A machine-learning (ML) assisted approach revealing p-p-s electronic coupling descriptor

A mathematical parameter is proposed to describe the p-p-s electronic coupling strength in transition metal dichalcogenides (TMDCs). Two key descriptors, Iband(p−s)Iband(p−s) and Cband(p−p′)Cband(p−p′), are defined as follows:

Iband(p−s)=ϵp−ϵsϵp,Cband(p−p′)=ϵp′−ϵpϵp′Iband(p−s)=ϵpϵp−ϵs,Cband(p−p′)=ϵp′ϵp′−ϵp

where ϵϵ represents the p-band or s-band center positions of the atoms. Here, pp, p′p′, and ss refer to the p-band of the doped anion atom, the p-band of the first neighboring six S/Se atoms around the doped anion atom, and the s-band of Li atoms, respectively. Iband(p−s)Iband(p−s) characterizes the energy gap between the doped TMDCs and lithium polysulfides (LiPS), where a smaller value indicates a reduced band center energy gap, leading to enhanced interfacial electron transfer dynamics and a stronger interaction between the doped TMDCs and LiPS. On the other hand, Cband(p−p′)Cband(p−p′) quantifies the coupling strength between the p-band of the doped anion atoms and the neighboring S/Se atoms, where a smaller value indicates stronger coupling.

The relationship between the Gibbs energy barrier (ΔGΔG) and the coupling descriptors Iband(p−s)Iband(p−s) and Cband(p−p′)Cband(p−p′) is established through a machine learning approach, represented as:

ΔGi=f(Iband(i)(p−s),Cband(i)(p−p′))ΔGi=f(Iband(i)(p−s),Cband(i)(p−p′))

The model demonstrates that Iband(p−s)Iband(p−s) and Cband(p−p′)Cband(p−p′) effectively capture the relationship between the p-p-s coupling strength and the Gibbs free energy barrier, with a fitting result achieving an average Root Mean Square Error (RMSE) of approximately 0.07 eV.

本研究提出一项数学参数，用于描述过渡金属硫族化合物（transition metal dichalcogenides, TMDCs）中的p-p-s电子耦合强度。本研究定义了两个关键描述符：Iband(p−s)与Cband(p−p′)，具体形式如下：
Iband(p−s)=(ε_p−ε_s)/ε_p，Cband(p−p′)=(ε_{p'}−ε_p)/ε_{p'}
其中ε代表原子的p带或s带中心能级位置；此处p、p′与s分别指代掺杂阴离子原子的p带、掺杂阴离子原子周围第一近邻的六个硫/硒原子的p带，以及锂原子的s带。

Iband(p−s)用于表征掺杂型TMDCs与多硫化锂（lithium polysulfides, LiPS）之间的能级差：其数值越小，代表带中心能级差越小，可强化界面电子转移动力学，增强掺杂TMDCs与LiPS之间的相互作用强度。与之相对，Cband(p−p′)用于量化掺杂阴离子原子的p带与邻近硫/硒原子的p带之间的耦合强度，其数值越小则代表耦合作用越强。

本研究通过机器学习方法建立了吉布斯能垒（ΔG）与上述两个描述符Iband(p−s)和Cband(p−p′)之间的关联关系，表达式如下：
ΔG_i = f(Iband^{(i)}(p−s), Cband^{(i)}(p−p′))

该模型证实，Iband(p−s)与Cband(p−p′)能够有效捕捉p-p-s耦合强度与吉布斯自由能垒之间的内在关联，其拟合结果的平均均方根误差（Root Mean Square Error, RMSE）约为0.07 eV。