Efficient Calculations with Multisite Local Orbitals in a Large-Scale DFT Code CONQUEST

Abstract

Multisite local orbitals, which are formed from linear combinations of pseudo-atomic orbitals from a target atom and its neighbor atoms, have been introduced in the large-scale density functional theory calculation code CONQUEST. Multisite local orbitals correspond to local molecular orbitals so that the number of required local orbitals can be minimal. The multisite support functions are determined by using the localized filter diagonalization (LFD) method [Phys. Rev. B 2009, 80, 205104]. Two new methods, the double cutoff method and the smoothing method, are introduced to the LFD method to improve efficiency and stability. TheHamiltonian and overlap matrices with multisite local orbitals are constructed by efficient sparse-matrix multiplications in CONQUEST. The investigation of the calculated energetic and geometrical properties and band structures of bulk Si, Al and DNA systems demonstrate the accuracy and the computational efficiency of the present method. The representability of both occupied and unoccupied band structures with the present method has been also confirmed.3

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

“…17 To accelerate the Hessian evaluation for a subset of atoms, usually, in a numeric fashion, a number of partial schemes is available. [18][19][20][21] The linearscaling QM algorithms [22][23][24][25] have primarily been developed for energy and gradient evaluations; the efficiency of Hessian computations has also been improved. [26][27][28] Some fragment based approaches [29][30][31][32][33][34][35][36][37][38][39][40] feature analytic second derivatives.…”

Large scale and linear scaling DFT with the CONQUEST code

“…Multi-site support functions (MSSF) [29,30] offer one way to reduce the number of support functions. The MSSF are constructed as linear combinations of the PAOs not only on the target atom, but also on its neighbouring atoms, defined by a cutoff radius r MS ,…”

“…where S sub is the overlap matrix and f ( sub ) is a Fermi function with a local Fermi level sub , used to exclude high energy unoccupied local molecular orbitals. Since the MSSF will depend on the charge density of the system, which will in turn depend on the MSSF, the linear-combination coefficients need to be determined self-consistently [29]. r MS should be equal to or smaller than the subspace region in the LFD method r LFD .…”

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

“…The localized filter diagonalization (LFD) method builds an adaptive basis on-the-fly by contracting the atomic Gaussian functions within a local region, with contraction coefficients determined by diagonalizing a block of the Hamiltonian matrix corresponding to that region 98,99 . This algorithm has also been used to construct multisite local support functions 100 , and the general philosophy has been extended by Lin et al 101 , including another model with more rigorous optimization 102 . While clearly promising, to our knowledge, the accuracy and performance of these methods on chemical systems have not been systematically assessed yet.…”