2.4. Single configuration free energy

Nearly all the functions in this module have been speeduped by Numba package, which means they are fast.

qha.single_configuration.free_energy(temperature, q_weights, static_energies, frequencies, static_only=False)

The total free energy at a certain temperature.

Parameters

• temperature (float64) – A float that represents the temperature at which the total free energy is calculated. This value is in unit ‘Kelvin’.

• q_weights (array(float64, 1d, A)) – An \(m \times 1\) vector that represents the weight of each q-point in Brillouin zone sampling. This vector can be non-normalized since a normalization will be done internally.

• static_energies (array(float64, 1d, A)) – An \(n \times 1\) vector that represents the static energy of the system with \(n\) different volumes. This should be the same unit as user-defined in the “settings” file.

• frequencies (array(float64, 3d, A)) – An \(n \times m \times l\) 3D array that represents the frequency read from file.

• static_only (bool) – If True, directly return the static energies, i.e., the static_energies parameter itself. This is useful when the user just wants to see static result while keeping all other functions unchanged.

Return type

array(float64, 1d, A)

Returns

An \(n \times 1\) vector that represents the total free energy of the system with \(n\) different volumes. The default unit is the same as in function ho_free_energy.

class qha.single_configuration.HOFreeEnergySampler(temperature, q_weights, frequencies)

A harmonic oscillator free energy sampler. The differences between free_energy and HOFreeEnergySampler are

• HOFreeEnergySampler provides several ways to compute free energies on different q-points, bands or

  volumes, which could be used to check the correctness of the data.

• HOFreeEnergySampler can make calculation lazy, rather than directly calculates the values immediately.

• free_energy is usually enough for computing the final free energy results. HOFreeEnergySampler only calculates its vibrational part, static energies are not taken into account.

Parameters

• temperature (float) – A float that represents the temperature at which the total free energy is calculated. This value is in unit ‘Kelvin’.

• q_weights (array(float64, 1d, A)) – An \(m \times 1\) vector that represents the weight of each q-point in Brillouin zone sampling. This vector can be non-normalized since a normalization will be done internally.

• frequencies (array(float64, 3d, A)) – An \(n \times m \times l\) 3D array that represents the frequencies read from a file, usually in unit \(\text{cm}^{-1}\).

property on_all_volumes

Sample free energies on every volume.

Returns

A vector with length equals the number of volumes. Each element is the free energy of one volume.

on_band(i)

Sample free energy on the \(i\) th band.

Parameters

i (int) – An integer labeling \(i\) th band.

Return type

array(float64, 2d, A)

Returns

The accumulated free energy on the :math:`i`th q-point.

on_q_point(i)

Sample free energy on the \(i\) th q-point.

Parameters

i (int) – An integer labeling \(i\) th q-point.

Return type

array(float64, 2d, A)

Returns

The accumulated free energy on the \(i\) th q-point.

on_volume(i)

Sample free energy on the \(i\) th volume.

Parameters

i (int) – An integer labeling \(i\) th volume.

Return type

float64

Returns

The accumulated free energy on the \(i\) th volume.