Wodyński Artur, Glodny Kilian, Kaupp Martin
Technische Universitát Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin D-10623, Germany.
J Chem Theory Comput. 2025 Jan 28;21(2):762-775. doi: 10.1021/acs.jctc.4c01503. Epub 2025 Jan 13.
Local hybrid functionals (LHs) use a real-space position-dependent admixture of exact exchange (EXX), governed by a local mixing function (LMF). The systematic construction of LMFs has been hampered over the years by a lack of exact physical constraints on their valence behavior. Here, we exploit a data-driven approach and train a new type of "n-LMF" as a relatively shallow neural network. The input features are of meta-GGA character, while the W4-17 atomization-energy and BH76 reaction-barrier test sets have been used for training. Simply replacing the widely used "t-LMF" of the LH20t functional by the n-LMF provides the LH24n-B95 functional. Augmented by DFT-D4 dispersion corrections, LH24n-B95-D4 remarkably improves the WTMAD-2 value for the large GMTKN55 test suite of general main-group thermochemistry, kinetics, and noncovalent interactions (NCIs) from 4.55 to 3.49 kcal/mol. As we found the limited flexibility of the B95c correlation functional to disfavor much further improvement on NCIs, we proceeded to replace it by an optimized B97c-type power-series expansion. This gives the LH24n functional. LH24n-D4 gives a WTMAD-2 value of 3.10 kcal/mol, the so far lowest value of a rung 4 functional in self-consistent calculations. The new functionals perform moderately well for organometallic transition-metal energetics while leaving room for further data-driven improvements in that area. Compared to complete neural-network functionals like DM21, the present more tailored approach to train just the LMF in a flexible but well-defined human-designed LH functional retains the possibility of graphical LMF analyses to gain deeper understanding. We find that both the present n-LMF and the recent x-LMF suppress the so-called gauge problem of local hybrids without adding a calibration function as required for other LMFs. LMF plots show that this can be traced back to large LMF values in the small-density region between the interacting atoms in NCIs for n- and x-LMFs and low values for the t-LMF. We also find that the trained n-LMF has relatively large values in covalent bonds without deteriorating binding energies. The current approach enables fast and efficient routine self-consistent calculations using n-LMFs in Turbomole.
局域杂化泛函（LHs）使用由局域混合函数（LMF）控制的精确交换（EXX）的实空间位置相关混合。多年来，由于缺乏对价态行为的精确物理约束，LMF的系统构建受到了阻碍。在这里，我们采用数据驱动的方法，将一种新型的“n-LMF”训练为相对较浅的神经网络。输入特征具有元广义梯度近似（meta-GGA）特征，同时使用W4-17原子化能和BH76反应势垒测试集进行训练。简单地用n-LMF取代LH20t泛函中广泛使用的“t-LMF”，就得到了LH24n-B95泛函。通过DFT-D4色散校正增强后，LH24n-B95-D4显著提高了通用主族热化学、动力学和非共价相互作用（NCIs）的大型GMTKN55测试集的WTMAD-2值，从4.55千卡/摩尔降至3.49千卡/摩尔。由于我们发现B95c相关泛函的灵活性有限，不利于NCIs的进一步大幅改进，我们接着用优化的B97c型幂级数展开式取代了它。这就得到了LH24n泛函。LH24n-D4给出的WTMAD-2值为3.10千卡/摩尔，这是自洽计算中到目前为止 rung 4泛函的最低值。新泛函在有机金属过渡金属能量学方面表现适中，同时在该领域仍有进一步数据驱动改进的空间。与像DM21这样的完整神经网络泛函相比，目前在灵活但定义明确的人工设计的LH泛函中仅训练LMF的更具针对性的方法，保留了通过图形化LMF分析以获得更深入理解的可能性。我们发现，当前的n-LMF和最近的x-LMF都抑制了局域杂化的所谓规范问题，而无需像其他LMF那样添加校准函数。LMF图表明，这可以追溯到n-LMF和x-LMF在NCIs中相互作用原子之间的小密度区域具有较大的LMF值，而t-LMF的值较低。我们还发现，经过训练的n-LMF在共价键中具有相对较大的值，而不会降低结合能。当前的方法能够在Turbomole中使用n-LMF进行快速高效的常规自洽计算。
