Inspired by MXene nanosheets and their regulation of surface functional groups,a series of Ti_(2)C‐based single‐atom electrocatalysts(TM@Ti_(2)CT_(x),TM=V,Cr,Mn,Fe,Co,and Ni)with two dif‐ferent functional groups(T=...Inspired by MXene nanosheets and their regulation of surface functional groups,a series of Ti_(2)C‐based single‐atom electrocatalysts(TM@Ti_(2)CT_(x),TM=V,Cr,Mn,Fe,Co,and Ni)with two dif‐ferent functional groups(T=–O and–S)was designed.The CO_(2)RR catalytic performance was stud‐ied using well‐defined ab initio calculations.Our results show that the CO_(2) molecule can be more readily activated on TM@Ti_(2)CO_(2) than the TM@Ti_(2)CS_(2) surface.Bader charge analysis reveals that the Ti_(2)CO_(2) substrate is involved in the adsorption reaction,and enough electrons are injected into the 2π*u orbital of CO_(2),leading to a V‐shaped CO_(2) molecular configuration and partial negative charge distribution.The V‐shaped CO_(2) further reduces the difficulty of the first hydrogenation reac‐tion step.The calculatedΔG of the first hydrogenation reaction on TM@Ti_(2)CO_(2) was significantly lower than that of the TM@Ti_(2)CS_(2) counterpart.However,the subsequent CO_(2) reduction pathways show that the UL of the potential determining step on TM@Ti_(2)CS_(2) is smaller than that of TM@Ti_(2)CO_(2).Combining the advantages of both TM@Ti_(2)CS_(2) and TM@Ti_(2)CO_(2),we designed a mixed functional group surface with–O and–S to anchor TM atoms.The results show that Cr atoms an‐chored on the surface of mixed functional groups exhibit high catalytic activity for the selective production of CH4.This study opens an exciting new avenue for the rational design of highly selec‐tive MXene‐based single‐atom CO_(2)RR electrocatalysts.展开更多
Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace ...Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.展开更多
文摘Inspired by MXene nanosheets and their regulation of surface functional groups,a series of Ti_(2)C‐based single‐atom electrocatalysts(TM@Ti_(2)CT_(x),TM=V,Cr,Mn,Fe,Co,and Ni)with two dif‐ferent functional groups(T=–O and–S)was designed.The CO_(2)RR catalytic performance was stud‐ied using well‐defined ab initio calculations.Our results show that the CO_(2) molecule can be more readily activated on TM@Ti_(2)CO_(2) than the TM@Ti_(2)CS_(2) surface.Bader charge analysis reveals that the Ti_(2)CO_(2) substrate is involved in the adsorption reaction,and enough electrons are injected into the 2π*u orbital of CO_(2),leading to a V‐shaped CO_(2) molecular configuration and partial negative charge distribution.The V‐shaped CO_(2) further reduces the difficulty of the first hydrogenation reac‐tion step.The calculatedΔG of the first hydrogenation reaction on TM@Ti_(2)CO_(2) was significantly lower than that of the TM@Ti_(2)CS_(2) counterpart.However,the subsequent CO_(2) reduction pathways show that the UL of the potential determining step on TM@Ti_(2)CS_(2) is smaller than that of TM@Ti_(2)CO_(2).Combining the advantages of both TM@Ti_(2)CS_(2) and TM@Ti_(2)CO_(2),we designed a mixed functional group surface with–O and–S to anchor TM atoms.The results show that Cr atoms an‐chored on the surface of mixed functional groups exhibit high catalytic activity for the selective production of CH4.This study opens an exciting new avenue for the rational design of highly selec‐tive MXene‐based single‐atom CO_(2)RR electrocatalysts.
基金The second author is supported by National Natural Science Foundation of China(Grant Nos.11550110172 and 11771164)。
文摘Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.
