The Drude oscillator model represents induced electronic polarization by introducing an auxiliary particle attached to each polarizable atom via a harmonic spring. The advantage with the Drude model is that it preserves the simple particle-particle Coulomb electrostatic interaction employed in nonpolarizable force fields, thus its implementation in NAMD is more straightforward than alternative models for polarization. NAMD performs the integration of Drude oscillators by employing a novel dual Langevin thermostat to freeze the Drude oscillators while maintaining the warm degrees of freedom at the desired temperature . Use of the Langevin thermostat enables better parallel scalability than the earlier reported implementation which made use of a dual Nosé-Hoover thermostat acting on, and within, each nucleus-Drude pair . Performance results show that the NAMD implementation of the Drude model maintains good parallel scalability, with an increase in computational cost by not more than twice that of using a nonpolarizable force field .
The Drude polarizable force field requires some extensions to the CHARMM force field. The Drude oscillators differ from typical spring bonds only in that they have an equilibrium length of zero. The Drude oscillators are optionally supplemented by a maximal bond length parameter, beyond which a quartic restraining potential is also applied. The force field is also extended by an anisotropic spring term that accounts for out-of-plane forces from a polarized atom and its covalently bonded neighbor with two more covalently bonded neighbors (similar in structure to an improper bond). The screened Coulomb correction of Thole is calculated between pairs of Drude oscillators that would otherwise be excluded from nonbonded interaction and optionally between non-excluded, nonbonded pairs of Drude oscillators that are within a prescribed cutoff distance [71,72].
Also included in the Drude force field are the use of off-centered massless interaction sites, so called ``lone pairs'' (LPs), to avoid the limitations of centrosymmetric-based Coulomb interactions . The coordinate of each LP site is constructed based on three ``guide'' atoms. The calculated forces on the massless LP must be transferred to the guide atoms, preserving total force and torque. After an integration step of velocities and positions, the position of the LP is updated based on the three guide atoms, along with additional geometry parameters that give displacement and in-plane and out-of-plane angles. See our research web page (http://www.ks.uiuc.edu/Research/Drude/) for additional details and parallel performance results.
No additional files are required by NAMD to use the Drude polarizable force field. However, it is presently beyond the capability of the Psfgen tool to generate the PSF file needed to perform a simulation using the Drude model. For now, CHARMM is needed to generate correct input files.
The CHARMM force field parameter files specific to the Drude model are required. The PDB file must also include the Drude particles (mass between 0.1 and 1.0) and the LPs (mass 0). The Drude particles always immediately follow their parent atom. The PSF file augments the ``atom'' section with additional columns that include the ``Thole'' and ``alpha'' parameters for the screened Coulomb interactions of Thole. The PSF file also requires additional sections that list the LPs, including their guide atoms and geometry parameters, and list the anisotropic interaction terms, including their parameters. A Drude-compatible PSF file is denoted by the keyword ``DRUDE'' given along the top line.
The NAMD logging to standard output is extended to provide additional temperature data on the cold and warm degrees of freedom. Four additional quantities are listed on the ETITLE and ENERGY lines:
The Drude model should be used with the Langevin thermostat enabled (Langevin=on). Doing so permits the use of normal sized time steps (e.g., 1 fs). The Drude model is also compatible with constant pressure simulation using the Langevin piston. Long-range electrostatics may be calculated using PME. The nonbonded exclusions should generally be set to use either the 1-3 exclusion policy (exclude=1-3) or the scaled 1-4 exclusion policy (exclude=scaled1-4).
The Drude water model (SWM4-NDP) is a 5-site model with four charge sites and a negatively charged Drude particle , with the particles ordered in the input files as oxygen, Drude particle, LP, hydrogen, hydrogen. The atoms in the water molecules should be constrained (rigidBonds=water), with use of the SETTLE algorithm recommended (useSettle=on). Explicitly setting the water model (waterModel=swm4) is optional.