A new density functional theory (DFT) exchange-correlation functional for the exploration of reaction mechanisms is proposed. This new functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a general-purpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct `back' the excess exact exchange mixing for ground-state properties, possibly simulating variable exchange.
Accurately predicting key combustion phenomena in reactive-flow simulations, e.g., lean blow-out, extinction/ignition limits and pollutant formation, necessitates the use of detailed chemical kinetics. The large size and high levels of numerical stiffness typically present in chemical kinetic models relevant to transportation/power-generation applications make the efficient evaluation/factorization of the chemical kinetic Jacobian and thermochemical source-terms critical to the performance of reactive-flow codes. Here we investigate the performance of vectorized evaluation of constant-pressure…
Since the seminal works of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting Kinetic Energy, $T_s[ρ]$, the subject of this work. The typical paradigm is to first approximate the energy functional, and then take its functional derivative, $\frac{δT_s[ρ]}{δρ(r)}$, yielding a potential that can be used in orbital-free DFT, or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional …
Development of the electronic kinetic-energy density functional is a subject of major interest in theoretical physics and chemistry. In this work, the nonlocal kinetic-energy functional is developed in terms of the response function for the molecular system to realize the orbital free density-functional theory(OF-DFT) to be utilized in the hybrid QM/MM(quantum mechanical/molecular mechanical) method. The present approach shows a clear contrast to the previous functionals where the homogeneous electron gas serves as a reference to build the response function. As a benchmark test we apply the me…
We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple approximation strategies lead to very accurate results. Here we promote the kinetic-energy density to a fundamental variable along side the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-e…
Kinetic energy density functionals (KEDFs) are central to orbital-free density functional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We point out a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows tha…
We investigate whether the entropic regularisation of the strictly-correlated-electrons problem can be used to build approximations for the kinetic correlation energy functional at large coupling strengths and, more generally, to gain new insight in the problem of describing and understanding strong correlation within Density Functional Theory.
We present a non-decomposable approximation for the non-additive non-interacting kinetic energy (NAKE) for covalent bonds based on the exact behavior of the von Weizsäcker (vW) functional in regions dominated by one orbital. This covalent approximation (CA) seamlessly combines the vW and the Thomas-Fermi (TF) functional with a switching function of the fragment densities constructed to satisfy exact constraints. It also makes use of ensembles and fractionally-occupied spin-orbitals to yield highly accurate NAKE for stretched bonds while outperforming other standard NAKE approximations near equ…
Orbital-Free Density Functional Theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the approximation made for the kinetic energy (KE) functional. To date, the most accurate KE functionals are non-local functionals based on the linear-response kernel of the homogeneous electron gas, i.e. the jellium model. Here, we use the linear-response kernel of the jellium-with-gap model, to construct a simple non-local KE functional (named KGAP) which depends …
We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-Generalized Gradient Approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory. Both types of functionals can thus be subsumed as special cases of a novel functional form that is naturally placed on the third rung of Jacob's ladder. Moreover, the kinetic energy tensor is related to the exchange hole curvature, is gauge invariant, and has very clearcut $N$-representability conditions. The latter conditions enable the definition of effecti…
A simple, novel, non-empirical, constraint-based orbital-free generalized gradient approximation (GGA) non-interacting kinetic energy density functional is presented along with illustrative applications. The innovation is adaptation of constraint-based construction to the essential properties of pseudo-densities from the pseudo-potentials that are essential in plane-wave-basis {\it ab initio} molecular dynamics. This contrasts with constraining to the qualitatively different Kato-cusp-condition densities. The single parameter in the new functional is calibrated by satisfying Pauli potential po…
