Molecular Mechanics Part 2

Potential Energy Surfaces Input File Types Successes, Limitations & Caveats Glossary of Terms

Energy MinimizationEnergy Minimization

Local minimum vs global minimum Many local minima; only ONE global minimum Methods: Newton-Raphson (block diagonal),

steepest descent, conjugate gradient, others.

global minimumglobal minimum

Potential Energy SurfacePotential Energy Surface

minimum

maximasaddle point

Extrema (stationary points, where the gradient is zero):

PES and Energy MinimizationPES 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.

Approaches to Global MinimumApproaches to Global Minimum

Dihedral driving (manual or automated; 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!

Input File StructureInput 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.

PDB (protein data bank) file of propane (C3H8)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)

…bottom of .PDB file…bottom of .PDB file

CONECT 1 2 4 5 11CONECT 2 1 3 6 7CONECT 3 2 8 9 10CONECT 4 1CONECT 5 1CONECT 6 2CONECT 7 2CONECT 8 3CONECT 9 3CONECT 10 3CONECT 11 1END

Cartesian coordinate (XYZ) fileCartesian 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)

Internal Coordinates (for NH3)Internal Coordinates (for NH3)

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)

(sometimes called Z-matrix)

File Interconversion MethodsFile 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) -> Alchemy2000 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

Uses of “Steric Energy”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).

Successes of Molecular Mechanics CalculationsSuccesses 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.

Successes of Molecular Mechanics...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).

Limitations of Molecular MechanicsLimitations 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 electron systems

Only ground states are considered...not T.S. or *

MM2 Atom Types (more than 60!)MM2 Atom Types (more than 60!)

1 C sp3 carbon2 C sp2 carbon (C=C)3 C sp2 carbon (C=O)4 C sp carbon5 H hydrogen (see others)6 O oxygen (single

bonded)7 O oxygen (double

bonded)8 N sp3 nitrogen9 N sp2 nitrogen10 N sp nitrogen11 F fluorine12 Cl chlorine

13 Br bromine14 I iodine15 S sulfide (-S-)16 S+ sulfonium17 S sulfoxide (use S=O)18 S sulfone (use two S=O)19 Si silane20 LP lone pair of electrons21 H hydroxyl hydrogen22 C cyclopropane carbon23 H amine hydrogen24 H carboxylic acid

hydrogen

Uses of Molecular MechanicsUses 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).

Caveats about Minimum Energy StructuresCaveats 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).

Molecular Mechanics GlossaryMolecular Mechanics Glossary

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

Glossary...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.