Fig. 4: Transition dipoles of the many-body dispersion (MBD) modes for crambin.
From: Second quantization of many-body dispersion interactions for chemical and biological systems
The figure illustrates the orientationally averaged transition dipole moment denoted as \(| {\bar{\mu }}_{\tilde{{{{{{{{\boldsymbol{0}}}}}}}}}{\tilde{{{{{{{{\boldsymbol{1}}}}}}}}}}_{k}}|\) for the kth MBD eigenmode as a function of the corresponding MBD excitation energy \(\hslash {\tilde{\omega }}_{k}\). The MBD energies on the x-axis are expressed in units relative to the lowest frequency eigenmode, i.e. \(\hslash {\tilde{\omega }}_{1}\). In the insets, the matrix elements of the square of the orientationally averaged transition dipole for the interacting residues. In particular, for two fixed residues α and β, \({(| {\bar{\mu }}_{\tilde{{{{{{{{\boldsymbol{0}}}}}}}}}{\tilde{{{{{{{{\boldsymbol{1}}}}}}}}}}_{k}}{| }^{2})}_{\alpha \beta }=1/3{\sum }_{A\in {{{{{{{{\mathcal{F}}}}}}}}}_{\alpha },B\in {{{{{{{{\mathcal{F}}}}}}}}}_{\beta }}\mathop{\sum }\nolimits_{i=1}^{3}\,{\mu }_{\tilde{{{{{{{{\boldsymbol{0}}}}}}}}}{\tilde{{{{{{{{\boldsymbol{1}}}}}}}}}}_{k};{A}_{{x}_{i}}}{\mu }_{\tilde{{{{{{{{\boldsymbol{0}}}}}}}}}{\tilde{{{{{{{{\boldsymbol{1}}}}}}}}}}_{k};{B}_{{x}_{i}}}^{*}\) are shown. Transition dipoles are expressed in Debyes. Source data are provided as a Source Data file.
