non-additive kinetic potential as in DFT embedding theories. can be computed using Thomas-Fermi, von Weizs\"acker, or more sophisticated kinetic energy functionals. The proposed model introduces as a novel interaction term in existing ion-correlation models, which include interactions beyond the central atom. We have applied this model to hydrogen at 5 eV and densities ranging 0.008 to 0.8 g/cm, and investigated the effects of on electron densities, Kohn-Sham energy level shifts, mean ionization, and total energies.
... Density functional theory (DFT) is an approximated method to compute the electronic structures of systems with multiple electrons [2]. It regards the electrons as a continuous density distribution over space and solves the Schrödinger equation of one electron experiencing an effective potential caused by the atoms and the electron density [3]: ...
Electron distributions in drug molecules are crucial in drug design and can be predicted using density functional theory (DFT). We propose a comprehensive scheme to perform DFT calculations in real space instead of using the conventional orbital basis set. We detail the implementation of spherical space and basis, Pulay's density mixing, Hamiltonian matrix construction, Kohn-Sham equation solution, and Bader's charge analysis in discretized coordinate basis. We demonstrate that the demanding computation can be carried out in a highly parallel manner with simple codes by exploiting efficient algorithms in the PyTorch and NumPy packages. We perform calculations on the drug acyclovir and predict the electron distribution, partial charges, and energy levels in the molecule. The study may facilitate research in computational molecular science and structure-based drug design.
... The gold and sulpher attached MMF system (C4N3H5S2Au2) was geometrically minimized for the zero and higher applied electric fields with five field steps within the range of ±0.26VÅ -1 using density functional method [6] incorporated in Gaussian09 program package [7]. For the optimization, permutation of Becke's three-parameter exchange function with non-local correlation of Lee, Yang and Parr (B3LYP hybrid function) [8] is used along with Los Alamos National Laboratory of double zeta basis set [LANL2DZ], as it delivers the complete explanation of heavy metal atoms [9] in the MMF molecular wire. ...
The effect of metal electrodes on methylene-methyliminomethyl formamidine (MMF) molecule has been calculated by Density functional analysis using Gaussian09 program package. The various applied electric fields (0.00 – 0.26 VÅ-1) altered the geometrical parameters and the corresponding electrostatic and transport properties of the molecule has been analyzed. The variations in the atomic charges (MPA, NPA) of the molecule for the various applied electric fields have been compared. The HOMO-LUMO gap of the molecule for zero bias is 1.904 eV, as the field increases this gap decreases to 0.272 eV. The ESP shows the potential difference between charges accumulated of the molecule for various applied electric fields. The applied electric field polarizes the molecule, in consequence of that the dipole moment of the molecule decreases from 9.65 to 8.82 Debye. The small decrease of dipole moment shows that the molecule exhibits smaller conductivity.
... A fundamental requirement to perform such simulations is the knowledge about the atomic interactions, i.e., the potential energy and the forces, which in principle can be obtained by solving the Schrödinger equation. Unfortunately, such quantum mechanical calculations are computationally very demanding, even if relatively efficient methods like density functional theory (DFT) [1,2] are used. Therefore, the accessible time and length scales of ab initio molecular dynamics (MD) simulations [3,4], in which the energies and forces are determined by DFT for each visited atomic configuration, are limited to a few hundred atoms and tens to hundreds of picoseconds. ...
The introduction of modern Machine Learning Potentials (MLP) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form the construction of MLPs has to be done with great care. In this tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs.
... The solution to (27) depends on the value of r s . For r s < a/ 3 √ 2 ≈ 0.4872, there are 3 real roots but only 1 is positive and for larger r s there is only 1 real root. ...
... A4 forward from r = r 0 to r = R with typical values r 0 = 0.05r s and R = 8r s , respectively. Following [27] the boundary condition used at r = r 0 is ...
... As discussed above, we only expect (27) to be valid at high densities. Nonetheless, it can used to get an initial approximation for z 0 at all densities. ...
Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy functional. We present details on how to generate accurate exchange-correlation energies for the ground-state uniform gas. We also use the exchange hole in a CP antiparallel spin calculation to extract the high-density limit. We give a highly accurate analytic solution to the Thomas-Fermi model for this problem, showing its performance relative to Kohn-Sham and may be useful at high temperatures. We explore several approximations to the CP potential. Results are compared to accurate parameterizations for both exchange-correlation energies and holes.
... All geometric structures of the zinc complexes were fully optimized at the B3LYP/6-311G* density functional (DFT) level [48] by using the Gaussian 03 Rev. E.01-SMP program [49]. The obtained geometry was visualized with the GaussView 4.1 program [50]. ...
The paper presents a synthesis of poly(l-lactide) with bacteriostatic properties. This polymer was obtained by ring-opening polymerization of the lactide initiated by selected low-toxic zinc complexes, Zn[(acac)(L)H2O], where L represents N-(pyridin-4-ylmethylene) tryptophan or N-(2-pyridin-4-ylethylidene) phenylalanine. These complexes were obtained by reaction of Zn[(acac)2 H2O] and Schiff bases, , the products of the condensation of amino acids and 4-pyridinecarboxaldehyde. The composition, structure, and geometry of the synthesized complexes were determined by NMR and FTIR spectroscopy, elemental analysis, and molecular modeling. Both complexes showed the geometry of a distorted trigonal bipyramid. The antibacterial and antifungal activities of both complexes were found to be much stronger than those of the primary Schiff bases. The present study showed a higher efficiency of polymerization when initiated by the obtained zinc complexes than when initiated by the zinc(II) acetylacetonate complex. The synthesized polylactide showed antibacterial properties, especially the product obtained by polymerization initiated by a zinc(II) complex with a ligand based on l-phenylalanine. The polylactide showed a particularly strong antimicrobial effect against Pseudomonas aeruginosa, Staphylococcus aureus, and Aspergillus brasiliensis. At the same time, this polymer does not exhibit fibroblast cytotoxicity.
