# Molecular Simulation/Polarizable force fields

This is a placeholder for a page on polarizable force fields

## Polarizability

When a molecule is placed in various environment, the charge distribution in a molecule changes. This is what defines Polarizability. Force field plays a key role in molecular dynamics so that if these force fields are more accurate, they are able to describe physical reality. Consequently, the output which obtains from the simulation will be more precise. So, this is crucial to have a good approximation for magnitude of the partial charge, and its position at the nucleus. On the other hand, non-polarizable (fixed charge) models offer poor explanation or effective potential with approximations that cannot fully capture many-body effects.In other words, fixed charge models offer tractable descriptions and are fit for equilibrium properties for homogeneous systems.In contrast, since polarizable empirical force fields consist of many-body effects, it provides a clear and systematic development in functional form.

## Drude Model (also known as Charges on Springs)

The Drude polarizable force field approximates the effect of induced polarization by adding negatively charged "Drude" particles to the system. These particles are tethered to the non-hydrogen atoms of the system with a harmonic potential. Electrostatic interactions with other charged particles cause the Drude particles to move in response, mimicking the effect of induced electron polarization. In this theory, Lennard-Jones potential is used to demonstrate dispersion interactions. Some positive features for Drude model are that it is relatively easy to implement within existing force fields, and also it is chemically instinctive.The serious of its weakness is that by using many extra charges, the number of interaction calculations increases. Atomic polarizability,${\displaystyle \alpha }$, of a given atom can be obtained from equation (1) where ${\displaystyle r_{D}}$ is the charge on a Drude particle and ${\displaystyle k_{D}}$ is the force constant for the spring that connects this Drude particle to its parent nucleus.

${\displaystyle \alpha =q_{D}^{2}/k_{D}}$ (1)
Schematic of the SWM4-NDP Drude polarizable water molecule. The Drude particle and its harmonic tether is shown in red. The lone-pair particle (LP) is on the H-O-H bisector.
A SWM4-NDP Drude polarizable model water molecule is polarized by the electric field created by a neighbouring potassium ion. The Drude particle (red) is negatively charged and moves to maximize its interaction with the potassium.

## AMOEBA Model (Atomic Multipole Optimized Energetics for Biomolecular Applications)

AMOEBA is one of the various force fields with the ability to describe electronic polarization. AMOEBA treats electrostatics using a combination of fixed and polarizable multipoles. In AMOEBA, the polarizable force field are modeled by an interactive atomic induced dipole. The induced dipole at each atom is the product of its atomic polarizability and the electrostatic field at this atom produced by permanent multipoles and induced dipoles of all other atoms. As a consequence, this future results in calculating of electrostatic interactions differ from the previous one which used a Coulomb potential to evaluate the charge–charge interactions. So, in AMOEBA should be added extra terms into the force field to account for the charge–dipole and dipole–dipole interactions. One advantage of the AMOEBA model is its emphasis on replication of molecular polarizability and electrostatic potentials, instead of just interaction energies.

Difference between AMOEBA and fixed charge force fields:

• Conventional force fields have point charges on each atom.
• AMOEBA puts a point charge, dipole, and quadrupole on each atom. Each atom needs to have its own coordinate system.
• AMOEBA also adds a polarizable dipole to each atom.

## References

Baker, chrietopher M. (2015). "Polarizable Force Fields for Molecular Dynamics Simulations of Biomolecules". Comput.Mol.Sci.

"Current Status of the AMOEBA Polarizable Force Field". J.Phys.Chem 114,8: 2549–2564. 2019. doi:doi.org/10.1021/jp910674d.