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Force-on-Nuclei
v2.1

Force-on-Nuclei [FN] attempts to calculate the force acting on a nucleus in a molecule, using the electron-density specifying 'cube' file for the given molecule. As per the Hellmann-Feynman electrostatic theorem, this force is simply the resultant of the Coulombic force of attraction by the smeared-out electron cloud and of repulsion by all other nuclei. The cube file may be obtained using packages such as PC GAMESS. 
However, FN may also be used to learn about the kind and pattern of data hidden within the cube files, such as the associated nuclear-framework orientation, maximum electron density values and locations, grid point and density value nearest to each nucleus and so on. 
Calculation of Coulombic force by the actual electron-cloud continuum approximated (in cube files) as a set of discrete grid-points naturally is prone to substantial error. To avoid it, FN allows creation of tailor-made PC GAMESS inputs to form cube files with a grid-point sitting just at the chosen nucleus.

This Windows package (screenshot shown below) has been developed (using the Visual FoxPro 6 platform) by Rituraj Kalita of Guwahati (India) first in 2007 as a part of a theoretical-chemistry package, but since 2008 it is also available as a separate freeware (i.e., free software). 


Fig.: Force-on-Nuclei Screenshot 

 

Frequently Asked Questions:

01. I know that we may run Force-on-Nuclei by double-clicking at the desktop icon named Force-on-Nuclei v2. How do I get that desktop icon?
 This icon should automatically appear at your Windows desktop. If it didn't, open the working folder (e.g., C:\Force_Nuc), starting from, say, My Computer. From that working folder find and copy the link file named Force-on-Nuclei v2, and then paste that to your Windows desktop to facilitate running the Force-on-Nuclei application in future.

02. I keep getting an error message: Row or column position is off the screen!  whenever I try to run (i.e., open) Force-on-Nuclei. Where is the problem?
 Most probably your monitor (VDU) screen resolution (screen area in Windows terminology) is not set to a level high enough (i.e., at least to a level of 800 by 600 pixels). You may try improving this particular Windows setting (via Control Panel - Display) -- it should work in most cases. The Windows XP 'themes' and the Windows display font-size (either 'small' or 'normal' font-size is the desired one) may also matter in some situations.

 

Tutorials: 
I. Calculating Force Acting on the Carbon Nucleus within a Methane Molecule

Step 0 (optional): Employing the PC GAMESS freeware (along with the free DblClkPCGAMESS kit-interface, if necessary) and using the (HF/6-31G level structure-optimized) coordinates-set for the methane molecule contained in the CH4_Cub1.inp (PC GAMESS input) file kept within the tutorials subfolder of this package, obtain the cube file (say, CH4_Cub1.cube) for this molecule (already available within the tutorials subfolder). Hyperlinks to a good collection of reading materials about basic computational chemistry, as well as about working with PC GAMESS, is available in the aforesaid DblClkPCGAMESS page.
Note: PC GAMESS stores the content of the cube file within the Punch file generated by it. Opening the Punch file, delete all other lines other than those embedded within the $Cube and subsequent $End markers (delete the two marker lines also), then save the file as CH4_Cub1.cube, say (may now compare your obtained contents with the those in the package-contained cube file). Next, find out what keywords within the PC GAMESS input file caused to create the cube output: for that, open the CH4_Cub1.inp file, and note the two following additional lines not found in usual PC GAMESS input files not generating a cube file (the MESH keyword below may have values Coarse, Medium or Fine, depending on the resolution of grid-points you prefer): 
$ELDENS IEDEN=1 $END
$CUBE CUBE=.T. MESH=Coarse $END

Step 1: Open Force-on-Nuclei by double-clicking at its desktop icon. Click at Choose File button, then choose the CH4_Cub1.cube file. As this cube file was generated (by PC GAMESS) with the molecular net charge (corresponding to the ICHARG parameter in PC GAMESS) zero, so keep the Net Charge entry as 0. Click Continue. You'll be asked whether to overwrite the pre-existing FN-Output (.FNO.txt) file: click Yes. 

