CONUNDrum: A program for orbital-free density functional theory calculations

We present a new code for energy minimization, structure relaxation and evaluation of bulk parameters in the framework of orbital-free density functional theory (OF-DFT). The implementation is based on solving the Euler–Lagrange equation on an equidistant real space grid on which density dependent variables and derivatives are computed. Some potential components are computed in Fourier space. The code is able to use semilocal and non-local kinetic energy functionals (KEF) as well as neural network based KEFs thus facilitating testing and development of emerging machine-learned KEFs. For semi-local and machine-learned KEFs the kinetic energy potentials are evaluated with real-space differentiation of the components, which are partial derivatives of the KE with respect to the electron density, its gradient and Laplacian.

本研究提出一款全新的代码，用于轨道自由密度泛函理论(orbital-free density functional theory, OF-DFT)框架下的能量最小化、结构弛豫以及体相参数评估。该代码的实现基于在等间距实空间网格上求解欧拉-拉格朗日方程，在此网格上完成与密度相关的变量及其导数的计算；部分势能分量则在傅里叶空间中完成计算。此代码支持使用半局域与非局域动能泛函(kinetic energy functionals, KEF)，以及基于神经网络的动能泛函，从而为新兴机器学习动能泛函的测试与开发提供便利。针对半局域和机器学习动能泛函，其动能势通过对各分量进行实空间微分进行求值，这些分量为动能相对于电子密度、其梯度以及拉普拉斯算子的偏导数。