Abstract
We present a real-space method for performing the operations that involve the nonlocal parts of the Kohn-Sham Hamiltonian in a first-principles plane-wave total-energy calculation. In contrast to the conventional reciprocal-space formulation, where the number of operations required to compute the nonlocal contributions to the energies, forces, and stresses scales as the cube of the system size, the numerical work to compute these quantities with our real-space algorithm scales as the square of the number of atoms in the unit cell. The scheme, which can be applied to any potential expressible as a sum of separable terms, uses an approximate method to project the nonlocal potential on the core region of each atom. Errors introduced in the projection step are extremely well controlled and will not be a cause of problems in practical calculations. We have implemented the method in a conjugate-gradient total-energy program and, for illustrative purposes, demonstrate that the method produces excellent results on a two-atom cell of silicon.
Keywords
Hamiltonian (control theory)Separable spacePhysicsSpace (punctuation)Cube (algebra)ReciprocalAtom (system on chip)Work (physics)Total energyMathematicsMathematical analysisQuantum mechanicsComputer scienceMathematical optimizationGeometry
Affiliated Institutions
Related Publications
Analysis of separable potentials
Soft, fully separable ab initio pseudopotentials, introduced some years ago by Kleinman and Bylander [Phys. Rev. Lett. 48, 1425 (1982)], have proven to be very useful for large-...
Nonlocal pseudopotentials in molecular-dynamical density-functional theory: Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">SiO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
Silicon dioxide is fundamental in geology, in the electronic materials industry, and in the glass industry. We have carried out an ab initio total energy minimization study of t...
Variational Quantum Monte Carlo Nonlocal Pseudopotential Approach to Solids: Cohesive and Structural Properties of Diamond
A new method of calculating total energies of solids which uses nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented. By use o...
Separable dual-space Gaussian pseudopotentials
We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numeric...
<i>Ab initio</i>study of the ferroelectric transition in cubic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Pb</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">GeTe</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
In the substitutionally disordered narrow-gap semiconductor Pb1−xGexTe, a finite-temperature cubic-rhombohedral transition appears above a critical concentration x ≈ 0.005. As a...
Publication Info
- Year
- 1991
- Type
- article
- Volume
- 44
- Issue
- 23
- Pages
- 13063-13066
- Citations
- 143
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
143
OpenAlex
Cite This
R. D. King-Smith,
M. C. Payne,
J. S. Lin
(1991).
Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations.
Physical review. B, Condensed matter
, 44
(23)
, 13063-13066.
https://doi.org/10.1103/physrevb.44.13063
Identifiers
- DOI
- 10.1103/physrevb.44.13063