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Register a new userFast periodic Gaussian density fitting by range separation
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We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real space and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method -- which we call range-separated GDF (RSGDF) -- scales sublinearly to linearly with the number of $k$-points for small to medium-sized $k$-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about $10$-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about $10^{-5}~E_{textrm{h}}$ in the converged Hartree-Fock energy with default auxiliary basis sets and can be systematically reduced by increasing the size of the auxiliary basis with little extra work. [The article has been accepted by The Journal of Chemical Physics.]
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We introduce a mixed density fitting scheme that uses both a Gaussian and a plane-wave fitting basis to accurately evaluate electron repulsion integrals in crystalline systems. We use this scheme to enable efficient all-electron Gaussian based periodic density functional and Hartree-Fock calculations.
The evaluation of exact (Hartree--Fock, HF) exchange operator is a crucial ingredient for the accurate description of electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient formulation of periodic HF exchange in LCAO representation presented here is based on the concentric atomic density fitting (CADF) approximation, a domain-free local density fitting approach in which the product of two atomic orbitals (AOs) is approximated using a linear combination of fitting basis functions centered at the same nuclei as the AOs in that product. Significant reduction in the computational cost of exact exchange is demonstrated relative to the conventional approach due to avoiding the need to evaluate four-center two-electron integrals, with sub-millihartree/atom errors in absolute Hartree-Fock energies and good cancellation of fitting errors in relative energies. Novel aspects of the evaluation of the Coulomb contribution to the Fock operator, such as the use of real two-center multipole expansions and spheropole-compensated unit cell densities are also described.
We introduce an approximation to the short-range correlation energy functional with multide-terminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density, the density gradient, and the on-top pair density, which locally interpolates between the standard Perdew-Burke-Ernzerhof correlation functional at vanishing range-separation parameter and the known exact asymptotic expansion at large range-separation parameter. When combined with (selected) configuration-interaction calculations for the long-range wave function, this approximation gives accurate dissociation energy curves of the H2, Li2, and Be2 molecules, and thus appears as a promising way to accurately account for static correlation in range-separated density-functional theory.
We present a simple, top-down approach for the calculation of minimum energy consumption of electrosorptive ion separation using variational form of the (Gibbs) free energy. We focus and expand on the case of electrostatic capacitive deionization (CDI), and the theoretical framework is independent of details of the double-layer charge distribution and is applicable to any thermodynamically consistent model, such as the Gouy-Chapman-Stern (GCS) and modified Donnan (mD) models. We demonstrate that, under certain assumptions, the minimum required electric work energy is indeed equivalent to the free energy of separation. Using the theory, we define the thermodynamic efficiency of CDI. We explore the thermodynamic efficiency of current experimental CDI systems and show that these are currently very low, less than 1% for most existing systems. We applied this knowledge and constructed and operated a CDI cell to show that judicious selection of the materials, geometry, and process parameters can be used to achieve a 9% thermodynamic efficiency (4.6 kT energy per removed ion). This relatively high value is, to our knowledge, by far the highest thermodynamic efficiency ever demonstrated for CDI. We hypothesize that efficiency can be further improved by further reduction of CDI cell series resistances and optimization of operational parameters.
By combining density-functional theory (DFT) and wave function theory (WFT) via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction (SCI) known as emph{configuration interaction using a perturbative selection made iteratively} (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of $mu=0.5$~bohr$^{-1}$ provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.
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