Theoretical Study on the Grafting Reaction of Maleimide to Polyethylene in the UV Radiation Cross-Linking Process

Theoretical investigation of the reaction of graft maleimide to polyethylene in the UV radiation cross-linking process is accomplished at the B3LYP/6-311+G(d,p) level for high-voltage cable insulation materials. The reaction potential energy surface of the nine reaction channels is identified. The results show that the N,N′-ethylenedimaleimide can connect two 4-methylheptane molecules and act as the cross-linking agent. The calculated reaction potential barrier of forming 4-methylheptane radical by maleimide is higher than that of maleic anhydride. The study is expected to provide a basis for optimizing the UV radiation cross-linking polyethylene process and development more than 500 kV high-voltage cable insulation materials in practical applications.


Introduction
With the fast development of new renewable energies, the highly efficient transmission of electricity is becoming more and more important. Offshore wind power and photovoltaic power transmission call for long distance and large capacity high-voltage direct current (HVDC) cable power transmission. This will promote the rapid development of polymeric HVDC cables in the near future. One of the most important issues is the insulation materials. Except for the electrical tree, cross-linked polyethylene (XLPE) insulation for HVDC cable also faces the problem raised by space charge accumulation in the bulk of the insulation. Under high electrical fields, charge carriers and ions in HVDC cable insulation can be trapped by either polymer defects and or polar molecules, forming non-uniform accumulation. Space charge accumulation can affect the operation of the direct current (DC) cable insulation in many ways, such as by distorting local electric field, accelerating material aging, or triggering electrical trees [1][2][3], etc. At present, there are three ways to solve this problem. The first is to manufacture the XLPE insulation cable materials with "chemical purity", e.g., reducing chemical impurities, such as the antioxidant and cross-linking agent. They may be the origin of the traps for space charge. However, the trap centers in the XLPE include not only the polar group of small molecules, but also the structure defects generated from the polyethylene (PE) molecular chain and its crystallization, such as free volumes and polar groups connected to the chain. The second solution is to introduce nanoparticles to XLPE materials, where the interface between nanoparticles and the polymer matrix may form the deep traps of charge carriers [4][5][6]. However, this strategy has many obstacles In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.

Stationary Point Geometries
The excitation energies (S1, S2, and S3) of two kinds of polar molecules have been calculated at the B3LYP/6-311+G(d,p) level. The computational results are listed in Table 1 together with the molecular formulas and corresponding abbreviations (ab.). In Table 1, the results show that maleimide derivatives, which have lower electron excitation energy levels than Bp, would be moreeasily grafted to the PE molecule by UV radiation without the help of Bp, and could be selected as a new candidate for a highly efficient space charge inhibitor. The excitation energies of EH, MHF, and the acrylic acid derivatives are all higher than that of Bp. This means that they would be grafted to PE by UV radiation with the help of Bp if their energy level of frontier molecular orbitals accords with sensitization conditions. The cross-linking byproduct from Bp and TAIC will affect some electrical properties such as increasing conductivity of the insulation. EEM, which has two ethylene groups, would act as the cross-linking agent and connect two PE molecules when it is excited by UV initiated without the help of Bp and TAIC. In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the first triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively.  In Table 2, hydrogen abstraction reactions for the grafting of maleimides to PE by UV radiation are listed. The optimized geometric structures at the triplet state of the reactants, the transition states involved in the nine ultraviolet light induced reactions, and other stationary points at the ground state are presented in Figure 1. The optimized lengths for the breaking and forming bonds in nine transition states, and the corresponding values for C-H bonds in both the reactant and the product, as well as the imaginary frequency values, are also listed in Table 2. In this paper, R, TS, and P refer to the reactant, the transition state, and the product, respectively. In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T 1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f ), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation Reactant b/f Product Frequency
Polymers 2018, 10, x FOR PEER REVIEW 4 of 11 In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Reaction Equation
Reactant In Table 2, it can be seen that among the nine studied reactions, the transition state structures at the T1 state of the hydrogen abstraction reaction have a common characteristic in that the breaking elongation of the reactant (C-H in model molecule Pe) is less than the bond elongation of the products (C-H in PCMM, PEEM, PEEM-g-Pe4 and PPe4-g-EEM-g-Pe4), indicating that the transition states are closer to the reactant and belong to the "early" transition state. According to Hammond's postulate [31], this kind reaction should be exothermic. Table 2. Hydrogen abstraction reaction equations for the grafting of maleimides to PE by UV radiation at the triplet state, the lengths of the reaction-involved C-H bonds in reactants, transition states (the breaking bond/the forming bond, b/f), products (in angstrom) and the imaginary frequency values (in cm −1 ) of the transition states.

