Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark.
J Chem Phys. 2018 Feb 14;148(6):064113. doi: 10.1063/1.5016259.
We present an approach to treat sets of general fit-basis functions in a single uniform framework, where the functional form is supplied on input, i.e., the use of different functions does not require new code to be written. The fit-basis functions can be used to carry out linear fits to the grid of single points, which are generated with an adaptive density-guided approach (ADGA). A non-linear conjugate gradient method is used to optimize non-linear parameters if such are present in the fit-basis functions. This means that a set of fit-basis functions with the same inherent shape as the potential cuts can be requested and no other choices with regards to the fit-basis functions need to be taken. The general fit-basis framework is explored in relation to anharmonic potentials for model systems, diatomic molecules, water, and imidazole. The behaviour and performance of Morse and double-well fit-basis functions are compared to that of polynomial fit-basis functions for unsymmetrical single-minimum and symmetrical double-well potentials. Furthermore, calculations for water and imidazole were carried out using both normal coordinates and hybrid optimized and localized coordinates (HOLCs). Our results suggest that choosing a suitable set of fit-basis functions can improve the stability of the fitting routine and the overall efficiency of potential construction by lowering the number of single point calculations required for the ADGA. It is possible to reduce the number of terms in the potential by choosing the Morse and double-well fit-basis functions. These effects are substantial for normal coordinates but become even more pronounced if HOLCs are used.
我们提出了一种在单个统一框架中处理通用拟合基函数集的方法，其中功能形式在输入时提供，即使用不同的函数不需要编写新的代码。拟合基函数可用于对自适应密度引导方法 (ADGA) 生成的单点网格进行线性拟合。如果拟合基函数中存在非线性参数，则使用非线性共轭梯度方法进行优化。这意味着可以请求一组与潜在切割具有相同固有形状的拟合基函数，而无需对拟合基函数进行其他选择。在与模型系统、双原子分子、水和咪唑相关的非谐势中探索了通用拟合基框架。比较了 Morse 和双阱拟合基函数与非对称单极小值和对称双阱势的多项式拟合基函数的行为和性能。此外，还使用正则坐标和混合优化和局部坐标 (HOLC) 对水和咪唑进行了计算。我们的结果表明，选择合适的拟合基函数集可以通过降低 ADGA 所需的单点计算数量来提高拟合例程的稳定性和整体势构建效率。通过选择 Morse 和双阱拟合基函数，可以减少势中的项数。这些效果对于正则坐标来说是显著的，但如果使用 HOLC，则效果更为明显。
