Derivatives w.r.t. electric field (qcip_tools.derivatives_e)
Tools to help the manipulation of derivatives of the energy with respect to a static (F) or dynamic (D) electric field (though the first one is a special case of the second).
Theory
Light can be described as an electromagnetic radiation, with time and space varying components. Generally, only the phenomena associated with its electric components, because dominant, are considered. If the space-dependent term is left constant, the electric part of the field reads
where \(\mathbf{f}^0\) is the amplitude of the the electric field, \(\omega\) is the pulsation (equals to \(2\pi\nu\), with \(\nu\) the frequency in \(s^{-1}\)) and \(t\) the time (in \(s\)). This situation refers to the electric dipole approximation.
A material is an ensemble of particles, negatively (electrons) and positively (nuclei) charged. An oscillating electric field interacts with all particles, though the motion of the electrons is the most significant part (because nuclei have a smaller speed). This leads to an oscillating induced dipole moment, or, at the macroscopic scale, a (change of) polarization. The total dipole of a molecule (sum of the induced and permanent dipole, \(\vec{\mu}_0\)), can be described using a Taylor series. For the \(i\)-components of the dipole moment,
where \(\alpha\) and \(\beta\) are tensors of rank 2 and 3, called the polarizability and the first hyperpolarizability, respectively (generaly expressed in atomic units, au). \(\omega_1\), \(\omega_2\) and \(\omega_3\) are the pulsations of the fields applied in the \(j\), \(k\) and \(l\) directions, while \(\omega_\sigma = \sum_i \omega_i\). For small electric fields, the polarizability term is dominant, but the hyperpolarizability terms becomes non-negligible when the field gets large.
Sources
R.W. Boyd, « Nonlinear Optics (3rd edition) ». Elsevier (2008).
F. Castet et al. J. Chem. Phys. 136, 024506 (2012).
F. Castet et al. Acc. Chem. Res. 46, 2656 (2013).
API documentation
- class qcip_tools.derivatives_e.BaseElectricalDerivativeTensor(tensor=None, input_fields=None, frequency='static')
Base for all derivatives of the energy with respect to the electric field.
- rank()
Alias for the order
- Return type:
int
- response_to_electric_field(field)
Response to an electric field, located at the (0, 0, 0) position and for which the direction is given by
field.\[E_i = \sum_{ij\ldot}^{x,y,z} \chi_{ij\ldots}\,F_i\,F_j\,\ldots\]- Parameters:
field (numpy.array) – The electric field
- Return type:
numpy.array
- to_name(simplified=False)
Get the name of the tensor from its representation, by using
REPRESENTATION.- Return type:
str
- to_string(threshold=1e-05, **kwargs)
Rewritten to get a better output with this kind of tensor
- class qcip_tools.derivatives_e.ElectricDipole(dipole=None)
Dipole moment, commonly written \(\mu\).
- compute_properties()
Function to compute the tensor’s properties
- norm()
Norm of the dipole
- Return type:
float
- to_string(threshold=1e-05, disable_extras=False, **kwargs)
Rewritten to add information
- class qcip_tools.derivatives_e.FirstHyperpolarisabilityTensor(tensor=None, input_fields=(1, 1), frequency='static')
First hyperpolarisability tensor, commonly written \(\beta(-\omega_\sigma;\omega_1,\omega_2)\).
- beta_hrs()
Hyper-Rayleigh scattering quantity:
\[\beta_{HRS}=\sqrt{\langle\beta^2_{ZZZ}\rangle + \langle\beta^2_{ZXX}\rangle}\]- Return type:
float
- beta_kerr(dipole)
Measured quantity in a dc-Kerr \(\beta(-\omega;\omega,0)\) experiment.
\[\beta^K = \frac{3}{2}\,(\beta_{||}-\beta_{\perp})\]- Parameters:
dipole (numpy.ndarray) – dipole moment
- Returns:
beta dc-Kerr
- Return type:
float
- beta_parallel(dipole)
Fetch beta value under parallel polarization of all fields:
\[\begin{split}\begin{align} \beta_{||} &= \frac{1}{5}\,\sum_i \frac{\mu_i}{||\vec{\mu}||}\,\sum_{j} \beta_{ijj} + \beta_{jij} + \beta_{jji} \\ &= \frac{3}{5}\,\sum_i\frac{\mu_i\,\beta_{i}}{||\vec{\mu}||} \end{align}\end{split}\]where \(\beta_{i}\) is a component of the beta “tensor”.
