Polarization is the ability of a molecule’s electron density to respond to and influence its environment and is the leading order many-body interaction for advanced electrostatics used in classical molecular simulation. It has proven to be an important interaction that is necessary to accurately simulate certain molecular systems. Polarization helps to capture intermolecular interactions of ligand-macromolecule complexes, heterogeneity at interfaces, electric field environments of heterogeneous systems such as proteins, and structure and dynamics of peptide-water solutions. In general, systems that can benefit most from the inclusion of polarization effects are heterogeneous, non-bulk systems that give rise to asymmetric environments. Additionally, polarization has been shown to be more transferable across the phase diagram beyond regions where the force field was initially parameterized.
The main drawback of including polarization in molecular simulation, however, is the computational expense of calculating explicit polarization interactions. The most common approach is to approximate the polarization solution using an iterative self- consistent field (SCF) method, which accounts for about half the cost of a polarizable simulation. Another approach is that of extended Lagrangians (EL), which treat polarization degrees of freedom dynamically and do not require iterations. EL methods, however, suffer from instability and require prohibitively small simulation time steps.
The focus of this dissertation is the reduction of the computational cost of polarizable classical molecular simulations while maintaining the high level of accuracy associated with these simulations. I present several new methods that combine the stability of SCF methods with the iteration-free dynamics of EL methods into a hybrid EL/SCF framework. The key to these EL/SCF methods is the introduction of auxiliary polarization degrees of freedom, which can be dynamically integrated and drive the real polarization degrees of freedom. The first approach is a relatively simple method for polarization that reduces the number of iterative cycles required for an SCF solution. This method also introduces thermostat control of auxiliary variables and is called iEL/SCF. A more sophisticated approach that eliminates the need for SCF iteration altogether, iEL/0-SCF, is also presented. This method is developed for both induced dipole and Drude polarization models. I also present a generalized and complete theory for classical iteration-free polarizable EL/SCF dynamics and explore combining iteration- free dynamics with other advanced high efficiency methods such as RESPA multi-time stepping and stochastic-isokinetic integration, which work complementarily with EL/SCF to further increase computational efficiency.
In summary, the developments presented in this dissertation are methods and theories that significantly reduce the cost of classical polarizable molecular dynamics without sacrificing accuracy. This work represents an important step in moving the scientific community toward the broader adoption of advanced potential energy surfaces embodied by polarizable force fields.