Frontier MOs and NBO Charge Population
According to our previous study [32], the SixOy nanoclusters have been proved to be efficient in accumulating electrons and protecting the PE chain. Our previous study also showed that the calculated vertical and adiabatic values of the ionization potentials (IPs) and the electron affinities (EAs) of MAH at the B3LYP/6-311+G(d,p) level are higher than those of the other two polar molecules (MA and AA) [15]. In this work, the calculated IPs and EAs for polar molecules CMM and EEM at the same level are higher than those of MAH. When grafted by CMM or EEM, the polymer would have a much stronger ability to suppress space charge injection and accumulation than if grafted by MAH under divergent electrical field stress in-service XLPE cables. CMM (1.80 eV) and EEM (1.76 eV) have higher EA(a) values than MAH (1.72 eV), suggesting that when grafted to PE, CMM and EEM would have much stronger abilities of capturing the hot electron with C=O groups in the insulation materials than MAH. The calculated highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO) energy gaps, Eg, values of 4.36 and 4.68 eV for CMM and EEM, respectively, are lower than 5.01 eV for MAH, although all are α,β-unsaturated carbonyl compounds. Because there are acylamino groups (-NC=O) in CMM and EEM, the conjugative effect between C=O groups and the N atom in maleimides is larger than that of C=O groups and the O atom in MAH. The electronic density on the C=C double bond relates to the electronegativity of the atom linked to acyl groups: the larger the electronegativity, the stronger the electron-withdrawing capability. Because the electronegativity of the O atom is larger than that of the N atom, the electronic density on the C=C double bond of MAH obviously decreases. Therefore, the reactivity of CMM or EEM to PE would be lower than that of MAH.

Frontier MOs and NBO Charge Population
According to our previous study [32], the Si x O y nanoclusters have been proved to be efficient in accumulating electrons and protecting the PE chain. Our previous study also showed that the calculated vertical and adiabatic values of the ionization potentials (IPs) and the electron affinities (EAs) of MAH at the B3LYP/6-311+G(d,p) level are higher than those of the other two polar molecules (MA and AA) [15]. In this work, the calculated IPs and EAs for polar molecules CMM and EEM at the same level are higher than those of MAH. When grafted by CMM or EEM, the polymer would have a much stronger ability to suppress space charge injection and accumulation than if grafted by MAH under divergent electrical field stress in-service XLPE cables. CMM (1.80 eV) and EEM (1.76 eV) have higher EA(a) values than MAH (1.72 eV), suggesting that when grafted to PE, CMM and EEM would have much stronger abilities of capturing the hot electron with C=O groups in the insulation materials than MAH. The calculated highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO) energy gaps, E g , values of 4.36 and 4.68 eV for CMM and EEM, respectively, are lower than 5.01 eV for MAH, although all are α,β-unsaturated carbonyl compounds. Because there are acylamino groups (-NC=O) in CMM and EEM, the conjugative effect between C=O groups and the N atom in maleimides is larger than that of C=O groups and the O atom in MAH. The electronic density on the C=C double bond relates to the electronegativity of the atom linked to acyl groups: the larger the electronegativity, the stronger the electron-withdrawing capability. Because the electronegativity of the O atom is larger than that of the N atom, the electronic density on the C=C double bond of MAH obviously decreases. Therefore, the reactivity of CMM or EEM to PE would be lower than that of MAH. The natural charge population on nine sites of MAM, CMM, and EEM at S 0 , S 1 , and T 1 states is given in Table 3. The maleimide molecules at the excited triplet state, T 1 , have double radicals which can reconstruct π bonds. The natural charge density on C1 and C2 of the CMM molecule at the excited triplet state, T 1 , is higher than that of EEM. As a result, C1 and C2 in EEM show higher reactivity on the excited triplet state than in CMM. The reaction potential barrier heights of EEM would be lower than those of CMM. Table 3. Natural charge population of maleimide at S 0 , S 1 , and T 1 states. The natural charge population on nine sites of MAM, CMM, and EEM at S0, S1, and T1 states is given in Table 3. The maleimide molecules at the excited triplet state, T1, have double radicals which can reconstruct π bonds. The natural charge density on C1 and C2 of the CMM molecule at the excited triplet state, T1, is higher than that of EEM. As a result, C1 and C2 in EEM show higher reactivity on the excited triplet state than in CMM. The reaction potential barrier heights of EEM would be lower than those of CMM.

