Teaching vibrational spectra to assign themselves

Abstract

A new paradigm for assigning vibrational spectra is described. Instead of proceeding from potential to Hamiltonian to eigenvalues/eigenvectors/intensities to spectrum, the new method goes “backwards” directly from spectrum to eigenvectors. The eigenvectors then “assign” the spectrum, in that they identify the basis states that contribute to each eigenvalue. To start, we demonstrate an algorithm that can obtain useful estimates of the eigenvectors connecting a real, symmetric Hamiltonian to its eigenvalues even if the only available information about the Hamiltonian is its diagonal elements. When this algorithm is augmented with information about transition intensities, it can be used to assign a complex vibrational spectrum using only information about (1) eigenvalues (the peak centers of the spectrum) and (2) a harmonic basis set (taken to be the diagonal elements of the Hamiltonian). Examples will be discussed, including application to the vibrationally complex spectral region of the formic acid dimer.