. Author manuscript; available in PMC: 2017 Apr 15.

Published in final edited form as: J Comput Chem. 2016 Jan 20;37(10):927–939. doi: 10.1002/jcc.24280

Table 2.

Layout of the 4 Born energy kernels.

kernel	no. blocks	no. threads per block	description
Calculate Born radii for hydrogens	number of atoms	500	Each block attends one hydrogen atom, each thread attends one quadrature point. The atom density V_solute at each quadrature point is calculated. Then those densities are integrated to generate the Born radius R^Born and the derivative ∂R^Born / ∂r from eq. 13 and eq. 19 respectively.
Calculate Born radii for heavy atoms	number of atoms	350	Each block attends one non-hydrogen atom, each thread attends one quadrature point. This kernel functions the same as the “Calculate Born radii for hydrogens” kernel and calculates R^Born, and the derivative ∂R^Born / ∂r for heavier atoms. The differences lie in the integration offsets and number of threads used to accommodate the larger radii of heavier atoms.
Calculate neighbor-atom force	number of neighbor-atom tiles	256	Each block attends one atom-atom comparison tile of the OpenMM neighbor-atom list, and each thread attends one atom-atom pair in that tile. The atom-atom interactions of all atoms, their Born radii, and charges are combined to calculate (∂ΔG^elec / ∂r)(∂r / ∂r) and (∂ΔG^elec / ∂R^Born) from eq. 16 and eq. 18 respectively. Additionally, the GBSW free energy of solvation ΔG^elec is calculated for the system.
Born force gradient	number of atoms	256	Each block attends an atom, and each thread attends a contribution of $Δ R_{b}^{B o r n} ∕ Δ r_{a}$ . The final value of (∂ΔG^elec / ∂R^Born)(∂R^Born / ∂r) from eq. 15 is calculated and added to the total force on each atom. If the option for calculating the nonpolar contribution to the solvation free energy is requested, it is calculated in this kernel following eq. 14.