Random phase approximation up to the melting point: Impact of anharmonicity and nonlocal many-body effects on the thermodynamics of Au

Abstract

Application of the generalized gradient corrected functional within standard density-functional theory results in a dramatic failure for Au, leading to divergent thermodynamic properties well below the melting point. By combining the upsampled thermodynamic integration using Langevin dynamics technique with the random phase approximation, we show that inclusion of nonlocal many-body effects leads to a stabilization and to an excellent agreement with experiment. Most present-day ab initio databases contain results from T = 0 K density-functional-theory (DFT) calculations using standard exchange-correlation functionals. This is a limitation in two respects: (a) First, materials development and application takes place at finite temperatures at which entropic contributions become important. In particular, anharmonic phonon-phonon excitations have been revealed to strongly modify materials properties, e.g., for dynamically unstable systems [2] or for defect formation [3]. (b) Second, standard functionals are known to have intrinsic deficiencies, e.g., for elements with nearly full electron shells. Hybrid functionals provide an improvement by introducing a fraction of exact exchange [4][5][6], but the corresponding mixing parameter is not always well defined, especially for composite systems. Further improvement requires also the correlation energy to include nonlocal many-body effects. A possible route utilizes the random phase approximation (RPA) within the adiabatic-connection-fluctuation-dissipation theorem (ACFDT) [7]. RPA has been successfully applied to various systems [8][9][10] and recent developments aim at improving the computational efficiency [11,12]. However, despite the various developments and applications, RPA has been employed only at T = 0 K, whereas the impact of nonlocal many-body interactions at finite temperatures has remained unknown.In this Rapid Communication, we compute the material properties of Au-a prototype closed shell element-using the RPA within the ACFDT formalism up to the melting point. This is made possible by advancing our previously introduced upsampled thermodynamic integration using Langevin dynamics (UP-TILD) technique [13] towards a combination of molecular dynamics simulations performed at the standard DFT level in conjunction with upsampled snapshots computed within RPA. We shall demonstrate that the inclusion of nonlocal many-body effects remedies the deficiencies introduced by standard DFT.We start by investigating the thermodynamics of Au within the Perdew-Burke-Ernzerhof generalized gradient approximation ) in conjunction with the projectoraugmented-wave (PAW) formalism [15] as implemented in VASP [16,17] using the newly designed GW-PAW potentials [10]. We concentrate on the heat capacity, which is a representative thermodynamic quantity. The state-of-the-art approach to calculate its temperature dependence includes electronic excitations in conjunction with the quasiharmonic approximation. We find that electronic excitations give a negligible contribution [18] due to ...

Improved method of calculatingab initiohigh-temperature thermodynamic properties with application to ZrC

“…The same behavior has been reported previously for Au [35], where the heat capacity calculated within the quasiharmonic approximation diverged in a similar manner for the GGA results. In that work it was found that the inclusion of anharmonic contributions only partially corrected this unphysical divergence, which could be fully removed by including a treatment of exchange and correlation within the random phase approximation (RPA).…”

Fast anharmonic free energy method with an application to vacancies in ZrC

“…There are a number of approaches in the literature to calculate the anharmonic vibrational properties of crystals, [1][2][3][4][12][13][14][15][16][17][18][19][20][21][22] including thermodynamic integration 23 (TI), which is the method used in this work. In TI the anharmonic part of the full Hamiltonian, E − E qh , is switched on with the parameter λ ∈ [0, 1], in this instance linearly as E mix (λ) = E qh + λ(E − E qh ).…”

Atomistic Modeling‐Based Design of Novel Materials

“…As discussed above, the inclusion of magnetic excitations and their impact on vibrational properties for magnetic materials such as CrN is crucial. Advancements beyond the above described approximations are being developed, for example, to treat defected and/or disordered systems (e.g., to account at elevated temperatures for thermodynamically driven creation of vacancies [126,144,157] or temperature-driven partitioning of substitutionally alloyed steels [158] ), the delicate interplay between various magnetic excitations (e.g., longitudinal spin fluctuations) and lattice vibrations (e.g., explicit anharmonic contributions) [135,136] or for predictions in multi-component systems, such as the new class of high entropy alloys. [45] Taking the magnetic contributions properly into account, the standard GGA approximation yielded T N ¼ 428K.…”

“…[38] These results demonstrate the predictive power of current theoretical approaches, which can be applied to many systems of practical interest, in particular in light of the nowadays available and ongoing increasing computational power. Advancements beyond the above described approximations are being developed, for example, to treat defected and/or disordered systems (e.g., to account at elevated temperatures for thermodynamically driven creation of vacancies [126,144,157] or temperature-driven partitioning of substitutionally alloyed steels [158] ), the delicate interplay between various magnetic excitations (e.g., longitudinal spin fluctuations) and lattice vibrations (e.g., explicit anharmonic contributions) [135,136] or for predictions in multi-component systems, such as the new class of high entropy alloys. [140,141,159,160] An important application field for "ab initio" thermodynamic data is using them as input for the CALPHAD method [161][162][163][164][165][166] implemented in simulation packages, such as Thermocalc [167] and Matcalc.…”