Step 2: Let the Force-on-Nuclei process run. A question regarding whether to create a text-file form of the electron density database (with only one answer No shown) -- just ignore that question (as that text-file formed will be quite bulky) -- the question will very soon disappear (with No as its understood answer). May now view the electron density and the nuclear framework databases; close the database displays when finished viewing. Next you're asked on which nucleus (or set of nuclei) the net force (or forces) is/are to be calculated. As 1 is already shown as the answer, and as we aim to calculate the force only on the carbon nucleus which is numbered 1 in the coordinates-set for the methane molecule, so just click Continue.

Step 3: The force-calculation process will be soon over, and the calculated force with all the earlier cube-file analysis will be reported in the displayed Force-on-Nuclei output file. 
But alas, the force on the carbon nucleus is not found to be even approximately zero, though as the structure-optimized molecule is supposed to be in (spatial) equilibrium (with respect to the internuclear coordinates), this force should have been zero in theory. The substantial error in the above calculation has crept in mainly because of the asymmetry of the grid-point positions closest to the nucleus (as stated in the introduction above): as the distance to the closest grid points from the nucleus is very small, the inverse-square Coulombic force by the corresponding electron-density elements becomes large, and any asymmetry of the grid-point locations along the nucleus-surrounding directions matters a great deal. So to remove the asymmetry of the grid-point locations, we may proceed to form a corrected cube file as per the following steps.

Step 4: Close the displayed output file to quit FN, then again open FN (by double-clicking at its desktop icon). But this time, after choosing the same cube file, click at the Generate button instead to generate a tailor-made PC GAMESS input file (Work2Do.inp) so as to finally form a cube file with one grid-point sitting just at the chosen nucleus (i.e., at the carbon nucleus with nucleus number 1), so that the other nearest grid-points would symmetrically surround this grid-point as well as that nucleus. Press Space (or Enter) key, when asked, to let the tailor-made Work2Do.inp input file get generated. Delete the topmost blank line and the top instruction line as well as the bottom instruction line, then save and close this PC GAMESS input file to (automatically) quit Force-on-Nuclei. 

Step 5: Employing PC GAMESS with this Work2Do.inp input file, form a new, tailor-made cube file: let us save it as CH4_Cub2.cube, say (not available with the supplied package). Repeat Step-1 to Step-3 above to calculate more accurately the force on the carbon nucleus in methane using this new cube file.

Step 6: To perform even better calculations with fine-resolution cube files, replace the Coarse keyword in MESH=Coarse entry with the Fine keyword, then repeat Step-0 to Step-5 above.

Step 7: To perform even more accurate calculations with MP2 level computation generated (as well as fine-resolution) cube file, replace the RUNTYP=ENERGY entry in the PC GAMESS input file with the word-set MPLEVL=2 RUNTYP=GRADIENT within the FN-corrected Work2Do.inp file (which was obtained in Step-4 during the last run), and run PC GAMESS on it. The punch file now contains contents of two ($Cube....$End lines embedded) cube files, out of which only the lower, MP2-type one (beginning with the MP2 Density identifier) is to be kept and saved as a (suitably named) .cube file. Then repeat Step-1 to Step-3 above with this cube-file.
 

II. Visualizing the Electron Density Distribution within the Methane Molecule using gOpenMol

Step 0. Get gOpenMol v3.0 (or a higher version of gOpenMol, by Leif Laaksonen et al) free-downloaded (~27 MB) & installed in your PC. A good starting point to learn gOpenMol operations is probably the note on how to use gOpenMol by Lev Kantorovich. Here, we are going to visualize the  fine-resolution cube file for methane (as obtained in Step 6 of Tutorial I above), named as, say CH4_cub1 Fine.cube. As gOpenMol can't deal with file/folder names containing intervening spaces, such named cube file must be suitably renamed, say, to CH4_Fine.cube (i.e., to a name lacking any intervening space).  