- Parameters:
dipole (numpy.ndarray|qcip_tools.derivatives_e.ElectricDipole) – dipole moment of the molecule
- Return type:
float
- beta_perpendicular(dipole)
Fetch beta value under perpendicular polarization of optical and static field.
\[\beta_{\perp} = \frac{1}{5}\,\sum_i \frac{\mu_i}{||\vec{\mu}||}\,\sum_{j} 2\beta_{ijj} - 3\beta_{jij} + 2 \beta_{jji}.\]- Parameters:
dipole (numpy.ndarray|qcip_tools.derivatives_e.ElectricDipole) – the dipole moment
- Return type:
float
- beta_squared_zxx()
Compute \(\langle\beta^2_{ZXX}\rangle\):
\[\begin{split}\begin{align} \langle\beta^2_{ZXX}\rangle &= \frac{1}{105}\, \sum_{ijk}^{xyz} 6\,\beta_{ijk}^2 + 3\,\beta_{ijj} \beta_{ikk} -2\, (\beta_{iij} \beta_{jkk} +\beta_{iij} \beta_{kjk} +\beta_{ijk} \beta_{jik})\\ &\approx \frac{1}{105}\,\sum_{ijk}^{xyz}4\, \beta_{ijk}^2-\beta_{ijj} \beta_{ikk} \end{align}\end{split}\](actually computed using the polarization dependant intensity)
- Return type:
float
- beta_squared_zzz()
Compute \(\langle\beta^2_{ZZZ}\rangle\):
\[\begin{split}\begin{align} \langle\beta^2_{ZZZ}\rangle &= \frac{1}{105}\,\sum_{ijk}^{xyz} 2\, \beta_{ijk}^2 + \beta_{ijj} \beta_{ikk} + 4\, (\beta_{iij} \beta_{jkk} + \beta_{iij} \beta_{kjk} + \beta_{ijk} \beta_{jik})\\ &\approx \frac{1}{35}\,\sum_{ijk}^{xyz} 2\,\beta_{ijk}^2 + 3 \beta_{ijj} \beta_{ikk} \end{align}\end{split}\](actually computed using the polarization dependant intensity)
- Return type:
float
- beta_vector()
return the hyperpolarizability vector
\[\beta_i = \frac{1}{3} \sum_j \beta_{ijj} + \beta_{jij} + \beta_{jji}\]- Return type:
numpy.ndarray
- compute_properties(**kwargs)
Function to compute the tensor’s properties
- compute_sum(what)
Shorthand to simplify the computation of invariant quantities.
whatis the list of quantities to compute:beta_tensor.compute_sum([(2/5, 'ijjikk'), (3/5, 'iijkjk'])is equivalent to\[\sum_{ijk}^{xyz} \frac{2}{5}\,\sbb{ijj}{ijj} + \frac{2}{5}\,\sbb{iij}{kjk}.\]- Parameters:
what (list) – what to compute ? list of tuple of the form (fraction, string of 6 char [either i, j or k])
- Return type:
float
- depolarization_ratio()
Hyper-Rayleigh depolarization ratio:
\[DR = \frac{\langle\beta^2_{ZZZ}\rangle}{\langle\beta^2_{XZZ}\rangle}\]
- dipolar_contribution(old_version=True)
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version (coherent with betaprint’s g16)
- Return type:
float
- dipolar_contribution_squared(old_version=True)
Compute the square of the dipolar contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- is_shg()
Check if the tensor correspond to a SHG one
- Return type:
bool
- nonlinear_anisotropy(old_version=True)
Compute the nonlinear anisotropy:
\[\rho_{3/1}^2 = \frac{|\beta_{J=3}|^2}{|\beta_{J=1}|^2}\]- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- octupolar_contribution(old_version=True)
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- octupolar_contribution_squared(old_version=True)
Compute the square of the octupolar contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version (coherent with betaprint’s g16)
- Return type:
float
- polarization_angle_dependant_intensity(angle)
Compute the angle (\(\Psi\)) dependant intensity in the SHS setup.
