Compressive sensing lattice dynamics. I. General formalism

Abstract

Ab initio calculations have been successfully used for evaluating lattice dynamical properties of solids within the (quasi-)harmonic approximation (i.e., assuming non-interacting phonons with infinite lifetimes), but it remains difficult to treat anharmonicity in all but the simplest compounds. We detail a systematic information theory based approach to deriving ab initio anharmonic force constants: compressive sensing lattice dynamics (CSLD). The non-negligible terms that are necessary to reproduce the first-principles calculated interatomic forces are automatically selected by minimizing the 1 norm (sum of absolute values) of the scaled force constants. By using efficient sampling of the configuration space using a modest number of atomic configurations with quasirandom displacements, CSLD is well suited for deriving accurate anharmonic potentials for complex multicomponent compounds with large unit cells. We demonstrate the power and generality of CSLD by calculating the phonon lifetimes and thermal transport properties of Type-I Si clathrates. arXiv:1805.08904v2 [physics.comp-ph]

Efficient construction of linear models in materials modeling and applications to force constant expansions

“…The latter perform consistently better than the second-order-only models. The inclusion of a few third-order terms thus stabilizes the extraction of the second-order FCs, an observation that has also been made in other situations 9,15 . These terms enable one to account for anharmonicity in the vicinity of the reference positions that would otherwise be effectively included in the second-order FCs.…”

“…Instead, one can consider general displacement patterns, involving many (or all) atoms in the supercell, and then employ regression techniques to reconstruct the underlying FCs. This approach has been shown to produce accurate higher order FCs 1,7,9,10,[30][31][32][33] but can also be used to construct effective FC models 20,21,30,34 . The force acting on atom i along α can be written as…”

“…The usefulness of regression with regularization for the construction of physical models has been demonstrated, using the least absolute shrinkage and selection operator (LASSO) 5 as well as the split-Bregman technique [6][7][8][9][10] . There is, however, a much larger pool of potentially useful regression techniques, including various other forms of regularization and feature selection.…”

“…This direct enumeration scheme becomes, however, tedious or impractical for larger systems (e.g., point defects, interfaces or nanoparticles [16][17][18] ) and/ or materials that require expansions beyond third order (e.g., metastable phases of transition metals or oxides 19 ). Accordingly linear regression techniques have been applied including ordinary least squares (OLS) 1,[20][21][22] , LASSO 5 , and split-Bregman 7,9 . As noted above, there are various other linear regression techniques and feature selection algorithms that could be suitable for FC regression such as recursive feature elimination (RFE), automatic relevance determination regression (ARDR), and adaptive LASSO (ad-LASSO).…”

Microscopic mechanism of unusual lattice thermal transport in TlInTe2

“…To renormalize the phonon frequencies at finite temperature, and to calculate the lattice thermal conductivity (κ l ) using the PBTE, an accurate estimation of anharmonic IFCs, namely the third-order and fourth-order IFCs are required. We obtain these anharmonic IFCs using the compressive sensing lattice dynamics (CSLD) method 28,29,65,66 using 2 × 2 × 2 supercell and 6 × 6 × 6 Γ-centered k-point mesh. While constructing the third and fourth order IFCs, a cut-off radius (r c ) is chosen, above which all three-body and four-body atomic interactions are discarded, respectively.…”