Mechanical, Structural and Electronic Properties of CO2 Adsorbed Graphitic Carbon Nitride (g-C3N4) under Biaxial Tensile Strain

We investigate mechanical, structural and electronic properties of CO2 adsorbed graphitic carbon nitride (g-C3N4) system under biaxial tensile strain via first-principles calculations. The results show that the stress of CO2 adsorbed g-C3N4 system increases and then decreases linearly with the increasing biaxial strain, reaching maximum at 0.12 strain. This is primarily caused by the plane N–C stretching of the g-C3N4. Furthermore, both the Perdew-Burke-Ernzerhof (PBE) and Heyd- Scuseria-Ernzerhof screened hybrid functional (HSE06) band gaps show direct-indirect transitions under biaxial tensile strain and have the maximum also at 0.12 strain. It is found that there is large dipole transition matrix element around Γ point, leading high optical absorption coefficients of the deformed adsorption system, which would be of great use for the applications of new elastic nanoelectronic and optoelectronic devices.


Introduction
The greenhouse effect is the rise in temperature caused by the rapid energy consumption on the global scale. This situation commits us to exploring effective methods for developing renewable energy. One of the most promising methods is to boost photocatalytic CO 2 reduction into hydrocarbon solar fuels, which can solve energy crisis and simultaneously protect our environment [1][2][3][4]. In 1979 [5], Inoue and his coworkers reported photocatalytic CO 2 reduction fuels using several semiconductors. After this, wide band gap semiconductor materials for CO 2 photoreduction have been studied, including CuO, TiO 2 and NiO and some metal sulfides [6][7][8][9]. All these photocatalysts are usually inorganic semiconductors, which distinguishes from the natural enzymes in plant tissues. Hence it is noted that biomimetic photocatalytic materials for photocatalytic CO 2 reduction are widely studied [10,11]. As an organic semiconductor photocatalyst, graphitic carbon nitride (g-C 3 N 4 ) has attracted much attention due to its visible-light activity, nontoxic resource, low-cost, promising applications in water splitting and what matters more is its appropriate band positions for CO 2 photoreduction [2,12,13].
Adsorption of CO 2 on the g-C 3 N 4 is critical for the photocatalytic activity [14,15]. In addition, the adsorption structure, stability and strength are very important for the electronic behavior. In recent years, the research on CO 2 photoreduction by g-C 3 N 4 -based photocatalysts has aroused a lot of concern and discussion [2, [12][13][14]. For instance, sulfur doped g-C 3 N 4 are designed to improve photocatalytic CO 2 reduction performance [15]. g-C 3 N 4 nanocomposites have been designed for effective CO 2 photoreduction, since the e−/h+ separation efficiency has risen, including Cu-NPs/g-C 3 N 4 [14], g-C 3 N 4 /Ag/m-CeO 2 [16] and Sr 2 Ta 2 O 7 /S-doped g-C 3 N 4 [17] heterojunctions.
In addition, Caux et al. [18] have studied Pt-g-C 3 N 4 for CO 2 photoreduction to improve the catalytic performance ascribed to the charge-separation efficiency. Different from these composite photocatalysts prepared by expensive metal salts, the preparation of pristine g-C 3 N 4 photocatalyst can be made facilely by thermally polycondensing the cheap N-rich precursors, such as cyanamide, dicyanamide, urea and melamine [19,20]. The outstanding characteristics of g-C 3 N 4 can be very beneficial in water splitting, CO 2 photoreduction, catalytic organic synthesis, organic contaminants purification and fuel cells [20]. In previous years, there are several excellent research on the g-C 3 N 4 preparation and applications [21,22]. In addition, all these studies result from the changes of the local atomic structure, electronic states and mechanical behavior of materials. Furthermore, strain is almost inevitable and the strain effects on the structural and electronic properties of two-dimensional materials have been studied for decades. Sometimes, strain is intentionally applied to improve mobility, as in the strained silicon technology, which is used in modern microelectronics [23]. Thus, it is crucial to understand how the strain affects the further deformation, electronic structures and mechanical properties for the CO 2 adsorbed g-C 3 N 4 .
In present paper, we investigate the mechanical, structural and electronic properties of biaxial tensile strain tuned CO 2 adsorbed g-C 3 N 4 system based on first-principles density functional theory (DFT) [24,25] calculations. The rest of the paper is organized as follows. Section 2 shows the calculation methods and optimized structures of CO 2 adsorbed g-C 3 N 4 system. Section 3 is devoted to the effects of biaxial strain regulated mechanical, structural and electronic properties of the adsorption system. Section 4 presents the conclusions.

