hqs_nmr.utils
Helper routines for nmr spectra calculations.
Functions
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Check in a simple way, if local SU2 symmetry could be helpful. |
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Evaluate intensity from spin contributions. |
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Obtain a guess for a frequency window for a molecule. |
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Obtain a guess for a frequency window for a molecule. |
Broadening of lorentzian is half of the fwhm. |
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Estimate the Lorentzian broadening from spin parameters. |
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Rediscretize the frequency axis in NumStep frequency points. |
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Normalize the correlator. |
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Check if a correlator has to be normalized or scaled depending on user input. |
Reduce the list of spin contributions to those associated with the reference isotope. |
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Simplify a fermions expression into a normalized expression containing only spin operators. |
- hqs_nmr.utils.lorentzian_broadening_from_spin_parameters(isotopes: list[Isotope], j_couplings: list[tuple[tuple[int, int], float]], reference_isotope: Isotope) float[source]
Estimate the Lorentzian broadening from spin parameters.
- Parameters:
isotopes – List of isotopes for every nucleus, in the same ordering as shifts. Every isotope is defined as Isotope(mass, symbol).
j_couplings – List containing J-coupling constants between nuclei. It contains tuples of pairs of integers and the associated coupling value, representing the respective nuclei indices (via their positions in the isotopes lists, starting counting with 0).
reference_isotope – Isotope specified as Isotope(mass, symbol) to define the frequency (w=gamma*field) of the rotating frame. For example, Isotope(1, ‘H’).
- Returns:
The broadening in rad / s.
- hqs_nmr.utils.lorentzian_broadening_from_fwhm(fwhm: float | ndarray) float | ndarray[source]
Broadening of lorentzian is half of the fwhm.
- Parameters:
fwhm – Full width half maximum.
- Returns:
Broadening of the Lorentzian in same unit as fwhm.
- hqs_nmr.utils.nmr_rescale_frequencies(omegas: ndarray, intensity: ndarray, number_steps: int = 100, limit: float = 0.0008) ndarray[source]
Rediscretize the frequency axis in NumStep frequency points.
Perform an equal area partitioning of intensity. Intensity should be >= 0.
- Parameters:
omegas – Original reference frequencies.
intensity – Reference spectral intensity.
number_steps – Number of frequency points.
limit – Portion of spectrum to be skipped for defining the start and end point.
- Returns:
An array with number_steps frequency points of the spectral function for each frequency.
- hqs_nmr.utils.guess_frequency_window_ppm(isotopes: list[Isotope], shifts: npt.ArrayLike, reference_isotope: Isotope) tuple[float, float][source]
Obtain a guess for a frequency window for a molecule.
- Parameters:
isotopes – List of isotopes; each given as Isotope(mass, symbol).
shifts – List of chemical shifts in parts-per-million (ppm).
reference_isotope – Isotope specified as Isotope(mass, symbol) to define the frequency (w=gamma*field) of the rotating frame. For example, Isotope(1, ‘H’).
- Returns:
Suggested (omega_min, omega_max) in ppm.
- hqs_nmr.utils.guess_spectrum(isotopes: list[Isotope], shifts: npt.ArrayLike, reference_isotope: Isotope, broadening_ppm: np.ndarray, frequency_window_ppm: tuple[float, float] | None = None, broadening_scaling_factor: float = 250.0, number_frequency_points: int = 500) tuple[np.ndarray, np.ndarray][source]
Obtain a guess for a frequency window for a molecule.
- Parameters:
isotopes – List of isotopes, each specified as Isotope(mass, element).
shifts – List of chemical shifts in parts per million (ppm).
reference_isotope – Isotope specified as Isotope(mass, symbol) to define the frequency (w=gamma*field) of the rotating frame. For example, Isotope(1, ‘H’).
broadening_ppm – Broadening in ppm.
frequency_window_ppm – Optional upper and lower bound of user defined energy window in ppm.
broadening_scaling_factor – Scaling factor of broadening_ppm to include frequencies, where potential multiplet peaks could be. Defaults to 250.
number_frequency_points – Number of frequency points for the estimated spectrum. Defaults to 500.
- Returns:
Omegas and estimate of correlator.
- hqs_nmr.utils.reduce_contributions_to_relevant_spins(spin_contributions: list[int], molecule_parameters: NMRParameters, reference_isotope: Isotope, solver_settings: NMRSolverSettings) list[int][source]
Reduce the list of spin contributions to those associated with the reference isotope.
- Parameters:
spin_contributions – List with indices of spin contributions that are supposed to be calculated.
molecule_parameters – The molecular isotopes, shifts and J-coupling values.
reference_isotope – Isotope specified as Isotope(mass, symbol) to define the frequency (w=gamma*field) of the rotating frame. Defaults to Isotope(1, ‘H’).
solver_settings – NMRSolverSettings object storing information on the cluster and solver methods. If None, the default solver parameters are used. Defaults to None.
- Returns:
When solver_settings.only_relevant_spins is True (default), spin contributions list without spin indices of a different isotope than the reference_isotope are returned. Otherwise the unaltered spin contributions.
- hqs_nmr.utils.evaluate_intensity(spin_contributions: ndarray) ndarray[source]
Evaluate intensity from spin contributions.
No additional normalization is performed
- Parameters:
spin_contributions – Spin contributions from which to evaluate the intensity.
- Returns:
The intensity.
- hqs_nmr.utils.normalize_correlator(omegas: ndarray, correlator: ndarray, number_relevant_spins: int | None = None) ndarray[source]
Normalize the correlator.
After normalization the correlator integrates to the number of times the reference isotope appears in the correlator. If correlator is a Green’s function the normalize is only performed with respect to its imaginary part.
- Parameters:
omegas – Frequencies at which the correlator was evaluated.
correlator – Correlator which is supposed to be normalized.
number_relevant_spins – Number of times the reference isotope appears in the molecule.
- Returns:
Normalized correlator.
- hqs_nmr.utils.normalize_or_scale(molecule_parameters: NMRParameters, calculation_parameters: NMRCalculationParameters, omegas_ppm: np.ndarray, correlator: np.ndarray) np.ndarray[source]
Check if a correlator has to be normalized or scaled depending on user input.
If normalize_spectrum is set to True, the spectrum is normalized with respect to the number of spins with the same isotope as the reference isotope. Otherwise a scaling with respect to the Boltzmann distribution is performed or if the complete_nmr_solver was used, nothing is done.
- Args.:
molecule_parameters: The molecular isotopes, shifts, and J-coupling values. calculation_parameters: Object containing all parameters needed to perform a NMR correlator function calculation. omegas_ppm: Frequencies at which to evaluate the correlator in ppm. correlator: Correlator to normalize or scale.
- Returns:
Normalized or scaled correlator.
- hqs_nmr.utils.check_local_su2(cluster_size: int, solver_settings: NMRSolverSettings) bool[source]
Check in a simple way, if local SU2 symmetry could be helpful.
This check does not search for groups, but just checks, if local SU2 symmetry could at all be beneficial. Further checks are done in the actual solver routine.
- Parameters:
cluster_size – Size of the cluster.
solver_settings – NMRSolverSettings object storing information on the clustering and solver method.
- Returns:
If local SU2 should be exploited True, otherwise False.
- hqs_nmr.utils.simplify_spin_expression(expression: fermions.ExpressionSpinful, num_spins: int, threshold: float = 1e-05) fermions.ExpressionSpinful[source]
Simplify a fermions expression into a normalized expression containing only spin operators.
- Args.:
expression: Expression to be converted. num_spins: number of spins in the expression. threshold: Threshold for the normalization.
- Returns:
Simplified expression.