We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.
Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. We evaluate our model against different families of XC approximations and show that, for non-empirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define a nov…
In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well-suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The la…
Adaptive Expansions of the Optimized Effective Potential in Physically Motivated Response Spaces
Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń（托伦哥白尼大学物理、天文学与信息学学院物理研究所）；Institute of Advanced Studies, Nicolaus Copernicus University in Toruń（托伦哥白尼大学高等研究院）
Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method
我们介绍了一个轨道优化的双杂交（DH）计划使用优化有效势（OEP）方法。使用对应于完整的交换相关能量表达式的局部势优化轨道，包括二阶M{\displaystyle M {\math}ller-Plesset（MP2）相关贡献。我们已经实现了一个单参数版本的基于OEP的自洽DH计划使用BLYP密度泛函近似，并将其与相应的非自洽DH计划进行比较，用于计算一些闭壳层原子和分子。虽然基于OEP的自洽性并没有为基态总能量和电离势的计算提供任何改进，但它确实提高了电子亲和势的准确性，并恢复了LUMO轨道能量与中性激发能相关的含义。此外，基于OEP的自洽DH方案提供了相当准确的交换相关势和相关密度。
We determine the correlation energy of BN, SiO$_2$ and ice polymorphs employing a recently developed RPAx (random phase approximation with exchange) approach. The RPAx provides larger and more accurate polarizabilities as compared to the RPA, and captures effects of anisotropy. In turn, the correlation energy, defined as an integral over the density-density response function, gives improved binding energies without the need for error cancellation. Here, we demonstrate that these features are crucial for predicting the relative energies between low- and high-pressure polymorphs of different coo…
Over the past few years it has been pointed out that direct inversion of accurate but approximate ground state densities leads to Kohn-Sham exchange-correlation (xc) potentials that can differ significantly from the exact xc potential of a given system. On the other hand, the corresponding wavefunction based construction of exchange-correlation potential as done by Baerends et al. and Staroverov et al. obviates such problems and leads to potentials that are very close to the true xc potential. In this paper, we provide an understanding of why the wavefunction based approach gives the exchange-…
We extend the range-separated double-hybrid RSH+MP2 method [J. G. Angyan et al., Phys. Rev. A 72, 012510 (2005)], combining long-range HF exchange and MP2 correlation with a short-range density functional, to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter $μ=0.5$ bohr$^{-1}$, we find that self-co…
Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital optimized DFT (OO-DFT) with the spin-free exact two-component (X2C) model for scalar relativistic effects, to study K-edge spectra of third period elements. OO-DFT/X2C is found to be quite accurate at predicting energies, yielding $\sim 0.5$ eV RMS error vs experiment with the modern SCAN (and related) functionals. This marks a significant improvement over the $>50$ eV deviations that are typical for the popular time-dependent DFT (TDDFT) approach. Consequently, …
We propose a new generalised Kohn-Sham or constrained hybrid method, where the exchange potential is the (equally weighted) average of the nonlocal Fock exchange term and the self-interaction-corrected exchange potential, as obtained from our constrained minimisation method of semi-local approximations. The new method gives an accurate single-particle eigenvalue spectrum with an average deviation between (the negative of) the valence orbital eigenvalues and the experimental ionisation potentials of about 0.5eV, while the deviation of core orbitals is within 2eV. The improvement in the eigenval…
In this work, we propose the Prony fitting decomposition (PFD) as an accurate and efficient exponential series method, applicable to arbitrary interacting bath correlation functions. The resulting hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in extremely low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.
Due to several attractive features, the meta-generalized-gradient approximations (meta-GGAs) are considered to be the most advanced and potentially accurate semilocal exchange-correlation functionals in the rungs of the Jacob's ladder of Density Functional Theory. So far, several meta-GGA are proposed by fitting to the test sets or/and satisfying as many as known exact constraints. Although the density overlap is treated by modern meta-GGA functionals efficiently, for non-covalent interactions, a long-range dispersion correction is essential. In this work, we assess the benchmark performance o…
We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent setting. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density funct…
Machine learning (ML) has recently gained attention as a means to develop more accurate exchange-correlation (XC) functionals for density functional theory, but functionals developed thus far need to be improved on several metrics, including accuracy, numerical stability, and transferability across chemical space. In this work, we introduce a set of nonlocal features of the density called the CIDER formalism, which we use to train a Gaussian process model for the exchange energy that obeys the critical uniform scaling rule for exchange. The resulting CIDER exchange functional is significantly …
We have studied the correlation potentials produced by various adiabatic connection models (ACM) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials, and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-inte…
