[Prediction and estimation on molar response values of alkanes by using molecular path vector]

A new method based on a novel molecular topological index vector, called the molecular path vector (MPV), of alkane molecules is proposed and employed for estimation and prediction of the molar response values of various alkanes. The novel MPV, p = (P1, P2, P3, P4, P5, P6, P7, P8, P9, P10)', which derived directly from the interaction terms of molecular graph, is used to characterize well molecular structures of all alkanes from one through ten or eleven carbon atoms. It showed that there exists very good correlation between the MPV elements and molar response values on both FID and TCD detectors in classical gas chromatography. Based on the given calibration set with different sample numbers and by using the practical multiple linear regression, the quantitative structure-response relationship (QSRR) equations, for the molar response values (SM) on both FID and TCD, are respectively given as follows: SM(FID) = 15.4004881 + 17.9905995 X1 - 0.1652116 X2 - 0.6974103 X3 - 0.8452390 X4 - 0.2671000 X5 - 1.5657273 X6 + 0.0944440 X7, n = 50, m = 7, r = 0.9976, ST = 26.132, SR = 1.965 1, Ev = 99.72%, RMS = 1.801, F = 1231.71 SM(TCD) = 11.9946996 + 29.1490916 X1 - 4.7451669 X2 - 3.7673385 X3 - 1.4948330 X4 - 1.6278831 X5 - 0.7934611 X6 - 3.0566093 X7, n = 32, m = 7, r = 0.9968, ST = 15.72, SR = 1.4310, Ev = 99.59%, RMS = 1.239, F = 531.227 where the independent descriptor variables, X1-X7, refer to the elements, P1, P2, P3, P4, P5, P6, P7 in the molecular path vector for all samples in both FID and TCD training sets; n, r, ST, SR, Ev, RMS and F are the sample number, regression coefficient, total standard deviation, standard residual deviation, explained variance, rooted mean squared error and F-statistic value, respectively. To test both models by using back-propagation neural network (BPNN) with the topological structure NN(7-4-2) and the cross validation through leave-one-out (LOO) procedure, the correlation coefficient of cross validation is over 0.96. Because there exists a quite good linear relationship between the molar responses and molecular path parameters, BPNN (r = 0.989 and 0.968) does not show its nonlinear advantage over multiple linear regression(MLR) (r = 0.9976 and 0.9968) in both presently examined cases, FID and TCD in the GC technique, for molecular modelling and quantitative prediction.