Notice The Electronic Supplementary Material for J. Phys. Chem. A 129,11032-11040 (2025) has been relocated to this public repository in an effort to keep the development of the pySCO library independent from those files.
Please ensure that the following external libraries are installed beforehand:
We use the International System of Units as follows:
| Property | Symbol | Unit |
|---|---|---|
| Temperature | K | |
| Spin-Crossover Energy | kJ mol-1 | |
| Enthalpy Change | kJ mol-1 | |
| Entropy Change | J mol-1 K-1 | |
| Gibbs Free Energy | kJ mol-1 | |
| Interaction Parameter | kJ mol-1 | |
| High-Spin Population |
- Reading Outputs from Electronic Structure Codes
- Thermodynamic models
The library currently is compatible with VASP, Gaussian, ORCA, NWChem, and pySCF.
Since VASP produces several output files, each collecting different data, we need to locate the folder with the outputs and pass it to pySCO. Before proceeding any further, please keep in mind that this is a three-step process, namely,
- relax the geometry using a
$k$ -point mesh, - run a single-point energy calculation with a
$k$ -point mesh, and - compute the vibrational frequencies with a
$q$ -point mesh.
Here we are interested in the EIGENVAL, POSCAR, and OUTCAR files from step (2), and in the OUTCAR file from step (3). There are two additional files we need to prepare for every spin state, namely, MAGCAR and VIBCAR. The first one simply contains the analogous magnetization as reported in the OUTCAR from step (2), but with the correct rounded magnetic moments, e.g.
magnetization (x)
# of ion s p d tot
------------------------------------------
1 0.000 0.000 4.000 4.000
2 0.000 0.000 4.000 4.000
3 0.000 0.000 0.000 0.000
...
256 0.000 0.000 0.000 0.000
--------------------------------------------------
tot 0.000 0.000 8.000 8.000
where the first two atoms are assigned four unpair electrons each, whereas the rest show no magnetic moment. The second file, VIBCAR, is the OUTCAR that contains the harmonic vibrational frequencies computed with the chosen set of
grep 2PiTHz OUTCAR > VIBCARNow we can pass the location to the directory that contains the OUTCAR, EIGENVAL, POSCAR, MAGCAR, and VIBCAR files. Remember that we need to do this for each spin state.
import pysco
low_spin = pysco.read_vasp( 'path/to/the/low/spin/state/directory' )
high_spin = pysco.read_vasp( 'path/to/the/high/spin/state/directory' )There are several approaches to generate the output files. The most straightforward is to run a geometry relaxation followed by a frequency analysis in the same job. However, this usually is discuraged by most exprienced users and, instead, a two-step approach is preferred, where we first do the geometry relaxation and then, on a separate run, compute the frequency analysis. Here we will favor this second approach and hence the output of interest is that for the frequency analysis.
The file extension for the electronic structure codes Gaussian, ORCA, and NWChem, in particular, is irrelevant for as long as you include the complete file name.
import pysco
low_spin = pysco.read_gaussian( 'path/to/the/low/spin/state/gaussian/output.log' )
high_spin = pysco.read_gaussian( 'path/to/the/high/spin/state/gaussian/output.log' )import pysco
low_spin = pysco.read_orca( 'path/to/the/low/spin/state/orca/output.out' )
high_spin = pysco.read_orca( 'path/to/the/high/spin/state/orca/output.out' )Advise to the user: ORCA sometimes truncates the number of molecular orbitals written in the output, which is not helpful in our case, therefore including ! PrintMOs in your input ensures that all orbitals are printed.
