Electron Correlations in Molecules and Solids

Jozef T. Devreese, F. Brosens

N. H. March

Rodney J. Bartlett

P. Fulde, H. Stoll, K. Kladko

Gaurav Harsha, Vibin Abraham, Dominika Zgid

For molecules and solids containing heavy elements, accurate electronic-structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all-electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis sets, particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.

Lizhong Fu, Yangjun Wu, Honghui Shang +1 more

Recent advancements in neural networks have led to significant progress in addressing many-body electron correlations in small molecules and various physical models. In this work, we propose QiankunNet-Solid, which incorporates periodic boundary conditions into the neural network quantum state (NNQS) framework based on generative Transformer architecture along with a batched autoregressive sampling (BAS) method, enabling the effective ab initio calculation of real solid materials. The accuracy of this method is demonstrated in one-, two-, and three-dimensional periodic systems, with results comparable to those of full configuration interaction and coupled-cluster method, even in the strongly correlated regime. Furthermore, we compute the band structures and density of states for silicon crystal. The successful incorporation of periodic boundary conditions into the NNQS framework through QiankunNet-Solid opens up new possibilities for the accurate and efficient study of electronic structure properties in solid-state physics.