Molecular Mechanics Part 2

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 1 C 1 -1.129 1.281 -0.000
• HETATM 2 C 2 -2.558 1.772 -0.000
• HETATM 3 C 3 -3.519 0.606 -0.000
• HETATM 4 H 4 -0.596 1.637 0.890
• HETATM 5 H 5 -0.596 1.637 -0.890
• HETATM 6 H 6 -2.733 2.392 0.890
• HETATM 7 H 7 -2.733 2.392 -0.890
• HETATM 8 H 8 -4.558 0.952 0.000
• HETATM 9 H 9 -3.359 -0.017 -0.890
• HETATM 10 H 10 -3.359 -0.017 0.890
• HETATM 11 H 11 -1.110 0.183 -0.000
  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
• CONECT 3 2 8 9 10
• CONECT 4 1
• CONECT 5 1
• CONECT 6 2
• CONECT 7 2
• CONECT 8 3
• CONECT 9 3
• CONECT 10 3
• CONECT 11 1
• END

9
Cartesian coordinate (XYZ) file

• C 1 -1.129 1.281 -0.000
• C 2 -2.558 1.772 -0.000
• C 3 -3.519 0.606 -0.000
• H 4 -0.596 1.637 0.890
• H 5 -0.596 1.637 -0.890
• H 6 -2.733 2.392 0.890
• H 7 -2.733 2.392 -0.890
• H 8 -4.558 0.952 0.000
• H 9 -3.359 -0.017 -0.890
• H 10 -3.359 -0.017 0.890
• H 11 -1.110 0.183 -0.000
• (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 0.0000 0 0.0000 0 0.0000
  0 0 0 0
• H 1.0200 1 0.0000 0 0.0000
  0 1 0 0
• H 1.0200 1 104.5368 1 0.0000 0
  1 2 0
• H 1.0200 1 104.5368 1 109.5796 1
  1 2 3
• 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) -gt HyperChem (.pdb .ent) -gt
  (save as .hin) -gt Alchemy2000 or
• Titan (.pdb) -gt 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 (CC)
• 3 C sp2 carbon (CO)
• 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 SO)
• 18 S sulfone (use two SO)
• 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 (Hookes Law)
• non-bonded (VdW) interactions
• conformational search
• atom type
• cutoff (e.g., for van der Waals interactions)
• dielectric constant permitivity of free space.