Gaussian-Based Coupled-Cluster Theory for Solids
The paper examines the implementation of Gaussian-based coupled-cluster (CC) theory for calculating the ground state and band structure properties of three-dimensional solids, specifically diamond and silicon. These materials serve as model covalent semiconductors, providing a robust benchmark for computational methods in materials science.
Methodology Overview
The authors employ Gaussian-based atomic orbitals to perform CC calculations for solids, presenting a detailed framework for handling integrals and employing Hartree-Fock (HF) methods within periodic systems. The approach is distinguished by sampling the Brillouin zone extensively with up to 64 k-points and using norm-conserving pseudopotentials alongside polarized double- and triple-zeta basis sets, culminating in computational tasks involving as many as 256 electrons distributed across 2,176 orbitals.
Density Functional and Wavefunction Methods
While density functional theory (DFT) is a staple in computational materials science, especially for weakly correlated systems, this paper emphasizes wavefunction-based techniques from quantum chemistry for condensed-phase materials. These methods, including time-dependent HF and second-order M\o ller-Plesset perturbation theory (MP2), are now applied to assess properties in periodic systems, demonstrating superior predictive capabilities compared to DFT in certain regimes, particularly for charge excitations manifesting in band structures.
Ground-State CCSD and Excited-State EOM-CCSD
The paper deploys CCSD theory for ground states and excited-state equation-of-motion CCSD (EOM-CCSD) for predicting quasiparticle band structures. EOM-CCSD distinguishes itself by providing a more accurate treatment of charged excitations, which are crucial for understanding material band gaps and electronic properties. Intriguingly, the EOM-CCSD approach reveals spectral function behaviors and eliminates fictive plasmaron poles noted in GW approximations, presenting significant improvements in treating excitations coupled to bosonic plasmon dynamics, especially in metallic environments.
Numerical Results and Convergence
The calculations highlight a clear trajectory towards convergence with respect to basis sets and Brillouin zone sampling. For diamond, the ground-state calculation indicates an extrapolated MP2 correlation energy per unit cell of -8.36 eV and a CCSD correlation energy of -7.86 eV, aligning closely with prior studies utilizing different computational frameworks. The cohesive energy results show robust alignment against experimental values, providing confidence in the predicted structural and energetic properties.
In the field of excited states, the indirect band gap predictions for diamond and silicon closely approximate experimental data, offering 5.37 eV for diamond and 1.19 eV for silicon post k-point mesh convergence. Highlighting the computational fidelity, EOM-CCSD demonstrations are credited with aligning predicted values substantially better than MP2, while self-consistent GW presents a typical underestimation.
Implications and Future Research Directions
The presented work opens avenues for routine application of coupled-cluster calculations to weakly correlated solids, where accuracy in predicting electronic structures is paramount. Future investigation is anticipated to focus on refining the interplay of pseudopotential and all-electron approximations, expanding basis set optimization for coupled-cluster methodologies, and integrating perturbative corrections such as CCSD(T) for increased precision.
Ultimately, this research paves the way for integrating reliable quantum chemical wavefunction methods into the computational toolkit for materials science, suggesting promising outcomes for high fidelity prediction in semiconductor and potentially metallic systems.