Sałek Paweł, Hesselmann Andreas
Laboratory of Theoretical Chemistry, The Royal Institute of Technology, Stockholm, Sweden.
J Comput Chem. 2007 Dec;28(16):2569-75. doi: 10.1002/jcc.20758.
A major unresolved problem of density functional theory is the yet unknown exchange-correlation functional, which leads to a proliferation of its less or more successful approximations. A practical implementation of these numerous functionals can present a substantial challenge particularly if the higher order functional derivatives are required. We present a systematic method of functional implementation. The method allows a clean handling of a large number of functionals in a mutually independent way. We developed an extensive set of automatic test routines to facilitate functional and derivative testing with respect to the implementation correctness and numerical stability. An integral part of the presented solution is a program for automatic code generation from analytical formulas that uses only freely available tools. Code for evaluation of functionals and their first, second, third, and fourth derivatives can be generated, which accelerates the development, implementation, and testing of new functionals.
密度泛函理论一个主要的未解决问题是尚未知晓的交换关联泛函，这导致了其或多或少成功的近似方法大量涌现。这些众多泛函的实际实现可能带来巨大挑战，特别是在需要高阶泛函导数的情况下。我们提出了一种系统的泛函实现方法。该方法允许以相互独立的方式清晰地处理大量泛函。我们开发了一套广泛的自动测试程序，以促进关于实现正确性和数值稳定性的泛函及导数测试。所提出解决方案的一个重要组成部分是一个仅使用免费可用工具从解析公式自动生成代码的程序。可以生成用于评估泛函及其一阶、二阶、三阶和四阶导数的代码，这加速了新泛函的开发、实现和测试。