Energetics
During the thermo-crosslinking process of PE, dicumyl peroxide takes a homolytic reaction and forms radicals [33], which initiate a hydrogen abstraction reaction with the PE chain to form PE radicals [26]. In the process of grafting MAH to PE by UV radiation, the benzophenone Bp is excited to the excited singlet state at first, and then to the excited triplet state through the intersystem crossing (ISC). Bp at the excited triplet state can sensitize MAH from the ground state to the excited triplet state, and return to the ground state. MAH at excited triplet state abstracts the hydrogen from the PE to form PE and MAH radicals. These PE radicals can react quickly with each other to produce a crosslinked network XLPE, through which mechanical properties and heat resistance are significantly enhanced, and MAH can also be grafted to the PE chain [26]. The radical reactions are induced by Bp, and the cross-linking rate is graded by TAIC [34]. Compared with the process of thermal initiated grafting with peroxide as initiator, photoinitiated grafting provides higher grafting efficiency [10]. In Table 4, at the B3LYP/6-311+G(d,p) level, the calculated reaction enthalpies at 298 K (Δ H 0 298 ) and the potential barrier heights (ΔE TS ) with zero-point energy (ZPE) corrections at T1 state are presented; the relative bond dissociation energies ( 0 298 D ) are also provided. Bond dissociation energies have good correlations with the corresponding reaction potential barrier heights. The calculated relative energy margin between S0 and T1 states (ΔE T1-S0 ) of acetophenone was 74.92 kcal/mol at the QCISD(T)/B3LYP level in our previous work [35], which is consistent with the experimental value of 73.74 kcal/mol [36]. Here, we aim at investigating the possible reactions of maleimides with Pe by UV radiation. Which can easily graft to PE chain, CMM or EEM? Can EEM act as the cross-linking agent and connect two Pe molecules? The natural charge population on nine sites of MAM, CMM, and EEM at S0, S1, and T1 states is given in Table 3. The maleimide molecules at the excited triplet state, T1, have double radicals which can reconstruct π bonds. The natural charge density on C1 and C2 of the CMM molecule at the excited triplet state, T1, is higher than that of EEM. As a result, C1 and C2 in EEM show higher reactivity on the excited triplet state than in CMM. The reaction potential barrier heights of EEM would be lower than those of CMM.

Energetics
During the thermo-crosslinking process of PE, dicumyl peroxide takes a homolytic reaction and forms radicals [33], which initiate a hydrogen abstraction reaction with the PE chain to form PE radicals [26]. In the process of grafting MAH to PE by UV radiation, the benzophenone Bp is excited to the excited singlet state at first, and then to the excited triplet state through the intersystem crossing (ISC). Bp at the excited triplet state can sensitize MAH from the ground state to the excited triplet state, and return to the ground state. MAH at excited triplet state abstracts the hydrogen from the PE to form PE and MAH radicals. These PE radicals can react quickly with each other to produce a crosslinked network XLPE, through which mechanical properties and heat resistance are significantly enhanced, and MAH can also be grafted to the PE chain [26]. The radical reactions are induced by Bp, and the cross-linking rate is graded by TAIC [34]. Compared with the process of thermal initiated grafting with peroxide as initiator, photoinitiated grafting provides higher grafting efficiency [10]. In Table 4, at the B3LYP/6-311+G(d,p) level, the calculated reaction enthalpies at 298 K (Δ H 0 298 ) and the potential barrier heights (ΔE TS ) with zero-point energy (ZPE) corrections at T1 state are presented; the relative bond dissociation energies ( 0 298 D ) are also provided. Bond dissociation energies have good correlations with the corresponding reaction potential barrier heights. The calculated relative energy margin between S0 and T1 states (ΔE T1-S0 ) of acetophenone was 74.92 kcal/mol at the QCISD(T)/B3LYP level in our previous work [35], which is consistent with the experimental value of 73.74 kcal/mol [36]. Here, we aim at investigating the possible reactions of maleimides with Pe by UV radiation. Which can easily graft to PE chain, CMM or EEM? Can EEM act as the cross-linking agent and connect two Pe molecules? The natural charge population on nine sites of MAM, CMM, and EEM at S0, S1, and T1 states is given in Table 3. The maleimide molecules at the excited triplet state, T1, have double radicals which can reconstruct π bonds. The natural charge density on C1 and C2 of the CMM molecule at the excited triplet state, T1, is higher than that of EEM. As a result, C1 and C2 in EEM show higher reactivity on the excited triplet state than in CMM. The reaction potential barrier heights of EEM would be lower than those of CMM.

