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Geometry Optimization	Version 5.2
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Molecular Mechanics (MM2, MOLY)	Conformational Analysis
MOPAC version 6	Manual geometry adjustments

Three geometry optimization methods are provided with the program: molecular mechanics (MM2 and MOLY), conformational analysis and the semi-empirical quantum methods found in MOPAC. Of these, MOPAC's AM1 and PM3 methods are the most sophisticated, although used alone they are likely to find only a local minimum.

Understanding the difference between a local and global minimum, and which methods finds which, is key. The global minimum is the lowest minimum energy conformation of the molecule possible. A local minimum is the low energy conformation closest to what is pictured on the screen. In the latter case lower minimum energy conformations are likely to be obtained from a different starting geometry. Standard MM2, MOLY or MOPAC used alone will find local minima. To find global minima use either the Quick MM2 method (watch out, it changes stereochemistry!) or conformational analysis in conjunction with standard MM2, MOLY or MOPAC.

Conformational Analysis and Molecular Mechanics minimizers are accessed from the Geometry menu. MOPAC is entered from the Tools menu.

Molecular Mechanics Minimizers

The Molecular Mechanics routines are entered through the Geometry menu. The goal of the molecular mechanics is to obtain a low energy geometry of the molecule. This geometry is often not the lowest energy geometry possible, but is a local minimum close to the starting geometry. To obtain a global energy minimum you will most likely have to also use Conformational Analysis iteratively with the minimizers.

Molecular Mechanics minimizers do not use quantum mechanics or other chemical theory to obtain minima. Instead, they look up in a table, ideal values for combinations of atoms to obtain bond lengths, bond angles and torsional (dihedral) angles. In addition, unbonded atom-atom overlap is kept to a minimum.

Clicking on the "Minimize" menu item in the Geometry menu will begin the process of minimizing strain energy in one of the molecules by moving atoms randomly and by gradients determined by the energy changes.

The MM2 minimizer originated with Norman Allinger and coworkers (3) in the early 1980s (with later improvements included here). This implementation comes from the developers of the DOS program Molgen (P. Baracic and M. Mackov). The MM2 minimizer is the industry standard for geometry optimization and is known to do a very good job minimizing organic molecules. It is parameterized for H, C, N, O, F, Si, P, S, Cl, Br and I.

With Version 5, a standard ("Full") MM2 minimization is the default. It finds a local minimum for the molecule as drawn. It does not find a global minimum unless you first run conformational analyses on the freely rotating bonds. The Quick MM2 minimizer does find global minima, but will effect stereochemistry in an unpredictable fashion.

The Quick MM2 version has some non-standard features:

it first breaks the molecules into smaller fragments and performs an MM2 minimization on them
it reassembles the molecule, using conformational analysis to set the dihedral angles in the low energy conformation (finds a global minimum conformation)
it uses a library of pre-optimized rings.

The full version of MM2 will find a local minimum for the molecule in its current conformation and will return the strain energies.

MOLY minimizer: Strain energy due to bond lengths, bond angles, dihedral angles, unbonded atom overlap and hybrid strain are calculated. The MMP minimizer is a classical mechanical force field molecular model based on the model (reference 1 and 2 below):

E_total= E_bond+ E_angle + E_nonbonded + E_tor + E_hyb

The bond-length and bond angle strain terms are calculated using standard Hooke's law type functions. The default method of calculating unbonded strain is:

	n-1	n
E_unbonded =	S	S	14.68(d⁶) [i and j are not bonded]
	I=1	J=i+1

where d is the overlap = (radius of i + radius of j) - the distance from i to j))

A "6-12" Lennard-Jones potential function from MOLY can be used as an alternative to the above function:

	n-1	n
E_unbonded =	S	S	(B/d⁶ - A)/d⁶ + C/d [i and j are not bonded]
	I=1	J=i+1

d = distance between i and j)

A, B and C = constants for the combinations of atoms found in the file "LenJones.txt" in your MMP directory. The B term is usually larger than the square of the A term (H, H: A = 71.7, B = 6389). The C term is quite small in comparison (H, H: C = 0.0092). Atom types supported = H, C, N, O, F, P, S, Cl, Br, I -otherwise the default method is used.

The torsional function tries to stagger butane-type interactions, keep double bonds, amides and esters planar, allenes perpendicular etc. The hybridization term is used to keep strained carbonyls flat and to automatically increase the angle between the appendages of strained rings. This minimizer is a modification of the MOLY minimizer (1) which was itself a descendent of one developed by Wipke et.al. (2). The version presented here has been both simplified and added to, and programmed into new languages (Visual Basic and the Power Basic DLL Compiler). Minimization can take a while for very large molecules (several minutes to an hour). Minimization can be done with any of 4 starting energy gradients. The gradients are:

Make extreme changes: This should only be used when the starting geometry is nearly random. This gradient has the ability to change chirality of your molecules.
Make large changes: This option will greatly disturb the starting geometry. It will especially make larger changes to dihedral angles. It is very useful for a large ring made with the 2-D generic ring-maker. It can be less useful for small non-ring molecules, which should be nearly optimized when made with MMP. It will not rotate bonds 180 degrees though and distinguish between gauche and anti conformations. Exploring the effects of large bond rotations on strain energy should be done with the Conformational Analysis routine found under the Calculate menu.
Make Moderate changes: This is a good compromise for molecules with mostly correct starting geometry, but with perhaps one ring needing moderate tweaking.
Refine: Starts with the last stage of minimization and will more quickly minimize a molecule that starts with low energy. It does not change dihedral angles much.

