Introduction

About half of the carbon dioxide emitted from the anthropogenic activities such as fossil fuel combustion remains in the atmosphere [1]. On the other hand, incomplete combustion of fossil fuels will lead to the formation of carbon monoxide. These two gases, i.e., CO2 and CO are major pollutant gases which are responsible for the greenhouse effect [2, 3], global warming [4,5,6,7], and climate change [8]. The continuous increase in the amount of CO2 is also responsible for the change in the pH level of oceans [9]. Moreover, carbon monoxide is more dangerous than CO2 because the hemoglobin that is present in our bloodstreams reacts easily with carbon monoxide and forms a stable compound which prevents oxygen to enter in our body [10]. The economic and industrial development of the developing countries is also contributing to the emission of these gases [11]. Cement industries are also contributing to the emission of CO2 [12, 13]. Limestone and decomposition of limestone are also responsible for the emission of CO2 [14]. As we all know that symmetry of bonds in CO2 is such that it is non-polar in nature [15]. So activation of CO2 and its conversion into important chemicals at room temperature was an important research by Y. Toda et al. [15]. The TPD (temperature-programmed desorption) yield for CO2 adsorption on C12A7:e− surface was greater than any other gas species [15]. Therefore, we need a special type of instrument, material etc. that can store or capture these gases easily [16,17,18].

Reaction of CO and CO2 with different clusters of metal proved to be a very important step to reduce the emission of CO and CO2 [19,20,21,22,23]. Si Zhou et al. [24] in their research took germanium clusters as a catalyst for the catalysis of CO oxidation. Their dual transition metal clusters were stable during the reaction process. In 2018, Qi- Yan Zhang et al. [25] showed the electrochemical reduction of CO2 to CH4 with the help of density functional theory (DFT). The storage of CO and CO2 over gas-phase clusters requires a special container that will be expensive and will require large storage area. Therefore, cluster in solid-state phase will have many benefits over the cluster in the gas phase. E. Durgun et al. [26] found that C2H4Ti2 cluster could hold ten H2 molecules at 300 K. They checked the stability of C2H4Ti2 with the help of vibrational frequencies analysis. Shevlin et al. [27] in their research took ethylene complexes to store hydrogen molecules. They took transition metal–doped carbon systems to store hydrogen molecules. They dimerize C2H4Ti2 to form C4H8Ti4 through the formation of Ti–Ti bond. In this letter, using density functional theory, we report the adsorption of 8 molecules, each of CO2 and CO on the C4H8Ti4 cluster. Due to the ferromagnetic nature of this cluster, it has advantages over the gas phase cluster. We can hold the cluster over a metal plate and can be easily made for reuse.

Computational methods

All the calculations were performed with the GAMESS [28] package. The density functional used was Becke’s three-parameter hybrid method combined with the Lee, Yang, and Parr correlation functional (B3LYP). The 6-31G (d,p) basis set was chosen for the considered atoms. The calculations were considered to be converged when the density change between two consecutive SCF cycles was less than 10−5. In the first step, we obtain the optimized geometry of C4H8Ti4 presented in Fig. 1. In the subsequent calculations, we allow eight molecules, each of CO and CO2, to react with the cluster. During the geometry optimization, all the coordinates of C4H8Ti4 cluster were fixed and CO and CO2 molecules were allowed to relax. The graphical package Ghemical was used to draw the molecules and Macmolplt was used to visualize the results.

Fig. 1
figure 1

Optimized geometry of C4H8Ti4 cluster

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Results and discussion

The adsorption of CO2 and CO on different transition metal–doped clusters has been studied by different researchers in past few years. In our research, we take 8 molecules each of CO and CO2 that are adsorb on the C4H8Ti4 cluster. We will divide our result and discussion into different parts. First, we discuss the optimized structure of C4H8Ti4 cluster and after that, we will discuss various parameters such as atomic orbital coefficient, HOMO-LUMO analysis, dipole moment, Mulliken population analysis, and binding energy.