import pysco
low_spin = pysco.read_nwchem( 'path/to/the/low/spin/state/nwchem/output.out' )
high_spin = pysco.read_nwchem( 'path/to/the/high/spin/state/nwchem/output.out' )Since pySCF already runs in Python, we simply need to provide the mean-field object we created for our run, and the harmonic analysis dictionary that we obtained from the hessian matrix. For the sake of clarity, please keep in mind that the mean-field object commonly is referred to as mf in the pySCF documentation, whereas the harmonic analysis is available through the thermo module using
from pyscf.hessian import thermo
hessian = spin_state_mean_field_object.Hessian( ).kernel( )
spin_state_harmonic_analysis = thermo.harmonic_analysis( spin_state_mean_field_object.mol, hessian )Then we use those outputs from our generic example in pySCO as follows,
import pysco
low_spin = pysco.read_pyscf( low_spin_mean_field_object, low_spin_harmonic_analysis )
high_spin = pysco.read_pyscf( high_spin_mean_field_object, high_spin_harmonic_analysis )The read module also allows for the inclusion of additional options when reading output files. These are specified as keyword arguments, namely, jahnteller, orbit, and configs. These keywords are not mutually exclusive and hence may be included simultaneously.
jahnteller:int = 1. By default pySCO assumes no Jahn-Teller distortions. The argument jahnteller may be used to specify the number of distortions in the structure. The following is an example using the Gaussian reader,
import pysco
low_spin = pysco.read_gaussian( 'path/to/the/low/spin/state/output.log', jahnteller=1 )
high_spin = pysco.read_gaussian( 'path/to/the/high/spin/state/output.log', jahnteller=3 )orbit:int = 0. By default pySCO assumes no spin-orbit coupling. The argument orbit may be used to specify the orbital angular momentum,
where LS and HS label the low- and high-spin state, respectively. The following is an example using the NWChem reader,
import pysco import
low_spin = pysco.read_nwchem( 'path/to/the/low/spin/state/output.out', orbit=1 )
high_spin = pysco.read_nwchem( 'path/to/the/high/spin/state/output.out', orbit=3 )configs:int = 1. By default pySCO assumes a unique spin configuration. But for the cases where a given spin state may exhibit more that one spin configuration related by symmetry, we use configs to specify the total number of such configurations,
The following is an example using the Gaussian reader,
import pysco import
low_spin = pysco.read_gaussian( 'path/to/the/low/spin/state/output.out', configs=1 )
high_spin = pysco.read_gaussian( 'path/to/the/high/spin/state/output.out', configs=2 )set_spin(list[int]). Here we refer to spin, set_spin() property can therefore be used to override the default behavior and specify the desired spin for each metal center, or any other atom in particular.
- It is a list of integers with the same size as the total number of atoms in the metal-complex.
- The order of the elements in this list must be consistent with the ordering of the atoms in the geometry.
The following is an example using the Orca reader,
import pysco
low_spin = pysco.read_orca( 'path/to/the/low/spin/state/output.out' )
high_spin = pysco.read_orca( 'path/to/the/high/spin/state/output.out' )
low_spin.set_spin( 2*[5] + 98*[0] )
high_spin.set_spin( 2*[1] + 98*[0] )It is important to note that we do not need the set_spin atribute for VASP because we already provide the MAGCAR. Keep in mind that pySCO will overwrite the contents read from MAGCAR should set_spin be specified.
set_orbit(list[int]). Specify the orbital angular momentum per atom from a predifined list.
- It is a list of integers with the same size as the total number of atoms in the metal-complex.
- The order of the elements in this list must be consistent with the ordering of the atoms in the geometry.
The following is an example using the NWChem reader,
import pysco
low_spin = pysco.read_nwchem( 'path/to/the/low/spin/state/output.out' )
high_spin = pysco.read_nwchem( 'path/to/the/high/spin/state/output.out' )
low_spin.set_orbit( 2*[1] + 98*[0] )
high_spin.set_orbit( 2*[3] + 98*[0] )The library offers the possibility to define a spin state independent of an ouput file, or files, from electronic structure calculations. This is handy for toy problems or for more in-depth analyses. The following list gathers all the necessary attributes for such purpose.
