Skip to content

Thermodynamic Properties

Purpose: Energies, forces, pressure, temperature, and thermodynamic state functions

In scope:

  • Energy hierarchy: BaseEnergy → specific energy types
  • Free energies: Gibbs, Helmholtz
  • Force hierarchy: BaseForce → TotalForce
  • Thermodynamic state variables: pressure, volume, temperature
  • Entropy and heat capacities
  • Virial tensor for stress calculations
  • Hessian matrices for phonon calculations

Relationship map

Hold "Alt" / "Option" to enable pan & zoom
classDiagram
    class BaseEnergy
    class BaseForce
    class ChemicalPotential
    class Enthalpy
    class Entropy
    class GibbsFreeEnergy
    class Heat
    class HeatCapacity
    class HelmholtzFreeEnergy
    class Hessian
    class InternalEnergy
    class KineticEnergy
    class MassDensity
    class PotentialEnergy
    class Pressure
    class Temperature
    class TotalEnergy
    class TotalForce
    class VirialTensor
    class Volume
    class Work
    BaseEnergy <|-- ChemicalPotential
    BaseEnergy <|-- Enthalpy
    BaseEnergy <|-- GibbsFreeEnergy
    BaseEnergy <|-- Heat
    BaseEnergy <|-- HelmholtzFreeEnergy
    BaseEnergy <|-- InternalEnergy
    BaseEnergy <|-- KineticEnergy
    BaseEnergy <|-- PotentialEnergy
    BaseEnergy <|-- TotalEnergy
    BaseForce <|-- TotalForce
    BaseEnergy <|-- VirialTensor
    BaseEnergy <|-- Work
    TotalEnergy --> BaseEnergy : contributions
    TotalForce --> BaseForce : contributions

Legend

Parent <|-- Child inheritance (Child extends Parent)
Owner --> SubSection containment/subsection

Key sections

Section Description MetaInfo
BaseEnergy Abstract class used to define a common value quantity with the appropriate units for different types of energies, which avoids repeating the definit... Open in MetaInfo browser
TotalEnergy The total energy of a system. Open in MetaInfo browser
KineticEnergy Physical property section describing the kinetic energy of a (sub)system. Open in MetaInfo browser
PotentialEnergy Physical property section describing the potential energy of a (sub)system. Open in MetaInfo browser
Heat The transfer of thermal energy into a system. Open in MetaInfo browser
Work The energy transferred to a system by means of force applied over a distance. Open in MetaInfo browser
InternalEnergy The total energy contained within a system, encompassing both kinetic and potential energies of the particles. Open in MetaInfo browser
Enthalpy The total heat content of a system, defined as 'InternalEnergy' + 'Pressure' * 'Volume'. Open in MetaInfo browser
GibbsFreeEnergy The energy available to do work in a system at constant temperature and pressure, given by Enthalpy - Temperature * Entropy. Open in MetaInfo browser
HelmholtzFreeEnergy The energy available to do work in a system at constant volume and temperature, given by InternalEnergy - Temperature * Entropy. Open in MetaInfo browser
ChemicalPotential Free energy cost of adding or extracting a particle from a thermodynamic system. Open in MetaInfo browser
VirialTensor A measure of the distribution of internal forces and the overall stress within a system of particles. Open in MetaInfo browser
BaseForce Base class used to define a common value quantity with the appropriate units for different types of forces, which avoids repeating the definitions f... Open in MetaInfo browser
TotalForce The total force of a system. Open in MetaInfo browser
Pressure The force exerted per unit area by gas particles as they collide with the walls of their container. Open in MetaInfo browser
Volume the amount of three-dimensional space that a substance or material occupies. Open in MetaInfo browser
Temperature Open in MetaInfo browser
Entropy A measure of the disorder or randomness in a system. Open in MetaInfo browser
HeatCapacity Amount of heat to be supplied to a material to produce a unit change in its temperature. Open in MetaInfo browser
MassDensity Mass per unit volume of a material. Open in MetaInfo browser
Hessian A square matrix of second-order partial derivatives of a potential energy function, describing the local curvature of the energy surface. Open in MetaInfo browser

Quantities by section

BaseEnergy

Quantity Type Description
value m_float64(float64) No description available.

TotalEnergy

This section has no direct quantities.

KineticEnergy

This section has no direct quantities.

PotentialEnergy

This section has no direct quantities.

Heat

This section has no direct quantities.

Work

This section has no direct quantities.

InternalEnergy

This section has no direct quantities.

Enthalpy

This section has no direct quantities.

GibbsFreeEnergy

This section has no direct quantities.

HelmholtzFreeEnergy

This section has no direct quantities.

ChemicalPotential

Quantity Type Description
temperature m_float64(float64) Temperature at which the chemical potential is calculated. Essential for finite-temperature calculations.
particle_number m_float64(float64) Number of particles (or particle density) for which the chemical potential applies. Can represent electron number, atom number, or other relevant particle count.
fermi_energy m_float64(float64) Fermi energy at T=0K, used as reference for finite-temperature chemical potential. At T=0, the chemical potential equals the Fermi energy.
type m_str(str) Type of chemical potential calculation. Examples: 'electronic', 'atomic', 'ionic', 'molecular'. Helps identify what kind of particles this applies to.

VirialTensor

This section has no direct quantities.

BaseForce

Quantity Type Description
value m_float64(float64) (shape: ['', '']) No description available.

TotalForce

This section has no direct quantities.

Pressure

Quantity Type Description
value m_float64(float64) No description available.

Volume

Quantity Type Description
value m_float64(float64) No description available.

Temperature

Quantity Type Description
points m_float64(float64) (shape: ['n_points']) Points in which the temperature is discretized.

Entropy

Quantity Type Description
value m_float64(float64) No description available.

HeatCapacity

Quantity Type Description
value m_float64(float64) No description available.

MassDensity

Quantity Type Description
value m_float64(float64) No description available.

Hessian

Quantity Type Description
n_hessian_dim m_int_bounded(int)
Matrix dimension (number of degrees of freedom) of the square Hessian in theMatrix dimension (number of degrees of freedom) of the square Hessian in the
coordinate basis used by the parser. For Cartesian atomic Hessians this is
typically 3 * N_atoms; constrained/filtered coordinates should use the
remaining degrees of freedom.
value m_float64(float64) (shape: ['n_hessian_dim', 'n_hessian_dim']) No description available.
n_negative_eigenvalues m_int_bounded(int)
Number of negative Hessian eigenvalues (imaginary vibrational frequencies).Number of negative Hessian eigenvalues (imaginary vibrational frequencies).
A value of 0 indicates a local minimum, 1 a first-order saddle point, and
>1 a higher-order saddle point. Leave unset if the Hessian was evaluated
away from a stationary point.
eigenvalues m_float64(float64) (shape: ['*'])
Eigenvalues of the Hessian.Eigenvalues of the Hessian. Sorted during normalization with positive values
descending, followed by zeros, then negative values ascending (most negative
first). Very low-magnitude modes in solid-state phonon calculations
(e.g., <100 cm-1) or when using RI/DF approximations often reflect numerical
artifacts rather than true instabilities.
stationary_point_type Enum
Stationary-point classification (requires zero gradient) based on HessianStationary-point classification (requires zero gradient) based on Hessian
eigenvalue signs. Use 'saddle_point' for any stationary point with one or
more negative eigenvalues (a transition state corresponds to exactly one).
Use 'maximum' when all eigenvalues are negative (negative-definite Hessian).
Use 'non_stationary' if the Hessian was evaluated where the gradient is
non-zero and no stationary point classification applies. Use 'unavailable'
when no classification could be determined from the data.