Structural analysis

Figure 1 shows the optimized geometry of C4H8Ti4 cluster that is formed after the dimerization of C2H4Ti2. The cluster is stable and has dipole moment of 0.001 Debye. The bond distance between Ti4–Ti5 is 2.265 Å. The bond length between Ti6–C8 and Ti3–C1 is 1.996 Å. The bond length between C8–H15 and C1–H9 is 1.116 Å. The bond length of H–C varies from 1.10 to 1.11 Å approximately. In Fig. 2a and b, we have shown the HOMO and LUMO of cluster C4H8Ti4. Their energies are equal to − 3.15 eV and − 1.90 eV respectively. The difference of energy between HOMO and LUMO is 1.25 eV. As we know that the actual total charge of four Ti atoms is 88 electrons but our calculations show that four Ti atoms in C4H8Ti4 cluster contain electronic charge equal to 86.12 electrons. Similarly, the total charge on four C atoms and eight H atoms was found to be 26.96 and 6.91 electrons respectively. It means hydrogen and titanium both loses electrons that were gained by carbon atoms. The total electrons gain by carbon atoms from titanium and hydrogen atoms are 2.96 electrons.

Fig. 2
figure 2

a HOMO and b LUMO representation of C4H8Ti4 cluster

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Figures 3 and 4 are showing the adsorption of CO2 and CO molecules respectively on the C4H8Ti4 cluster. The average bond length of Ti–O in C4H8Ti4–CO2 complex varies from 2.005 to 4.786 Å approximately and nearest bond length between Ti–O is 2.005 Å. In C4H8Ti4–CO2 complex, CO2 is linked with titanium generally via oxygen atom while in C4H8Ti4–CO complex, CO is linked to titanium generally via carbon atom. The average bond length of Ti–C in C4H8Ti4–CO complex varies from 2.15 to 5 Å approximately. The nearest distance between Ti–C is 2.155 Å. The adsorption configuration of CO2 on cluster in Fig. 3 is such that the O–C–O angle is not exactly 180° but all O–C–O in complex are tilted by certain degrees to get the stable configuration. The tilted angle of O–C–O varies from 116 to 178° approximately. Similarly, this trend was observed in the adsorption of CO molecules and is presented in Fig. 4 having different Ti–C–O angle ranging between 171 and 178° approximately.

Fig. 3
figure 3

Optimized geometry of C4H8Ti4–CO2 complex

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Fig. 4
figure 4

Optimized geometry of C4H8Ti4–8CO complex

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HOMO-LUMO analysis

The atomic orbital coefficient helps in finding the dominant factor of an orbital over other orbitals. In our work, we find that for HOMO, the p orbital of 1C atom of C4H8Ti4 cluster has the highest occupancy among all other orbitals. For 2C and 3Ti atom, the s orbital has the highest occupancy. For 4Ti and 5Ti atom, the p orbital has the highest occupancy. For 6Ti, 7C, and 8C atoms, the s orbital has the highest occupancy. The hydrogen atom orbitals show negligible contribution in occupancy. Similarly, if we talk about LUMO, the s orbitals of 1C, 2C, 3Ti, 6Ti, 7C, and 8C atoms have the highest occupancy among all other orbitals while for 4Ti and 5Ti atoms, the d orbital has the highest occupancy.

In Fig. 3, we can see that six out of eight molecules of CO2 are attached with our cluster C4H8Ti4. CO2 molecules are mainly attached with titanium atoms of the cluster. The HOMO and LUMO orbital energies of C4H8Ti4–8CO2 complex come out to be − 132.610 and − 81.372 eV respectively. The difference in their energy is equal to 51.238 eV. We can see from Fig. 4 that all eight CO molecules are attached with our cluster having different bond length. CO molecules are also mainly attached with titanium atoms of the cluster same as in case of CO2. The HOMO and LUMO orbital energies of C4H8Ti4–8CO complex come out to be − 111.878 and − 78.781 eV respectively. The difference in their energy is approximately equal to 33 eV. The difference between HOMO and LUMO of cluster C4H8Ti4 was approximately equal to 34 eV. The difference between HOMO and LUMO that is known as HOMO–LUMO gap helps us in knowing the strength and stability of our cluster C4H8Ti4 upon complexion with CO.