-
elements:list[str]. No units. All the elements for the species at hand. It is possible to use a short-hand notation to group the elements, e. g.,['Mn'] + ['C'] + ['H']. -
atoms:list[int]. No units. Atom counts for the species at hand. Use of a short-hand notation is possible, e. g.,[1] + [12] + [14]. -
spin:list[int]. No units. Difference between spin-up electrons and spin-down electrons on a per atoms basis. The ordering must be consitent with the attributeelements. A short-hand notation also is possible for this attribute, e. g.,[5] + 12*[0] + 14*[0]. -
energy:float. In units of electronvolt. The self-consistent total energy of the species for the spin state at hand. -
volume:float. In units of$\mathring A$ 3. The volume for the unit cell for species with periodic boundary conditions and zero otherwise. -
frequencies:list[float]. In units of Hertz. The set of harmonic frequencies for the species at hand. Beware that by setting this atribute to zeros, e. g.,3*[0.0]the library will ignore all the vibrational contributions for the calculation of both spin-crossover energies and temperatures. -
orbital_energies:list[float]. In units of electronvolt. Single particle energies subtracted by the Fermi energy for the species at hand. -
rotational_symmetry:float. No units. The rotational symmetry number for the species at hand. Given that the use of symmetry most often is not utilized, the rotational symmetry number likely is one. Beware that by setting this attribute to zero, the library will ignore the contributions to the rotational entropy. -
rotational_temperature:float. In units of Kelvin. The rotational temperature for the species at hand. It is defined as$\theta_r = \hbar/(2\,k_B\,I)$ , where$I$ is the moment of inertia for the species. Beware that by setting this attribute to zero, the library will ignore the contributions to the rotational entropy.
The definition of a custom spin state also allows for the inclusion of additional options that are specified as keyword arguments, namely, jahnteller and configs. These keywords are not mutually exclusive and hence may be included simultaneously. The orbital angular momentum, orbit, on the other hand, must be set as in the following example, that further illustrates the use of the configs option during the creation of the generic spin_state object.
import pysco
spin_state = pysco.read.reader( configs=1 )
spin_state.elements = ['Fe'] + ['O'] + ['N'] + ['C'] + ['H']
spin_state.atoms = [4] + [8] + [16] + [192] + [216]
spin_state.spin = 4*[4] + 8*[0] + 16*[0] + 192*[0] + 216*[0]
spin_state.energy = -2749.21532786
spin_state.volume = 4699.15
spin_state.frequencies = [ 3.329835e+13, 3.328946e+13, ..., 5.569565e+12, 5.566312e+12 ]
spin_state.orbital_energies = [ -89.566276, -89.566270, ..., 6.221009, 6.240796 ]
spin_state.rotational_symmetry = 0.0 # Ignore contribution
spin_state.rotational_temperature = 0.0 # Ignore contribution
# IMPORTANT: Set internal variables
spin_state.orbit = spin_state._set_orbital_momentum( 0 )
spin_state.zero_point_energy = spin_state._set_zero_point_energy( )
# IMPORTANT: Sanity check
spin_state._check_attributes( )This model consists of assuming that the spin state mixture for a given molecular aggregate is distributed statistically and forms a regular solution. For a given material at constant pressure, the conversion from low to high spin is a thermal equilibrium between the spin configurations. The state function therefore is the Gibbs free energy
Where the basic assumption is that the inter-molecular coupling has negligible dependence on those spin states, and that the ideal entropy of mixing,
where
There are two optional arguments that modify the behavior of the model:
-
metals:tuple(str) = ('Cr', 'Mn', 'Fe', 'Co). By default the reported spin-crossover energy is normalized to the total number of spin conversion centers. This number is determined internally by comparing which transition metals undergo a spin transition. This list of metals can be modified by the user. -
centers:float = 1.0. The automatic normalization also may be overruled by means of this optional keyword that fixes the total number of spin-crossover centers. This is useful for multi-center metal complexes were not all metals switch their spin state. Alternatively, the use of set_spin also fixes internally the number of spin-crossover centers.
We may use this regular solution model in pySCO by creating an object which, for practical purposes we will be calling model, in the form
import pysco
# Default use
model = pysco.RegularSolution( ls=low_spin, hs=high_spin )
# Specify the metals of interest
model = pysco.RegularSolution( ls=low_spin, hs=high_spin, metals=('Fe') )
# Fix a different number of metallic centers
model = pysco.RegularSolution( ls=low_spin, hs=high_spin, centers=2.0 )
# Specify the local spins for both the low- and high-spin states
low_spin.set_spin( [1, 0], 98*[0] )
high_spin.set_spin( [1, 2], 98*[0] )
model = pysco.RegularSolution( ls=low_spin, hs=high_spin)where low_spin and high_spin are the objects we created previously by either reading the output from an electronic structure code, or by including the information ourselves.
