Rungs 1 to 4 of DFT Jacob's ladder: extensive test on the lattice constant, bulk modulus, and cohesive energy of solids (1603.01504v1)

Abstract: A large panel of old and recently proposed exchange-correlation functionals belonging to rungs 1 to 4 of Jacob's ladder of density functional theory are tested (with and without a dispersion correction term) for the calculation of the lattice constant, bulk modulus, and cohesive energy of solids. Particular attention will be paid to the functionals MGGA_MS2 [J. Sun et al., J. Chem. Phys. 138, 044113 (2013)], mBEEF [J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014)], and SCAN [J. Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] that are approximations of the meta-generalized gradient type and were developed with the goal to be universally good. Another goal is also to determine for which semilocal functionals and groups of solids it is beneficial (or not necessary) to use the Hartree-Fock exchange or a dispersion correction term.

Analysis of Exchange-Correlation Functionals on Solids Across Rungs of Density Functional Theory

The paper authored by Tran, Stelzl, and Blaha presents a comprehensive evaluation of exchange-correlation (XC) functionals from rungs 1 to 4 of Jacob's ladder within the framework of Kohn-Sham Density Functional Theory (DFT) with respect to their applicability to the lattice constant, bulk modulus, and cohesive energy of solids. The functionals span from the local density approximation (LDA) to generalized gradient approximation (GGA), meta-GGA (MGGA), hybrid functionals, and their variants incorporating dispersion corrections.

Testing Framework

Two distinctly categorized test sets were used: one comprising strongly bound solids and another including weakly bound systems. In aligning results with known experimental data and benchmark methods such as CCSD(T) and RPA, several notable functionals were analyzed:

• GGA functionals have been traditional choices for modeling solid properties. Despite their reasonable accuracy within certain contexts, this class perpetuates significant limitations, such as failing to accurately account for nonlocal electron correlation effects.
• MGGA functionals, particularly MGGA_MS2 and SCAN, have shown a marked ability to close the performance gap between solids’ predictive accuracy and their computational cost. These functionals leverage the kinetic energy density to augment performance for both intra-molecular and inter-molecular forces without necessarily requiring HF exchange, ensuring more universal applicability.
• Hybrid functionals are typically reserved for their improved bandgap predictions in semiconductors and insulators. However, their usage, especially in pure metallic systems, can cause misleading results, given the added computational overhead of HF exchange.
• Adding dispersion corrections like D3/D3(BJ) leads to remarkable improvements in capturing non-covalent interactions in both layered materials and molecular complexes, underscoring the importance of these corrections, particularly for systems where van der Waals forces predominate.

Numerical Observations

The paper highlights several key numerical insights:

• Among functionals without explicit dispersion corrections, MGGAs (notably SCAN and MGGA_MS2) surpass GGAs and even some hybrids in predicting structural properties such as lattice constants for both finite and extended systems.
• Dispersion corrected functionals—PBE-D3, PBE-D3(BJ), and their ilk—offer improved predictions across the board, with particular emphasis on rare-gas solids and interlayer interactions within graphite and h-BN.
• While hybrid functionals paired with dispersion terms manifest considerable potential for graphene and similar layered structures, their expanded computational cost remains a drawback.
• For weakly bound systems, an ordinary GGA or hybrid GGA without further adjustments underrepresents dispersion forces, a gap prominently addressed by modern functionals that include intrinsic nonlocal correlations or dispersion terms.

Theoretical and Practical Implications

From a theoretical perspective, these functionals, especially the advanced MGGAs and hybrid functionals augmented with van der Waals corrections, signify a shift towards methods that integrate increased molecular-like accuracy into the solid state model without drastically increasing computational expense. Practically, this underscores the need for choosing an XC functional based on the specific application domain, optimizing computational resources while attaining reliable predictions.

Speculation on Future AI Developments

As AI continues to impact computational chemistry, the demand for accurate yet efficient functionals grows. The synthesis of machine learning techniques with reliable functionals can pave the way for producing functionals with improved predictive power and generalization across varying chemical spaces.

Conclusion

This work aggregates an extensive and invaluable benchmark across multiple classes of functionals. It compartmentalizes the critical need for dispersion treatments in modeling molecular and solid-state systems, which customary functionals struggle to represent adequately. The discourse significantly informs chemists and material scientists on the tactical deployment of functionals concerning specific interactions, geometries, and electronic properties.