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.

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

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_2 = \begin{cases} 1.0, & \mbox{if }r \le 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}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_3 = \begin{cases} 0.0, & \mbox{if }r \le 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:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle E_\text{elec} = \frac{q_iq_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}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 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}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 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