This section is dealing with specific types of analysis performed by MDANSE. If you are not sure where these fit into the general workflow of data analysis, please read Workflow.

Infrared#

This section contains background theory for following plugins:

Infrared#

Calculates the molecular infrared spectrum averaged over all molecules in the trajectory. The infrared spectrum is calculated from the Fourier transform of the autocorrelation of the time-derivative of the molecular dipole:

(92)#\[I(\omega) \propto \frac{1}{N_{m}}\sum_{m} \frac{1}{6\pi} \int \mathrm{d}t \, \left\langle \dot{\vec{\mu}}_{m}(0) \cdot \dot{\vec{\mu}}_{m}(t) \right\rangle e^{-i\omega t}\]

where \(N_{m}\) is the number of molecules and \(\dot{\vec{\mu}}_{m}(t)\) is the time-derivative of the molecular dipole moment of molecule \(m\).

Dipole Autocorrelation Function#

Calculates the molecular dipole autocorrelation function which is closely related to the molecular infrared spectrum

(93)#\[\mathrm{DACF}(t) = \frac{1}{3 N_{m}}\sum_{m} \left\langle \vec{\mu}_{m}(0) \cdot \vec{\mu}_{m}(t) \right\rangle\]

where \(N_{m}\) is the number of molecules \(m\) and \(\vec{\mu}(t)\) is the molecular dipole moment of molecule \(m\).