View of CORRELATION OF EFFECTIVE CHARGE WITH SCHULTZ AND RANDIC MOLECULAR TOPOLOGICAL INDICES

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CORRELATION OF EFFECTIVE CHARGE WITH SCHULTZ AND RANDIC MOLECULAR

TOPOLOGICAL INDICES S. Khatri

Professor, Shri RGP Gujarati Professional Institute, Indore P. A. Kekre

Professor of Physics P. M. B. Gujarati Science College, 01, Nasia Road, Indore

Abstract: Effective charge as a total charge within a certain molecular volume around the nucleus. Some Co (II) complexes were used to establish correlation between effective charge with some topological indices like Schultz and Randic. Many studies have been made where the various physico – chemical properties are correlated with the topological indices because the properties of a molecular system are affected by the topology of molecule. These studies have shown a very good correlation demonstrating the utility of the graph theoretical approach. The result obtained in these studies shows that the topological indices of organic molecule acting as a legend can be used for estimating effective charge theoretically.

1 INTRODUCTION

Earlier, we have established a correlation between topological index (Winer and Balaban Index) and X-Ray parameter1, 2, 3, 4 in present works we have now established a correlation between effective charge with Schultz5 and Randic6 index.

2. GENERATION OF SCHULTZ AND RANDIC INDEX –

The Schultz molecular topological index of G denoted by MTI, is defined as MTI = Σ𝑒𝑖𝑛𝑖=1

Where ei’s, (1, 2, 3 …n) represents the elements of the following row matrix of order n.

V (G) [A (G) + D (G)] = [e1, e2, ---en]

Where V (G) is the valence row matrix, A (G) and D (G) are adjacency and distance matrix respectively.

The Randic Index makes use of vertices present in the chemical graph and therefore, it is sensitive to the shape also. Hence this index is also known as molecular connectivity index .

It is equal to the some of the values of all molecular edge

The variables m and n are the valencies of the bond end points of each edge.

3. RESULTS AND DISCUSSION

Table 1 contains name of complexes and their molecular graph. Table 2 contains effective charge, Schultz and Randic Index.

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Table 1 Name of the Complexes and their molecular graphs.

Table 2 Effective charge, Schultz Index and Randic Index Co (II)- Substituted Pyrazolm – 5 One complex.

The position of X-ray absorption edge depends upon the valence of the absorbing ion the effective charge on the central atom and also upon the geometry of the complex. 7, 8 in the present work the K-absorption edge for all Co (II) complexes is found to be higher energy side.

The order of effective charge for complexes as indicated by their values has been found to be as follows:

CoPN > CoPZ > CoPT > CoPZ5 > CoPS

The order is due to fact that - NH and –C=O stretching frequencies are observed at 3380 and 1750 cm-1 respectively. However, upon complexation the bond due to the –NH stretching is again retained at 3380 cm-1 because of the presence of another –NH group.

The larger values of effective charge in all Co (II) complexes show that the complexes are more ionic in character. As the edge shift is taken to be proportional to the ionic character9.

According to suchet10 the effective charge is a result of two factors –

1. Electro negativity difference between the constituent atoms which tends to bring them to complete ionic electronic configuration and

2. Polarizations due to the inter penetrations of the electron clouds.

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Not only ligation of a particular type e.g. Co-O or Co-N is responsible in imparting ionic character to the complex, but their position in the planer ring / axial position also contributes to the ionic character. We used gianturco and Coulson method11. For calculating effective charge.

Figure 1 and 2 shows correlation between effective charge (Zeff) with Schultz Index and Randic Index respectively

The correlation assumes the general form

Where TI stands for a particular topological index and a is constant.

The figure 1 represents the correlation for effective charge and Schultz Index. While figure 2 demonstrates the correlation for Randic Index and effective charge. Both the plots yield excellent parabola (Second order polynomial)

It is gratifying that the correlation between effective charges of Co (II) complexes with Schultz Index is better than that with Rendic Index. We can say that the effective charge thus estimated indicates that topological indices of the organic molecules acting as ligands can be used for estimating effective charge theoretically.

4. CONCLUSION

Schultz and Randic molecule topological indices contain important structural information.

Thus the topological understanding of molecular properties can lead to the development of new area of the present and future interest i.e. designing of drugs and tracking the effect of pollutants in the environment.

REFERENCES

1. Kekre PA, Joshi KP, Khatri S and Mishra A 1996 Bull Soc Belg. 105169

2. Mishra A, Khatri S, Joshi KP and Kekre PA 2000 Asian Journal of Physics 9 345.

3. Kekre PA, Khatri S, Mishra A and Joshi K.P. 2012, Journal of Physics, conference series 36501201

4. Khatri S, And Kekre PA, Jun, 2018, Global Journal of Engineering Science and Researches 10-5281/

Zenoda1293875.

5. Schultz H.P. 1989 J. Chem. Inf. Computer Sci 29, 227.

6. Randic M 1975, J Am Chem Soc 97i6609.

7. Agrawal BK and Verma L.P. 1970 J. Phy C3535.

8. Shrivastava US, Nigam H.L. and Vishnoi A.N. 1971 Ind. J. Pure and applied Phy 963.

9. Barinskii R.L. 1967, J Struet Chem USSR, 8 , 805 10. Suchet J.P. 1965, Am. Chem. 10, 512.

11. Gianturco F.A. and Coulson C.A. 1968, Mol. Phys 14223