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Register a new userA Generic Approach to Electronic Structure Calculations in Nanoscopic Systems
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Authors
Jordan Kyriakidis
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We outline a generic, flexible, modular, yet efficient framework to the computation of energies and states for general nanoscopic systems with a focus on semiconductor quantum dots. The approach utilizes the configuration interaction method, in principal obtaining all many-body correlations in the system. The approach exploits the powerful abstracting mechanisms of C++s template facility to produce efficient yet general code. The primary utility of the present approach is not in the resulting raw computational speed, but rather in minimizing the time from initial idea to final results.
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The generation of input files for density functional theory (DFT) programs must often be manually done by researchers. If one wishes to produce a maximally localized wannier functions (MLWFs) the calculation consists of several separate files that must be formatted correctly in order for the program to work properly. Many of the inputs are repeated throughout the files and can be easily automated. In this work, a program is presented to generate all of the input files needed to produce wannier functions with Wannier90 starting from open source DFT programs such as Quantum Espresso, Abinit, and Siesta. In addition, the input files for WannierTools are also included for those that wish to produce surface greens functions for the generation of surface state bands. The program presented allows for users new to DFT to use the programs with minimal understanding of parameters needed to produce good results, in addition, this program allows for researchers who are advanced DFT users to utilize this program for high throughput wannier calculations.
We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into account and we present an optimization scheme for the occupation numbers that ensures that the constraints remain satisfied. We also compare sequential and simultaneous quasi-Newton and nonlinear conjugate gradient optimization procedures, and demonstrate that simultaneous optimization of the electronic orbitals and occupation numbers improve performance compared to the sequential approach.
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy cut-off for planewave discretizations, for both linear and nonlinear eigenvalue problems. The method is error controllable for linear eigenvalue problems in the sense that for a given required accuracy, an energy cut-off for which the solution matches the target accuracy can be reached efficiently. Further, the method is particularly promising for nonlinear eigenvalue problems in electronic structure calculations as it shall reduce the cost of early iterations in self-consistent algorithms. We present some numerical experiments for both linear and nonlinear eigenvalue problems. In particular, we provide electronic structure calculations for some insulator and metallic systems simulated with Kohn--Sham density functional theory (DFT) and the projector augmented wave (PAW) method, illustrating the efficiency and potential of the algorithm.
We consider a minimization scheme based on the Householder transport operator for the Grassman manifold, where a point on the manifold is represented by a m x n matrix with orthonormal columns. In particular, we consider the case where m >> n and present a method with asymptotic complexity mn^2. To avoid explicit parametrization of the manifold we use Householder transforms to move on the manifold, and present a formulation for simultaneous Householder reflections for S-orthonormal columns. We compare a quasi-Newton and nonlinear conjugate gradient implementation adapted to the manifold with a projected nonlinear conjugate gradient method, and demonstrate that the convergence rate is significantly improved if the manifold is taken into account when designing the optimization procedure.
Motivated by the recently proposed parallel orbital-updating approach in real space method, we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers
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