# Difference between revisions of "OBForceFieldGhemical"

## OBForceFieldGhemical class

This class is an implementation of the molecular mechanics force field used in the Ghemical program. It is an all-atom method similar to the Tripos-5.2 force field.

### Parameters

Parameters for the Gehmical force field can be found in data/ghemical.prm.

### Bonded Interactions

#### Bond Stretching

$E_{bond}=k_{b}(r_{ab}-r_{ab}^0)^2$

$k_b$: bond stretching force constant (ghemical.prm)

$r_{ab}^0$: ideal bond length (ghemical.prm)

$r_{ab}$: bond length between atoms a and b

#### Angle Bending

$E_{angle}=k_a(\theta_{abc}-\theta_{abc}^0)^2$

$k_a$: angle bending force constant (ghemical.prm)

$\theta_{abc}^0$: ideal angle (ghemical.prm)

$\theta_{abc}$: angle

#### Torsional

$E_{torsion}= V_1(1 + cos(\omega_{abcd})) + V_2(1 - cos(2\omega_{abcd})) + V_1(1 + cos(3\omega_{abcd}))$

$V_t$: rotational barrier (ghemical.prm)

$s_t$: +1 if staggered minimum, -1 if eclipsed minimum (ghemical.prm)

$n_t$: multiplicity (ghemical.prm)

$\omega_{abcd}$: torsion angle

$V_1$, $V_2$ and $V_3$ can be derived from $V_t$, $s_t$ and $n_t$ using this table:

 $s_tn_t=+3$ $s_tn_t=+2$ $s_tn_t=+1$ $s_tn_t=-1$ $s_tn_t=-2$ $s_tn_t=-3$ $V_1$ 0 0 $V_t$ $-V_t$ 0 0 $V_2$ 0 $-V_t$ 0 0 $V_t$ 0 $V_3$ $V_t$ 0 0 0 0 $-V_t$

### Non-Bonded Interactions

#### Van der Waals

$E_{vdw}=k_{ab}\left(\frac{1}{\sigma_{ab}^{12}} - \frac{2}{\sigma_{ab}^6}\right)$

$k_{ab} = \sqrt{k_a k_b}$: force constant (ghemical.prm)

$\sigma_{ab} = \frac{r_{ab}}{R_a + R_b}$

$R_a$: vdw radius of atom a (ghemical.prm)

$r_{ab}$: separation (calulated in the same way as bondlengths)

#### Electrostatic

$E_{ele}=332.17 \frac{Q_a Q_b}{r_{ab}}$

$Q_a$: net atomic charge on atom a

$Q_b$: net atomic charge on atom b

$r_{ab}$: separation (calulated in the same way as bondlengths)

$332.17$: unit conversion factor

#### 1,4-Scaling

Non bonded interations between atoms in a 1,4 relationship are scaled with a factor 0.5.

### Validation

In progress... (1,4-scaling problem)