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Libro: Espectroscopia no lineal y bidimensional (Tokmakoff)
5: Espectroscopia bidimensional
5.6: Apéndice- Diagramas de tercer orden correspondientes a picos en un espectro 2D de vibraciones acopladas

5.6: Apéndice- Diagramas de tercer orden correspondientes a picos en un espectro 2D de vibraciones acopladas

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*Diagramas que no contribuyen a experimentos de doble resonancia, pero sí contribuyen a las mediciones de transformada de Fourier. Los diagramas de refase corresponden a los términos en la ecuación (9.14).

Usando un propagador fenomenológico, los diagramas de\(S_{II}\) no refase conducen a las siguientes expresiones para los ocho picos en el espectro 2D.

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