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Register a new userApplying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit
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Added by
Andreas Gr\\\"uneis
Publication date
2020
fields
Physics
and research's language is
English
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Modern electronic structure theories can predict and simulate a wealth of phenomena in surface science and solid-state physics. In order to allow for a direct comparison with experiment, such ab initio predictions have to be made in the thermodynamic limit, substantially increasing the computational cost of many-electron wave-function theories. Here, we present a method that achieves thermodynamic limit results for solids and surfaces using the gold standard coupled cluster ansatz of quantum chemistry with unprecedented efficiency. We study the energy difference between carbon diamond and graphite crystals, adsorption energies of water on h-BN, as well as the cohesive energy of the Ne solid, demonstrating the increased efficiency and accuracy of coupled cluster theory for solids and surfaces.
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Accelerating the calculations of finite-temperature thermodynamic properties is a major challenge for rational materials design. Reliable methods can be quite expensive, limiting their effective applicability in autonomous high-throughput workflows. Here, the 3-phonons quasi-harmonic approximation (QHA) method is introduced, requiring only three phonon calculations to obtain a thorough characterization of the material. Leveraging a Taylor expansion of the phonon frequencies around the equilibrium volume, the method efficiently resolves the volumetric thermal expansion coefficient, specific heat at constant pressure, the enthalpy, and bulk modulus. Results from the standard QHA and experiments corroborate the procedure, and additional comparisons are made with the recently developed self-consistent QHA. The three approaches - 3-phonons, standard, and self- consistent QHAs - are all included within the automated, open-source framework AFLOW, allowing automated determination of properties with various implementations within the same framework.
Classical turning surfaces of Kohn-Sham potentials, separating classically-allowed regions (CARs) from classically-forbidden regions (CFRs), provide a useful and rigorous approach to understanding many chemical properties of molecules. Here we calculate such surfaces for several paradigmatic solids. Our study of perfect crystals at equilibrium geometries suggests that CFRs are absent in metals, rare in covalent semiconductors, but common in ionic and molecular crystals. A CFR can appear at a monovacancy in a metal. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators. This classical picture is confirmed in the limits of extreme uniform compression of the internuclear distances, where all materials become metals without CFRs, and extreme expansion, where all materials become insulators with disconnected and widely-separated CARs around the atoms.
Recent calculations using coupled cluster on solids have raised discussion of using a $N^{-1/3}$ power law to fit the correlation energy when extrapolating to the thermodynamic limit, an approach which differs from the more commonly used $N^{-1}$ power law which is (for example) often used by quantum Monte Carlo methods. In this paper, we present one way to reconcile these viewpoints. Coupled cluster doubles calculations were performed on uniform electron gases reaching system sizes of $922$ electrons for an extremely wide range of densities ($0.1<r_s<100.0$) to study how the correlation energy approaches the thermodynamic limit. The data were corrected for basis set incompleteness error and use a selected twist angle approach to mitigate finite size error from shell filling effects. Analyzing these data, we initially find that a power law of $N^{-1/3}$ appears to fit the data better than a $N^{-1}$ power law in the large system size limit. However, we provide an analysis of the transition structure factor showing that $N^{-1}$ still applies to large system sizes and that the apparent $N^{-1/3}$ power law occurs only at low $N$.
Successful modern generalized gradient approximations (GGAs) are biased toward atomic energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves equilibrium properties of densely-packed solids and their surfaces.
We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.
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