Efficient pseudopotentials for plane-wave calculations¶
Why this mattered¶
Troullier and Martins mattered because they made norm-conserving pseudopotentials substantially more practical for plane-wave density-functional calculations. Earlier norm-conserving pseudopotentials had the formal advantage of transferability, but many were too “hard”: their rapidly varying pseudo-wavefunctions required large plane-wave cutoffs, especially for first-row atoms, transition metals, and rare-earth elements. The paper’s central contribution was a systematic construction of smooth first-principles pseudopotentials that retained norm conservation while sharply reducing basis-set cost. In effect, it helped turn plane-wave pseudopotential DFT from a method best suited to relatively simple solids into a more broadly usable computational framework.
The shift was not merely technical efficiency. By lowering the cost of converged plane-wave calculations for chemically and structurally difficult systems, Troullier-Martins pseudopotentials expanded what could be treated routinely: covalent materials such as diamond and quartz, transition-metal systems such as copper, oxides such as rutile, and even challenging rare-earth cases such as cerium. This supported a broader movement in the 1990s toward predictive first-principles materials modeling, where total energies, forces, structures, phonons, defects, and surfaces could be computed with controlled convergence rather than fitted empirical potentials.
Its influence is visible in the infrastructure of later electronic-structure work. Troullier-Martins pseudopotentials became a standard reference point for plane-wave codes and pseudopotential libraries, alongside later developments such as separable Kleinman-Bylander forms, ultrasoft pseudopotentials, and the projector augmented-wave method. Those later approaches relaxed or reworked parts of the norm-conserving framework to gain still more efficiency, but they addressed the same bottleneck the 1991 paper made unavoidable: the quality of the pseudopotential largely determines whether plane-wave first-principles simulation is merely possible or practically scalable.
Abstract¶
We present a simple procedure to generate first-principles norm-conserving pseudopotentials, which are designed to be smooth and therefore save computational resources when used with a plane-wave basis. We found that these pseudopotentials are extremely efficient for the cases where the plane-wave expansion has a slow convergence, in particular, for systems containing first-row elements, transition metals, and rare-earth elements. The wide applicability of the pseudopotentials are exemplified with plane-wave calculations for copper, zinc blende, diamond, \ensuremath{\alpha}-quartz, rutile, and cerium.
Related¶
- cite → Ground State of the Electron Gas by a Stochastic Method — Troullier and Martins cite Ceperley and Alder's quantum Monte Carlo electron-gas results as the source of correlation energies used in density-functional calculations.
- cite → Unified Approach for Molecular Dynamics and Density-Functional Theory — Troullier and Martins build norm-conserving pseudopotentials for the plane-wave density-functional molecular dynamics framework introduced by Car and Parrinello.
- cite → Self-Consistent Equations Including Exchange and Correlation Effects — Troullier and Martins rely on the Kohn-Sham self-consistent density-functional equations as the electronic-structure framework for their pseudopotentials.
- enables → Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility — Efficient plane-wave pseudopotentials enabled tractable density-functional simulations of phosphorene's atomic and electronic structure.
- cite ← Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility — The phosphorene simulations rely on Vanderbilt ultrasoft pseudopotentials to make plane-wave electronic-structure calculations computationally efficient.
- cite ← Projector augmented-wave method — The PAW method responds to Troullier-Martins efficient norm-conserving pseudopotentials by offering an all-electron reconstruction with plane-wave efficiency.
- enables ← Ground State of the Electron Gas by a Stochastic Method — Diffusion quantum Monte Carlo supplied stochastic ground-state electronic benchmarks used to validate efficient plane-wave pseudopotentials.
- enables ← Unified Approach for Molecular Dynamics and Density-Functional Theory — Car-Parrinello combined molecular dynamics with density-functional theory in plane-wave calculations, motivating pseudopotentials optimized for efficient plane-wave use.
- enables ← Self-Consistent Equations Including Exchange and Correlation Effects — Kohn-Sham self-consistent density-functional equations provided the electronic-structure framework in which plane-wave pseudopotentials are constructed and tested.