A new approach to calculate the vibrational distribution function of molecules in a medium providing energy for vibrational excitation is proposed and demonstrated. The approach is an improvement of solution methods based on the drift-diffusion Fokker-Planck (FP) equation for a double differentiable function representing the vibrational populations on a continuum internal energy scale. A self-consistent numerical solution avoids approximations used in previous analytical solutions. The dissociation flux, a key parameter in the FP equation, is fixed using the kinetics of molecular dissociation …
Laplacian-level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory
A new Green's function formalism for kinetic energy density functional for atomic and molecular system: Emergence of $N-$dependence using model potentials
本文提出一种基于 Green 函数的精确动能密度泛函形式体系，通过新颖微扰级数支持系统改进，并在模型势中再现正确的动能 $N$-依赖性。
Local Behavior of the First-Order Gradient Correction to the Thomas-Fermi Kinetic Energy Functional
由Haq、Chattaraj和Deb（Chem. Phys. Lett. Vol.81，8031，1984）已经通过评估总动能和局部动能密度来研究。为了测试动能密度，我们通过品质因数来评估其与精确结果的偏差，质量因子是一个比其相对误差更好地反映泛函质量的参数。该研究是在两个不同的系统上进行的：轻原子（Z=18）和限制在库仑型势中的费米子的非相互作用模型。结果表明，这种近似比一般的广义梯度近似半局部动力学密度泛函具有很低的相对误差和更好的局部性质。
The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $ρ_{\rm B}$ and $ρ_{\rm tot} = ρ_{\rm A} + ρ_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singular…
The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizsäcker functional in the region of low density/high density gradient. This behavior is crucial when these functionals are employed in subsystem DFT simulations to approximate the nonadditive kinetic energy. We propose a GGA nonadditive kinetic energy functional which mimics the good behavior of nonlocal functionals retaining the computational complexity of typical semilocal functionals. The new functional reproduces Kohn-Sham DFT and…
Approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversi…
First-principles calculation of the standard formation enthalpy, $ΔH_f^\circ$ (298K), in such large scale as required by chemical space explorations, is amenable only with density functional approximations (DFAs) and some composite wave function theories (cWFTs). Alas, the accuracies of popular range-separated hybrid, `rung-4' DFAs, and cWFTs that offer the best accuracy-vs.-cost trade-off have as yet been established only for datasets predominantly comprising small molecules, hence, their transferability to larger datasets remains vague. In this study, we present an extended benchmark dataset…
Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals
The distribution of noncollinear magnetism in an electronic system provides information about the kinetic energy as well as some kinetic energy densities. Two different everywhere-positive kinetic densities related to the Schrödinger--Pauli Hamiltonian are considered. For one-electron systems described by a single Pauli spinor, the electron density, spin density and current density completely determines these kinetic energy densities. For many-electron systems, lower bounds on the kinetic energy densities are proved. These results generalize a lower bound due to von Weizsäcker, which is based …
Kohn-Sham Kinetic Energy Density in the Nuclear and Asymptotic Regions: Deviations from the Von Weizsäcker Behavior and Applications to Density Functionals
For orbital-free {\it ab initio} molecular dynamics, especially on systems in extreme thermodynamic conditions, we provide the first pseudo-potential-adapted generalized gradient approximation (GGA) functional for the non-interacting free energy. This is achieved by systematic finite-temperature extension of our recent LKT ground state non-interacting kinetic energy GGA functional (Phys. Rev. B \textbf{98}, 041111(R) (2018)). We test the performance of the new functional first via static lattice calculations on crystalline aluminum and silicon. Then we compare deuterium equation of state resul…
By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy. Even though, semilocal nonadditive functionals find a broad range of applications, their accuracy is somewhat limited especially for those systems where achieving balance between exchange-correlation interactions on one side and nonadditive kinetic energy on the other is crucial. In eQE 2.0, we improve drama…
The quest for an approximate yet accurate kinetic energy density functional is central to the development of orbital-free density functional theory. While a recipe for closed-shell systems has been proposed earlier, we have shown that it cannot be naïvely extended to open-shell atoms. In this present work, we investigated the efficacy of an ad-hoc recipe to compute the kinetic energy densities for open-shell atoms by extending the methodology used for closed-shell systems. We have also analyzed the spin-dependent features of Pauli potentials derived from two previously devised enhancement fact…
We show how to incorporate the possibility of kinetic control in the conceptual Density Functional Theory formalism. This allow us to prove that the hard/soft acid/base principle will likely fail when the reactions are not thermodynamically-driven.
