How to read TINKER's force field parameters

Question

I'm going to parameterize AMBER force field for the simulation of some small molecules. I have found the parameter sets provided by TINKER at here.

I'm stuck here because I couldn't find any explanations about the parameter values. They should be the parameters that appear in the formula of AMBER force field. However, I have no idea which numbers mean $k_b$, $l_0$, $k_a$, $θ_0$, or the rest parameters.

Answer 1

Okay I will take a stab at this.

Consider the following bond stretching parameters in the TINKER FF file:

      ##################################
      ##                              ##
      ##  Bond Stretching Parameters  ##
      ##                              ##
      ##################################


bond          1    1          310.00     1.5260

This tells you that this is a bond parameter between atom 1 and atom 1. The index of atoms is given in the FF file as

   #####################################################
   ##                                                 ##
   ##  TINKER Atom Class Numbers to Amber Atom Types  ##
   ##                                                 ##
   ##    1  CT      11  CN      21  OW      31  HO    ##
   ##    2  C       12  CK      22  OH      32  HS    ##
   ##    3  CA      13  CQ      23  OS      33  HA    ##
   ##    4  CM      14  N       24  O       34  HC    ##
   ##    5  CC      15  NA      25  O2      35  H1    ##
   ##    6  CV      16  NB      26  S       36  H2    ##
   ##    7  CW      17  NC      27  SH      37  H3    ##
   ##    8  CR      18  N*      28  P       38  HP    ##
   ##    9  CB      19  N2      29  H       39  H4    ##
   ##   10  C*      20  N3      30  HW      40  H5    ##
   ##                                                 ##
   #####################################################

So clearly this is a bond parameter between CT and CT. What do these atom notations stand for? They are outlined in Table 1 of this paper. The value 310.00 is $K_r$ (in kcal mol$^{-1}$) and 1.5260 is $r_{\mathrm{eq}}$ (in Ang).

---

For angle bends:

      ################################
      ##                            ##
      ##  Angle Bending Parameters  ##
      ##                            ##
      ################################


angle         1    1    1      40.00     109.50

angle denotes what you'd expect. The last two parameters, 40.00 ($K_{\theta}$ in kcal (mol radian$^2$)$^{-1}$) and 109.50 ($\theta_{\mathrm{eq}}$ in deg.) are for CT-CT-CT (atom1-atom1-atom1).

---

For torsional angles:

      ############################
      ##                        ##
      ##  Torsional Parameters  ##
      ##                        ##
      ############################


torsion       1    1    1    1            0.156    0.0  3

This is clearly a torsion between CT-CT-CT-CT. Here is where it gets a little tricky. If anyone finds this to be erroneous, please let me know and I will correct it. The parameter, 0.156 is simply determined by the following formula:

$$\frac{\frac{V_n}{2}}{\mathrm{no.~of~paths}}$$

where $V_n/2$ is the magnitude of torsion in kcal mol$^{-1}$. In Table 14 of the previously cited paper, for Torsional Parameters you find for X-CT-CT-X:

• no. of paths = 9
• $V_n/2$ = 1.40

Therefore, $1.40/9$ $\approx$ 0.156 which is exactly what is given in the TINKER FF file. I've done this with a few other torsional parameters and it seems to add up. I believe footnote $f$ in Table 14 explains this.

The 0.0 is simply $\gamma$ (phase offset in deg.) and 3 is $n$ (the periodicity of the torsion).

Functional Form of Amber94 FF

It may be useful (and convenient) to spell out the functional form as presented in the cited paper here.

$$E_{\mathrm{tot}} = \sum_{\mathrm{bonds}} K_r(r-r_{\mathrm{eq}})^2 +$$ $$~~~~~~~~~~~~\sum_{\mathrm{angles}} K_{\theta}(\theta - \theta_{\mathrm{eq}} ) ^2 + $$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~\sum_{\mathrm{dihedrals}} \frac{V_n}{2}[1+\cos(n\phi - \gamma)] + $$ $$~~~~~~~~~~~~~~~~~~~~~~~\sum_{i<j} \left[ \frac{A_{ij}}{R_{ij}^2} - \frac{B_{ij}}{R_{ij}^6} + \frac{q_i q_j}{\epsilon R_{ij}} \right]$$

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Reference: Cornell and co-workers. J. Am. Chem. Soc. 1995, 117, 5179.