# Density Functional Theory Study on the Adsorption of Co(II) in Aqueous Solution by Graphene Oxide
## 4 Study on the Mechanism of GO Adsorption Process
### Influence of External Environment on Adsorption
#### 4.2.1 pH  
The pH value of the adsorption solution is closely related to the existence of hydrogen functional groups and metal ions on GO. When the acid is strong, a large amount of H\({}^{+}\) in the solution surrounds the material, increasing the protonation degree of GO, and the functional groups on the surface of GO exist in their original form. In this case, metal ions and adsorbents may be combined through coordination. When the pH of the solution gradually increases, H\({}^{+}\) on the GO surface gradually decreases, and some hydroxyl and carboxyl groups even remove H\({}^{+}\) in the form of -O- and -COO-, which are directly combined with positively charged metal ions through electrostatic adsorption. If the pH continues to increase to more than 7, cobalt and manganese ions will be hydrolyzed and precipitated, which can also maintain a high removal rate, but it loses the significance of studying adsorption, so this paper only considers the case that the solution is acidic. In the acidic solution, GO(COOH), GO(OH)s, GO(OH)\({}_{b}\) and their structures after hydrogen ion removal, GO(COO)\({}^{-}\), GO(O)s\({}^{-}\), GO(O)\({}_{b}\)\({}^{-}\) and Co\({}^{2+}\), were placed in the same space, and Gaussian software was used to calculate the following results:  
1. When GO(COOH), GO(OH)s and GO(OH)\({}_{b}\) form complexes with Co\({}^{2+}\), the adsorption energy is negative, which means that the adsorption process requires external energy absorption, indicating that it is difficult for the complexes formed to exist stably. 2. When the pH gradually rises in the acidic range, GO(COO)\({}^{-}\) and GO(O)s\({}^{-}\) can rapidly combine with Co\({}^{2-}\) to form a stable structure. However, the existence form of GO(O) is not affected by pH changes and can also combine with Co\({}^{2+}\) to form a stable configuration. When GO(COO)\({}^{-}\) combines with Co\({}^{2+}\), the hydroxyl oxygen atom on the carboxyl group is connected with a metal ion, the structure is recorded as [GO(COO)...Co]\({}^{+}\), and the energy of the stable structure is \(-\)1561.056966 Hartree. The stable structure formed by GO(O)s\({}^{-}\) and Co\({}^{2+}\) is written as [GO(O)s...Co]\({}^{+}\), its energy is \(-\)1448.23174 Hartree, and the stable structure formed by GO(O) and Co\({}^{2+}\) is written as [GO(O)...Co] with energy of \(-\)1449.352687 Hartree. 3. When GO(O)\({}_{b}\)\({}^{-}\) and Co\({}^{2+}\) are placed in the same space, they also can form a stable configuration, but the Gaussian calculation shows that no chemical bond is formed between Co\({}^{2+}\) and GO. Since the chemical bond type shown in the Gaussian calculation does not correspond to the actual situation one by one, in order to further determine whether there is a bond between them, this paper calculates the Mayer bond level of the complex through a powerful file-processing software Multifwn [18]. The Mayer bond level is calculated based on the wave function in quantum chemistry, which can be physically understood as the logarithm of electrons shared between atoms [18]. For single/double/triple bonds, the Mayer level is closer to 1.0/2.0/3.0, while for atoms with no or little bonding, the Mayer level is closer to 0. If the Mayer level is less than 0.5, it is considered weak bonding [19]. The Mayer bond level between the hydroxyl oxygen and Co\({}^{2+}\) at the edge of the GO lamella is calculated to be close to 0, which proves that the chelation between the metal and the O atom is weak, which also corresponds to the weak electronegativity of the hydroxyl group at the edge of the graphene lamella. After calculation, in a stable configuration, the energy of Co\({}^{2+}\) is \(-\)144.742875 Hartree, and the energies of GO(COO)\({}^{+}\), GO(O)s\({}^{-}\) and GO(O) are \(-\)1415.785741 Hartree, \(-\)1302.989132 Hartree and \(-\)1304.337224 Hartree. The binding energy between GO and metal ions = metal energy + GO energy \(-\) energy after binding. The calculated adsorption energies of GO containing different functional groups on metal ions are shown in Table 2.