Drude Oscillators

Drude oscillators, Fluctuating charge, Molecular dynamics, CHARMM... 

The total electric field, E, is composed of the external electric field from the permanent charges E° and the contribution from other induced dipoles. This is the basis of most polarizable force fields currently being developed for biomolecular simulations. In the present chapter an overview of the formalisms most commonly used for MM force fields will be presented. It should be emphasized that this chapter is not meant to provide a broad overview of the field but rather focuses on the formalisms of the induced dipole, classical Drude oscillator and fluctuating charge models and their development in the context of providing a practical polarization model for molecular simulations of biological macromolecules [12-21], While references to works in which the different methods have been developed and applied are included throughout the text, the major discussion of the implementation of these models focuses... 

The Drude oscillators are typically treated as isotropic on the atomic level. However, it is possible to extend the model to include atom-based anisotropic polarizability. When anisotropy is included, the harmonic self-energy of the Drude oscillators becomes... 

Molecular Dynamics Using the Classical Drude Oscillator... 

From this point of view it is of interest to examine the consequences of full ther-malization of the classical Drude oscillators on the properties of the system. This is particularly important given the fact that any classical fluctuations of the Drude oscillators are a priori unphysical according to the Bom-Oppenheimer approximation upon which electronic induction models are based. It has been shown [12] that under the influence of thermalized (hot) fluctuating Drude oscillators the corrected effective energy of the system, truncated to two-body interactions is... 

In addition to the static induction effects included in I/scf, the hot Drude oscillators give rise to a 1/r6, temperature-dependent, attractive term. This jkg Ta2/r6 term is the classical thermodynamic equivalent of the London quantum dispersive attraction IEa2/r6. It corresponds to a small perturbation to the London forces, because k T is at least two orders of magnitude smaller than the typical ionization energy IE. The smaller the temperature of the Drude motion, the closer the effective potential is to the SCF potential, making Eq. (9-57) independent of mo, the mass of the oscillators. 

Lamoureux G, MacKerell AD, Roux B (2003) A simple polarizable model of water based on classical Drude oscillators. J Chem Phys 119(10) 5185—5197... 

Lamoureux G, Roux B (2003) Modeling induced polarization with classical Drude oscillators theory and molecular dynamics simulation algorithm. J Chem Phys 119(6) 3025-3039... 

Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD (2005) Determination of electrostatic parameters for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput 1 (1) 153—168... 

Lopes PEM, Lamoureux G, MacKerell AD, Polarizable Empirical Force Field for Nitrogen-containing Heteroaromatic Compounds Based on the Classical Drude Oscillator. Accepted for publication on J Comput Chem... 

Vorobyov IV, VM Anisimov, AD MacKerell Jr (2005) Polarizable empirical force field for alkanes based on the classical drude oscillator model. J. Phys. Chem. B 109 (40) 18988-18999... 

Another way to include polarization into force fields is via a classical Drude oscillator ( charge on a spring or COS [156]). Here, an additional particle with an associated charge is attached at the nucleus of each atom. The charge on the particle is added to the static charge of the atom. The polarizability is then determined via Eq. (3.30c),... 

Explicit Inclusion of Induced Polarization in Atomistic Force Fields Based on the Classical Drude Oscillator Model... 

Current polarizable models can be classified into three major categories (1) induced dipole, [2] fluctuating charge, and [3] classical Drude oscillator (or Shell models]. 

In the Drude polarizable model, the only relevant adjustable parameter is the combination q /KD that corresponds to the atomic polarizability. In the limit of large Kd, the treatment of induced polarization based on Drude oscillators is formally equivalent to a point-dipole treatment such as used by AMOEBA. In practice, the magnitude of Kd is commonly chosen to achieve small displacements of Drude particles from their corresponding atomic positions, as required to remain close to the point-dipole approximation for the induced dipole associated with the atom-Drude pair [150] while preserving a stable integration of the equation of motion with a reasonable time step. For a fixed force constant Kd the atomic polarizability is determined by the amount of chaise assigned to the Drude particle. In the current implementation, the classical Drude model introduces atomic polarizabilities only to non-hydrogen atoms for practical considerations, as discussed below. However, this is adequate to accurately reproduce molecular polarizabilties, as seen in a number of published studies [127,142,146]. 

The total potential energy of the Drude polarizable model contains the terms representative of the interaction with the static electric field, interaction with other dipoles and the self-energy associated with the Drude oscillators, in addition to the standard contributions representing bonding terms (bonds, angles, dihedrals, etc.) and intermolecular interactions represented by Lennard-Jones (Lj) "6-12" term ... 

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