... Even though the underlying physics is translationally invariant, we note that the numerical solution to the Kohn-Sham equations does not need to fully obey this. For instance, if the grid in real space is too coarse, this might lead to and egg-box effect 54 , resulting in a small translation-dependent spurious potential. As a result, combining a DFT method whose parameters are not finely tuned together with a very tight threshold for the optimization step can result in the optimizer failing to converge. ...
Local optimization of adsorption systems inherently involves different scales: within the substrate, within the molecule, and between molecule and substrate. In this work, we show how the explicit modeling of the different character of the bonds in these systems improves the performance of machine learning methods for optimization. We introduce an anisotropic kernel in the Gaussian process regression framework that guides the search for the local minimum, and we show its overall good performance across different types of atomic systems. The method shows a speed-up of up to a factor two compared with the fastest standard optimization methods on adsorption systems. Additionally, we show that a limited memory approach is not only beneficial in terms of overall computational resources, but can result in a further reduction of energy and force calculations.
... Thus. apart from the last case, the HF orbitals do not follow the orbital-specific exponential decay exp(− nl r) (where nl = √ −2 nl ) characteristic for the solutions of the Schrödinger equation with a local multiplicative spherical potential vanishing at r → ∞ . In particular, such a decay is found for atomic orbitals satisfying the Kohn-Sham equation within the density-functional theory [72], but it is not valid for the solution of the HF equation which includes the nonlocal (integral) exchange operator defined by Eqs. (3)- (5). ...
The Hartree–Fock (HF) equation for atoms with closed (sub)shells is transformed with the pseudospectral (PS) method into a discrete eigenvalue equation for scaled orbitals on a finite radial grid. The Fock exchange operator and the Hartree potential are obtained from the respective Poisson equations also discretized using the PS representation. The numerical solution of the discrete HF equation for closed-(sub)shell atoms from He to No is robust, fast and gives extremely accurate results, with the accuracy superior to that of the previous HF calculations. A very moderate number of 33 to 71 radial grid points is sufficient to obtain total energies with 14 significant digits and occupied orbital energies with 12 to 14 digits in numerical calculations using the double precision (64-bit) of the floating-point format.The electron density at the nucleus is then determined with 13 significant digits and the Kato condition for the density and s orbitals is satisfied with the accuracy of 11 to 13 digits. The node structure of the exact HF orbitals is obtained and their asymptotic dependence, including the common exponential decay, is reproduced very accurately. The accuracy of the investigated quantities is further improved by performing the PS calculations in the quadruple precision (128-bit) floating-point arithmetic which provides the total energies with 25 significant digits while using only 80 to 130 grid points.
... The electronic structure is modeled via the DFT that provides a framework for calculating electronic properties of materials [14]. In DFT, Schrodinger wave equation and Poisson equation are solved self-consistently until convergence is achieved. ...
This paper presents B-splines and nonuniform rational B-splines (NURBS)-based finite element method for self-consistent solution of the Schrödinger wave equation (SWE). The new equilibrium position of the atoms is determined as a function of evolving stretching of the underlying primitive lattice vectors and it gets reflected via the evolving effective potential that is employed in the SWE. The nonlinear SWE is solved in a self-consistent fashion (SCF) wherein a Poisson problem that models the Hartree and local potentials is solved as a function of the electron charge density. The complex-valued generalized eigenvalue problem arising from SWE yields evolving band gaps that result in changing electronic properties of the semiconductor materials. The method is applied to indium, silicon, and germanium that are commonly used semiconductor materials. It is then applied to the material system comprised of silicon layer on silicon-germanium buffer to show the range of application of the method.
... However, it is reported in [11] that the complimentary change in conductance for P-type and N-type doped NWs due to same organic molecules, which indicates that electrostatic interaction dominates the response. In this paper, we consider the analysis of sensitivity of Si nanowire with different cross sections only and neglect the effect of any surface states, as the response of a sensor is characterized in terms of its selectivity, settling time, and sensitivity. ...
Nanowire field effect transistors can be modeled for ultrasensitive charge detection based bio- or chemical sensors. As critical dimensions of the nanowire sensor can be of the same order of size of biological molecules or chemical species yielding exceptional sensing possibilities. In addition, the large surface/volume ratio will give high sensitivities simply because surface effects dominate over bulk properties. Thus, we modeled Si nanowire with different geometries in the different chemical environment using NEGF approach. To analyze the performance, the sensitivity of Si nanowire with different cross sections including circular, rectangular, and triangular is derived by two definitions. It is calculated that the sensitivity of Si nanowire with different structures is a function of geometrical parameters and doping density. It is illustrated that the sensitivity varies inversely with cross-section area, doping density, and also the length of nanowire.