The regular solution model includes two main attributes that are accesible to the user:
-
min_nhs:float = 1.00e-06. The lower bound for the relative high-spin population of interest. To prevent numerical inestabilities, the lower bound should not equal exactly zero. -
max_nhs:float = 9.99e-01. The upper bound for the relative high-spin population of interest. To prevent numerical inestabilities, the upper bound should not equal exactly one.
set_min_nhs(float). Specify the lower bound for the relative high-spin population of interest.
- It is a float close to zero, but not exactly zero that helps preventing numerical inestabilities during the evaluation of the natural logarithm.
set_max_nhs(float). Specify the upper bound for the relative high-spin population of interest.
- It is a float close to one, but not exactly one that helps preventing numerical inestabilities during the evaluation of the natural logarithm.
The list of points for the thermal evolution of the high-spin population determined internally by pySCO is meant to produce a uniform sampling of the relative high-spin population to preserve the quality of the plot,
set_nhs_list:Callable. It is possible to change the default uniform sampling by specifying a callable function with the positional arguments points, min_nhs, and max_nhs. The following code snipt exepmplifies its use with the Gaussian reader,
import pysco
import numpy as np
from matplotlib import pyplot as plt
def mod_nhs_list( points, min_nhs, max_nhs ):
nhs_points = np.linspace( min_nhs, max_nhs, num=points )
return nhs_points
low_spin = pysco.read_gaussian( 'path/to/the/low/spin/state/gaussian/output.log' )
high_spin = pysco.read_gaussian( 'path/to/the/high/spin/state/gaussian/output.log' )
model = pysco.RegularSolution( ls=low_spin, hs=high_spin )
# Specify the modified callable function
model.set_nhs_list = mod_nhs_list
nhs_T_dH_dS_dG = model.high_spin_population( )
plt.scatter( nhs_T_dH_dS_dG['T'], nhs_T_dH_dS_dG['nhs'], c='b' )
plt.xlabel( 'Temperature [K]' )
plt.ylabel( 'High-Spin Population' )
plt.show( )that produces the following result
The energy difference between the high-spin and low-spin states,
where
There is one optional argument that modifies the behavior of the function:
-
zero_point_energy:bool = False. If set toTrue, the zero-point energy correction will be included, as in${\Delta E}_\mathrm{sco}$ . Otherwise the energy difference${\Delta E}_\mathrm{HL}$ will be reported.
import pysco
# Default
Ehl = model.spin_crossover_energy( )
# Include the zero-point energy correction
Esco = model.spin_crossover_energy( zero_point_energy=True )The equilibrium temperature at which the populations of the high-spin and low-spin states are equal defines the transition temperature,
where
There are two optional arguments that modify the behavior of the function:
-
guess:float = 298.15. A rough estimate of$T_{1/2}$ , in Kelvin, can be provided to accelerate the numerical procedure. -
tol:float = 1.0e-03. The accuracy threshold for the calculation of$T_{1/2}$ .
import pysco
# Default
Thalf, dH, dS = model.transition_temperature( )
# Modify the initial temperature guess
Thalf, dH, dS = model.transition_temperature( guess=120.0 )
# Modify the convergence threshold for the temperature
Thalf, dH, dS = model.transition_temperature( tol=0.01 )
# Simultaneous choices
Thalf, dH, dS = model.transition_temperature( guess=120.0, tol=0.01 )Compute the thermal evolution of the relative high-spin population, also known as magnetization, in the form
Returns dict[str:ndarray], a dictionary with NumPy arrays with keys 'nhs': relative high-spin population, 'T': temperature, 'dH': change in enthalpy, 'dS': change in entropy, 'dG': change in Gibbs free enrgy.
