Auto VDW determination

This pages explains how DL_FIELD can use Slater-Kirkwood (SK) approximation to automatically determine the vdw parameters for any pair of atoms, in situations where there is no defined vdw mixing rules, nor standard parameters available in the literatures.

For this reason, this method only applies to systems that contain more than one FF scheme (multiple potential) such as the bio-inorganic models, where one atom is from one FF scheme and the other atom is from the other FF scheme.

../../_images/Orange_bar6.png

SK approximation

Van der Waals (vdw) forces are combination of several non-covalent intermolecular forces that arise due to change in electron clouds, resulting in dipole moments. The strongest component being those of permanent dipoles, while the London dispersion force is the weakest component. The latter is predominantly present in nonpolar atoms such as noble gases. It arises due to instantaneous electron cloud fluctuations that form temporary dipoles. Therefore, London force is also called the induced dipole-induced dipole attraction.

For this reason, vdw forces are closely related to atomic polarisability (\(\alpha\)), or the ability to deform the electron clouds, especially those of electron valence.

Recall that a typical vdw LJ12-6 function consists of a repulsive parameter, A, and a dispersive parameter, B.

\[V \left(r \right) = \frac{A}{r^{12}} - \frac{B}{r^{6}}\]

Consider two atoms, of type i and j, DL_FIELD can determine the dispersive parameter by using the Slater-Kirkwood approximation.

\[B_{ij} = \frac{3}{2}\frac{ \alpha_{i} \alpha_{j}}{\sqrt{\frac{\alpha_{i}}{N_{i}}} + \sqrt{\frac{\alpha_{j}}{N_{j}}}}\]

where N is the number of electron in an atom. In the case of the repulsive parameter, this can be obtained from the sum of atomic radii, w.

\[A_{ij} = \frac{1}{2}B_{ij}(w_{i} + w_{j})^{6}\]
../../_images/Orange_bar6.png

The dl_field.atom_data file

The equations show that \(\alpha\) and w are the only adjustable parameters and they are listed in the file called dl_field.atom_data in the /lib folder. A portion of this data, with illustrations, is shown below:

../../_images/dl_f_23_1.png

To determine the vdw parameters, DL_FIELD will look for exact match of ATOM_KEYs expressed in DL_F Notation between the input system and the data list, to obtain the corresponding \(\alpha\) and w. If there is no match, DL_FIELD will obtain values from generic entries, with a symbol ‘*’. For example, the generic entry for fluorine is F*.

For more details about data sources, please look into the content of the file.

Note

The information listed in dl_field.atom_data cannot be overriden by the udff file. You would need to change values or add new entries directly in the file.

../../_images/Orange_bar6.png

Using SK approximation

Consider a model consistis of an octane molecule trapped within silicalite (SiO2) framework, which is a zeolite.

../../_images/dl_f_23_2.jpg

Below shows a portion of the configuration input file (in xyz format), showing the relevant directives.

 2330
CRYST1   40.180   39.476   26.284  90.00  90.00  90.00        None   1
# POTENTIAL opls2005  MOLECULAR_GROUP A1
C  20.211000  16.483000  6.365000
C  19.789000  15.207000  5.635000
H  19.897000  17.379000  5.822000
H  19.770000  16.534000  7.366000
H  21.298000  16.534000  6.483000
C  20.209000  13.924000  6.361000
H  18.700000  15.207000  5.500000
H  20.216000  15.207000  4.624000
...
...
# POTENTIAL inorganic_zeolite  MOLECULE_KEY Z4s     MOLECULAR_GROUP A2
Si  28.853000  21.319000  23.108000
Si  26.862000  20.447000  25.183000
Si  25.482000  20.758000  14.855000
Si  22.341000  20.661000  14.791000
Si  21.865000  20.552000  24.931000
Si  24.413000  21.421000  23.522000
Si  28.824000  36.228000  22.852000
...
...

It shows OPLS2005 FF is applied to the octane molecule, while an inorganic_zeolite FF is applied to silicalite. Potential parameters are available for both the octane molecule and the silicalite structure. However, there is no vdw parameter available between atoms of both components. We will use the SK approximation to determine these missing parameters.

Below show a portion of DL_FIELD control, showing the relevant input options, as highlighted.

Control file title - octane in silicalite
1        * Construct DL_POLY output files
none        * Secodary output files (Gromacs, Chemshell or none). 
multiple  * Type of force field require (see list below for choices).
kj/mol  * Energy unit: kcal/mol, kJ/mol, eV, or K.
normal  * Conversion criteria (strict, normal, loose)
1        * Bond type (0=default, 1=harmonic , 2=Morse)
1        * Angle type (0=default, 1=harmonic, 2=harmonic cos)
none   * Include user-defined information. Put 'none' or a .udff filename
1       * Verbosity mode: 1 = on, 0 = off
octane_zeolite.xyz   * Configuration file.
none   * Output file in PDB. Put 'none' if not needed.
0 5 molecules  10.0 * Solution Maker: on/off, density, unit, cutoff)
1        * Optimise FIELD output size, if possible? 1=yes  0=no
1         * Atom display: 1 = DL_FIELD format. 2 = Standard format
1         * Vdw display format: 1 = 12-6 format   2 = LJ format
default * Epsilon mixing rule (organic FF only) : default, or 1 = geometric, 2 = arithmatic
default   * Sigma mixing rule (organic FF only) : default, or 1 = geometric, 2 = arithmatic
1        * Epsilon mixing rule (inorganic FF only) : 1 = geometric   2 = arithmatic
1        * Sigma mixing rule (inorganic FF only) : 1 = geometric   2 = arithmatic
6    * Epsilon mixing rule (BETWEEN different FF) : 1 = geometric   2 = arithmatic
6     * Sigma mixing rule (BETWEEN different FF): 1 = geometric 2 = arithmatic
0         * Display additional info. for protein 1=Yes  0=No
0         * Freeze atoms? 1 = Yes (see below)  0 = No
0         * Tether atoms? 1 = Yes (see below)  0 = No
...
...

The control file shows this is a multiple potential model and DL_FIELD will extract the require FF schemes from the input file, octane_zeolite.xyz. The options (6) are selected for the LJ12-6 mixing rules to obtain the LJ \(\epsilon\) and \(\sigma\) parameters by meanis of SK approximation. Note that atom display mode must be that of DL_FIELD format (or DL_F Notation), to carry out correct matching against the data in the dl_field.atom_data.

When DL_FIELD is run, the following information will be reported in the dl_field.output file:

...
...
Use SK combination rule to determine vdw parameters between pairs
of atoms from different FF schemes. Reading data from dl_field.atom_data.

Selected atomic polarisabilities and vdw radii are shown in brackets).
C1p_A(pol=0.960 rvdw=1.800) - Si#101_B(pol=0.000 rvdw=2.100)
A = 0.0000e+00   B = 0.0000e+00
Eps = 0.000   Sigma = 0.000
================
C1p_A(pol=0.960 rvdw=1.800) - O#c101_B(pol=0.000 rvdw=0.000)
A = 0.0000e+00   B = 0.0000e+00
Eps = 0.000   Sigma = 0.000
================
C1p_A(pol=0.960 rvdw=1.800) - O#s101_B(pol=0.850 rvdw=1.520)
A = 1.1410e+06   B = 1.7041e+03
Eps = 0.636   Sigma = 2.958
================
...
...

Note

For more information about SK approximation, please consult DL_FIELD manual, Section 3.10.2

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