Analytical Model for Rates of Electron Attachment and Intramolecular Electron Transfer in Electron Transfer Dissociation Mass Spectrometry

A new physical model is put forth to allow the prediction of electron transfer rates and distances for (i) intramolecular transfer from an n >= 3 Rydberg orbital on a positive site to a disulfide or amide bond site and (ii) intermolecular transfer from an anion donor to an n a 3 Rydberg orbital of a positively charged polypeptide. Although ab initio methods have proven capable of handling such electron transfer events when the Rydberg orbital has principal quantum number n = 3, they have proven to be incapable of handling Rydberg states having quantum number n > 3, so having a new tool capable of handling n > 3 Rydberg states is important. The model (i) focuses on each Rydberg orbital's large peak of high amplitude, (ii) approximates the electron density within this peak as constant within a radial shell characterized by a radius < r > and thickness T both of which depend on the quantum number n, and (iii) assumes that strong coupling (either with an orbital of an anion donor or to a disulfide sigma* or a backbone amide pi* orbital) occurs when the valence orbital penetrates fully within the radial shell of the Rydberg orbital. These assumptions permit a derivation of the ratios of rates of electron transfer for n > 3 to those for n = 3. Combining these ratios with ab initio rates for n = 3 allows one to make rate predictions for inter- and intramolecular electron transfer involving Rydberg orbitals appropriate to the electron transfer dissociation process. One important prediction of this model is that the combination of large-penetration and Landau-Zener surface-crossing conditions places very severe limitations on which Rydberg levels can initially be populated in electron transfer dissociation. Another prediction is that a Rydberg orbital of a given principal quantum number n has a limited range of distances over which it can transfer an electron; sigma* or pi* orbitals either too far from or too close to a given Rydberg orbital cannot accept an electron from that orbital.