There are three optional arguments that modify the behavior of the function:
-
points:int = 128. The number of temperature points at which the high-spin population will be evaluated. -
guess:float = 298.15. The initial temperature guess, in Kelvin, for the numerical procedure. -
tol:float = 1.0e-03. The accuracy threshold for the calculation of the temperatures.
import pysco
# Default
nhs_T_dH_dS_dG = model.high_spin_population( )
# Modify the number of points
nhs_T_dH_dS_dG = model.high_spin_population( points=512 )
# Modify the initial temperature guess
nhs_T_dH_dS_dG = model.high_spin_population( guess=120.0 )
# Modify the convergence threshold
nhs_T_dH_dS_dG = model.high_spin_population( tol=0.01 )
# Simultaneous choices
nhs_T_dH_dS_dG = model.high_spin_population( points=512, guess=120.0, tol=0.01 )Compute the Gibbs free energy for a given isotherm in the form
Returns dict[str:ndarray], a NumPy array with keys 'nhs': relative high-spin population, 'dG': change in Gibbs free energy.
There is a single mandatory argument:
temperature:float. Specify the choice of temperature for the isotherm.
There is one optional argument that modifies the behavior of the function:
points:int = 128. The total number of point for the curve.
import pysco
# Default
nHS_G = model.gibbs_free_energy( 120.0 )
# Modify the number of points
nHS_G = model.gibbs_free_energy( 120.0, points=512 )Slichter and Drickamer proposed the addition of a non-linear mean-field term independent of the temperature to the regular solution model to parametrize the splitting in the form
That represents the simplest approximation to modeling inter-molecular interactions by means of a second-order term,
There are three optional arguments that modify the behavior of the model:
-
interaction:float = 0.0. Define the phenomenological interaction parameter that will we used as the default during runtime evaluations. Use set_interaction to modify its value after the creation of the object. -
metals:tuple(str) = ('Cr', 'Mn', 'Fe', 'Co). By default the reported spin-crossover energy is normalized to the total number of spin conversion centers. This number is determined internally by comparing which transition metals undergo a spin transition. This list of metals can be modified by the user. -
centers:float = 1.0. The automatic normalization also may be overruled by means of this optional keyword that fixes the total number of spin-crossover centers. This is useful for multi-center metal complexes were not all metals switch their spin state. Alternatively, the use of set_spin also fixes internally the number of spin-crossover centers.
We may use the Slichter-Drickamer model in pySCO by creating an object which, for practical purposes we will be calling model, in the form
import pysco
# Default use
model = pysco.SlichterDrickamer( ls=low_spin, hs=high_spin, interaction=2.0 )
# Specify the metals of interest
model = pysco.SlichterDrickamer( ls=low_spin, hs=high_spin, interaction=2.0, metals=('Fe') )
# Fix a different number of metallic centers
model = pysco.SlichterDrickamer( ls=low_spin, hs=high_spin, interaction=2.0, centers=2.0 )
# Specify the local spins for both the low- and high-spin states
low_spin.set_spin( [1, 0], 98*[0] )
high_spin.set_spin( [1, 2], 98*[0] )
model = pysco.SlichterDrickamer( ls=low_spin, hs=high_spin )where low_spin and high_spin are the objects we created previously by either reading the output from an electronic structure code, or by including the information ourselves.
Keep in mind that by letting
The Slichter-Drickamer model includes two main attributes that are accesible to the user:
-
min_nhs:float = 1.00e-06. The lower bound for the relative high-spin population of interest. To prevent numerical inestabilities, the lower bound should not equal exactly zero. -
max_nhs:float = 9.99e-01. The upper bound for the relative high-spin population of interest. To prevent numerical inestabilities, the upper bound should not equal exactly one.
set_min_nhs(float). Specify the lower bound for the relative high-spin population of interest.
- It is a float close to zero, but not exactly zero that helps preventing numerical inestabilities during the evaluation of the natural logarithm.
set_max_nhs(float). Specify the upper bound for the relative high-spin population of interest.
- It is a float close to one, but not exactly one that helps preventing numerical inestabilities during the evaluation of the natural logarithm.