With the help of Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO), we can predict the electronic properties of clusters and complexes. In the process of chemical reactions, HOMO-LUMO plays an important role and hence HOMO-LUMO analysis is useful in determining the chemical stability of complexes and clusters. Furthermore, with smaller the HOMO-LUMO gap, the excitation of electrons in cluster and complex will be more easy in comparison with the cluster that has large HOMO-LUMO gap. The HOMO-LUMO gap for C4H8Ti4–8CO2 complex is larger than the C4H8Ti4–8CO complex, which reveals that the C4H8Ti4–8CO2 complex requires more energy to excite electrons. The HOMO-LUMO gap of 51.238 eV and 33 eV for C4H8Ti4–8CO2 and C4H8Ti4–8CO complexes respectively indicates that C4H8Ti4–8CO2 complex has relatively higher kinetic stability.

Dipole moment analysis

Dipole moment helps in the characterization of chemical bonds and it also helps in determining the ionic character of a molecule. The site which is highly charged is the most reactive site in a molecule. The dipole moment of C4H8Ti4–8CO complex is 2.336 Debye. Previously, this dipole moment of our cluster alone was 0.001 Debye. In Fig. 3b, we have shown the CO2 molecules attached to our cluster. The dipole moment of C4H8Ti4–8CO2 complex is 3.837 Debye. So, larger the dipole moment greater will be the stability of our cluster with CO2. The dipole moment of C4H8Ti4–8CO2 is greater than C4H8Ti4–8CO. So complexion of C4H8Ti4 cluster is more stable with CO2 in comparison with CO. The redistribution of charge is the main reason behind this dipole moment change.

Binding energy analysis

Binding energy, as we all know, is the minimum energy required to breakdown a system of particles into separate segments. The binding energy of CO with C4H8Ti4 cluster which was calculated as the difference of total energy between the C4H8Ti4–CO complex and C4H8Ti4 cluster and CO molecule separately is equal to 1.1573 eV. Similarly, the binding energy of cluster C4H8Ti4 with CO2 is 2.14 eV. We all know that greater the binding energy, greater will be the energy required to separate the particles from each other. This means that if we want to separate CO2 from a cluster, we have to supply more energy in comparison with CO. So we can say that complexion with CO2 is rather more stable in comparison with complexion with CO.

Mulliken population analysis

In computational chemistry, Mulliken population analysis is used to calculate partial atomic charges that are based on the linear combination of atomic orbitals. According to Mulliken population analysis, in C4H8Ti4–8CO2 complex, the carbon atoms of CO2 lose 5.13 electrons while carbon atom of cluster C4H8Ti4 gains 2.87 electrons, hydrogen atoms lose 1.24 electrons, and titanium atoms lose 3.38 electrons. Overall, the oxygen atom of CO2 in C4H8Ti4–CO2 complex gains 6.89 electrons. Similarly, in C4H8Ti4–8CO complex, the 4Ti loses 2.22 electrons approximately. The overall charge gain by carbon is 0.67 electrons. The charge transfers from all hydrogen atoms are 1.20 electrons. The total charge gain by oxygen is 2.75 electrons. So if we add the total charge of carbon and oxygen and subtract it from hydrogen charge, then we get the 2.22 electrons that are equal to the value of the 4Ti charge which was transfer or loses by 4Ti.

Conclusions

Optimized geometry, dipole moment, and binding energy of C4H8Ti4 cluster with CO and CO2 were calculated with the help of DFT by using B3LYP functional. In our study, we find that C4H8Ti4 transition metal cluster is very emphatic and useful for CO and CO2 adsorption. The binding energy of C4H8Ti4–CO2 complex was greater than C4H8Ti4–CO complex which indicates that C4H8Ti4 cluster holds CO2 molecules more strongly in comparison with CO molecules. The dipole moment of C4H8Ti4–CO2 complex was greater than C4H8Ti4–CO complex which indicates that C4H8Ti4–CO2 complex is more polar. The structural analysis of C4H8Ti4 cluster complexes with CO2 and CO indicates the strong binding of CO2 and CO. The low cost, stable, non-toxic, and ferromagnetic nature of transition metal C4H8Ti4 cluster provides a great scope for CO and CO2 adsorption and will help in reducing the harmful effects.