Scheme 1
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Jeffrey John Gosper and
Conor McMenamin
Chemistry Department
Brunel University
Uxbridge, Middx
UB8 3PH, UK
GridView is a Windows program that enables the potential energy surfaces generated by MOPAC (6 and 93) GRID calculations to be visualized and analyzed. The program facilitates the exploration of these surfaces by producing contour and feature maps. The maps are 'live' in that single/multiple points can be selected for structure viewing/animation (requires an XYZ file viewer such as Re_View). A series of sample simulations have been used to test GridView and both the executable (16 bit and 32 bit) and source codes (Visual BASIC 4) are included in the full paper.
Potential Energy Surface, Semi-Empirical QM calculations, MOPAC6, MOPAC93, Contour maps, Hypermolecules, MNDO, Windows Program, GridView, visualization, GRID calculations.
One important field of computational chemistry is the study of chemical reactions that involves structures of highly distorted geometries. These structures are not modelled well using typical parabolic energy functions, thus molecular mechanics is not well suited to the study of chemical reactions. Various quantum mechanical methods may be applied to such studies however semiempirical methods offer reasonable results and have the advantage that they can used for the study of medium sized systems of up to a few hundred atoms.
The Born-Oppenheimer approximation is key to the theoretical description of chemical phenomena,1 it asserts that the motion of electrons in a molecule is uncoupled from that of the nuclei. This approximation has lead to the concept of a Potential Energy Surface (PES). As it is assumed that electronic motion is separated from nuclear motion, by solving the quantum mechanical motion for the electrons a potential energy can be determined for each possible arrangement of the nuclei in a molecule. A PES is a function that describes how the potential energy of a molecule changes as the nuclei move relative to one another.
To fully describe the orientation in 3-dimensional space of an N-atom system requires 3N numbers, but as we are only concerned with relative positions we can ignore the six overall degrees of freedom that result in no relative change (i.e. only effect the molecule as a whole), leaving 3N-6 internal degrees of freedom (3N-5 for linear systems). Therefore, in order to carry out an complete investigation of the PES for even a modest sized molecule, a prohibitively large number of calculations need to be performed, hence approximations must be made for multinuclear systems. Useful information can be learned from examining selected regions of the PES, such as PES derived from the variation of one (linear synchronous transit method) or two geometrical parameters.2 These latter types of PES calculation are tenable and if semiempirical methods are employed even reasonably large systems can be studied.
The problem is not so much running these calculations but in the analysis of the copious amount of information produced. For example, the output from a typical calculation on a molecule containing 25 atoms (using a 23x23 grid to sample the variation of two geometric parameters) can be in excess of 1000 pages. The data generated for each point in the grid includes atomic charges, coordinates, energy and other information from which the user must extract the information they seek. MOPAC63 and MOPAC933 are widely used semi-empirical general purpose molecular orbital packages, and have the ability to generate such PESs. In the case of these programs the generation of a PES via this method is known as a GRID calculation. Such calculation are readily run by supplying an initial structure and indicating which internal variables are to be altered. The size of the step and the number of points used to sample the PES are also entered. Note that for MOPAC6 and MOPAC93 the maximum number of grid point is 23*23 and the default grid size is 11*11.
The electrocyclic 1,3-dipolar addition of azide to a double bond4 can be used to illustrate PES calculations (such
reactions have been extensively studied by molecular orbital calculations
5). The MOPAC (either 6 or 93) input file
for this reaction (Scheme 1) is included below:
PM3 GEO-OK STEP1=0.2 STEP2=0.2 2d search of reaction N C 1.50468 -1 1 H 1.10682 1 113.37726 1 2 1 H 1.10573 1 108.12396 1 117.87269 1 2 1 3 C 1.53079 1 101.82756 1 -122.34158 1 2 1 3 H 1.10509 1 114.43521 1 124.73661 1 5 2 1 H 1.10547 1 113.81799 1 -111.84138 1 5 2 1 N 1.49628 -1 103.29593 1 6.37604 1 5 2 1 H .99475 1 116.35622 1 -13.18362 1 1 2 3 N 1.22770 1 113.31689 1 -1.61680 1 8 5 2
Part of the output generated by MOPAC6 from the above Z-matrix is included in Appendix I.
