CPMD
Encyclopedia
The Car–Parrinello Molecular Dynamics,, also known as CPMD, is a method to follow the classical motion of point-like atomic nuclei in time, i.e. for performing molecular dynamics
(MD), while at the same time solving ab-initio and efficiently the quantum mechanical motion of electrons. Unlike classical MD
, CPMD includes the motion of electron
s in the calculations of energy, forces and motion.
s are usually described by a pseudopotential
, and the wavefunction
of the valence electron
s are approximated by a plane wave
basis set
.
The ground state electronic density (for fixed nuclei) is calculated self-consistently, usually using the density functional theory
method. Then, using that density, forces on the nuclei can be computed, to update the trajectories (using, e.g. the Verlet integration
algorithm). In addition, however, the coefficients used to obtain the electronic orbital functions can be treated as a set of extra spatial dimensions, and trajectories for the orbitals can be calculated in this context.
(BOMD) method. In BOMD the electrons must be minimized via matrix diagonalization
at every step in the trajectory. CPMD uses fictitious dynamics to keep the electrons in the ground state, preventing the need for a costly self-consistent iterative minimization at each time step. The fictitious dynamics relies on the use of a fictitious electron mass (usually in the range of 400 - 800 a.u.
) to ensure that there is very little energy transfer from nuclei to electrons, i.e. to ensure adiabaticity
. Any increase in the fictitious electron mass resulting in energy transfer would cause the system to leave the ground-state BOMD surface.
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
(MD), while at the same time solving ab-initio and efficiently the quantum mechanical motion of electrons. Unlike classical MD
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
, CPMD includes the motion of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in the calculations of energy, forces and motion.
General Approach
In CPMD the core electronCore electron
Core electrons are the electrons in an atom that are not valence electrons and therefore do not participate in bonding. An example: the carbon atom has a total of 6 electrons, 4 of them being valence electrons. So the remaining 2 electrons must be core electrons.They are so tightly bound to the...
s are usually described by a pseudopotential
Pseudopotential
In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering.- Atomic physics :...
, and the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
of the valence electron
Valence electron
In chemistry, valence electrons are the electrons of an atom that can participate in the formation of chemical bonds with other atoms. Valence electrons are the "own" electrons, present in the free neutral atom, that combine with valence electrons of other atoms to form chemical bonds. In a single...
s are approximated by a plane wave
Plane wave
In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....
basis set
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
.
The ground state electronic density (for fixed nuclei) is calculated self-consistently, usually using the density functional theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
method. Then, using that density, forces on the nuclei can be computed, to update the trajectories (using, e.g. the Verlet integration
Verlet integration
Verlet integration is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics...
algorithm). In addition, however, the coefficients used to obtain the electronic orbital functions can be treated as a set of extra spatial dimensions, and trajectories for the orbitals can be calculated in this context.
Fictitious Dynamics
CPMD is an approximation of the Born-Oppenheimer MDMolecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
(BOMD) method. In BOMD the electrons must be minimized via matrix diagonalization
Diagonalizable matrix
In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1AP is a diagonal matrix...
at every step in the trajectory. CPMD uses fictitious dynamics to keep the electrons in the ground state, preventing the need for a costly self-consistent iterative minimization at each time step. The fictitious dynamics relies on the use of a fictitious electron mass (usually in the range of 400 - 800 a.u.
Atomic units
Atomic units form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, which one might name Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article...
) to ensure that there is very little energy transfer from nuclei to electrons, i.e. to ensure adiabaticity
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
. Any increase in the fictitious electron mass resulting in energy transfer would cause the system to leave the ground-state BOMD surface.
See also
- Born-Oppenheimer molecular dynamics
- Car-Parrinello methodCar-Parrinello methodThe Car–Parrinello method is a type of ab initio molecular dynamics, usually employing periodic boundary conditions, planewave basis sets, and density functional theory, proposed by Roberto Car and Michele Parrinello in 1985, who were subsequently awarded the Dirac Medal by ICTP in 2009.In...
- CP2KCP2KCP2K is a freely available program, written in Fortran 95, to perform atomistic and molecular simulations of solid state, liquid, molecular and biological systems...
- Density functional theoryDensity functional theoryDensity functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
- Fractional coordinatesFractional coordinatesIn crystallography, a fractional coordinate system is a coordinate system in which the edges of the unit cell are used as the basic vectors to describe the positions of atomic nuclei...
- Quantum chemistry computer programsQuantum chemistry computer programsQuantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry. Most include the Hartree–Fock and some post-Hartree–Fock methods. They may also include density functional theory , molecular mechanics or semi-empirical quantum...
- Folding@HomeFolding@homeFolding@home is a distributed computing project designed to use spare processing power on personal computers to perform simulations of disease-relevant protein folding and other molecular dynamics, and to improve on the methods of doing so...