Computational Methods
Our calculations are performed using DFT with the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) form [26], as implemented in the Vienna ab initio Simulation Package (VASP) code [24][25][26][27][28][29]. In addition, the projector augmented wave (PAW) [26] approach is derived. 5 × 5 × 1 Monkhorst-Pack k-point meshes [30] are used to sample the Brillouin zone. The PBE and HSE06 exchange-correlation functionals are adopted. The wave functions are expanded in a plane-wave basis set with an energy cutoff of 450 eV. The total energy and atomic forces are converged to 10 −6 eV and 0.02 eV/Å. The biaxial strain can be calculated with the following equation [31]: where a, b and a 0 , b 0 are the deformed (stretched or shrunken) and initial equilibrium lattice constants of unit cell. Figure 1a,b show the top and side views of unit cell for the CO 2 adsorbed g-C 3 N 4 system, respectively, which are represented by the dashed black parallelogram. The green, yellow and red balls represent C, N and O atoms, respectively. In addition, the orientation of biaxial tensile strain is marked with black arrows. The unit cell of pristine g-C 3 N 4 contains three types of N atoms and two types of C atoms (N1, N2, N3, C1 and C2), therefore there are four kinds of N-C bonds (N1-C1, C1-N2, N2-C2 and N3-C2) (shown in Figure 1). The optimized lattice constant of pristine g-C 3 N 4 turns out to be 7.15 Å, which is consistent with the previous studies [32,33]. We investigate optimization of adsorption system under biaxial tensile strain from 0 to 0.2 with an increment of 0.01 per step. Upon CO 2 adsorption, the planar g-C 3 N 4 structure of becomes buckled (puckered). Previous research has shown that CO 2 prefers to adsorb nearly parallel to the g-C 3 N 4 plane [34]. In this work, gas-phase calculations have proven useful because they provide in an unperturbed way rather detailed insight into the elementary steps of numerous transformations mediated by the catalysts. The green, yellow and red balls represent C, N and O atoms, respectively. In addition, the orientation of biaxial tensile strain is signed with black arrows. For the pristine g-C3N4, there are three types of N and two types of C (N1, N2, N3, C1 and C2).

Mechanical and Structural Properties
The stress-strain relations of CO2 adsorbed g-C3N4 system are displayed in Figure 2a. The stress increases almost linearly with the increasing biaxial tensile strain and reaches maximum at about 0.12 strain, then it suddenly drops as the strain increases. The phenomenon of linear elasticity in the CO2 adsorbed g-C3N4 system suggests that its stretchability may not reach high values, because its stretching of bonds have limitations. In order to study the deformation mechanism in more details, we display the bond lengthsstrain curves in Figure 2b,c. It has been found that the C-O bond lengths change relatively little with the increasing strain, so we only consider the N-C bonds here. It can be noticed that the outside N3-C2 bond (signed in Figure 1) is stretched more than the inner ones (N1-C1, N2-C1 and N2-C2 in Figure 1), because of the stronger stress concentration around the pore tip. From Figure 2b, we can see that the growth of all the inner bonds (N1-C1, N2-C1 and N2-C2) start to fall at 0.12 strain and show opposite changes of up and down at around 0.16 strain, resulting the decrease of stress-strain curve in Figure 2a. However, the outside N3-C2 bond continues to grow until strain of 0.18, as shown in Figure 2c. are the top and side views of the optimized CO 2 adsorbed g-C 3 N 4 (without strain) system within the unit cell, respectively, which is represented by the dashed black parallelogram. The green, yellow and red balls represent C, N and O atoms, respectively. In addition, the orientation of biaxial tensile strain is signed with black arrows. For the pristine g-C 3 N 4 , there are three types of N and two types of C (N1, N2, N3, C1 and C2).

