Abstract
We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.
Highlights
Where the matrix K, which we call the density kernel, is the representation of the density matrix in the basis of the localized orbitals as follows: Kαβ = ∑ MαifiMi∗β
The density functional theory (DFT) energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc functions
We perform the Fast Fourier Transforms (FFTs) on NGWFs in a miniature simulation cell, which we call the “FFT box.”12 In order to preserve important properties of the integrals [such as hermiticity and uniformity of the quantum mechanical (QM) operators] computed with the FFT box, particular care must be taken in how this box is defined and used, as we have described in early publications
Summary
To take practical advantage of this principle and develop methods with reduced or linear-scaling computational cost, we need to truncate the exponentially decaying tail of the density matrix. As the system size (number of atoms) increases, we will eventually reach the point where the remaining amount of information increases linearly with the size of the system This is not straightforward to implement if we use the KS orbitals directly. A more practical approach is to work with a set of localized orbitals {φα} that, in general (but not necessarily), are non-orthogonal as non-orthogonality can result in better localization.4 These localized orbitals can be considered to be connected to the KS orbitals via a linear transformation M as follows: φα(r) = ∑ ψi(r)Miα and ψi(r) = φα(r)Mαi,. Which is equivalent to the necessary requirements of KS orbital orthonormality and integer occupancies of 1 or 0 (for calculations in materials with a gap)
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