1. Molecular Mechanics Part 2
Potential Energy Surfaces
Input File Types
Successes, Limitations & Caveats
Glossary of Terms

2. Energy Minimization Local minimum vs global minimum
Many local minima; only ONE global minimum
Methods: Newton-Raphson (block diagonal), steepest descent, conjugate gradient, others.
global minimum

3. Potential Energy Surface
Extrema (stationary points, where the gradient is zero):
maxima
saddle point
minimum

4. PES and Energy Minimization
First, some caveats:
extrema (stationary points) are located by most methods; this includes maxima, minima, and saddle points.
among the minima, local minima are found, not necessarily the global minimum.
with shallow minima (flat PES), a lot of cpu time can be spent seeking the lowest energy structure.

5. Approaches to Global Minimum
Dihedral driving (manual or automated; a 3n)
Randomization-minimization (Monte Carlo)
Molecular dynamics
Trial & error (poor)
All methods are tedious, but some attempt at searching for the minimum is absolutely necessary if the result is to be meaningful!

6. Input File Structure
Input is usually done graphically (by sketching or building structures atom-by-atom or by assembling component parts).
This graphical model is converted to a mathematical model by the software.
Each software package has its own file type, but most have some common features.
The .pdb file is most common denominator.

7. PDB (protein data bank) file of propane (C3H8)
HETATM C
HETATM C
HETATM C
HETATM H
HETATM H
HETATM H
HETATM H
HETATM H
HETATM H
HETATM H
HETATM H continued...
(not all columns utilized/recognized by all software)

8. …bottom of .PDB file CONECT 1 2 4 5 11 CONECT 2 1 3 6 7
END

9. Cartesian coordinate (XYZ) fileH H H H H H H H
(this MAY be the same as the .PDB file, as shown here, or the orientation of the molecule may be different, making the numbers different)

10. Internal Coordinates (for NH3)
(sometimes called Z-matrix)
distance angle dihedral ref. atom # N H H H
0 (end of file)
(1 means optimize, 0 means keep constant, -1 means vary according to a designated pattern)

11. File Interconversion Methods
Many modeling programs will read and write several file types (Titan, Alchemy2000 and HyperChem will read and write .pdb files, but with slightly different formats
Titan (.pdb) -> HyperChem (.pdb = .ent) -> (save as .hin) -> Alchemy or
Titan (.pdb) -> WebLabViewer (to visualize, copy into MS.doc for lab reports)
Conversion programs exist: most common is BABEL
Gaussian 03, which we will use for ab initio calculations, has a conversion utility called newzmat

12. Uses of “Steric Energy”
“Steric energy” has NO physical meaning, and it is defined differently in different programs
Therefore it CAN NOT be used to compare structures calculated by different programs
Its use is limited to comparing ISOMERIC structures having the SAME number and kinds of bonds (conformers, stereoisomers).

13. Successes of Molecular Mechanics Calculations
Calculations are very fast
Geometry optimizations of small to medium- size molecules can be accomplished on a pc
Conformations of macromolecules (including biomacromolecules such as peptides and polysaccharides) can be calculated using workstations or parallel processing computers.

14. Successes of Molecular Mechanics...
Reasonable geometries are usually obtained:
Bond lengths within 0.1 Angstrom of experimental values
Bond angles within 2° of experimental values.
Calculated energies are usually quite good:
Enthalpies of formation within 2 kcal/mol (8 kJ/mol) of experimental values
Provides input structure for more involved calculations (molecular orbital methods).

15. Limitations of Molecular Mechanics
The calculations do not account for electrons! Orbital interactions are ignored!
The selection of “atom type” is crucial to the computational result:
e.g., AMBER has 5 types of Oxygen: carbonyl , alcohol, acid, ester/ether, water (see next slide)
No consideration is given to the importance of delocalized p electron systems
Only ground states are considered...not T.S. or *

16. MM2 Atom Types (more than 60!)
1 C sp3 carbon
2 C sp2 carbon (C=C)
3 C sp2 carbon (C=O)
4 C sp carbon
5 H hydrogen (see others)
6 O oxygen (single bonded)
7 O oxygen (double bonded)
8 N sp3 nitrogen
9 N sp2 nitrogen
10 N sp nitrogen
11 F fluorine
12 Cl chlorine
13 Br bromine
14 I iodine
15 S sulfide (-S-)
16 S+ sulfonium
17 S sulfoxide (use S=O)
18 S sulfone (use two S=O)
19 Si silane
20 LP lone pair of electrons
21 H hydroxyl hydrogen
22 C cyclopropane carbon
23 H amine hydrogen
24 H carboxylic acid hydrogen

17. Uses of Molecular Mechanics
Obtaining a reasonably good geometry (in structures where pi electrons are not involved.
As a starting point for further calculations, such as semi-empirical, ab initio, or density functional.
Searching the potential energy surface for minimum energy conformations (it is usually too expensive to do this using MO methods).

18. Caveats about Minimum Energy Structures
What does the global minimum energy structure mean?
Does reaction/interaction of interest necessarily occur via the lowest energy conformation?
What other low energy conformations are available? (Boltzmann distribution and probability/entropy considerations may be important).

19. Molecular Mechanics Glossary
energy minimization, geometry optimization
potential energy surface
gradient
global vs. local minimum
force field
steric energy
bond length
bond angle

20. Glossary... dihedral (torsional) angle
harmonic oscillator (Hooke’s Law)
non-bonded (VdW) interactions
conformational search
atom type
cutoff (e.g., for van der Waals interactions)
dielectric constant; permitivity of free space.