Welcome to the Absorption/Emission Spectrum Learning Tool!
Developers: Matthew Capaldi, Maximillian Thomas, Nikolay Golubev
This interactive tool visualizes the vibronic structure of an electronic absorption or emission spectrum. When a molecule undergoes a transition between two electronic states, the transition intensity to each vibrational level of the final state is governed by the Franck-Condon principle: it is proportional to the squared overlap (the Franck-Condon factor) between the vibrational wavefunction of the initial state and that of the final state. Because the two electronic states generally have different equilibrium geometries and vibrational frequencies, this produces a characteristic series of vibronic peaks rather than a single sharp line.
The interface is organized into two main sections: the Control Panel and the Plot section. The Control Panel lets the two potential energy surfaces be adjusted, in either a 1D (single vibrational coordinate) or 2D (two coupled vibrational coordinates) model. As these parameters are modified, the Plot section updates in real time to show the resulting stick and convolved spectra, together with the underlying potentials and vibrational wavefunctions.
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This panel controls how the calculated vibronic spectrum is displayed. The Convolution Width parameter specifies the spectral broadening applied to the discrete Franck-Condon transitions, allowing finite linewidths arising from instrumental resolution or other broadening mechanisms to be simulated. The Show Convolved Spectrum option toggles the display of the broadened spectrum in addition to the underlying stick spectrum, making it easier to compare the discrete transition intensities with the continuous spectral profile observed experimentally.
This panel controls the vibrational frequencies of the initial and final electronic states through the Omega Initial and Omega Final parameters. Changing these frequencies modifies the curvature of the corresponding harmonic potential energy surfaces and the spatial extent of the vibrational wavefunctions. As a result, the Franck-Condon factors and the resulting vibronic spectrum change, reflecting the different vibrational structures of the two electronic states.
This panel controls the relative displacement between the initial- and final-state potential energy surfaces. The Horizontal Shift parameter changes the displacement of the equilibrium geometry along the vibrational coordinate, while the Vertical Shift parameter adjusts the energy offset between the two electronic states. Together, these parameters determine the overlap of the vibrational wavefunctions and therefore strongly influence the Franck-Condon factors and the resulting vibronic spectrum.
This panel controls the vibrational frequencies of the initial electronic state along the two normal-mode coordinates through the Omega X and Omega Y parameters. These frequencies determine the curvature of the two-dimensional harmonic potential energy surface and the localization of the corresponding vibrational wavefunctions. Modifying either frequency changes the vibrational level spacing and influences the Franck-Condon overlaps with the final-state vibrational wavefunctions.
This panel controls the vibrational parameters of the final electronic state. The Omega X' and Omega Y' parameters are analogous to those of the initial state and define the vibrational frequencies along the two normal-mode coordinates X' and Y' for the final-state potential energy surface.
This panel controls the relative displacement and orientation of the initial and final potential energy surfaces. The Shift X and Shift Y parameters define the displacement between the equilibrium geometries of the initial and final electronic states, while the Vertical Shift controls the energy separation between the two electronic states. In the two-dimensional model, the additional Rotation parameter introduces the so-called Duschinsky rotation, which describes the change in orientation between the normal modes of the initial and final states and influences the resulting Franck-Condon factors.
This plot displays the calculated vibronic absorption or emission spectrum. Positive transition energies correspond to absorption processes, while negative energies relative to the initial state represent emission transitions. Individual stick peaks represent transitions between specific vibrational levels, with intensities determined by the corresponding Franck-Condon factors. The broadened spectrum provides a more realistic representation of the experimentally observed spectral profile, illustrating how the relative geometry and vibrational properties of the two electronic states shape the overall vibronic structure.
This plot displays the potential energy surfaces of the initial and final electronic states together with their corresponding vibrational energy levels and wavefunctions. The vibrational states represent the quantized nuclear motion within each electronic state, while their spatial overlap determines the Franck-Condon factors governing the vibronic transition intensities. The relative displacement and curvature of the two potentials illustrate how differences in equilibrium geometry and vibrational frequencies shape the resulting absorption or emission spectrum.
This plot displays the two-dimensional potential energy surface of the initial electronic state together with its ground-state vibrational wavefunction. The surface defines the energy landscape for nuclear motion, while the wavefunction illustrates the spatial distribution of the nuclei in the lowest vibrational level. The shape and localization of the ground-state wavefunction are determined by the curvature of the potential and the corresponding vibrational frequencies along the two normal-mode coordinates.
This plot displays the two-dimensional potential energy surface of the final electronic state together with a selected vibrational wavefunction. The vibrational state can be adjusted using the nX' and nY' controls, which select the vibrational quantum numbers along the two normal-mode coordinates. The resulting wavefunction illustrates the spatial structure of the vibrational state, whose overlap with the initial-state wavefunction determines the corresponding Franck-Condon transition intensity.