Best Ordinate and Best Equations for the Position and Shape of an Absorption Maximum

Abstract

Accurate values for the location of absorption maxima are important in qualitative analysis by spectrophotometry and for theoretical calculations. Accuracy should increase with sharpness of curvature. For instruments recording linearly in one of three ordinates (T, A, or logA), experience shows that optimum peak sharpness occurs respectively at intermediate transmittance and high absorbance, but independent of logA. Using an empirical equation for the shape of a maximum, the curvature is measured by the second derivative, which can be maximized by inspection or by taking the derivative of this with respect to the ordinate, equating to zero, and solving. When nine published equations are put into the three ordinate forms and differentiated, six give results consistent with experience. On the basis of this result and other factors, four of the equations are recommended as superior, namely the Cauchy function, the Gaussian function, and two combinations of these. Comparison of numerical values for curvatures with the three ordinates predict accuracy to be about equal at T = 37%, A =0.43, and any value of logA, but greatest for A linear if A is increased.