Mechanical and Structural Properties
The stress-strain relations of CO 2 adsorbed g-C 3 N 4 system are displayed in Figure 2a. The stress increases almost linearly with the increasing biaxial tensile strain and reaches maximum at about 0.12 strain, then it suddenly drops as the strain increases. The phenomenon of linear elasticity in the CO 2 adsorbed g-C 3 N 4 system suggests that its stretchability may not reach high values, because its stretching of bonds have limitations. In order to study the deformation mechanism in more details, we display the bond lengths-strain curves in Figure 2b,c. It has been found that the C-O bond lengths change relatively little with the increasing strain, so we only consider the N-C bonds here. It can be noticed that the outside N3-C2 bond (signed in Figure 1) is stretched more than the inner ones (N1-C1, N2-C1 and N2-C2 in Figure 1), because of the stronger stress concentration around the pore tip. From Figure 2b, we can see that the growth of all the inner bonds (N1-C1, N2-C1 and N2-C2) start to fall at 0.12 strain and show opposite changes of up and down at around 0.16 strain, resulting the decrease of stress-strain curve in Figure 2a. However, the outside N3-C2 bond continues to grow until strain of 0.18, as shown in Figure 2c.
In Figure 3a,b, we draw the CO 2 adsorbed g-C 3 N 4 system along with its the electron localization function (ELF) [35] contour at biaxial strain of 0 and 0.12, and the ELF takes a value between 0 and 1. From the representation of the bond in the CO 2 adsorbed g-C 3 N 4 system, it can be determined that the outside N3-C2 bond breaks at 0.12 and 0.2 strain. It is clear that the ELF contour agrees with the study of the bond length variations, suggesting that these bonds are very active under biaxial strain, because the ELF values of the inner bonds are about 0.85, showing integrity of covalent bonding. Figure 3c shows the adsorption energy-strain curve to analyze the stability, and the adsorption energy Eads is calculated by the following equation [36]: where E total , E g-C 3 N 4 and E co 2 are the total energy of CO 2 adsorbed g-C 3 N 4 system, g-C 3 N 4 and CO 2 , respectively. It is worthwhile to note that the adsorption of CO 2 on g-C 3 N 4 is highly exothermic (negative adsorption energy) with strain less than 0.05, suggesting that g-C 3 N 4 can be an excellent gas sensor. In addition, the adsorption energy increases with the increasing strain, indicating stronger interaction between CO 2 and g-C 3 N 4 . It is interesting to see that energy-strain curve has a maximum slope at 0.12 strain, which means that there is the biggest deformation. Furthermore, the adsorption energy increases almost quadratically with increasing biaxial strain, showing an elastic behavior rather than a viscous one. This study also demonstrates that the CO 2 adsorbed g-C 3 N 4 system without strain is more stable. This is because the tensile strain weakens the bonds of the CO 2 adsorbed g-C 3 N 4 system, resulting in higher chemical reactivity. This distinct behavior can be ascribed to the adsorption configuration and charge transfer, which will be systematically discussed below. In Figure 3a,b, we draw the CO2 adsorbed g-C3N4 system along with its the electron localization function (ELF) [35] contour at biaxial strain of 0 and 0.12, and the ELF takes a value between 0 and 1. From the representation of the bond in the CO2 adsorbed g-C3N4 system, it can be determined that the outside N3-C2 bond breaks at 0.12 and 0.2 strain. It is clear that the ELF contour agrees with the study of the bond length variations, suggesting that these bonds are very active under biaxial strain, because the ELF values of the inner bonds are about 0.85, showing integrity of covalent bonding. Figure 3c shows the adsorption energy-strain curve to analyze the stability, and the adsorption energy Eads is calculated by the following equation [36]: (2) where , and are the total energy of CO2 adsorbed g-C3N4 system, g-C3N4 and CO2, respectively. It is worthwhile to note that the adsorption of CO2 on g-C3N4 is highly exothermic (negative adsorption energy) with strain less than 0.05, suggesting that g-C3N4 can be an excellent gas sensor. In addition, the adsorption energy increases with the increasing strain, indicating stronger interaction between CO2 and g-C3N4. It is interesting to see that energy-strain curve has a maximum slope at 0.12 strain, which means that there is the biggest deformation. Furthermore, the adsorption energy increases almost quadratically with increasing biaxial strain, showing an elastic behavior rather than a viscous one. This study also demonstrates that the CO2 adsorbed g-C3N4 system without strain is more stable. This is because the tensile strain weakens the bonds of the CO2 adsorbed g-C3N4 system, resulting in higher chemical reactivity. This distinct behavior can be ascribed to the adsorption configuration and charge transfer, which will be systematically discussed below.

Electronic Properties
Band structures calculated with PBE and HSE06 methods for CO2 adsorbed g-C3N4 are shown in Figure 4a-d,i-l. The conduction band minimum (CBM) and valance band maximum (VBM) band edge positions are denoted by the red and blue points, which are signed with A and B, respectively. Apparently, both PBE and HSE06 band gaps exhibit direct (K to K) to indirect (K to Γ) transitions at strain from 0 to 0.04 [see Figure 4a,b,i,j],