The list of points for the thermal evolution of the high-spin population determined internally by pySCO is meant to produce a uniform sampling of the relative high-spin population to preserve the quality of the plot,
set_nhs_list:Callable. It is possible to change the default uniform sampling by specifying a callable function with the positional arguments points, min_nhs, and max_nhs. The following code snipt exepmplifies its use with the VASP reader,
import pysco
import numpy as np
from matplotlib import pyplot as plt
def mod_nhs_list( points, min_nhs, max_nhs ):
nhs_points = np.linspace( min_nhs, max_nhs, num=points )
return nhs_points
low_spin = pysco.read_vasp( 'path/to/the/low/spin/state/directory' )
high_spin = pysco.read_vasp( 'path/to/the/high/spin/state/directory' )
model = pysco.SlichterDrickamer( ls=low_spin, hs=high_spin, interaction=2.0 )
# Specify the modified callable function
model.set_nhs_list = mod_nhs_list
nhs_T_dH_dS_dG = model.high_spin_population( )
plt.scatter( nhs_T_dH_dS_dG['T'], nhs_T_dH_dS_dG['nhs'], c='b' )
plt.xlabel( 'Temperature [K]' )
plt.ylabel( 'High-Spin Population' )
plt.show( )that produces the following result
set_interaction(float). Fix the default value for the phenomenological interaction parameter during runtime calculations. This value will be overruled should the optional argument interaction be used for the thermal evolution of the high-spin population or the Gibbs free energy. Likewise while fitting an interaction parameter.
The energy difference between the high-spin and low-spin states,
where
There is one optional argument that modifies the behavior of the function:
-
zero_point_energy:bool = False. If set toTrue, the zero-point energy correction will be included, as in${\Delta E}_\mathrm{sco}$ . Otherwise the energy difference${\Delta E}_\mathrm{HL}$ will be reported.
import pysco
# Default
Ehl = model.spin_crossover_energy( )
# Include the zero-point energy correction
Esco = model.spin_crossover_energy( zero_point_energy=True )The equilibrium temperature at which the populations of the high-spin and low-spin states are equal defines the transition temperature,
where
There are two optional arguments that modify the behavior of the function:
-
guess:float = 298.15. A rough estimate of$T_{1/2}$ , in Kelvin, can be provided to accelerate the numerical procedure. -
tol:float = 1.0e-03. The accuracy threshold for the calculation of$T_{1/2}$ .
import pysco
# Default
Thalf, dH, dS = model.transition_temperature( )
# Modify the initial temperature guess
Thalf, dH, dS = model.transition_temperature( guess=120.0 )
# Modify the convergence threshold for the temperature
Thalf, dH, dS = model.transition_temperature( tol=0.01 )
# Simultaneous choices
Thalf, dH, dS = model.transition_temperature( guess=120.0, tol=0.01 )Compute the thermal evolution of the relative high-spin population, also known as magnetization, in the form
Returns dict[str:ndarray], a dictionary with NumPy arrays with keys 'nhs': relative high-spin population, 'T': temperature, 'dH': change in enthalpy, 'dS': change in entropy, 'dG': change in Gibbs free enrgy.
There are three optional arguments that modify the behavior of the function:
-
points:int = 128. The number of temperature points at which the high-spin population will be evaluated. -
guess:float = 298.15. The initial temperature guess, in Kelvin, for the numerical procedure. -
tol:float = 1.0e-03. The accuracy threshold for the calculation of the temperatures. -
interaction:float = None. When povided, the temporary specified interaction parameter will be used on the fly. To fix an interaction parameter see set_interaction.
import pysco
# Default
nhs_T_dH_dS_dG = model.high_spin_population( )
# Modify the number of points
nhs_T_dH_dS_dG = model.high_spin_population( points=512 )
# Modify the initial temperature guess
nhs_T_dH_dS_dG = model.high_spin_population( guess=120.0 )
# Modify the convergence threshold
nhs_T_dH_dS_dG = model.high_spin_population( tol=0.01 )
# Use temporary interaction parameter
nhs_T_dH_dS_dG = model.high_spin_population( interaction=2.1 )
# Simultaneous choices
nhs_T_dH_dS_dG = model.high_spin_population( points=512, guess=120.0, tol=0.01, interaction=2.1 )Compute the Gibbs free energy for a given isotherm in the form
Returns dict[str:ndarray], a NumPy array with keys 'nhs': relative high-spin population, 'dG': change in Gibbs free energy.