An alternative minimization routine, "downhill simplex minimization" was added to address some problems with the MOLY minimizer. The MOLY minimizer uses the "steepest descent" method of minimization. This method does not always find local minima. The downhill simplex method has the reputation of being slow, but always finds a minimum. Using the downhill simplex method instead of the make Extreme, Large or Moderate changes options of MOLY seems to give better results most of the time. The terms used to calculate the energy are exactly the same ones used with MOLY with one exception. If you have more than one molecule then the electrostatic coulomb charge interactions between the atoms in the different molecules will also be calculated. This can be helpful in docking a molecule on the surface of another molecule.
Another new feature added with version 2 is the "approximate hydrogens" option. This option deletes the hydrogens from carbons and readjusts the van der Waal's radii of the carbons to account for the missing hydrogens. Using this option will speed up the minimization. After minimizing with this option you may want to add the hydrogens back, get them in a reasonable conformation, and use the Refine option to get the final molecular geometry.
You may also take into account electrostatic interaction and hydrogen bonding during minimization. The hydrogen bonding function is the same simple routine described in "Dock molecule with molecule" above. The electrostatic model is described above under "Conformational analysis". If using electrostatics, you must run CNDO first to get the charges. If you want to use the minimizer to dock a molecule on the surface of another molecule, setting the dielectric constant will change the effect of the electrostatics (the larger this number, the larger the effect: air = 1, water = 78.54 at 25 C).
If you own recent versions of the product "Chemsite" you can use the Chemsite Amber (4) minimizer from within MMP. Amber was designed to model biopolymers, so is fast with larger molecules. Chemsite also has a molecular dynamics routine that can be used iteratively with minimization to optimize geometry. When Chemisite is called from within MMP's minimization window, Chemsite will start with the molecule currently displayed in MMP, with the Amber minimizer running. Quitting Chemsite will cause the minimized geometry to be read into MMP, replacing whatever is in MMP at the time. This option will only work with Chemsite versions sold after May 15, 1996.

References:

1. T.M. Dyott, A.J. Stuper and G.S. Zander, 1980. "MOLY - an interactive system for molecular analysis", J. Chem. Inf. Comput. Sci., 20: 28-35.

2. Wipke, W.T., P. Gund, J.M. Verbalis and T.M. Dyott, Abstracts, 162nd National Meeting of the American Chemical Society, Washington D.C., Sept. 1971, No. ORGN-17.

3. Allinger, N.L. J. Am. Chem. Soc. 99:8127 (1977)(original MM2 paper)

4. Weiner, S.J. , P.A. Kollman, D.A. Case, U. C. Singh, C. Ghio, G. Alagona, S. Profeta, Jr. And P. Weiner, J. Am. Chem. Soc. 106: 765 (1984) abd S,H, Wuberm O,A, Jikknabm D,T, Nguyen and D.A. Case, J. Comp. Chem. 7:230 (1986)(Description of AMBER)

Conformational Analysis

The goal of conformational analysis is to find the low energy torsional angle of rotating bonds. Conformational analysis is half of the process of finding global minima. Molecular Mechanics Routines or MOPAC is the other half of the process. This can be an iterative process. For instance, MM2 could be used to turn a 2-D structure obtained from a 2-D drawing program into a 3-D structure. Then conformational analysis can be used to set the molecule in the likely global low energy conformation. Finally, MOPAC can be invoked to get the final optimized geometry.

How the program works: Conformational analysis is invoked from the Geometry menu. The user selects one or two bonds to rotate. The bonds will rotate and the strain energy due to non-bonded atom overlap, torsional barriers, Coulombic electrostatic charge interactions, and hydrogen bonding will be computed in user specified degree increments. The unbonded overlap is calculated by a Lennard-Jones 6-12 function or the MOLY minimizer unbonded strain term (see discussion on minimization for the formulas). The MOLY unbonded model, coupled with a dielectric constant of 1 seems to give better answers, but some readers will probably feel more comfortable using the familiar Lennard-Jones function. The Coulombic electrostatic charge interaction is calculated by Coulomb's law:

	n-1	n
E_charge= 332.17 (	S	S	[Q_iQ_j]/[D_ij d_ij])
	I=1	J=i+1

where Q is the partial charge, D the dielectric constant and d the distance between atoms i and j.

