1. “Topological Index Calculator” A JavaScript application to introduce quantitative structure-property relationships (QSPR) in undergraduate organic chemistry Irvin J. Levy, Departments of Chemistry & Computer Science, Gordon College, Wenham, MA 01984, ijl@gordon.edu Steven D. Granz, Departments of Mathematics & Computer Science, Gordon College Since the development of the Wiener Index, numerous topological indices have been described. These methods convert molecular structure to a mathematical representation (a chemical graph) and then define computations to be performed on the resulting graph. Statistical correlations between those results and physical properties serve as a predictive tool. In organic chemistry, students are taught the relationship between molecular structure and boiling point but generally do not investigate the phenomenon because tools to support the tedious calculations are lacking. We have developed a JavaScript program, "Topological Index Calculator," which computes key indices rapidly. Use of JavaScript benefits instructors who may wish to modify or extend the program's capabilities and students who may want to use the tool easily both in and out of the laboratory. With this program, students may work cooperatively to develop correlations between topological indices and physical properties of alkanes. Background: A topological index is a value that is dependent on the molecular structure of a molecule. They are used to approximate physical properties of molecules, such as the boiling point. To get a better understanding of how indices are used, we will examine how to calculate the Wiener Index of a molecule. Two very important graph-theoretical matrices are the adjacency matrix and the distance matrix. Both of these can be used to find the Weiner Index of a molecule. The adjacency matrix A of a labelled connected graph G with N vertices, is a square symmetric matrix of order N. It is defined as: A ij = 1;if vertices i and j are adjacent = 0; otherwise The distance matrix D of a labelled connected graph with N vertices, is a square symmetric matrix of order N. It is defined as: D ij =l ij ;if i ≠ j =0;otherwise where l ij is the length of the shortest path (the distance) between the vertices i and j in G. The Wiener Index is defined as one-half the sum of the elements of the distance matrix. N N W=1/2∑ ∑D ij i=1 i=1 For example: What is the Wiener Index of 2,3-dimethylbutane? Adjacency Matrix: 2,3-dimethylbutane 0 1 0 0 0 0 1 0 1 0 1 0 A =0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 Distance Matrix: 2,3-dimethylbutane 0 1 2 3 2 3 1 0 1 2 1 2 D=2 1 0 1 2 1 3 2 1 0 3 2 2 1 2 3 0 3 3 2 1 2 3 0 Wiener Index: 2,3-dimethylbutane 0 + 1 + 2 + 3 + 2 + 3 + 1 + 0 + 1 + 2 + 1 + 2 + 2 + 1 + 0 + 1 + 2 + 1 + 3 + 2 + 1 + 0 + 3 + 2 + 2 + 1 + 2 + 3 + 0 + 3 + 3 + 2 + 1 + 2 + 3 + 0= 58 Wiener Index = 58 / 2 = 29 Results: Topological indices can be calculated quickly using the “Topological Index Calculator.” This information can easily be used to create an index equation by plotting the experimental boiling point vs. the index computed for a set of molecules and performing a linear regression analysis on the data. For example, data in the table below can be used to generate index equations for alkanes. Index equations created for particular indices to predict approximate boiling point of molecules: N: BP = 177.38 ln(N) + 24.742 Average Error: 2.30% Polarity: BP = 10.16 (Polarity Index) + 323.6Average Error: 4.63% Wiener: BP = 56.81 ln(Wiener Index) + 157.99 Average Error: 2.85% Balaban: BP = 25.684 (Balaban Index) + 324.95Average Error: 7.69% Odd-Even: BP = 156.97 ln(Odd-Even Index) + 1.9792 Average Error: 4.53% Vertex Degree Distance: BP = 45.453 ln(VDD Index) + 313.74 Average Error: 8.95% Harary: BP = 15.036 (Harary Index) + 220.98 Average Error: 3.21% Randic: BP = 184.73 ln(Randic Index) + 150.09Average Error: 1.45% Future Directions: use the tool to verify values found in the literaure develop new indices with better approximations of the boiling point combine current indices with one another develop unique index References: Cao, C. "Topological Indices Based on Vertex, Distance and Ring: On Boiling Points of Paraffins and Cycloalkanes." J. Chem. Inf. and Comp. Sci., 2001, 41, 4. Mihalic, Z. "A Graph-Theoretical Approach to Structure-Property Relationships." J. Chem. Educ. 1992, 69, 9. Trinajstic, N. Chemical Graph Theory. Vol II. Florida: CRC Press, 1983. Abstract: http://www.math-cs.gordon.edu/courses/topo/