Notes on AMBER 12 interface

The AMBER 12 interface is based on pmemd rather than sander.

There are many limitations on pmemd, predominantly that it lacks:

• Analytical second derivatives;
• Smooth cutoffs;
• Non-periodic vacuum simulations.

However, it has built-in support for CUDA acceleration and its code is much, much simpler than the sander code.

Changes from pmemd code

amber_interface.F90

Based upon pmemd.F90, with the following changes:

• Split the code into 3 subroutines: amber_setup, energy_and_gradient, amber_finish

smooth_cutoff.F90

The module is named smooth_cutoff_mod and keeps track of ifswitch.

Implementing force switching cut-offs. Important variables to keep track of:

ifswitch determines which style of cut-offs is used.

ifswitch = 1

rc = sqrt(cut), i.e. ${\text{cut}}=r_{c}^{2}$

In generalised Born simulations, cut is a private variable. The publicly accessible variable is gb_cutoff. Note that this is different from rgbmax, which determines the cut-off for calculating gb radii.

We switch on the additional terms at $r_{\text{on}}$. This is arbitrarily set to 0.9 of the cut-off distance.

$r_{\text{on}}^{2}=(0.9r_{c})^{2}$

We have these other terms, term1(1:natom), term2(1:natom), term3(1:natom), which I shall represent as $c_{1},c_{2},c_{3}$ respectively.

$r^{2}=(x_{i}-x_{j})^{2}+(y_{i}-y_{j})^{2}+(z_{i}-z_{j})^{2}$

$c_{1}={\frac {c_{3}}{c_{2}}}={\begin{cases}0.0,&{\mbox{if }}r\leq r_{\text{on}}\\{\frac {-12(r_{\text{on}}^{2}-r^{2})}{(r_{c}^{2}-r^{2})(r_{c}^{2}+2r^{2}-3r_{\text{on}}^{2})}},&{\mbox{if }}r>r_{\text{on}}\end{cases}}$

$c_{2}={\begin{cases}1.0,&{\mbox{if }}r\leq r_{\text{on}}\\(r_{c}^{2}-r^{2})^{2}(r_{c}^{2}+2r^{2}-3r_{\text{on}}^{2}){\frac {1}{r_{c}^{6}}}{\frac {1}{(1-0.9^{2})^{3}}},&{\mbox{if }}r>r_{\text{on}}\end{cases}}$

$c_{3}={\begin{cases}0.0,&{\mbox{if }}r\leq r_{\text{on}}\\-12(r_{c}^{2}-r^{2})(r_{\text{on}}^{2}-r^{2}){\frac {1}{r_{c}^{6}}}{\frac {1}{(1-0.9^{2})^{3}}},&{\mbox{if }}r>r_{\text{on}}\end{cases}}$

The energies and their derivatives are given by:

$E_{\text{elec}}={\frac {q_{i}q_{j}}{\epsilon _{\text{int}}r}}c_{2}{\mbox{ and }}{\frac {-1}{r}}{\frac {dE_{\text{elec}}}{dr}}={\frac {E_{\text{elec}}}{r^{2}}}+E_{\text{elec}}c_{1}$

$E_{\text{gb}}=E_{\text{gb}}c_{2}{\mbox{ and }}{\frac {dE_{\text{gb}}}{dr}}={\frac {-1}{r}}{\frac {dE_{\text{gb}}}{dr}}c_{2}+E_{\text{gb}}c_{1}$

$E_{\text{vdW}}=\left({\frac {A}{r^{12}}}-{\frac {B}{r^{6}}}\right)c_{2}{\mbox{ and }}{\frac {-1}{r}}{\frac {dE_{\text{vdW}}}{dr}}=\left({\frac {12A}{r^{12}}}-{\frac {6B}{r^{6}}}\right){\frac {1}{r^{2}}}c_{2}+\left({\frac {A}{r^{12}}}-{\frac {B}{r^{6}}}\right)c_{3}$

mdin_ctrl_dat.F90

• Line 31: ifswitch added to declaration
• Line 45: ifswitch added to / mdin_ctrl_int / common block
• Line 49: mdin_ctrl_int_cnt = 56 (rather than 55, since there is one more integer variable now)
• Line 216: ifswitch added /cntrl/ namelist, for reading min.in files.
• Line 434: initialised ifswitch = 0