\[\begin{split}\langle\beta^2\rangle = \frac{1}{105}\,\begin{pmatrix} 4-26\cos^2\Psi+20\cos^4\Psi\\ 4+2\cos^2\Psi-8\cos^4\Psi \\ 1-10\cos^2\Psi+12\cos^4\Psi \\ 2+8\cos^2\Psi-4\cos^4\Psi \\ 4+2\cos^2\Psi-8\cos^4\Psi \end{pmatrix}^T\,\begin{pmatrix} [g\beta^2]_A\\ [g\beta^2]_B\\ [g\beta^2]_C\\ [g\beta^2]_D\\ [g\beta^2]_E\\ \end{pmatrix}.\end{split}\]- Parameters:
angle (float) – angle (in degree)
- Return type:
float
- spherical_J1_contribution_squared()
Compute the \(|\beta_{J=1}|^2\) contribution
\[\begin{align} |\beta_{J=1}|^2 &= |\beta_{J=1\alpha}|^2 + |\beta_{J=1\beta}|^2 + 2\,|\beta_{J=1\alpha\beta}|^2 &= \frac{1}{5}\,\sum_{ijk}^{xyz} 2\,\sbb{ijj}{ikk} + 3\,\sbb{iij}{kjk} - 2\,\sbb{iij}{jkk} \end{align}\]- Return type:
float
- spherical_J1a_contribution_squared()
Compute the \(|\beta_{J=1\alpha}|^2\) contribution
\[|\beta_{J=1\alpha}|^2 = \frac{1}{5}\,\sum_{ijk}^{xyz} 2\,\sbb{ijj}{ikk}\]- Return type:
float
- spherical_J1ab_contribution_squared()
Compute the \(|\beta_{J=1\alpha\beta}|^2\) contribution
\[|\beta_{J=1\alpha\beta}|^2 = -\frac{1}{5}\,\sum_{ijk}^{xyz} \sbb{iij}{jkk}\]- Return type:
float
- spherical_J1b_contribution_squared()
Compute the \(|\beta_{J=1\beta}|^2\) contribution
\[|\beta_{J=1\beta}|^2 = \frac{1}{5}\,\sum_{ijk}^{xyz} 3\,\sbb{iij}{kjk}\]- Return type:
float
- spherical_J2_contribution_squared()
Compute the \(|\beta_{J=2}|^2\) contribution
\[|\beta_{J=2}|^2 = \frac{1}{3}\,\sum_{ijk}^{xyz} 2\beta_{ijk}^2 -2\,\sbb{ijk}{jik}-\sbb{ijj}{ikk} -\,\sbb{iij}{kjk} +2\,\sbb{iij}{jkk}\]- Return type:
float
- spherical_J3_contribution_squared()
Compute the \(|\beta_{J=3}|^2\) contribution
\[|\beta_{J=3}|^2 = \frac{1}{15}\,\sum_{ijk}^{xyz} 5\beta_{ijk}^2 + 10\,\sbb{ijk}{jik}-\sbb{ijj}{ikk} -4\,\sbb{iij}{kjk} -4\,\sbb{iij}{jkk}\]- Return type:
float
- to_string(threshold=1e-05, disable_extras=False, dipole=None, **kwargs)
Rewritten to add information
- exception qcip_tools.derivatives_e.NotSHG
Raised when trying to compute a quantity from SHG experiment on a tensor which is not
- exception qcip_tools.derivatives_e.NotTHG
Raised when trying to compute a quantity from THG experiment on a tensor which is not
- class qcip_tools.derivatives_e.PolarisabilityTensor(tensor=None, input_fields=(1,), frequency='static')
Polarisability tensor, commonly written \(\alpha(-\omega_\sigma;\omega_1)\).
