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.