A Unified Theory for the Blue- and Red-Shifting Phenomena in Hydrogen and Halogen Bonds

Typical hydrogen and halogen bonds exhibit red-shifts of their vibrational frequencies upon the formation of hydrogen and halogen bonding complexes (denoted as D···Y-A, Y = H and X). The finding of blue-shifts in certain complexes is of significant interest, which has led to numerous studies of the origins of the phenomenon. Because charge transfer mixing (i.e., hyperconjugation in bonding systems) has been regarded as one of the key forces, it would be illuminating to compare the structures and vibrational frequencies in bonding complexes with the charge transfer effect "turned on" and "turned off". Turning off the charge transfer mixing can be achieved by employing the block-localized wave function (BLW) method, which is an ab initio valence bond (VB) method. Further, with the BLW method, the overall stability gained in the formation of a complex can be analyzed in terms of a few physically meaningful terms. Thus, the BLW method provides a unified and physically lucid way to explore the nature of red- and blue-shifting phenomena in both hydrogen and halogen bonding complexes. In this study, a direct correlation between the total stability and the variation of the Y-A bond length is established based on our BLW computations, and the consistent roles of all energy components are clarified. The n(D) → σ*(Y-A) electron transfer stretches the Y-A bond, while the polarization due to the approach of interacting moieties reduces the HOMO-LUMO gap and results in a stronger orbital mixing within the YA monomer. As a consequence, both the charge transfer and polarization stabilize bonding systems with the Y-A bond stretched and red-shift the vibrational frequency of the Y-A bond. Notably, the energy of the frozen wave function is the only energy component which prefers the shrinking of the Y-A bond and thus is responsible for the associated blue-shifting. The total variations of the Y-A bond length and the corresponding stretching vibrational frequency are thus determined by the competition between the frozen-energy term and the sum of polarization and charge transfer energy terms. Because the frozen energy is composed of electrostatic and Pauli exchange interactions and frequency shifting is a long-range phenomenon, we conclude that long-range electrostatic interaction is the driving force behind the frozen energy term.