Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

We present ab initio quantum-mechanical molecular-dynamics simulations of the liquid-metal--amorphous-semiconductor transition in Ge. Our simulations are based on (a) finite-temperature density-functional theory of the one-electron states, (b) exact energy minimization and hence calculation of the exact Hellmann-Feynman forces after each molecular-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nos\'e dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows us to perform simulations over more than 30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liquid and amorphous Ge in very good agreement with experiment. The simulation allows us to study in detail the changes in the structure-property relationship through the metal-semiconductor transition. We report a detailed analysis of the local structural properties and their changes induced by an annealing process. The geometrical, bonding, and spectral properties of defects in the disordered tetrahedral network are investigated and compared with experiment.

Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium.

CASTEP Computer program / Density functional theory / Pseudopotentials / ab initio study / Plane-wave method / Computational crystallography Abstract. The CASTEP code for first principles electro- nic structure calculations will be described. A brief, non- technical overview will be given and some of the features and capabilities highlighted. Some features which are un- ique to CASTEP will be described and near-future devel- opment plans outlined.

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First principles methods using CASTEP

We have developed and implemented a selfconsistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical linear combination of atomic orbitals basis set, which includes multiple-zeta and polarization orbitals. Exchange and correlation are treated with the local spin density or generalized gradient approximations. The basis functions and the electron density are projected on a real-space grid, in order to calculate the Hartree and exchange-correlation potentials and matrix elements, with a number of operations that scales linearly with the size of the system. We use a modified energy functional, whose minimization produces orthogonal wavefunctions and the same energy and density as the Kohn-Sham energy functional, without the need for an explicit orthogonalization. Additionally, using localized Wannier-like electron wavefunctions allows the computation time and memory required to minimize the energy to also scale linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, thus allowing structural relaxation and molecular dynamics simulations.

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The SIESTA method for ab initio order-N materials simulation

A simple way has been discovered to put model pseudopotentials, $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})={\ensuremath{\Sigma}}_{\mathrm{lm}}|{Y}_{\mathrm{lm}}〉{V}_{l}(r)\ifmmode\times\else\texttimes\fi{}〈{Y}_{\mathrm{lm}}|$, into a form which reduces the number of integrals of $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ required for an energyband calculation from $\frac{\mathrm{mn}(n+1)}{2}$ to $\mathrm{mn}$ for each $l$ in the sum (where $n$ is the number of plane waves used in the expansion and $m$ the number of points in the Brillouin zone at which the calculation is performed). The new form may be chosen to improve the accuracy of the pseudopotential when used in other chemical environments.

Efficacious Form for Model Pseudopotentials

The exchange operator is divided into two parts, a Thomas-Fermi screened exchange operator and the remainder. The remainder and correlation are treated in the local-density approximation, while the screened exchange matrix elements are exactly evaluated. Calculations for Si result in much improved band gaps as well as an improved exchange contribution to the binding energy.

Good semiconductor band gaps with a modified local-density approximation

Using a basis set of {similar to}3580 plane waves, we perform {ital ab} {ital initio} self-consistent calculations of the energy bands and cohesive energy of B{sub 12}C{sub 3}. Calculating stresses and forces, both the lattice constants and the positions of the atoms in the unit cell are determined. If trigonal symmetry is forced (i.e., all three carbons on the chain), the cohesive energy is 108.20 eV/(unit cell). In the experimentally observed structure with one boron on each chain and one carbon on each icosahedron, the cohesive energy is 109.48 eV/(unit cell). An indirect energy gap of 2.781 eV is obtained for this structure and charge-density--contour plots indicate that the ratio of the charge on the carbons to that on the borons is much greater than the 4:3 ratio of their valences.

Self-consistent calculations of the energy bands and bonding properties of B12C3.

Chou has recently presented an approximation to the norm-conserving form of Vanderbilt's nonlocal Hermitian pseudopotential. We point out two minor shortcomings of the Chou approximation and also show that it is actually easier to construct the Vanderbilt pseudopotential than to construct Chou's approximation to it. The all-electron silver d-electron logarithmic derivative is compared over a range of energies with that obtained from a Vanderbilt pseudopotential which is exact at two energies and with Chou's approximate pseudopotential. The agreement with the former is excellent and with the latter is only fair.

Nonlocal Hermitian norm-conserving Vanderbilt pseudopotential.

Hamann has shown how to construct a norm-conserving pseudopotential for the unbound 4f state in the Ba atom. This pseudopotential which was calculated at -1.877 eV, fails to yield the sharp 4f resonance found at +1.501 eV in the Dirac atom. We show that this is a consequence not of the energy at which the pseudopotential is calculated but rather of the cutoff radius used. We calculate the pseudopotential at -1.877 eV using a cutoff radius intermediate to those used by Hamann for the bound 4f state of the ${\mathrm{Ba}}^{+}$ ion and the unbound 4f state of Ba, and obtain the positive-energy resonance. When the [${\ensuremath{\partial}}^{2}$(\ensuremath{\psi}'/\ensuremath{\psi})/\ensuremath{\partial}${E}^{2}$]-preserving form of the norm-conserving pseudopotential recently developed by Shirley et al. is used, the resonance occurs at 1.507 eV and is actually larger than that of the Dirac atom. We also discuss the application of these new ideas to the separable form of the norm-conserving pseudopotential.

D. M. Bylander

Papers

Efficacious Form for Model Pseudopotentials

Good semiconductor band gaps with a modified local-density approximation

Self-consistent calculations of the energy bands and bonding properties of B12C3.

Nonlocal Hermitian norm-conserving Vanderbilt pseudopotential.

4f resonances with norm-conserving pseudopotentials