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Molecular Mechanics Part 2

Molecular Mechanics Part 2. Potential Energy Surfaces Input File Types Successes, Limitations & Caveats Glossary of Terms. Energy Minimization. Local minimum vs global minimum Many local minima; only ONE global minimum

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Molecular Mechanics Part 2

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  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) 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)

  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)-> 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

  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. 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 spnitrogen 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 MM2 Atom Types (more than 60!)

  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.

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