How to read TINKER's force field parameters

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](http://dasher.wustl.edu/tinker/distribution/params/).


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](http://en.wikipedia.org/wiki/AMBER#Functional_form). However, I have no idea which numbers mean $k\_b$, $l\_0$, $k\_a$, $θ\_0$, or the rest parameters.




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](http://ffamber.cnsm.csulb.edu/ffamber/pdfs/cornell_amber94_1995jacs.pdf). 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.


$$E\_{\mathrm{tot}} = \sum\_{\mathrm{bonds}} K\_r(r-r\_{\mathrm{eq}})^2 +$$
$$~~~~~~~~~~~~\sum\_{\mathrm{angles}} K\_{\theta}(\theta - \theta\_{\mathrm{eq}} ) ^2 + $$
$$~~~~~~~~~~~~~~~~~~~~~~~~~~\sum\_{\mathrm{dihedrals}} \frac{V\_n}{2}[1+\cos(n\phi - \gamma)] + $$
$$~~~~~~~~~~~~~~~~~~~~~~~\sum\_{i<j} \left[ \frac{A\_{ij}}{R\_{ij}^2} - \frac{B\_{ij}}{R\_{ij}^6} + 
\frac{q\_i q\_j}{\epsilon R\_{ij}} \right]$$




---


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


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