Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Energy densities in the strong-interaction limit of density functional theory

We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals.Comment: 12 page

Diffusion Monte Carlo Study of Para -Diiodobenzene Polymorphism Revisited

We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of p-DIB molecular crystal polymorphism. [J. Phys. Chem. Lett. 2010, 1, 1789-1794] We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest which are currently feasible using the resources of the K computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1×1×1) simulation cell considerably. We therefore repeated our DMC simulations with a 1×3×3 simulation cell, which is the largest such calculation to date. We used a DFT nodal surface generated with the PBE functional and we accumulated statistical samples with ∼6.4×105 core-hours for each polymorph. Our final results predict a polymorph stability consistent with experiment, but indicate that results in our previous paper were somewhat fortuitous. We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are far larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T-move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.Chemistry and Chemical Biolog