On analysis of thermodynamic properties of cuboctahedral bi-metallic structure

Porous materials, for example, metalnatural structures (MOFs) and their discrete partners metalnatural polyhedra (MOPs), that are built from coordinatively unsaturated inorganic hubs show incredible potential for application in gas adsorption/partition cycles, catalysis, and arising openings in hardware, optics, detecting, and biotechnology. A well-known hetero-bimetallic metalorganic polyhedra of this discrete partners metalnatural polyhedra (MOPs) class is cuboctahedral bi-metallic stricture. In this paper, we discuss the stricture of Heterobimetallic metalorganic polyhedra (cuboctahedral bi-metallic). Also, we computed the topological indices based on the degree of atoms in this cuboctahedral bi-metallic structure.


Introduction
Development of large molecules that are amiable to plan also, functionalization is of essential current interest as it speaks to a significant advance in the accomplishment of atomic complexity. We accept that enormous permeable atoms fill in as charming beginning protests toward this path since the openings to their voids might be helpful in directing the specific delivery and official of more modest molecules (Eddaoudi et al., 2001;Müller et al., 1998).
At present there are in any event two difficulties that must be tended to for bigger and more intricate frameworks to be figured it out. To begin with, single precious stones of huge particles are hard to get, accordingly blocking their full primary portrayal; second, plan of unbending substances that keep up their structure without visitors to take into consideration reversible admittance to the voids also as compound functionalization of their voids and outside surface remains generally unexplored (Fujita et al., 1999).
Given these difficulties and considering our ongoing work on metal-natural structures (MOFs), where we have illustrated the utilization of optional structure units (SBUs) as intends to the development of unbending organizations with perpetual porosity, we looked for to utilize the oar wheel group embraced by copper (II) acetic acid derivation, Cu 2 (CO 2 ) 4 , as an unbending SBU for tending to these difficulties. Fundamentally, the gathering of such SBUs with polytopic carboxylate linkers produced unbending permeable systems with open metal destinations where it is conceivable to functionalize the pores with various ligands (Day et al., 1989;Hong et al., 2000).
The clusters investigated of unit cell of cuboctahedral bi-metallic by DFT methods is dedicated in Figure 1. In which Hydrogen bound structures were advanced and checked to be at least on the potential energy surface with zero negative eigenvalue of the Hessian. Critically, the Pd site indicated no considerable cooperation with H 2 by and large no minima were found. The bimetallic groups were contrasted with the scandalous CuCu bunch, which was demonstrated in the trio state. All hydrogen communication energies were adjusted for premise set superposition error and zero-point energy commitments (Teo et al., 2016).
Here we depict the amalgamation and characterization of an arrangement of permeable metalnatural polyhedra developed from bimetallic paddle wheels that are, up to this point, uncommon building blocks for structure materials. The bimetallic metal units depend on a PdIIMII (M = Ni, Cu, or Zn) theme (Figure 2), where the Pd(II) particles transcendently dwell on the inside of the cuboctahedral confines. As an outcome, the outside of the MOPs can be specifically enhanced with a progression of first column change metals that can be responded to give open coordination locales. We misuse this element and decide the gas adsorption properties of these extraordinary materials tentatively, utilizing a hypothetical examination to additionally clarify the adsorption. Eminently, they show incredibly high take-up of hydrogen for discrete permeable particles (Teo et al., 2016).

Degree-based topological indices
Let G = (V; E) be a graph where V be the vertex set and E be the edge set of G. The degree of a vertex a is the number of edges of G incident with a. Mathematical chemistry connects graph theory to science and focuses its consideration on the ideas of chemical graphs known as a molecular graph where atoms in the molecules are represented by vertices and bonds by edges. In fact, topological theories have often been used in the field of chemistry, the topology of an atom determines the form of prominent Huckel sub-atomic orbitals. Normally the vertex degree is referred to its valency in a chemical graph.
The first degree-based index is introduced by Randic (1975) as: (1) Amic et al. (1998) and Bollobás and Erds (1988) proposed the general Randic index as: ( 2) The atom bond connectivity index is o introduced by Estrada et al. (1998) as: ( 3) The geometric arithmetic index is introduced by Vukicevic and Furtula (2009) as: (4)  The first and second Zagreb index is formulated by Gutman and Trinajsti (1972) and Gutman and Das (2004) as: In 2008, Došlić put forward the first Zagreb coindex and second Zagreb coindex (Došlić, 2008), defined as: For more details about these indices see Gao et al. (2016Gao et al. ( , 2017Gao et al. ( , 2018 Gutman and Trinajsti (1972) and Furtula and Gutman (2015) presented forgotten topological indices which was characterized as: (12) Furtula et al. (2010) defined augmented Zagreb index as: The Balaban index (Balaban, 1982;Balaban and Quintas, 1983) is defined as for a graph G of order n, size is defined as: (14) The redefined version of the Zagreb indices was defined by Ranjini et al. (2013), namely, the redefined first, second and third Zagreb indices for a graph G as:

Results for cuboctahedral bi-metallic (MOPs)
The number of vertices and edges of cuboctahedral bi-metallic (MOPs) are 196n and 240n, respectively. Since there are four type of vertices in cuboctahedral bi-metallic (MOPs) namely the vertices of degree 1, 2, 3, 4, respectively. The vertex partition of the vertex set cuboctahedral bi-metallic (MOPs) is presented in Table 1. Also, the edge partition of cuboctahedral bi-metallic (MOPs) based on degrees of end vertices of each edge are depicted in Table 2.

For
The numerical and graphical representation of above computed results are presented in Table 3 and Figures 3 and 4, respectively.

The geometric arithmetic index
The numerical and graphical representation of above computed results are presented in Table 4 and in Figure 5."  3.6 The first Zagreb coindex 3.7 The second Zagreb coindex

The hyper Zagreb index
The hyper Zagreb index is computed by using Table 2 as follows:

The forgotten index
The forgotten index is computed as:

The augmented Zagreb index
The augmented Zagreb index is computed as below:

The Balaban index
The numerical and graphical representation of above computed results are presented in Table 7 and in Figure 9.

The redefine Zagreb indices
The redefine Zagreb indices are computed as:  The numerical and graphical representation of above computed results are presented in Table 8 and in Figure 10.

Conclusion
In this paper, we discuss the structure of Hetero-bimetallic metalorganic polyhedra (cuboctahedral bi-metallic). Also, we computed the topological indices based on the degree of atoms in this cuboctahedral bi-metallic structure. More preciously we have computed, Randic indices, Zagreb type indices, forgotten index, geometric arithmetic index, and Balaban indices. Also, we provide the numerical and graphical representation of computed results, which leads us to describe the thermodynamics properties of hetero-bimetallic metalorganic polyhedra (cuboctahedral bi-metallic structure)." Funding information: The research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, 11601485).