Energetics
During the thermo-crosslinking process of PE, dicumyl peroxide takes a homolytic reaction and forms radicals [33], which initiate a hydrogen abstraction reaction with the PE chain to form PE radicals [26]. In the process of grafting MAH to PE by UV radiation, the benzophenone Bp is excited to the excited singlet state at first, and then to the excited triplet state through the intersystem crossing (ISC). Bp at the excited triplet state can sensitize MAH from the ground state to the excited triplet state, and return to the ground state. MAH at excited triplet state abstracts the hydrogen from the PE to form PE and MAH radicals. These PE radicals can react quickly with each other to produce a crosslinked network XLPE, through which mechanical properties and heat resistance are significantly enhanced, and MAH can also be grafted to the PE chain [26]. The radical reactions are induced by Bp, and the cross-linking rate is graded by TAIC [34]. Compared with the process of thermal initiated grafting with peroxide as initiator, photoinitiated grafting provides higher grafting efficiency [10]. In Table 4, at the B3LYP/6-311+G(d,p) level, the calculated reaction enthalpies at 298 K (Δ H 0 298 ) and the potential barrier heights (ΔE TS ) with zero-point energy (ZPE) corrections at T1 state are presented; the relative bond dissociation energies ( 0 298 D ) are also provided. Bond dissociation energies have good correlations with the corresponding reaction potential barrier heights. The calculated relative energy margin between S0 and T1 states (ΔE T1-S0 ) of acetophenone was 74.92 kcal/mol at the QCISD(T)/B3LYP level in our previous work [35], which is consistent with the experimental value of 73.74 kcal/mol [36]. Here, we aim at investigating the possible reactions of maleimides with Pe by UV radiation. Which can easily graft to PE chain, CMM or EEM? Can EEM act as the cross-linking agent and connect two Pe molecules?

Energetics
During the thermo-crosslinking process of PE, dicumyl peroxide takes a homolytic reaction and forms radicals [33], which initiate a hydrogen abstraction reaction with the PE chain to form PE radicals [26]. In the process of grafting MAH to PE by UV radiation, the benzophenone Bp is excited to the excited singlet state at first, and then to the excited triplet state through the intersystem crossing (ISC). Bp at the excited triplet state can sensitize MAH from the ground state to the excited triplet state, and return to the ground state. MAH at excited triplet state abstracts the hydrogen from the PE to form PE and MAH radicals. These PE radicals can react quickly with each other to produce a cross-linked network XLPE, through which mechanical properties and heat resistance are significantly enhanced, and MAH can also be grafted to the PE chain [26]. The radical reactions are induced by Bp, and the cross-linking rate is graded by TAIC [34]. Compared with the process of thermal initiated grafting with peroxide as initiator, photoinitiated grafting provides higher grafting efficiency [10]. In Table 4, at the B3LYP/6-311+G(d,p) level, the calculated reaction enthalpies at 298 K (∆H 0 298 ) and the potential barrier heights (∆E TS ) with zero-point energy (ZPE) corrections at T 1 state are presented; the relative bond dissociation energies (D 0 298 ) are also provided. Bond dissociation energies have good correlations with the corresponding reaction potential barrier heights. The calculated relative energy margin between S 0 and T 1 states (∆E T1-S0 ) of acetophenone was 74.92 kcal/mol at the QCISD(T)/B3LYP level in our previous work [35], which is consistent with the experimental value of 73.74 kcal/mol [36]. Here, we aim at investigating the possible reactions of maleimides with Pe by UV radiation. Which can easily graft to PE chain, CMM or EEM? Can EEM act as the cross-linking agent and connect two Pe molecules?  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  ), the potential barrier heights TSs (ΔE TS ) with zeropoint energy (ZPE) corrections at the T1 state at the B3LYP/6-311+G(d,p) level, and the bond dissociation energies of C-H bonds in the reactants (all in eV). During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the  ), the potential barrier heights TSs (ΔE TS ) with zeropoint energy (ZPE) corrections at the T1 state at the B3LYP/6-311+G(d,p) level, and the bond dissociation energies of C-H bonds in the reactants (all in eV). During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the During the UV radiation cross-linking PE process, the calculated reaction potential barrier of forming the Pe2 radical by MAH is 0.10 eV at the T 1 state at the B3LYP/6-311+G(d,p) level [15]. The calculated reaction potential barrier of forming the Pe2 radical by EEM is 0.26 eV at the T 1 state at the same level in this work, which is higher than that of MAH. This is consistent with a qualitative assessment based on the electronic density analysis above. Therefore, the electronic density on the C=C double bond in MAH is smaller than that of maleimide (EEM and CMM), leading to the more facile MAH radical with the lower energy barriers (0.10 eV) [15]. For the nine forming radical reactions with Pe in Table 4 at the T 1 state, all are exothermic, consistent with Hammond's postulate [31]. The reaction potential barrier of forming the Pe4 radical by EEM (0.19 eV) is the lowest among the nine reaction channels and the reaction enthalpy (∆H 0 298 = −0.47 eV) is also the