OBForceFieldGhemical

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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

BondEGhemical.png

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

AngleEGhemical.png

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

TorsionSingleEGhemical.png TorsionDoubleEGhemical.png

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

VDWEGhemical.png

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

EleAttrEGhemical.png EleRepEGhemical.png

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

Done. The energies were compared to the energies produced by the ghemical package. Analytical gradients are also implemented and their values have been compared to numerical derivatives. (The MMFF94 test set was used for the validation.)