Drude particle
Encyclopedia
Drude particles are model oscillators used to simulate the effects of electronic polarizability
in the context of a classical molecular mechanics
force field
. It is based on the Drude model
of mobile electrons. Molecular mechanics models, commonly used for computational calculations such as structural minimization and molecular dynamics
simulations, represent individual atom
s or other particles as hard spheres that interact according to the laws of Newtonian mechanics. These methods are often used in the computational study of protein
s, nucleic acid
s, and other biomolecule
s.
Most force fields in current practice use a fixed-charge model in which each atom in the simulation is assigned a single electric charge that does not change during the course of the simulation. This obviously cannot model induced dipole
s or other electronic effect
s of a changing local environment. Drude particles are massless virtual sites carrying partial electric charge and attached to individual atoms via a harmonic spring
. The spring constant and relative partial charges on the atom and associated Drude particle determine the extent to which the Drude particle responds to the local electrostatic field. The movement of the Drude particle thus serves as a proxy for the changing distribution of the electric charge associated with the corresponding atom.
The Drude particle method, and polarizable force fields in general, have not yet been widely applied due to their very high computational cost compared to the equivalent fixed-charge simulation. In the Drude model, this cost is largely due to the challenge in recalculating the local electrostatic field and repositioning the Drude particles at each time step; traditionally this is done using an iterative self consistent field (SCF) method, although a much more efficient method has been developed that assigns a very small mass to each Drude particle and applies a Lagrangian
transformation. Water model
s incorporating Drude sites have also been developed and refined for incorporation into a polarizable force field under development.
Polarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
in the context of a classical molecular mechanics
Molecular mechanics
Molecular mechanics uses Newtonian mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields...
force field
Force field (chemistry)
In the context of molecular modeling, a force field refers to the form and parameters of mathematical functions used to describe the potential energy of a system of particles . Force field functions and parameter sets are derived from both experimental work and high-level quantum mechanical...
. It is based on the Drude model
Drude model
The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials...
of mobile electrons. Molecular mechanics models, commonly used for computational calculations such as structural minimization and molecular dynamics
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...
simulations, represent individual atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s or other particles as hard spheres that interact according to the laws of Newtonian mechanics. These methods are often used in the computational study of protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
s, nucleic acid
Nucleic acid
Nucleic acids are biological molecules essential for life, and include DNA and RNA . Together with proteins, nucleic acids make up the most important macromolecules; each is found in abundance in all living things, where they function in encoding, transmitting and expressing genetic information...
s, and other biomolecule
Biomolecule
A biomolecule is any molecule that is produced by a living organism, including large polymeric molecules such as proteins, polysaccharides, lipids, and nucleic acids as well as small molecules such as primary metabolites, secondary metabolites, and natural products...
s.
Most force fields in current practice use a fixed-charge model in which each atom in the simulation is assigned a single electric charge that does not change during the course of the simulation. This obviously cannot model induced dipole
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
s or other electronic effect
Electronic effect
An electronic effect influences the structure, reactivity, or properties of molecule but is neither a traditional bond nor a steric effect. In organic chemistry, the term stereoelectronic effect is also used to emphasize the relation between the electronic structure and the geometry of a...
s of a changing local environment. Drude particles are massless virtual sites carrying partial electric charge and attached to individual atoms via a harmonic spring
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
. The spring constant and relative partial charges on the atom and associated Drude particle determine the extent to which the Drude particle responds to the local electrostatic field. The movement of the Drude particle thus serves as a proxy for the changing distribution of the electric charge associated with the corresponding atom.
The Drude particle method, and polarizable force fields in general, have not yet been widely applied due to their very high computational cost compared to the equivalent fixed-charge simulation. In the Drude model, this cost is largely due to the challenge in recalculating the local electrostatic field and repositioning the Drude particles at each time step; traditionally this is done using an iterative self consistent field (SCF) method, although a much more efficient method has been developed that assigns a very small mass to each Drude particle and applies a Lagrangian
Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
transformation. Water model
Water model
In computational chemistry, classical water models are used for the simulation of water clusters, liquid water, and aqueous solutions with explicit solvent. These models use the approximations of molecular mechanics...
s incorporating Drude sites have also been developed and refined for incorporation into a polarizable force field under development.