This
article primarily discusses the utility of vibrational perturbation
theory for the prediction of X–H stretching vibrations with
particular focus on the specific variant, second-order vibrational
perturbation theory with resonances (VPT2+K). It is written as a tutorial,
reprinting most important formulas and providing numerous simple examples.
It discusses the philosophy and practical considerations behind vibrational
simulations with VPT2+K, including but not limited to computational
method selection, cost-saving approximations, approaches to evaluating
intensity, resonance identification, and effective Hamiltonian structure.
Particular attention is given to resonance treatments, beginning with
simple Fermi dyads and gradually progressing to arbitrarily large
polyads that describe both Fermi and Darling–Dennison resonances.
VPT2+K combined with large effective Hamiltonians is shown to be a
reliable framework for modeling the complicated CH stretching spectra
of alkenes. An error is also corrected in the published analytic formula
for the VPT2 transition moment between the vibrational ground state
and triply excited states.