The dielectric constant can be set during the conformational analysis routine from within the conformational analysis window. The higher the dielectric constant, the stronger the electrostatic interactions (air = 1, water = 78.54). The simple hydrogen bonding function is calculated using a rather simple H-Bond algorithm:

E(hb)_ij = (R_ij¹⁰/d_ij¹⁰)((R_ij²/d_ij²) - 2)

where d = distance between i and j

R= optimum H bond distance between i and j

No account of H-bond angle is taken by this method (which in reality would play a part).

A list of the local minima (low energy conformations) will be displayed and a 2-D or 3-D graph of the results will follow. The list of minima is automatically output to a file (Confor.Out). This file will be erased and written over every time you do a conformational analysis. You can make a screen print of the graphs by selecting "Print molecule"and "Screen print" from the File menu. The program will also print to the screen a graph of dipole moment versus angle. With larger molecules, rotating 2 bonds may take as long as 1-4 hours to calculate if you use a low torsional angle increment (e.g. 5 degrees). The model used is a "rigid rotor" system. In rigid rotor systems, bond angles and bond lengths are not changed to minimize non-bonded atom overlaps. This will result in higher energy values for highly strained conformations than is found in nature. You can tell when this happens when peaks on the plots come to points instead of smooth curves. Hydrogen bonding energy will be underestimated by the simple Coulombic charge model. Torsional strain is only calculated for the rotating bonds. This means that the energy values will differ for the same conformation if you rotate different bonds, and that comparisons of energy values between different molecules will usually not be valid.

At the end of the routine, the molecule with the lowest conformational energy will we displayed. You may also choose to display up to 3 additional low energy confomers. If you wish to redisplay the molecule as it was before the conformational analysis, select the Undo menu item from the Edit menu.

Manual Geometry Adjustments

Invert

After selecting this item, click on the stereocenter that is to be changed. Two of the center's attached atoms will be inverted (positions exchanged).

Mirror

This causes the selected molecules mirror image to be substituted by changing the sign of the x coordinates.

Reference Bonds and Angles

Change bond length

After selecting this item, the user clicks (when prompted) on two atoms. The current bond length is displayed, and the user can type in a new length in the text box and hit OK, or cancel to keep the current value.

Change bond angle

After selecting this item, the user clicks (when prompted) on an atom. The current reference angle is displayed, and the user can type in a new angle in the text box and hit OK, or cancel to keep the current value. Reference angles and atoms can be found with the Geometry/Print bond lengths and angle option listed below.

Change torsional angle

After selecting this item, the user clicks (when prompted) on an atom. The current reference torsional angle is displayed, and the user can type in a new angle in the text box and hit OK, or cancel to keep the current value. Reference torsional angles and atoms can be found by selecting "Print bond lengths and angles" from the Geometry menu.

Hybridization

Make SP

After selecting this option, clicking on an atom with two attachments will cause it to change the reference bond angle of the second atom to 180 degrees.

Make SP2

Selecting this option, then clicking on an atom, will cause the second and third atoms attached to it to change to bond angles of 120 degrees with torsional angles of 180 and 0 degrees. It may not work for ring atoms (nothing may happen).

Make SP3

Selecting this option, then clicking on an atom, will cause the second, third and fourth atoms attached to it to change to bond angles of 109.5 degrees with torsional angles of 180, 60 and 300 degrees. It will not change angles if the attached atom is part of the same ring or fused ring system as the central atom.

Make center trigonal bipyrimid

Selecting this option, then clicking on an atom, will cause the second, third, and fourth atoms attached to it to change to bond angles of 90 degrees, with torsional angles of 180, 60 and 300 degrees, and cause the fifth attached atom to change to bond angle of 180 degrees.

2-D Geometry

Move atom

After selecting this item, the user clicks down on an atom, drags it with the mouse and releases the mouse button at the new location of the atom. This a 2-D drawing tool, which destroys the 3-D geometry of the molecule.

Move group

After selecting this item, the user clicks down on an atom, drags it with the mouse and releases the mouse button at the new location for the atom. Atoms attached to the moved atoms will move with it, with their old bond lengths and angles intact. This is a 2-D drawing tool, which destroys the 3-D geometry of the molecule. Non-ring atoms can be restored, sometimes, by clicking on Geometry/hybridization/ and selecting the appropriate hybridization for the reference atom for the selected atom (the reference atom is the attached atom which didn't move).

Make molecule 2-D

This routine will change the geometry of your molecule so that the molecule is drawn flat. Atoms connected to 4 other atoms, for instance, will have their bond angles and torsional angles changed to form a cross (90 degree bond angles). This is somewhat useful for clearly depicting all the atoms in a molecule, when they overlap or obscure each other. Changing the molecule back to 3-D can be laborious.

Convert 2-D to 3-D

This routine converts 2-D molecules to 3-D molecules by correcting the bond lengths and bond angles to standard 3-D values. Some atom overlap is possible, and minimization may be required to get an acceptable molecule. On occasion this routine has not worked properly and has resulted in poor molecular geometry. If you have any unsaved molecule you might want to save it before using this routine.

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