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16. Egg-box effect in CH4. The x-axis represents the distance of the carbon atom to the central point of the grid. E is the total energy, ε1 the Kohn-Sham eigenvalue of the HOMO-1 state, and ε2,3,4 the Kohn-Sham eigenvalues of the HOMO state (which is triply degenerate). For the sake of clarity, we plot the difference between these quantities and their values when the carbon atom is located at the central grid-point
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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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... 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]: ...
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... 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. ...
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... 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. ...
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... 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). ...
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... 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.