Step 1. To provide the electron-density visualization for a cube-file, gOpenMol at first requires the (Angstrom-unit) nuclear Cartesian coordinates of the molecule implicit within the cube file, in a form of an XMol XYZ file. However, if, coordinates for the same molecular structure but oriented differently, such as those found within the PC GAMESS input file generating the cube file, are used, the visualization will not be meaningful. Neither do the Bohr-unit nuclear coordinates found at the top part of the cube file (or within the corresponding PC GAMESS  'single-point-geometry' output file) serve this purpose. Force-on-Nuclei greatly helps here by directly providing (within its .FNO.txt output file) the (Angstrom-unit) contents of an XMol XYZ file, corresponding to the molecular structure implicit within the cube file on which it operates.
So, to get a proper XYZ file, open Force-on-Nuclei and choose the CH4_Fine.cube file to operate on, and let the usual FN process run. At the end, from the displayed contents of the CH4_Fine.FNO.txt output file, copy the contents (only non-blank lines) for the would-be XMol XYZ file, and paste those contents within a file named CH4_Fine.xyz (may compare contents of the same-named file to be found pre-existing within the Force-on-Nuclei package). 
Note: The contents of the aforesaid output-file (should go through those) provide a lot of other relevant information about the electron density characteristics within the cube file, such as:
    (i) Bohr-unit (x, y, z) values for the beginning (i.e., lowest x, y, z) and the ending (i.e., highest x, y, z) grid-points, the consecutive-grid positional increments (Dx, Dy, Dz) along the (x, y, z) axes, and the numbers of grid-points (Nx, Ny, Nz) along these three directions
    (ii) The electron probability (E-P) density integral ∫r dx dy dz (where r is the electron density), compared to the net number of electrons (i.e., the sum of constituent atomic numbers minus the net molecular charge) within the molecule  
    (iii) The maximum and the minimum values of the electron density r out of the grid-points, with their corresponding positions (i.e., their x, y, z values), that too specified further with the three nearest nuclei and their distances from grid-point
    (iv) The grid-point numbers (Nx, Ny, Nz) for the grid-point nearest to every nucleus, along with its electron density value 

Step 2. Open gOpenMol, then at its Tcl/Tk Interface click at File, then at Import (NOT at Open), then at Coords..., then in the newly opened window click at Browse button, then locate & open the aforesaid CH4_Fine.xyz file, and then click at the Apply button. You'll see the nuclear framework of the CH4 molecule appearing as a wire-frame in the main graphical window. You may mouse-drag (similar to what one does in Chime, ViewMol3D and ArgusLab etc.) along the empty black space (i.e., the background) to view that framework from different angles (note that mouse-dragging with the right-button pressed would resize the molecular display); choose a orientation (and size) that would give the best view for the electron-density figure, and leave it at that. Close this Import Coordinates window. Let us now change the black background to white: to do that, at the Tcl/Tk Interface click at View, then at Background colour, then at Colour..., then in the color-choosing window click at the white-colored square, and then at OK. 
Note: In gOpenMol, the C-atom color is green, which is rather uncommon, comparing the blackish color generally used. To change the C-atom color to a blackish one, at the Tcl/Tk interface of gOpenMol click at View, then at Atom colour..., then within the Define Atom Colour dialog box thus obtained click at the blank long space next to Atom: and put C (yes, uppercase C) there. Then click at the Colour... button, and choose a dark gray color. Click at the Apply button to let the change take place. Also, the H-atom color is white in gOpenMol, which is invisible against our white background. So, similarly change the H-atom color too, say into a light gray one.

Step 3. After the nuclear structure has been thus specified, we may next proceed to open and view the electron cloud. However to achieve that, at first we need to convert the cube file to a gOpenMol-intelligible plot (.plt) file. To do that, first click at Run, then at gCube2plt/...., then at the newly opened window, click at Browse button for the Input file name, then therein open the aforesaid CH4_Fine.cube file, then copy the whole pathname of this file from this Input file name text-box into the text box corresponding to the Output file name, then select the cube extension at the end of this output filename, delete that and manually type plt in its place (within gOpenMol, better not ever use the Backspace key). Next, click at the radio buttons corresponding to Gaussian94 and to g94cub2pl (this is because a cube file generated by PC GAMESS and extracted out of the Punch file just looks like a Gaussian94-generated one). Next, click at Apply (if the bottom-lying Apply button is not visible in your monitor, slightly push this window up by dragging at its top window-bar), which will result in a 'job done' message at the bottom -- now close this Run gCube2plt/.. window. [As the just-generated CH4_Fine.plt file will be available now onwards, you won't need to perform this Step 2 the next time you want to view the CH4 electron cloud -- may directly go to Step 3.] 

