Machine learning(ML)integrated with density functional theory(DFT)calculations have recently been used to accelerate the design and discovery of single-atom catalysts(SACs)by establishing deep structure–activity rela...Machine learning(ML)integrated with density functional theory(DFT)calculations have recently been used to accelerate the design and discovery of single-atom catalysts(SACs)by establishing deep structure–activity relationships.The traditional ML models are always difficult to identify the structural differences among the single-atom systems with different modification methods,leading to the limitation of the potential application range.Aiming to the structural properties of several typical two-dimensional MA_(2)Z_(4)-based single-atom systems(bare MA_(2)Z_(4) and metal single-atom doped/supported MA_(2)Z_(4)),an improved crystal graph convolutional neural network(CGCNN)classification model was employed,instead of the traditional machine learning regression model,to address the challenge of incompatibility in the studied systems.The CGCNN model was optimized using crystal graph representation in which the geometric configuration was divided into active layer,surface layer,and bulk layer(ASB-GCNN).Through ML and DFT calculations,five potential single-atom hydrogen evolution reaction(HER)catalysts were screened from chemical space of 600 MA_(2)Z_(4)-based materials,especially V_(1)/HfSn_(2)N_(4)(S)with high stability and activity(Δ_(GH*)is 0.06 eV).Further projected density of states(pDOS)analysis in combination with the wave function analysis of the SAC-H bond revealed that the SAC-dz^(2)orbital coincided with the H-s orbital around the energy level of−2.50 eV,and orbital analysis confirmed the formation ofσbonds.This study provides an efficient multistep screening design framework of metal single-atom catalyst for HER systems with similar two-dimensional supports but different geometric configurations.展开更多
A two-dimensional(2D)MA_(2)Z_(4)family with and phases has been attracting tremendous interest,the MoSi_(2)N_(4)and WSi_(2)N_(4)of which have been successfully fabricated(Science 369,670(2020)).Janus monolayers have b...A two-dimensional(2D)MA_(2)Z_(4)family with and phases has been attracting tremendous interest,the MoSi_(2)N_(4)and WSi_(2)N_(4)of which have been successfully fabricated(Science 369,670(2020)).Janus monolayers have been achieved in many 2D families,so it is interesting to construct a Janus monolayer from the MA_(2)Z_(4)family.In this work,Janus MSiGeN4(M=Zr and Hf)monolayers are predicted from-MA_(2)Z_(4),which exhibit dynamic,mechanical and thermal stabilities.It is found that they are indirect band-gap semiconductors by using generalized gradient approximation(GGA)plus spin-orbit coupling(SOC).With biaxial strain a/a0 from 0.90 to 1.10,the energy band gap shows a nonmonotonic behavior due to a change of conduction band minimum(CBM).A semiconductor to metal transition can be induced by both compressive and tensile strains,and the phase trans-formation point is about 0.96 for compressive strain and 1.10 for tensile strain.The tensile strain can change the positions of CBM and valence band maximum(VBM),and can also induce the weak Rashba-type spin splitting near CBM.For MSiGeN4(M=Zr and Hf)monolayers,both an in-plane and out-of-plane piezoelectric response can be produced,when a uniaxial strain in the basal plane is applied,which reveals the potential as piezoelectric 2D materials.The high absorption coefficients in the visible light region suggest that MSiGeN4(M=Zr and Hf)monolayers have potential photocatalytic applications.Our works provide an idea to achieve a Janus structure from the MA_(2)Z_(4)family,and can hopefully inspire further research exploring Janus MA_(2)Z_(4)monolayers.展开更多
This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--bre...This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--breaking bifurcation points. Two numerical examples are given. In addition, we show that there exist three quadratic pitchfork bifurcation point curves passing through corank-2 symmetry breaking bifurcation point.展开更多
基金supported by the National Key R&D Program of China(2021YFA1500900)National Natural Science Foundation of China(U21A20298,22141001).
文摘Machine learning(ML)integrated with density functional theory(DFT)calculations have recently been used to accelerate the design and discovery of single-atom catalysts(SACs)by establishing deep structure–activity relationships.The traditional ML models are always difficult to identify the structural differences among the single-atom systems with different modification methods,leading to the limitation of the potential application range.Aiming to the structural properties of several typical two-dimensional MA_(2)Z_(4)-based single-atom systems(bare MA_(2)Z_(4) and metal single-atom doped/supported MA_(2)Z_(4)),an improved crystal graph convolutional neural network(CGCNN)classification model was employed,instead of the traditional machine learning regression model,to address the challenge of incompatibility in the studied systems.The CGCNN model was optimized using crystal graph representation in which the geometric configuration was divided into active layer,surface layer,and bulk layer(ASB-GCNN).Through ML and DFT calculations,five potential single-atom hydrogen evolution reaction(HER)catalysts were screened from chemical space of 600 MA_(2)Z_(4)-based materials,especially V_(1)/HfSn_(2)N_(4)(S)with high stability and activity(Δ_(GH*)is 0.06 eV).Further projected density of states(pDOS)analysis in combination with the wave function analysis of the SAC-H bond revealed that the SAC-dz^(2)orbital coincided with the H-s orbital around the energy level of−2.50 eV,and orbital analysis confirmed the formation ofσbonds.This study provides an efficient multistep screening design framework of metal single-atom catalyst for HER systems with similar two-dimensional supports but different geometric configurations.
基金supported by Natural Science Basis Research Plan in Shaanxi Province of China(2021JM-456)。
文摘A two-dimensional(2D)MA_(2)Z_(4)family with and phases has been attracting tremendous interest,the MoSi_(2)N_(4)and WSi_(2)N_(4)of which have been successfully fabricated(Science 369,670(2020)).Janus monolayers have been achieved in many 2D families,so it is interesting to construct a Janus monolayer from the MA_(2)Z_(4)family.In this work,Janus MSiGeN4(M=Zr and Hf)monolayers are predicted from-MA_(2)Z_(4),which exhibit dynamic,mechanical and thermal stabilities.It is found that they are indirect band-gap semiconductors by using generalized gradient approximation(GGA)plus spin-orbit coupling(SOC).With biaxial strain a/a0 from 0.90 to 1.10,the energy band gap shows a nonmonotonic behavior due to a change of conduction band minimum(CBM).A semiconductor to metal transition can be induced by both compressive and tensile strains,and the phase trans-formation point is about 0.96 for compressive strain and 1.10 for tensile strain.The tensile strain can change the positions of CBM and valence band maximum(VBM),and can also induce the weak Rashba-type spin splitting near CBM.For MSiGeN4(M=Zr and Hf)monolayers,both an in-plane and out-of-plane piezoelectric response can be produced,when a uniaxial strain in the basal plane is applied,which reveals the potential as piezoelectric 2D materials.The high absorption coefficients in the visible light region suggest that MSiGeN4(M=Zr and Hf)monolayers have potential photocatalytic applications.Our works provide an idea to achieve a Janus structure from the MA_(2)Z_(4)family,and can hopefully inspire further research exploring Janus MA_(2)Z_(4)monolayers.
文摘This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--breaking bifurcation points. Two numerical examples are given. In addition, we show that there exist three quadratic pitchfork bifurcation point curves passing through corank-2 symmetry breaking bifurcation point.
