Second-Principles Density Functional Theory

The SPDFT approach is a large-scale electronic structure method, prepared to deal with 100000+ atoms, based on a systematical approximation of the full DFT energy and with a similar level of accuracy. This is achieved by separating the total density into a reference part, typically corresponding to the system’s neutral, geometry-dependent ground state, and a deformation contribution that takes into account the difference between the full density and the reference one.

Expanding the DFT energy in terms of the deformation density it is found that the zeroth-order term, corresponding to the DFT energy associated to the reference density, simply describes, in most cases, the energy surface of the unperturbed ground state. Higher order terms describe electron-hole excitations that allow obtaining the full range of electron properties like band, magnetic states, etc.

At difference with many other methods that are atom-based SPDFT is material -based. With this we mean that the basic construction block of a simulation is a model for a material. In particular, a SPDFT simulation requires the use of both a force-field and an electron Hamiltonian, formulated in a Wannier-function basis, that are obtained from first-principles simulations of a material in contrast with atom-atom potentials or electron basis based on atomic-functions typically used in other large-scale approaches. While this imposes the most important constraint to the method, the requirement of having a fixed bond topology – i.e. atoms cannot dissociate – this also allows the method to essentially match the accuracy of DFT even when dealing with very large number of atoms/electrons.

• Second-principles method for materials simulations including electron and lattice degrees of freedom, Pablo García-Fernández, Jacek C. Wojdeł, Jorge Íñiguez and Javier Junquera, Physical Review B 93, 195137 (2016). [arXiv:1511.07675]

 

Lattice potentials

In principles, SPDFT simulations can be based on any force field or effective potential treating all the atoms in the lattice. In SCALE-UP we implement a particular approach that adapts very well to our needs, as it can be trivially formulated for any material and permits a systematic improvement to reproduce a training set of first-principles data more and more accurately. This approach is based on the use of polynomial potentials that can be written as a Taylor series — in function of atomic distortions and lattice strains — around a convenient reference structure. The references describing this method, as implemented in SCALE-UP, are the following:

 

• First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides, Jacek C. Wojdeł, Patrick Hermet, Mathias P. Ljungberg, Philippe Ghosez and Jorge Íñiguez, Journal of Physics: Condensed Matter 25, 305401 (2013). [arXiv:1301.5731]The basic formulation of the polynomial potentials was introduced in this 2013 article, with applications to ferroic perovskites PbTiO₃ and SrTiO₃.
• Efficient systematic scheme to construct second-principles lattice-dynamical models, Carlos Escorihuela-Sayalero, Jacek C. Wojdeł and Jorge Íñiguez, Physical Review B 95, 094115 (2017). [arXiv:1608.06788]In this 2017 article, we implemented a new approach to the construction of polynomial models, taking advantage of one of its distinctive features — namely, that they are linear in the adjustable parameters — to introduce an ultra-fast fitting procedure that, in turn, allows us to select automatically the dominant interactions from a pool that includes essentially all impossible couplings. By doing this, we are able to routinely obtain very accurate models that reproduce a training set of DFT data within less than 1 meV per atom, and remain predictive (i.e., are cross-validated). This is the approach implemented in the utility to construct lattice models distributed with SCALE-UP.