spectrum

psi4.driver.p4util.spectrum(*, poles, residues, kind='opa', lineshape='gaussian', gamma=0.2, npoints=5000, out_units='nm')

One-photon absorption (OPA) or electronic circular dichroism (ECD) spectra with phenomenological line broadening.

This function gives arrays of values ready to be plotted as OPA spectrum:

$$\epsilon (\omega )=\frac{4{\pi }^2{N}_{\mathrm{A}}\omega }{3\times 1000\times \ln (10)(4\pi {ϵ}_0)n\hslash c}\sum _{i\to j}{g}_{ij}(\omega )|{\mu }_{ij}{|}^2$$

or ECD spectrum:

$$\mathrm{\Delta }\epsilon (\omega )=\frac{16{\pi }^2{N}_{\mathrm{A}}\omega }{3\times 1000\times \ln (10)(4\pi {ϵ}_0)n\hslash c^2}\sum _{i\to j}{g}_{ij}(\omega )\mathrm{\Im }({\mu }_{ij}\cdot {\mathbf{m}}_{ij})$$

in macroscopic units of $\mathrm{L}\cdot {\mathrm{mol}}^{-1}\cdot {\mathrm{cm}}^{-1}$. The lineshape function $g_{ij}(\omega )$ with phenomenological broadening $\gamma$ is used for the convolution of the infinitely narrow results from a linear response calculation.

Parameters:

• poles (Union[List[float], ndarray]) – Poles of the response function, i.e. the excitation energies. These are expected in atomic units of angular frequency.

• residues (Union[List[float], ndarray]) – Residues of the linear response functions, i.e. transition dipole moments (OPA) and rotatory strengths (ECD). These are expected in atomic units.

• kind (str) – {“opa”, “ecd”} Which kind of spectrum to generate, one-photon absorption (“opa”) or electronic circular dichroism (“ecd”). Default is opa.

• lineshape (str) – {“gaussian”, “lorentzian”} The lineshape function to use in the fitting. Default is gaussian.

• gamma (float) – Full width at half maximum of the lineshape function. Default is 0.2 au of angular frequency. This value is expected in atomic units of angular frequency.

• npoints (int) – How many points to generate for the x axis. Default is 5000.

• out_units (str) –

  Units for the output array x, the x axis of the spectrum plot. Default is wavelengths in nanometers. Valid (and case-insensitive) values for the units are:

  • au atomic units of angular frequency

  • Eh atomic units of energy

  • eV

  • nm

  • THz

Returns:

spectrum – The fitted electronic absorption spectrum, with units for the x axis specified by the out_units parameter. This is a dictionary containing the convoluted (key: convolution) and the infinitely narrow spectra (key: sticks).

{"convolution": {"x": np.ndarray, "y": np.ndarray},
 "sticks": {"poles": np.ndarray, "residues": np.ndarray}}

Return type:

Dict[str, numpy.ndarray]

Notes

• Conversion of the broadening parameter $\gamma$. The lineshape functions are formulated as functions of the angular frequency $\omega$. When converting to other physical quantities, the broadening parameter has to be modified accordingly. If ${\gamma }_{\omega }$ is the chosen broadening parameter then:

  • Wavelength: $gamm{a}_{\lambda }=\frac{{\lambda }_{ij}^2}{2\pi c}{\gamma }_{\omega }$

  • Frequency: $gamm{a}_{\nu }=\frac{{\gamma }_{\omega }}{2\pi }$

  • Energy: $gamm{a}_E={\gamma }_{\omega }\hslash$

References

A. Rizzo, S. Coriani, K. Ruud, “Response Function Theory Computational Approaches to Linear and Nonlinear Optical Spectroscopy”. In Computational Strategies for Spectroscopy. https://doi.org/10.1002/9781118008720.ch2