- anisotropic_value()
Ansotropic value:
\[\Delta\alpha= \left[\frac{1}{2}\sum_{ij} 3\,\alpha_{ij}^2 - \alpha_{ii}\,\alpha_{jj}\right]^{1/2}.\]- Return type:
float
- compute_properties()
Function to compute the tensor’s properties
- isotropic_value()
Isotropic value:
\[\bar{\alpha}=\frac{1}{3}\sum_i \alpha_{ii}.\]- Return type:
float
- to_string(threshold=1e-05, disable_extras=False, **kwargs)
Rewritten to add information
- qcip_tools.derivatives_e.REPRESENTATIONS = {'alpha(-w;w)': 'dD', 'alpha(0;0)': 'FF', 'beta(-2w;w,w)': 'XDD', 'beta(-w;w,0)': 'dDF', 'beta(0;0,0)': 'FFF', 'beta(0;w,-w)': 'FDd', 'gamma(-2w;w,w,0)': 'XDDF', 'gamma(-3w;w,w,w)': 'XDDD', 'gamma(-w;0,0,w)': 'dFFD', 'gamma(-w;w,0,0)': 'dDFF', 'gamma(-w;w,w,-w)': 'dDDd', 'gamma(0;0,0,0)': 'FFFF', 'mu': 'F'}
Correspondence between a name and a representation
- qcip_tools.derivatives_e.SIMPLIFIED_NAMES = {'alpha': 'α(0;0)', 'alpha(-w;w)': 'α(-w;w)', 'beta': 'β(0;0,0)', 'beta(-2w;w,w)': 'β(-2w;w,w)', 'beta(-w;w,0)': 'β(-w;w,0)', 'energy': 'E', 'gamma': 'γ(0;0,0,0)', 'gamma(-2w;w,w,0)': 'γ(-2w;w,w,0)', 'gamma(-3w;w,w,w)': 'γ(-3w;w,w,w)', 'gamma(-w;0,0,w)': 'γ(-w;0,0,w)', 'gamma(-w;w,0,0)': 'γ(-w;0,0,w)', 'gamma(-w;w,w,-w)': 'γ(-w;w,w,-w)', 'mu': 'µ'}
List of all simplified names
- class qcip_tools.derivatives_e.SecondHyperpolarizabilityTensor(tensor=None, input_fields=(1, 1, 1), frequency='static')
Second hyperpolarisability tensor, commonly written \(\gamma(-\omega_\sigma;\omega_1,\omega_2,\omega_3)\).
- compute_properties(**kwargs)
Function to compoute the tensor’s properties
- compute_sum(what)
Shorthand to simplify the computation of invariant quantities.
whatis the list of quantities to compute:gamma_tensor.compute_sum([(2/5, 'ijklijkl'), (3/5, 'iijjkkll'])is equivalent to\[\sum_{ijk}^{xyz} \frac{2}{5}\,\sgg{ijkl}{ijkl} + \frac{2}{5}\,\sgg{iijj}{kkll}.\]- Parameters:
what (list) – what to compute ? list of tuple of the form (fraction, string of 8 char [either i, j, k or l])
- Return type:
float
- depolarization_ratio()
Compute the depolarization ratio:
\[DR = \frac{\langle\gamma^2_{ZZZZ}\rangle}{\langle\gamma^2_{ZXXX}\rangle}\]- Return type:
float
- gamma_kerr()
Measured quantity in a dc-Kerr (-w;w,0,0) experiment
\[\gamma^K = \frac{3}{2}\,(\gamma_{||}-\gamma_{\perp})\]- Return type:
float
- gamma_parallel()
Fetch parallel isotropic average of gamma
\[\gamma_{||} = \frac{1}{15}\,\sum_{ij} \gamma_{iijj} + \gamma_{ijji} + \gamma_{ijij}\]- Return type:
float
- gamma_perpendicular()
Fetch perpendicular isotropic average of gamma
\[\gamma_{\perp} = \frac{1}{15}\,\sum_{ij} 2\gamma_{iijj} - \gamma_{ijij}\]- Return type:
float
- gamma_squared_zxxx()
Compute \(\langle\gamma^2_{ZXXX}\rangle\):