Determination of trends within the volumous data produced by such calculations, and extraction of important structures such as saddle points and minima can be difficult. The researcher must search through reams of output looking for relevant structures. If they wish to view a particular structure then an internal to Cartesian co-ordinate conversion is also probably required. Additionally, if further computational methods are to be applied to selected structures (e.g. for energy gradient optimisation) then the file must be manually edited. Both MOPAC6 and MOPAC93 assist in the analysis of type of data by summarising the energies of each point in a form suitable for plotting. However, no direct link is made from the plot to molecular structures and therefore manual processing of GRID output is required. This process is rather cumbersome and can be time-consuming, especially when a calculation fails to proceed in the fashion intended.
Given the importance of the PES to the understanding chemical phenomena, and the complexity of the data produced in PES calculations, a program that assists in the analysis of this type of data would be extremely useful. There are a several commercial programs (including Chem-X6, Nemesis7, CAChe8) that enable some types of PESs (mostly conformational) to be linked to structure viewing. However, none of these interface with MOPAC6/93, nor enable animation sequences of pathways across the PES to be viewed. It was therefore the objective of this project to develop an interactive tool for the PC that aids in the analysis of PESs that are obtained from MOPAC6/93 GRID calculations. By presenting the PES in the form of a contour map, and linking this to the visualisation of particular structures/pathways, as well as assisting in the formulation of input files for further calculations, reaction schemes can be studied in a fraction of the usual time. The software developed for this process is known as 'GridView'. Our initial intention was to develop a tool compatible with MOPAC6 and MOPAC93, however GridView can also be applied to the analysis of other 3D-data grids and PESs. To use GridView in this latter fashion it is necessary to construct an appropriate input file. Alternatively, GridView itself could be tailored for a particular need. To enable such possibilities, the structure of the GridView input file is presented and copies of the source code are attached.
GridView is a Visual Basic 4 program that runs under Windows 3.x (16 bit) or Windows95/NT (32 bit). The 16 bit and 32 bit setup files have been included with this paper. Also the source code for GridView is available in both zipped and text forms. The major features included in the program are discussed below.
GridView directly reads the lineprinter output file created by MOPAC63 or MOPAC933 GRID calculations. Typically these files are named 'FOR006' or 'filename.out'. The following is a list of requirements that a GridView input files must have.
" ATOM"must appear followed by three further lines (these can contain any information as they are skipped). Following this there must be N non-blank line, where N is the number of atoms. These lines must be followed by a blank line (i.e. a line containing a null string); and
The file "minout.txt" contains the minimum amount of information that is necessary for a contour map to be produced. If the structure viewing interface is to be used, than the file must also contain a MOPAC output 'Z-matrix' for each point on the grid. The file "minstruc.txt" is an example of such a file.
Once a file has been read by GridView a colour map is displayed. Figure 1 shows a typical display window. In this case the map have been derived from the MOPAC input file discussed above using MOPAC6. The output from this calculation (dipg1.out) will be used to exemplify GridView facilities thoughout this document.
Figure 1: A typical map produced by GridView using default values.
By default, three different graphs are superimposed on this map, however each of these can be eliminated from the display by selecting appropriate items in the 'Display Options' menu. The three different display elements include:
Apart from the ability to turn off the above display items a few other display options are available. These additional features include:
In feature maps maxima (hills), minima (valleys), (potential) saddle points,
troughs, and ridges are highlighted. The algorithm used for the identification
of these features is rather simple but effective. The trend in the energies of
the points that lie on the horizontal, vertical, and two diagonal axes
surrounding the point are determined. The following diagram depicts each of
these directions:
There are
three possibilities (types) for the trends in energies along these directions:
Using these trends it is possible to assign the feature to the central point using the following patterns:
An example of the feature map corresponding to Figure 1 shown above is provided in Figure 5.
Figure 3: An example feature map (using the default 'Display Options' settings).
One of the facilities offered in the 'Display Options' menu item is to
'Increase Resolution'. This has the effect of smoothing the data and contours.
