shnitsel.analyze.spectra

Functions

_get_fosc(energy_interstate, dip_trans_norm)

Internal function to actually calculate the oscillator frequency for energies and transition dipoles.

get_fosc(energy_per_or_interstate, dip_trans_norm)

Function to obtain a dataarray containing the oscillator strength as a dataarray.

assign_fosc(ds)

Function to calculate oscillator strength fosc and create a new dataset with this variable assigned.

broaden_gauss(delta_E, fosc[, agg_dim, width_in_eV, ...])

Applies a gaussian smoothing kernel to the fosc data.

ds_broaden_gauss(interstate[, width_in_eV, nsamples, xmax])

Function to Get the broadened spectrum of the interstate energy and oscillator strength data to plot

get_spectrum(data, t, sc[, rel_cutoff])

Function to calculate a gaussian-smoothed spectrum of an interstate dataset

calc_spectra(interstate[, times, rel_cutoff])

Function to calculate spectra

get_spectra_groups(spectra)

Group spectra results into spectra involving the ground state or only excited states.

sep_ground_excited_spectra(spectra[, excited_transitions])

Function to split Spectra into two groups.

spectra_all_times(inter_state)

Function to calculate the spectra at all times.

Module Contents

_get_fosc(energy_interstate, dip_trans_norm)

Internal function to actually calculate the oscillator frequency for energies and transition dipoles.

Parameters:

  • energy_interstate (DataArray) – The Array of Energies in the system.

  • dip_trans_norm (DataArray) – The array of associated norm of transition dipoles in the system.

Returns:

The resulting oscillation frequency (f_osc) array.

Return type:

DataArray

Notes

We use the following unitless form of f_osc: $$f_{osc} = frac{2}{3} frac{m_e}{hbar^2} cdot Delta E cdot frac{mu^2}{e^2}$$

get_fosc(energy_per_or_interstate, dip_trans_norm)

Function to obtain a dataarray containing the oscillator strength as a dataarray.

Parameters:

  • energy_interstate (DataArray) – The array of per- or inter-state energies in the system. If provided as a per-state energy, inter-state barriers will automatically be calculated.

  • dip_trans_norm (DataArray) – The array of associated transition dipoles in the system with their norm calculated across the direction dimension.

  • energy_per_or_interstate (xarray.DataArray)

Returns:

The resulting datarray of oscillator strength f_osc

Return type:

DataArray

assign_fosc(ds)

Function to calculate oscillator strength fosc and create a new dataset with this variable assigned.

Parameters:

ds (xr.Dataset) – Dataset from which to calculate fosc

Returns:

Dataset with the member variable fosc set

Return type:

xr.Dataset

broaden_gauss(delta_E, fosc, agg_dim='frame', *, width_in_eV=0.5, nsamples=1000, xmin=0, xmax=None)

Applies a gaussian smoothing kernel to the fosc data.

Aggregation is performed along the agg_dim dimension.

Parameters:

  • delta_E (xarray.DataArray) – values used for the x-axis, presumably $E_i$

  • fosc (xarray.DataArray) – values used for the y-axis, presumably $f_mathrm{osc}$

  • agg_dim (shnitsel.core.typedefs.DimName) – dimension along which to aggregate the many Gaussian distributions, by default ‘frame’

  • optional – dimension along which to aggregate the many Gaussian distributions, by default ‘frame’

  • width_in_eV (float) – the width of the Gaussian distributions used, by default 0.5 eV

  • optional – the width of the Gaussian distributions used, by default 0.5 eV

  • nsamples (int) – number of evenly spaced x-values over which to sample the distribution, by default 1000

  • optional – number of evenly spaced x-values over which to sample the distribution, by default 1000

  • xmax (float | None) – the maximum x-value, by default 3 standard deviations beyond the pre-broadened maximum

  • optional – the maximum x-value, by default 3 standard deviations beyond the pre-broadened maximum

  • xmin (float)

Return type:

xarray.DataArray

ds_broaden_gauss(interstate, width_in_eV=0.5, nsamples=1000, xmax=None)

Function to Get the broadened spectrum of the interstate energy and oscillator strength data to plot a nice and smooth spectrum.

Width of the smoothing kernel is given in eV and the energy is assumed to be in eV or will be converted to eV.

Parameters:

  • interstate (InterState) – Interstate dataset with energy_interstate and fosc information.

  • width_in_eV (float, optional) – Width of the gaussian smoothing kernel in eV. Defaults to 0.5 eV.

  • nsamples (int, optional) – Number of samples/steps in the range of the energy spectrum. Defaults to 1000.

  • xmax (float | None, optional) – Maximum of the energy range to consider for the spectrum. Defaults to None.

Returns:

Resulting broadened spectrum statistics.

Return type:

xr.DataArray

get_spectrum(data, t, sc, rel_cutoff=0.01)

Function to calculate a gaussian-smoothed spectrum of an interstate dataset

Parameters:

  • data (InterState) – An InterState dataset with fosc and energy data

  • t (float) – The time at which to evaluate the spectrum

  • sc (tuple[int, int]) – State combination identifier. Possibly an index or a tuple (from, to) of states.

  • rel_cutoff (float, optional) – Relative cutoff threshold. Values below the max of the resulting spectrum times this scale will be ignored. Defaults to 0.01.

Returns:

The Gauss-broadened spectrum of the provided data system.

If broadening across trajectories could not be performed, just returns the fosc array.

Return type:

xr.DataArray

calc_spectra(interstate, times=None, rel_cutoff=0.01)

Function to calculate spectra

Parameters:

  • interstate (InterState) – An InterState transformed Dataset.

  • times (Iterable[float]|None, optional) – The times at which the spectrum should be calculated. Defaults to None. If None, will be initialized as [0,10,20,30]

  • rel_cutoff (float, optional) – Factor for the cutoff of broadened/smoothened spectrum relative to maximum. Defaults to 0.01.

Returns:

Returns a dict of DataArrays indexed by (time, statecomb) tuples.

Return type:

SpectraDictType

get_spectra_groups(spectra)

Group spectra results into spectra involving the ground state or only excited states.

Parameters:

spectra (SpectraDictType) – The Spectral calculation results, e.g. from calc_spectra(). Indexed by (timestep, state_combination) and yielding the associated spectrum.

Returns:

First the spectra involving the ground state SpectraDictType: Second the spectra involving only excited states.

Return type:

SpectraDictType

sep_ground_excited_spectra(spectra, excited_transitions=None)

Function to split Spectra into two groups.

Can specify which state combinations should be grouped into excited transitions. If not provided a excited_transitions set, will assume all transitions not involving the ground state to be ‘excited’.

Parameters:

  • spectra (SpectraDictType) – The spectral results, e.g. from calc_spectra()

  • excited_transitions (set[tuple[int, int]] | None, optional) – An optional set specifying all state transitions that should be filtered as ‘excited. Defaults to None.

Returns:

First the spectra not involving excited state transitions SpectraDictType: Second the spectra involving only excited state transitions

Return type:

SpectraDictType

spectra_all_times(inter_state)

Function to calculate the spectra at all times.

Does not return a dict with only the relevant (t,sc) combinations as above but instead a full xr.DataArray with a time dimension that has spectrum data for all times within the dataset averaged across trajectories.

Parameters:

inter_state (xr.Dataset) – The InterState transformed Dataset.

Raises:

ValueError – If required variables or dimensions are missing

Returns:

The resulting spectra across all times.

Return type:

xr.DataArray