Step 4. To view the electron cloud, now click at Plot, then at Contour..., then in the resulting Contour Control window, click at Browse button to select (open) this newly generated CH4_Fine.plt file, then click at Import. You'll see the Contour levels entries for the user-definable probability-density values & colors (corresponding to the desired contour which will be a set of probability-density iso-surfaces)  appearing at the middle of this window. These entries may be made pretty elaborate, however as gOpenMol beginners, let us now go for a rather elementary set (see the left figure below). Type 1.0 (a rather high value of probability-density, observed near a non-H nuclei) for Value 1, 0.1 (a high value of probability-density, found near any nuclei) for Value 2, 0.01 for Value 3 and 0.001 (a rather low value found farther from nuclei) for Value 4. Next, click at the Colour.. button against Value 1 and select the deep red (see the illustration below) color out of the available colors, then similarly select the deep fuchsia (purple-red) color against Value 2 and the light greenish-blue color against Value 3, then finally the bright yellow color against Value 4. Then click Apply and wait for the windows to stabilize: you'll see the Details buttons appearing near the four defined colors (see figure below). Yes, we've also got an electron-cloud picture (not the refined one shown in the figure below) at the main graphical window, but as the four colored layers start appearing as opaque bodies by default, so the outermost yellow color is unfortunately, at present, concealing the inner colors as well as the innermost nuclear framework! 

       

Step 5. Now to get the desired multiple-color as well as nuclei-displaying electron-cloud view click at the four available Details buttons one by one, then in each of the resulting Contour 1, level x windows (for x = 1,2,3,4), move the Opacity slider to fix the opacity value at 0.10 for the all four colors (instead of the default 1.00, thus making all these colored layers a great deal transparent). Click at Apply and then close the corresponding (i.e., the Contour 1, level x) window. After all the four opacity values are thus changed and the windows gets stabilized, minimize (or close) the main Contour Control window to view the graphical window: you'll now see a four-color body similar to the above figure, but may be viewed from a different angle. [Note that because of some (present) limitations in gOpenMol, the layer colors may not appear just as directed -- say, the bright red color ultimately becomes brownish red, whereas the greenish light-blue color turns to light green.] Now, we may view zones within the methane molecule's electron density distribution as follows: 
    (i)  The innermost very-high-density region (brownish red) just surrounding the C-nucleus (with r > 1.0)
   (ii)  The inner high-density (pink) lobe encompassing the whole nuclear framework (with r within 0.1-1.0)
   (iii) The outer medium-density (greenish) lobe and the outermost low-density (yellowish) lobe.
Note: You may also save (say as CH4_Fine.gom file) the gOpenMol visualization-work for this molecule by choosing save or save as... from the file menu; in that case in any later gOpenMol session, may open that .gom (i.e., gOpenMol) file to make any changes to the visualization settings.

 

Cite use of this package as:
        Force-on-Nuclei 2.1 
        © 2008 Rituraj Kalita, Guwahati (India)  
        http://www.geocities.com/riturajkalita/Force_Nuc.htm  

 

References:        

1. PC GAMESS, version 7.1 (Tornado) – build number 4471, 2007, Alex A. Granovsky, Laboratory of Chemical Cybernetics, Moscow State University, Russia. <http://classic.chem.msu.su/gran/gamess/index.html>;
Schmidt, M.W., Baldridge, K.K., Boatz, J.A., Elbert, S.T., Gordon, M.S., Jensen, J.H., Koseki, S., Matsunaga, N., Nguyen, K.A., Su, S.J., Windus, T.L., with Dupuis, M., and Montgomery, J.A. The General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347-1363. 

2. DblClkPCGAMESS: The Tiny Kit for Running PC GAMESS, © 2008 Rituraj Kalita, Guwahati (India)  
  <http://www.geocities.com/riturajkalita/DClk_PCGM.htm> 

3. Kalita, R. Examples and Explanations of PC GAMESS Input Files. 
  <http://www.geocities.com/riturajkalita/PCGAMESS_Inputs.htm>