\[\begin{split}\langle\gamma_{ZXXX}^2\rangle &= \frac{1}{630}\sum_{ijkl}^{xyz} \left\{\begin{array}{l} 16\,\gamma_{ijkl}^2 +24\,\gamma_{ijjk} \gamma_{ikll} - 12\,\gamma_{iijk} \gamma_{jllk}\\ - 6\,(\gamma_{iijk} \gamma_{ljlk} + \gamma_{ijkl} \gamma_{jikl} ) -3\,(\gamma_{iijj} \gamma_{kllk}+\gamma_{ijjk} \gamma_{kill}) \end{array}\right\}\\ &\approx \frac{1}{630} \sum_{ijkl}^{xyz} 10\,\gamma^2_{ijkl} +3\,\gamma_{iijk}\gamma_{jkll} -3\gamma_{iijj}\gamma_{kkll}\end{split}\](actually computed using the polarization dependant intensity)
- Return type:
float
- gamma_squared_zzzz()
Compute \(\langle\gamma^2_{ZZZZ}\rangle\):
\[\begin{split}\langle\gamma_{ZZZZ}^2\rangle &= \frac{1}{315}\sum_{ijkl}^{xyz} \left\{\begin{array}{l} 2\,\gamma_{ijkl}^2 + 12\,\gamma_{iijk} \gamma_{jllk} + 6\,(\gamma_{iijk} \gamma_{ljlk} + \gamma_{ijkl} \gamma_{jikl} )\\ + 3\,(\gamma_{ijjk} \gamma_{ikll} +\gamma_{iijj} \gamma_{kllk} +\gamma_{ijjk} \gamma_{kill}) \end{array}\right\}\\ &\approx \frac{1}{315}\,\sum_{ijkl}^{xyz} 8\,\gamma^2_{ijkl} + 24\, \gamma_{iijk}\gamma_{jkll}+3\,\gamma_{iijj}\gamma_{kkll}\end{split}\](actually computed using the polarization dependant intensity)
- Return type:
float
- gamma_ths()
Compute \(\gamma_{THS}\), the quantity from a third harmonic scattering experiment.
\[\gamma_{THS} = \sqrt{\langle\gamma^2_{ZZZZ}\rangle + \langle\gamma^2_{ZXXX}\rangle}\]- Return type:
float
- hexadecapolar_contribution(old_version=True)
Compute the hexadecapolar contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- hexadecapolar_contribution_squared(old_version=True)
Compute the square of the hexadecapolar (bless you!) contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- is_thg()
Check if a tensor is a THG one
- Return type:
bool
- isotropic_contribution(old_version=True)
Compute the isotropic contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- isotropic_contribution_squared(old_version=True)
Compute the square of the isotropic contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- polarization_angle_dependant_intensity(angle)
Compute the angle (\(\Psi\)) dependant intensity in the THS setup.
\[\begin{split}\langle\gamma^2\rangle = \frac{1}{630}\, \begin{pmatrix} 6-81\cos^2\Psi+198\cos^4\Psi-126\cos^6\Psi\\ 24-108\cos^2\Psi-72\cos^4\Psi+144\cos^6\Psi\\ 12+54\cos^2\Psi-90\cos^4\Psi+18\cos^6\Psi\\ 6-54\cos^2\Psi+36\cos^4\Psi+36\cos^6\Psi\\ 4+36\cos^2\Psi-12\cos^4\Psi-12\cos^6\Psi \\ 6-81\cos^2\Psi+198\cos^4\Psi-126\cos^6\Psi\\ 12+54\cos^2\Psi-90\cos^4\Psi+18\cos^6\Psi \end{pmatrix}^T\,\begin{pmatrix} [g\gamma^2]_A\\ [g\gamma^2]_B\\ [g\gamma^2]_C\\ [g\gamma^2]_D\\ [g\gamma^2]_E\\ [g\gamma^2]_F\\ [g\gamma^2]_G\\ \end{pmatrix}.\end{split}\]- Parameters:
angle (float) – angle (in degree)
- Return type:
float
- quadrupolar_contribution(old_version=True)
Compute the quadrupolar contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- quadrupolar_contribution_squared(old_version=True)
Compute the square of the quadrupolar contribution
- Parameters:
old_version (bool) – Use the previous (with Kleinman’s conditions) version
