Quantum-Mechanical Calculations of Resonance Raman Intensities: The Weighted-Gradient Approximation

A framework of the weighted-gradient approach is developed for effective quantum-mechanical modeling of resonance Raman (RR) intensities with a view toward rationalizing enhancement patterns observed for histidine and tryptophan side chains. Unlike the single-state gradient approach, this new procedure utilizes the vertical gradients obtained for all computed excited states to produce an effective gradient and the RR intensity patterns for a particular frequency of the excitation photon. The dramatic spectral changes observed for the histidine ring upon its protonation, deprotonation, or deuterium substitution of exchangeable protons is well reproduced by this model. Spectral comparison for the tryptophan ring clearly demonstrated improved quality of the weighted-gradient over the single-state gradient approach. Computed spectra exemplify the potential application of this model to support vibrational studies of electronic and structural interactions of chromophores in proteins.