Electronic Properties
Band structures calculated with PBE and HSE06 methods for CO 2 adsorbed g-C 3 N 4 are shown in Figure 4a-d,i-l. The conduction band minimum (CBM) and valance band maximum (VBM) band edge positions are denoted by the red and blue points, which are signed with A and B, respectively. Apparently, both PBE and HSE06 band gaps exhibit direct (K to K) to indirect (K to Γ) transitions at strain from 0 to 0.04 [see Figure 4a,b,i,j], and then turns to be direct (Γ to Γ) again at 0.12 strain [see Figure 4c,d,k,l]. Moreover, in Figure 4e-h, we plot the PBE high transition probabilities between the topmost valence and the lowest conduction bands, which are revealed by the squares of the dipole transition matrix elements [37], P 2 , at all the k-points. It is found that the CO 2 adsorbed g-C 3 N 4 system has large dipole transition matrix elements around Γ point, especially at 0.2 strain, indicating strong optical absorption coefficients of photons with energies near the bandgap, which is essential in optoelectronic applications. However, at any strain, the transition matrix amplitudes between band edges are very weak around the M and K points. The rich tunable properties show tremendous potential applications of the biaxial strained CO 2 adsorbed g-C 3 N 4 system in elastic nanoelectronic and optoelectronic devices [38][39][40]. Moreover, comparison between the PBE and HSE06 shows that entire shape of band structures is independent of the functional. It is evident that the CBM and VBM are the same in PBE and HSE06. Both functionals show the same type (direct or indirect) of band structures. The band gap is the main difference of the band structures calculated using the two functionals. Therefore, one can qualitatively study the band structures of CO 2 adsorbed g-C 3 N 4 with PBE instead of calculating the band in expensive HSE06. In addition, we conducted computational studies (PBE and HSE06) on defected g-C 3 N 4 to elucidate how the biaxial strain is affected by CO 2 adsorption in the supporting information Figure S1. It is found that the band structures show metal states under 0 to 0.2 strain.  Figure 5 shows the PBE and HSE06 band gaps of CO2 adsorbed g-C3N4 as a function of strain. The HSE06 can provide a better prediction of band gap in general. In addition, the HSE06 band gaps are found to be higher than the PBE values under the same strain. Furthermore, the band gap-strain curves of the two methods have the same changing tendency that both methods reach the maximum at 0.12 strain, where the indirect-direct tran-  Figure 5 shows the PBE and HSE06 band gaps of CO 2 adsorbed g-C 3 N 4 as a function of strain. The HSE06 can provide a better prediction of band gap in general. In addition, the HSE06 band gaps are found to be higher than the PBE values under the same strain. Furthermore, the band gap-strain curves of the two methods have the same changing tendency that both methods reach the maximum at 0.12 strain, where the indirect-direct transition occurs, and it is the maximum tensile strength point of the CO 2 adsorbed g-C 3 N 4 system.

Conclusions
In this work, we have investigated mechanical, structural and electronic properties of CO2 adsorbed g-C3N4 system under biaxial tensile strain by performing first-principles calculations. The CO2 adsorbed g-C3N4 system shows linear elasticity and has high strength at 0.12 strain, which is mainly induced by the stretching of N-C bonds in the g-C3N4 plane. In addition, the outside N-C bonds are stretched more than the inner ones. The unstrained CO2 adsorbed g-C3N4 is more stable because of the bonds weakened by the stretching strain. Both the PBE and HSE06 band gaps exhibit direct-indirect transitions under biaxial tensile strain and reach maximum at 0.12 strain. There are large dipole transition matrix elements around Γ point, showing high optical absorption coefficients, which would be beneficial to the applications of elastic nanoelectronic and optoelectronic devices.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: (a-j) are PBE and HSE06 calculated band structures of the CO2 adsorbed on defective g-C3N4 system at 0, 0.05, 0.1, 0.15 and 0.2 strain. The Fermi energy is set at zero energy and indicated by the red dashed line. (k) is the optimized structure of the CO2 adsorbed on defective g-C3N4 system without strain.

Conclusions
In this work, we have investigated mechanical, structural and electronic properties of CO 2 adsorbed g-C 3 N 4 system under biaxial tensile strain by performing first-principles calculations. The CO 2 adsorbed g-C 3 N 4 system shows linear elasticity and has high strength at 0.12 strain, which is mainly induced by the stretching of N-C bonds in the g-C 3 N 4 plane. In addition, the outside N-C bonds are stretched more than the inner ones. The unstrained CO 2 adsorbed g-C 3 N 4 is more stable because of the bonds weakened by the stretching strain. Both the PBE and HSE06 band gaps exhibit direct-indirect transitions under biaxial tensile strain and reach maximum at 0.12 strain. There are large dipole transition matrix elements around Γ point, showing high optical absorption coefficients, which would be beneficial to the applications of elastic nanoelectronic and optoelectronic devices.