Data smoothing is achieved using a simple averaging algorithm that only
considers adjacent points. Although this is a rather primitive method it does
seem to be effective. Figure 4 shows a series of maps that arise from using this
facility.
Figure 4: Images A-D represent a series of images arising from increasing the
resolution of a GridView map.
One of the major features of GridView is the ability to link the display map to structures. This is achieved by selecting one or more points on the map, using a left-mouse button select, and then selecting the 'View | Launch XYZ Viewer' menu item. The program then finds the appropriate structure(s) in the MOPAC output file, converts these from internal to Cartesian co-ordinates (using code derived from the MNDO program9) and finally launches a viewer program such as Re_View 10 so that the structures can be viewed in 3D. If multiple structures have been selected then an animation of these can be displayed using Re_View10 .
An XYZ file11 has been generated using the structures the give rise to the lower-left to upper-right diagonal in Figure 1. This provides an example of the connection between the map and structure viewing possible in GridView. Figure 5 summarises the results obtained from this analysis, highlighting the structures of the starting material, approximate saddle point, and products. The structures and graph were generated using Re_View10 .
Figure 5: A summary of the link between the GridView map and structures viewed
by Re_View.
An mpeg animation of the structures running along the diagonal helps depict the power of GridView/Re_View combination.
To aid in the selection of points for viewing three utilities have been added to GridView. These enable the automatic selection of either:
This latter selection reveals the method employed by the MOPAC6/93 GRID calculation. MOPAC starts from the lower-left corner and works up the first column and then down the second. This up and down sequence is continued until the final structure is reached. A multistructure XYZ file and mpeg movie arising from the selection of all the points clearly shows this procedure.
A feature has been included in GridView that facilitates further MOPAC calculations on a selected point on the grid. This is normally used to aid energy or energy gradient optimisation on approximate saddle points or minima. After picking a point (using a left-mouse button click) and selecting the 'File | Write MOPAC (Internal) Input' menu item, the user is requested for a filename, the keywords to include in the file and the two comment lines to be added to the MOPAC Z-matrix. The generated Z-matrix can then be used to run MOPAC in the usual fashion.
GridView has been tested using a number of simple simulations including pericyclic and elimination reactions, as well as conformational analyses. These are discussed in turn below. It is not the purpose of this paper to evaluate the validity, or otherwise, of these simulation but to demonstrate the utility of the GridView/Re_View combination in the analysis of the results derived from MOPAC6/93 GRID calculations.
GRID calculations are very useful in the study of pericyclic reactions particularly cycloadditions. The reaction discussed above falls into this category and one further example will be discussed here.
Grierson et al.12 have published their findings concerning the semi-empirical GRID study of the 1,3-dipolar cycloaddition of nitrone to ethene. This was an excellent test for GridView as the PESs derived from the calculations were also published. The reaction shown in Scheme 2 was studied using MOPAC93 and the contour maps obtained from GirdView are depicted in Figure 6.
Figure 6: GridView contour maps obtained for the AM1 and MNDO MOPAC93 GRID
calculations for the reaction of nitrone and ethene. The '#' symbol represents
the location of the saddle point located in these calculations.
The transition state for the AM1 calculation is located on the diagonal, whereas the equivalent point on the MNDO grid is obviously unsymmetrical. Grierson et al.12 attribute this considerable difference to AM1 having excessive core-core repulsion for bond formation involving nitrogen. The power of MOPAC GRID calculations and GridView in transition state location for cycloaddition reactions is typified by the fact that refinement of the approximate AM1 transition state only required 5 cycles of gradient optimisation.
Figure 7 shows the GridView map produced from the output of a MOPAC93 GRID calculation for the elimination of H+ and Cl- from 2-chloropropane including COSMO solvation (EPS=78). The figure also includes the structures corresponding to important points on the map.
Figure 7: An augmented GridView map for the elimination of H+ and Cl-
from 2-chloropropane.
