Abstract 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. Program summary Program title: CONUNDrum. CPC Library link to program files: http://dx.doi.org/10.17632/phnz2gg8mz.1 Licensing provision: GNU GPL v3 Programming language: C++ External routines: Fastest Fourier Transform in the West (FFTW) library ( http://www.fftw.org/ ) Nature of problem: Calculation of the electronic and structural properties of molecules and extended systems in the framework of the orbital-free density functional theory. Evaluation of the bulk parameters of solid compounds. Solution method: High-order central finite-difference method and fast Fourier transform are used for calculation of different total energy components. Density optimization is performed with the steepest descent or the Polak–Ribiere variant of the non-linear conjugate-gradient method with a line search procedure based on the Armijo condition. A numerical approach is used for structural optimization — the total energies with respect to small variations in lattice geometries are computed directly, with subsequent evaluation of the force components via a high-order central-finite difference method. The same numerical procedure is used for evaluation of bulk properties. Restrictions: Local pseudopotentials.

中文翻译：

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难题：无轨道密度泛函理论计算程序

摘要 我们在无轨道密度泛函理论 (OF-DFT) 的框架内提出了一种用于能量最小化、结构松弛和体参数评估的新代码。该实现基于在等距实空间网格上求解 Euler-Lagrange 方程，在该网格上计算密度相关变量和导数。一些潜在的分量是在傅立叶空间中计算的。该代码能够使用半局部和非局部动能泛函 (KEF) 以及基于神经网络的 KEF，从而促进新兴机器学习 KEF 的测试和开发。对于半局部和机器学习的 KEF，动能势通过分量的实空间微分进行评估，这些分量是 KE 相对于电子密度、梯度和拉普拉斯算子的偏导数。程序概要 程序标题：CONUNDrum。CPC 库程序文件链接：http://dx.doi.org/10.17632/phnz2gg8mz.1 许可条款：GNU GPL v3 编程语言：C++ 外部例程：西方最快的傅立叶变换 (FFTW) 库（http:// www.fftw.org/ ) 问题性质：在无轨道密度泛函理论的框架内计算分子和扩展系统的电子和结构特性。评估固体化合物的整体参数。求解方法：采用高阶中心有限差分法和快速傅立叶变换计算不同的总能量分量。密度优化是通过最速下降法或非线性共轭梯度法的 Polak-Ribiere 变体和基于 Armijo 条件的线搜索程序来执行的。数值方法用于结构优化——直接计算与晶格几何形状微小变化相关的总能量，随后通过高阶中心有限差分法评估力分量。相同的数值程序用于评估整体特性。限制：局部赝势。