There is a single mandatory argument:
temperature:float. Specify the choice of temperature for the isotherm.
There are two optional arguments that modify the behavior of the function:
-
points:int = 128. The total number of point for the curve. -
interaction:float = None. When povided, the temporary specified interaction parameter will be used on the fly. To fix an interaction parameter see set_interaction.
import pysco
# Default
nHS_G = model.gibbs_free_energy( 120.0 )
# Modify the number of points
nHS_G = model.gibbs_free_energy( 120.0, points=512 )
# Use temporary interaction parameter
nHS_G = model.gibbs_free_energy( 120.0, interaction=2.1 )
# Simultaneous choices
nHS_G = model.gibbs_free_energy( 120.0, points=512, interaction=2.1 )Keep in mind that we need to sample a series of spin configurations within the interval ms:list[reader] that contains the objects generated by the reader modules.
The fitting procedure will use a least-squares approach. It returns the interaction parameter and the coefficient of determination,
There is a single mandatory argument:
ms:list[reader]. A list with the set of spin configurations that contains the objects generated by the reader modules for materials modeling.
There are three optional arguments that modify the behavior of the function:
-
guess:float = 298.15. The initial temperature guess, in Kelvin, for the numerical procedure. -
tol:float = 1.0e-03. The accuracy threshold for the calculation of the temperatures. -
interaction:float = None. When povided, the temporary specified interaction parameter will be used on the fly. To fix an interaction parameter see set_interaction.
import pysco
mixed_spin = [ spin_config_1, spin_config_2, spin_config_3, ... ]
# Default
interaction, R2 = model.fit_leastsqrs_interaction( mixed_spin )
# Modify the initial temperature guess
interaction, R2 = model.fit_leastsqrs_interaction( mixed_spin, guess=120.0 )
# Modify the convergence threshold
interaction, R2 = model.fit_leastsqrs_interaction( mixed_spin, tol=0.01 )
# Use temporary interaction parameter
interaction, R2 = model.fit_leastsqrs_interaction( mixed_spin, interaction=2.1 )
# Simultaneous choices
interaction, R2 = model.fit_leastsqrs_interaction( mixed_spin, guess=120.0, tol=0.1, interaction=2.1 )The fitting procedure will use a Boltzmann ensemble approach as in H. Paulsen Magnetochemistry 2, 14 (2016). This option remains in an experimental stage. It returns the interaction parameter and the weight for each spin configuration.
There is a single mandatory argument:
ms:list[reader]. A list with the set of spin configurations that contains the objects generated by the reader modules for materials modeling.
There are three optional arguments that modify the behavior of the function:
-
guess:float = 298.15. The initial temperature guess, in Kelvin, for the numerical procedure. -
tol:float = 1.0e-03. The accuracy threshold for the calculation of the temperatures. -
interaction:float = None. When povided, the temporary specified interaction parameter will be used on the fly. To fix an interaction parameter see set_interaction.
import pysco
mixed_spin = [ spin_config_1, spin_config_2, spin_config_3, ... ]
# Default
interaction, weights = model.fit_boltzmann_interaction( mixed_spin )
# Modify the initial temperature guess
interaction, weights = model.fit_boltzmann_interaction( mixed_spin, guess=120.0 )
# Modify the convergence threshold
interaction, weights = model.fit_boltzmann_interaction( mixed_spin, tol=0.01 )
# Use temporary interaction parameter
interaction, weights = model.fit_boltzmann_interaction( mixed_spin, interaction=2.1 )
# Simultaneous choices
interaction, weights = model.fit_boltzmann_interaction( mixed_spin, guess=120.0, tol=0.1, interaction=2.1 )