Force Field development
As an example, let us construct a force field compatible with the AMBER94
Draw the molecule with a mouse
Open the Free drawing panel in the Build > Free drawing
menu or by pressing the toolbar button
Select methane as a primer for the model by clicking the
button on the kernel box.
Right-click the hydrogen atom to transform it to carbon.
Click Add hydrogen button.
Choose fluoride from the list of elements and transform two hydrogen
atoms into it by right-clicking them.
A crude model of 1,2-difluoroethane is ready.
Let us transform it into two models in gauche- and trans-conformations.
To construct a gauche model, invoke the Geometry Editor.
Choose the Dihedral angle mode and the F-C-C-F angle by consecutively clicking the corresponding atoms. Specify the angle value of 60 degrees and press Enter.
The resulting model has a gauche conformation but wrong bond lengths.
Rapid preliminary optimization can be done by semiempirical
quantum chemical methods. Open the GAMESS panel in the
Tools > PC GAMESS or by pressing the toolbar button
Select the OPTIMIZE calculation.
Semiempirical method can be selected in the Assembly panel,
e.g., Basis > PM3. After optimization started, the molecule
rapidly changes its conformation.
The conformation can be further specified using Ab inition calculations.
Let us first use the 3-21+G basis with an electrons correlation at
the MP2 level.
Then, perform the optimization in MP2 / 6-311+G(2d,p).
AMBER94 was developed in the basis of 6-31G(d), but we will shift to
MP2 / 6-311+G(2d,p) since the 2d bases provide for
substantially better results, and current computers are powerful enough
to make such calculations routine. An MP2 / 6-311+G(2d,p)
optimization yields an accurate model in a gauche conformation.
Save it to a file.
Potential-derived charges on atoms
With a model in a sensible conformation, one can determine the partial charges on atoms. Since our molecule includes only four heavy atoms, the electrostatic field around it can be calculated using a relatively large basis, e.g., aug-cc-pVTZ. For typical calculations, aug-cc-pVDZ, can be recommended since it yields the dipole moments close to experimental (for MP2 electron correlation).
Select the Electrostatics calculation, MP2 correlation, and aug-cc-pVTZ basis.
After a calculation for about 1 hour, partial charges are assigned to the
model atoms. Do not forget to save the model after the calculation.
Repeat the above steps to generate a model of difluoroethane in a trans conformation.
The charges on atoms in the gauche and trans models slightly differ.
Fortunately, the differences in this case are not great and we can just
average the charges on equivalent atoms in both conformations.
The conformational dependence of charges is a serious problem of
parametrization of molecular mechanics force fields.
Some kind of averaging is a common solution.
Parameters of valence interactions
Construction of an accurate model includes a good torsion energy approximation.
This requires either valid experimental data or adequate quantum chemical
calculations. The torsion potentials cannot be specified by analogy with other
molecules, such analogies are not practicable. The torsion potentials should be
specified obligatorily after the partial charges on atoms are specified,
since they heavily depend the charges.
Let us calculate our optimized gauche and trans models in
MP4 / aug-cc-pVDZ. Select the aug-cc-pVDZ bases in the
Standard section, specify MP4 in the above panel,
and select the ENERGY calculation. Do not forget to test the settings
by the Check button, and start calculation.
(The calculation lasted 13 min on our PC).
| Gauche - Trans
Thus, at the MP4 / aug-cc-pVDZ approximation, the gauche conformation
proved more stable than the trans conformation by -0.0010739464 Hartree
(-0.674 kcal/mol or -2.82 kJ/mol). The experimental values are
0.83 kcal/mol (S. Nonoyama et al., 51st Annual Meeting of Chemical
Society, Kanazawa, Japan) and 0.57 ± 0.09 kcal/mol,
(K.B. Wiberg and M.A. Murcko, J. Phys. Chem., 1987, vol. 91).
Before selecting the force field parameters, we have to specify molecular
mechanics types for the atoms. Force fields by different authors have different
sets of types. Fine Types were introduced to allow switching between
them. Fine Types are the most specialized types for all supported
force fields. The /data/ForceField folder contains the
FineType.mlm file with a table of conversion from Fine Types
to particular force field types. Unique types can be created for all atoms
in the molecule, but we will use the -CH2- and H2C- types
for carbon and hydrogen, respectively.
Create a new Fine Type F-tutor for fluorine.
F-tutor - - - - F - - - - - - - - - - - - - - - - -
We specified that it should be converted to the F type of the
AMBER94 field. Restart the program to apply the FineType.mlm file changes.
Save the corresponding types to the model files.
The result can look as follows:
@Table Atoms 8
str str double double double double str str str str double double double str
ID Element X Y Z Q Type Mol Res Flag R* Epsilon Mass Comment
0 C -0.19366 -0.04181 -0.06123 0.1056 -CH2- 0 - - - - -
1 C 1.31260 0.05690 -0.12459 0.1056 -CH2- 0 - - - - -
2 H -0.51562 -1.08063 0.01309 0.0732 H2C- 0 - - - - -
3 H -0.65415 0.42715 -0.93092 0.0732 H2C- 0 - - - - -
4 F -0.61717 0.63461 1.08129 -0.2520 F-tutor 0 - - - - -
5 H 1.77308 -0.41205 0.74510 0.0732 H2C- 0 - - - - -
6 F 1.73611 -0.61953 -1.26711 -0.2520 F-tutor 0 - - - - -
7 H 1.63456 1.09571 -0.19893 0.0732 H2C- 0 - - - - -
@Table Bonds 7
str str str double double str
ID1 ID2 Order R-eqv Force Comment
0 1 s - -
0 2 s - -
0 3 s - -
0 4 s - -
1 5 s - -
1 6 s - -
1 7 s - -
Let us open the model and calculate its energy. A warning appears
"No such angle parameter: CT CT F", pointing to missing parameters
for the current force field (AMBER94). The full list of missing parameters
is specified in /Report/FF_error.txt. Another way to determine
the missing parameters is to save the model in the mmol format.
Specify the missing parameters in the
In this example, they will be chosen by analogy with those available in
AMBER94. For an accurate model, they can be determined by the approximation
of quantum mechanical calculations; however, they are not critical for many
tasks. Specify the following parameters:
CT CT F 40.0 109.50 tutor
HC CT F 50.0 109.50 tutor
Energy calculation finds no unspecified parameters. Although the torsion
angles have not been specified, AMBER94 has default values for the *-CT-CT-*
angles. We can specify the model by setting the F-CT-CT-F value.
Include the following line in the /data/ForceField/AMBER94_3_torsional.xls file:
F CT CT F 1 1.0 180.0 1 tutor
This line should follow the lines with asterisks to override the default value.
The force constant was temporarily set to unity. Its value should be selected
so that the difference between the trans and gauche conformation energies
approximates that obtained by quantum mechanics or experiment.
The comparison should be performed in local energy minima; accordingly,
both models should be optimized after each parameter change.
The Optimization panel is invoked from the
Compute > Optimize menu. The default parameters are suitable for
our task. Several experiments with the force constant demonstrate that the V/2
value of 2.02 kcal/mol provides for the desired energy difference.
F CT CT F 1 2.02 180.0 1 tutor
As a result, a simple model of 1,2-difluoroethane was constructed
using the following steps:
- Geometry determination by quantum mechanical calculations
- Potential derived charge determination
- Specification of force constants for valance bonds and angles
- Adjustment of the torsion potential for quantum chemical or experimental data
A finer model requires the calibration of van der Waals and electrostatic
interactions to fit the vaporization heat and density
of liquid 1,2-difluoroethane to experimental data.