A simulation roughly corresponding to an E1 elimination begins at the start material and runs up the left column and along the top. A further factor that makes these calculations and analyses important is that the COSMO solvation model is not recommended for use with FORCE calculations in MOPAC93 calculations.13 As such transition state vibrational analyses and intrinsic reaction coordinate calculations are problematical when the COSMO solvation model is included. Therefore reaction path and GRID calculations are two on the prime methods by which reaction simulations may be produced which include this solvation model.
Although MOPAC is not often used in conformational analyses it is possible to employ GRID calculations to generate conformational maps. Such map are of importance where molecular mechanics would be expected to give rise to faulty results; such as in cases where extended conjugation is important, where appropriate parameters are not available, or where full relaxed (diabatic) analysis are required. A couple of examples of the utility of GridView for a conformational analysis have been performed on 3-aminoprop-2-enal and substituted heterocycle (1) using MOPAC6 GRID calculations.
(1)
In the case of 3-aminoprop-2-enal the N-C and the C-C single bonds were each rotated in steps up to a total of 60o. Scheme 3 shows the relevant bonds and the range of values included in the calculation.
The GridView map for the above reaction is depicted in Figure 8. There are a number of interesting trends within this data such as the change in hybrization state of the nitrogen (as indicated by the HNH bond angle), as a function of the torsion angle between atoms 1-2-3-4.
Figure 8: A GridView conformational map obtained for 3-aminoprop-2-enal.
An augmented conformational map obtained by rotation about both C-C acyclic single bonds in heterocycle (1) is depicted in Figure 9. Here the subtle variation in energy as the two groups go in and out of conjugation with the aromatic heterocyclic ring can be readily seen. A single point near the lower left corner failed to optimise correctly, however overall this is provides an excellent diabatic surface.
The MOPAC input file used for the calculation is available.
Figure 9:
Conformational map produced for heterocycle (1). A few important structures are
included in the figure.
The aim of this project was to develop an interactive tool for the PC that facilitated the analysis of the results obtained from MOPAC6/93 GRID calculations. By presenting the PES in the form of a contour map, and linking this to the visualisation of particular structures/pathways, as well as assisting in the formulation of input files for further calculations, such calculations can be studied in a fraction of the usual time. The novel program GridView achieves this goal and can be used to facilitate such calculations. Additionally, by manipulating the output from other PES calculations, GridView can be used in their analysis. Further, provision of the source code with this paper enables others to develop new uses for GridView and tailor it to specific needs.
(1) Eying, H., Walter, J., and Kimball, G.E., Quantum Chemistry, Wiley, New York, 1944, p. 190.
(2) McKee, M.L. and Page, M., Reviews in Computational Chemistry, 1993, 4, 35 and reference therein.
(3) MOPAC6 - Stewart, J.J.P, MOPAC, QCPE 455MOPAC6 for DOS is available by anonymous FTP from ftp.osc.edu/pub/chemistry/software/msdos/mopac.for.dos/mopac6/mopacdos.zip; MOPAC93 - QCPE MOPAC93 Revision2.
(4) March, J., 'Advanced Organic Chemsitry', 4th Ed., p. 836, Wiley, New York, 1992 and references therein.
(5) For a review see Houk, K.N., and Yamaguchi, K. in '1,3-Dipolar Cycloaddition Chemistry', Ed. Padwa, A., Vol. 2, p.407, Wiley, New York, 1984.
(6) Chem-X, Chemical Design Limited, Oxon, England.
(7) Nemesis, Oxford Molecular Ltd, England.
(8) CAChe, CAChe Scientific, Beaverton Oregon.
(9) Dewar, M.J.S. and Theil, W., J. Am. Chem. Soc., 1977, 99, 4899.
(10) Gosper, J.J., 'Re_View - A Windows Molecular Animation Program', http://www.brunel.ac.uk/depts/chem/ch241s/re_view/re_view.htm, 1996.
(11) XMol Users Manual, Minnesota Supercomputer Center, Inc., Minneapolis MN, 1993.
(12) Grierson, L., Perkins, M.J., and Rzepa, H.S., J. Chem. Soc., Chem. Commun., 1779, 1987.
(13) Stewart, J.J.P, 'MOPAC93 Manual', QCPE MOPAC93 Revision2.