- Return type:
float
- spherical_J0_contribution_squared()
Compute the \(|\gamma_{J=0}|^2\) contribution:
\[|\gamma_{J=0}|^2 = \frac{1}{5} \sum^{xyz}_{ijkl} \sgg{iijj}{kllk}\]- Return type:
float
- spherical_J1_contribution_squared()
Compute the \(|\gamma_{J=1}|^2\) contribution:
\[|\gamma_{J=1}|^2 = \frac{1}{10} \sum^{xyz}_{ijkl} 3\,\sgg{ijjk}{ikll} - 3\,\sgg{ijjk}{kill}\]- Return type:
float
- spherical_J2_contribution_squared()
Compute the \(|\gamma_{J=2}|^2\) contribution:
\[\begin{split}\begin{align} |\gamma_{J=2}|^2 &= |\gamma_{J=2\alpha}|^2 + |\gamma_{J=2\beta}|^2 + 2\,|\gamma_{J=2\alpha\beta}|^2 \\ &= \frac{1}{14}\,\sum_{ijkl}^{xyz} 10\,\sgg{iijk}{ljlk}+5\,\sgg{ijjk}{kill} +5\,\sgg{ijjk}{ikll}-8\,\sgg{iijk}{jllk}-4\,\sgg{iijj}{kllk} \end{align}\end{split}\]- Return type:
float
- spherical_J2a_contribution_squared()
Compute the \(|\gamma_{J=2\alpha}|^2\) contribution:
\[|\gamma_{J=2\alpha}|^2 = \frac{1}{42}\,\sum_{ijkl}^{xyz} 15\,\sgg{ijjk}{kill}+15\,\sgg{ijjk}{ikll}-10\,\sgg{iijj}{kllk}\]- Return type:
float
- spherical_J2ab_contribution_squared()
Compute the \(|\gamma_{J=2\alpha\beta}|^2\) contribution:
\[|\gamma_{J=2\alpha\beta}|^2 =\frac{1}{21}\,\sum_{ijkl}^{xyz} 2\,\sgg{iijj}{kllk}-6\,\sgg{iijk}{jllk}\]- Return type:
float
- spherical_J2b_contribution_squared()
Compute the \(|\gamma_{J=2\beta}|^2\) contribution:
\[|\gamma_{J=2\beta}|^2 = \frac{1}{21} \sum_{ijkl}^{xyz} 15\,\sgg{iijk}{ljlk}-5\,\sgg{iijj}{kllk}\]- Return type:
float
- spherical_J3_contribution_squared()
Compute the \(|\gamma_{J=3}|^2\) contribution:
\[\begin{split}|\gamma_{J=3}|^2 = \frac{1}{20} \sum^{xyz}_{ijkl}\left\{ \begin{array}{l} 15\,\gamma_{ijkl}^2+20\,\sgg{iijk}{jllk}+\sgg{ijjk}{kill}\\ -10\,\sgg{iijk}{ljlk}-15\,\sgg{ijkl}{jikl}-11\sgg{ijjk}{ikll} \end{array} \right\}\end{split}\]- Return type:
float
- spherical_J4_contribution_squared()
Compute the \(|\gamma_{J=4}|^2\) contribution:
\[\begin{split}|\gamma_{J=4}|^2 = \frac{1}{140} \sum^{xyz}_{ijkl}\left\{ \begin{array}{l} 35\,\gamma_{ijkl}^2+105\,\sgg{ijkl}{jikl}+12\,\sgg{iijj}{kllk}\\ -60\,\sgg{iijk}{jllk}-30\,\sgg{iijk}{ljlk}-15\sgg{ijjk}{ikll}-15\sgg{ijjk}{kill} \end{array} \right\}\end{split}\]- Return type:
float
- to_string(threshold=1e-05, disable_extras=False, dipole=None, **kwargs)
Rewritten to add information
- qcip_tools.derivatives_e.convert_energy_to(e, unit)
Convert energy to something else
- Parameters:
e (float) – the energy (in atomic unit)
unit (str) – the unit (nm, ev, cm-1)
- qcip_tools.derivatives_e.convert_frequency_from_string(f)
Convert the string value to the value in atomic units.
- Parameters:
f (str|float) – the string value
- Return type:
float
- qcip_tools.derivatives_e.fields_to_str(input_)
Get the string representation of a series of fields and the response, such as “-3w;w,w,w”.
- Parameters:
input (tuple) – list of fields
- Returns:
representation
- Return type:
str