Efficient method for localised functions using domain transformation and Fourier sine series

Efficient method for localised functions using domain transformation and Fourier sine series" (2014). Taylor & Francis makes every effort to ensure the accuracy of all the information (the " Content ") contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. An efficient approach to handle localised states by using spectral methods (SM) in one and three dimensions is presented. The method consists of transformation of the infinite domain to the bounded domain in (0, π) and using the Fourier sine series as a set of basis functions for the SM. It is shown that with an appropriate choice of transformation functions, this method manages to preserve the good properties of original SMs; more precisely, superb computational efficiency when high level of accuracy is necessary. This is made possible by analytically exploiting the properties of the transformation function and the Fourier sine series. An especially important property of this approach is the possibility of calculating the Hartree energy very efficiently. This is done by exploiting the positive properties of the sine series as a basis set and conducting an extinctive part of the calculations analytically. We illustrate the efficiency of this method and implement it to solve the Poisson's and Helmholtz equations in both one and three dimensions. The efficiency of the method is verified through a comparison to recently published results for both one-and three-dimensional problems. 1. Introduction In atomistic calculations of molecules and clusters, it is essential to use localised basis sets, where the wavefunctions vanish exponentially at large distances. There are many used sets and the most common ones are Slater-type and Gaussian-type orbitals (STO and GTO, respectively) [1–6]. Practically, the sets dectate the accuracy and maximum possible size of the …