Molecular Dynamics Using Fluctuating Charges

Applications of the fluctuating charge model have relied on iterative methods to determine the converged charges [52, 159, 164, 196] and for very large-scale systems, multilevel methods have also been developed [197, 198], MC methods have also been used with fluctuating-charge models [116, 194], 

(9-62) MjL is the mass of atom //. The mass mq does not correspond to any physical mass and is simply set to a value small enough such that the charges follow the atomic coordinates adiabatically. The Lagrangian also includes an Nmoiec number of constraints to ensure that each molecule remains electrostatically neutral. 

Based on the Lagrangian of Eq. (9-62), the equations of motion for the positions and charges are 

These equations of motion can be integrated by many standard ensembles constant energy, constant volume, constant temperature and constant pressure. More complex forms of the extended Lagrangian are possible and readers are referred to Ref. [17] for a Lagrangian that allows intermolecular charge transfer. 

Although a direct comparison between the iterative and the extended Lagrangian methods has not been published, the two methods are inferred to have comparable computational speeds based on indirect evidence. The extended Lagrangian method was found to be approximately 20 times faster than the standard matrix inversion procedure [117] and according to the calculation of Bernardo et al. [208] using different polarizable water potentials, the iterative method is roughly 17 times faster than direct matrix inversion to achieve a convergence of 1.0 x 10-8 D in the induced dipole. 

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Patel S, Mackerell AD, Brooks CL (2004) CHARMM fluctuating charge force field for proteins II -Protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model. J Comput Chem 25(12) 1504-1514... 

Patel S, Brooks CL (2005) A nonadditive methanol force field bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model. J Chem Phys... 

A new molecular dynamics model in which the point charges on atomic sites are allowed to fluctuate in response to the environment has been developed in a previous work J. Chem. Phys.y 101 6151 (1994)). The model and its application to liquid water are briefly reviewed. Various properties of the model eire calculated, with emphasis on the bonding characteristics. The water model is also used to investigate the aqueous solvation of formaldehyde. 

Ab initio molecular dynamics simulations usually describe fluctuations of molecular electronic structures and can broaden knowledge of electric dipole moments, polarization processes, or possible charge-transfer effects, and complement classic MD methods. However, AIMD simulations are computationally demanding, and only relatively small systems of tens of ion pairs can be propagated over short time periods of tenths of picoseconds. These simulations typically begin from liquid state conflgurations that are equilibrated with classic MD using empirical interaction potentials. 

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