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5.6: Appendix- Third Order Diagrams Corresponding to Peaks in a 2D Spectrum of Coupled Vibrations

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    911figure1.png

    *Diagrams that do not contribute to double-resonance experiments, but do contribute to Fourier-transform measurements. Rephasing diagrams correspond to the terms in eq. (9.14).

    Using a phenomenological propagator, the \(S_{II}\) non-rephasing diagrams lead to the following expressions for the eight peaks in the 2D spectrum.

    \[\begin{aligned} S_{II}(\omega_1,\omega_3) &= \frac{2|\mu_{s,0}|^4+|\mu_{a,0}|^2|\mu_{s,0}|^2}{\left[-i(\omega_1+\omega_{s,0})+\Gamma_{s,0}\right]\left[i(\omega_3-\omega_{s,0})+\Gamma_{s,0}\right]} + \frac{2|\mu_{a,0}|^4+|\mu_{a,0}|^2|\mu_{s,0}|^2}{\left[-i(\omega_1+\omega_{a,0})+\Gamma_{a,0}\right]\left[i(\omega_3-\omega_{a,0})+\Gamma_{a,0}\right]} \\ &+ \frac{|\mu_{a,0}|^2|\mu_{s,0}|^2}{\left[-i(\omega_1+\omega_{s,0})+\Gamma_{s,0}\right]\left[i(\omega_3-\omega_{a,0})+\Gamma_{a,0}\right]} + \frac{|\mu_{a,0}|^2|\mu_{s,0}|^2}{\left[-i(\omega_1+\omega_{a,0})+\Gamma_{a,0}\right]\left[i(\omega_3-\omega_{s,0})+\Gamma_{b,0}\right]} \\ &- \frac{|\mu_{s,0}|^2|\mu_{2s,s}|^2+\mu_{s,0}\mu_{0,a}\mu_{as,s}\mu_{a,as}}{\left[-i(\omega_1+\omega_{s,0})+\Gamma_{s,0}\right]\left[i(\omega_3-\omega_{s,0}+\Delta_{s})+\Gamma_{2s,s}\right]} - \frac{|\mu_{a,0}|^2|\mu_{2a,a}|^2+\mu_{a,0}\mu_{0,s}\mu_{as,a}\mu_{s,as}}{\left[-i(\omega_1+\omega_{a,0})+\Gamma_{a,0}\right]\left[i(\omega_3-\omega_{a,0}+\Delta_{a})+\Gamma_{2a,a}\right]} \\ &-\frac{|\mu_{s,0}|^2|\mu_{as,s}|^2}{\left[-i(\omega_1+\omega_{s,0})+\Gamma_{s,0}\right]\left[i(\omega_3-\omega_{a,0}+\Delta_{as})+\Gamma_{as,s}\right]} - \frac{|\mu_{a,0}|^2|\mu_{as,a}|^2}{\left[-i(\omega_1+\omega_{a,0})+\Gamma_{a,0}\right]\left[i(\omega_3-\omega_{s,0}+\Delta_{as})+\Gamma_{as,a}\right]} \\ &\equiv {\bf 1+1'+2+2'+3+3'+4+4'} \end{aligned} \label{9.1.1}\]

    This page titled 5.6: Appendix- Third Order Diagrams Corresponding to Peaks in a 2D Spectrum of Coupled Vibrations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Andrei Tokmakoff via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.