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Register a new userComment on Density and Physical Current Density Functional Theory by Xiao-Yin Pan and Viraht Sahni, Int. J. Quant. Chem. 110, 2833 (2010)
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This comment criticizes the above paper by Xiao-Yin Pan and Viraht Sahni. It is shown that their formulation of Physical Current Density Functional Theory is, at best, a garbled reformulation of the Vignale-Rasolt current-density functional theory, and, at worst, a potential source of mistakes insofar as it complicates the formulation of the variational principle and prevents the constrained search construction of the universal functional.
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Exchange interactions are a manifestation of the quantum mechanical nature of the electrons and play a key role in predicting the properties of materials from first principles. In density functional theory (DFT), a widely used approximation to the exchange energy combines fractions of density-based and Hartree-Fock (exact) exchange. This so-called hybrid DFT scheme is accurate in many materials, for reasons that are not fully understood. Here we show that a 1/4 fraction of exact exchange plus a 3/4 fraction of density-based exchange is compatible with a correct quantum mechanical treatment of the exchange energy of an electron pair in the unpolarized electron gas. We also show that the 1/4 exact-exchange fraction mimics a correlation interaction between doubly-excited electronic configurations. The relation between our results and trends observed in hybrid DFT calculations is discussed, along with other implications.
We discuss the relationship between modern time-dependent density functional theory and earlier time-period
Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs. This code hosts the development of joint density-functional theory (JDFT) that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.
Due to their current and future technological applications, including realisation of water filters and desalination membranes, water adsorption on graphitic sp$^{2}$-bonded carbon is of overwhelming interest. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and non-covalent interactions in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed textbf{WaC18}), which includes a single water molecule interacting with a broad range of carbon structures, and various bulk (3D) and two dimensional (2D) ice polymorphs. The performance of 28 approaches, including semi-local exchange-correlation functionals, non-local (Fock) exchange contributions, and long-range van der Waals (vdW) treatments, are tested by computing the deviations from the reference interaction energies. The calculated mean absolute deviations on the WaC18 set depends crucially on the DFT approach, ranging from 135 meV for LDA to 12 meV for PBE0-D4. We find that modern vdW corrections to DFT significantly improve over their precursors. Within the 28 tested approaches, we identify the best performing within the functional classes of: generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, which are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, respectively.
A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation energies, the total energies, and the ionization energies of test atoms and molecules; and despite the unique simplicities, the functionals accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11. Therefore, we propose that, as guided by the simplicities and supported by the accuracies, the correlation energy is the energy that locally tends to drive the system toward the uniform electron gas.
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