TY  - JOUR
PB  - American Physical Society
ID  - 10.1103/PhysRevB.54.11169
DO  - 10.1103/PhysRevB.54.11169
TI  - Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
PY  - 1996/10/15/
UR  - https://link.aps.org/doi/10.1103/PhysRevB.54.11169
JF  - Physical Review B
JA  - Phys. Rev. B
J1  - PRB
VL  - 54
IS  - 16
SP  - 11169
EP  - 11186
A1  - Kresse, G.
AU  - Furthmüller, J.
AB  - We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay’s DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order N3atoms operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay’s scheme. A special ‘‘metric’’ and a special ‘‘preconditioning’’ optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order N2atoms scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. © 1996 The American Physical Society.
ER  -

TY  - JOUR
T1  - Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
AU  - Kresse, G.
AU  - Furthmüller, J.
JO  - Computational Materials Science
VL  - 6
IS  - 1
SP  - 15
EP  - 50
PY  - 1996
DA  - 1996/07/01/
SN  - 0927-0256
DO  - https://doi.org/10.1016/0927-0256(96)00008-0
UR  - https://www.sciencedirect.com/science/article/pii/0927025696000080
AB  - We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
ER  - 

TY  - JOUR
PB  - American Physical Society
ID  - 10.1103/PhysRevB.59.1758
DO  - 10.1103/PhysRevB.59.1758
TI  - From ultrasoft pseudopotentials to the projector augmented-wave method
PY  - 1999/01/15/
UR  - https://link.aps.org/doi/10.1103/PhysRevB.59.1758
JF  - Physical Review B
JA  - Phys. Rev. B
J1  - PRB
VL  - 59
IS  - 3
SP  - 1758
EP  - 1775
A1  - Kresse, G.
AU  - Joubert, D.
AB  - The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blöchl’s projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules (H2,H2O,Li2,N2,F2,BF3,SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
ER  -