Quantum chemical justification for an empirical correlation

A challenge to quantum chemistry is to describe many of the empirical correlations that experimentalists have painstakingly catalogued. For example, an earlier post discusses a correlation between the rate of a photoisomerisation reaction and the electron withdrawing ability of a substitutent. An important empirical rule for organic dye molecules is the Dewar-Knott rule which relates the frequency (wavelength) of maximum light absorption [the colour of the dye] to the electron withdrawing (or donating) ability of a substituent.

Seth Olsen recently published a nice paper which gives a high level quantum chemistry justification of the Dewar-Knott rule for a family of diarylmethane dyes, including Michler's hydrol blue. The graph below shows how the excitation energy varies with a parameter characterising the composition of the ground state many-body wavefunction, and which varies with the substituent X.