calc_self_mie_from_multipole

mapsci.multipole_mie_combining_rules.calc_self_mie_from_multipole

calc_self_mie_from_multipole(bead_dict, mie_vdw=None, temperature=298, lambda_r=12, distance_opts={}, distance_array=None, polarizability_opts={}, shape_factor_scale=False, nondimensional=False)[source]

Calculation of self-interaction parameters for the Mie potential from multipole moments.

Nondimensional parameters are scaled using the following physical constants: vacuum permittivity, \(\varepsilon_{0}\), Boltzmann constant, \(k_{B}\), and elementary charge, \(e\).

Parameters

  • bead_dict (dict) – Dictionary of Mie and multipole parameters for bead_A.

    • epsilon (float) Energy parameter scaled by \(k_{B}\) in [K], or nondimensionalized as \(\epsilon'=\epsilon/(3k_{B}T)\)

    • sigma (float) Size parameter in [Å], or nondimensionalized as \(\sigma'=\sigma (4 \pi \varepsilon_{0}) 3k_{B}T e^{-2}\)

    • lambdar (float) Repulsive exponent

    • lambdaa (float) Attractive exponent

    • charge (float) Charge of bead in [e], or nondimensionalized as \(q'=q/e\)

    • dipole (float) Dipole of bead in [Debye], or nondimensionalized as \(\mu'=\mu (4 \pi \varepsilon_{0}) 3k_{B}T e^{-3}\)

    • quadrupole (float) Quadrupole of bead in [Debye*Å], or nondimensionalized as \(Q'=Q (4 \pi \varepsilon_{0})^{2} (3k_{B}T)^{2} e^{-5}\)

    • ionization_energy (float) Ionization_energy of bead in [kcal/mol], or nondimensionalized as \(I'=I/(3k_{B}T)\)

    • polarizability (float) Polarizability of bead in [\(Å^3\)] or nondimensionalized with \(\alpha'=\alpha (4 \pi \varepsilon_{0}) 3k_{B}T e^{-6}\), where the dimensionalized version is the polarizability volume

  • mie_vdw (float, Optional, default=None) – This nondimensionalized attractive parameter for the Mie potential is related not only to the Mie exponents but also to the triple and critical temperatures of a substance. It can be used to specify the repulsive exponent, otherwise a value of 12 is assumed

  • lambda_r (float, Optional, default=12) – Assumed repulsive exponent. This quantity can be changed later as long as the energy parameter is scaled accordingly.

  • temperature (float, Optional, default=298) – Temperature in [K] for adding and removing dimensions, if the parameters are nondimensionalized, this value isn’t used.

  • shape_factor_scale (bool, Optional, default=False) – Scale energy parameter based on shape factor epsilon*Si*Sj

  • distance_opts (dict, Optional, default={}) – Optional keywords for creating r array used for calculation or fitting

  • polarizability_opts (dict, Optional, default={}) – Dictionary of keyword arguments for fit_polarizability() or solve_polarizability_integral()

  • nondimensional (bool, Optional, default=False) – Indicates whether the given bead library has been nondimensionalized by dict_dimensions()

  • distance_array (numpy.ndarray, Optional, default=None) – Array (or float) in either [Å] or nondimensionalized distance between two beads. \(r'=r (4 \pi \varepsilon_{0}) 3k_{B}T e^{-2}\), whatever is consistent with ‘bead_dict’. If None, ‘distance_opts’ are used to generate the array.

Returns

cross_dict – Dictionary with energy parameter and exponents for Mie cross interaction between the given beads.

  • epsilon (float) Fit energy parameter, scaled by \(k_{B}\) in [K], or nondimensionalized as \(\epsilon'=\epsilon/(3k_{B}T)\)

  • lambdar (float) Repulsive exponent, if mie_vdw is provided, otherwise this is the same value that was given.

  • lambdaa (float) Fit attractive exponent

Return type

dict