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Register a new userAn orbital-free density functional method based on inertial fields
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In this paper we revisit the Levy-Perdew-Sahni equation. We establish that the relation implicitly contains the conservation of energy density at every point of the system. The separate contributions to the total energy density are described in detail, and it is shown that the key difference to standard density functional methods is the existence of a general exchange-correlation potential, which does not explicitly depend on electron charge. We derive solutions for the hydrogen-like atoms and analyse local properties. It is found that these systems are stable due to the existence of a vector potential ${bf A}$, related to electron motion, which leads to two general effects: (i) The root of the charge density acquires an additional complex phase; and (ii) for single electrons, the vector potential cancels the effect of electrostatic repulsions. We determine the density of states of a free electron gas based on this model and find that the vectorpotential also accounts for the Pauli exclusion principle. Implications of these results for direct methods in density functional theory are discussed. It seems that the omission of vector potentials in formulating the kinetic energy density functionals may be the main reason that direct methods so far are not generally applicable. Finally, we provide an orbital free self-consistent formulation for determining the groundstate charge density in a local density approximation.
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Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of non-local functionals, possibly employing system dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that instead properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian-level of theory, can indeed achieve similar accuracy as non-local functionals and can be accurate for both metals and semiconductors, without the need of system-dependent parameters.
We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are two fold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10~meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
In first-principles calculations, hybrid functional is often used to improve accuracy from local exchange correlation functionals. A drawback is that evaluating the hybrid functional needs significantly more computing effort. When spin-orbit coupling (SOC) is taken into account, the non-collinear spin structure increases computing effort by at least eight times. As a result, hybrid functional calculations with SOC are intractable in most cases. In this paper, we present an approximate solution to this problem by developing an efficient method based on a mixed linear combination of atomic orbital (LCAO) scheme. We demonstrate the power of this method using several examples and we show that the results compare very well with those of direct hybrid functional calculations with SOC, yet the method only requires a computing effort similar to that without SOC. The presented technique provides a good balance between computing efficiency and accuracy, and it can be extended to magnetic materials.
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly-bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be$_2$ and Ne$_2$.
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