1. Molecular force field Lecture 3 – 4. October 2010

2. Molecular force field • What is a force field? • Based on QM and experimental data • Additive and non-additive (polarizable forcefields) • Components of intra- and inter molecular forces • Polarizable force fields • Optimization parameters • An iterative approach to obtain self-consistent inter- and intramolecular parameters • Analogy and experimentally optimized parameters

3. Specialized force fields • Most force fields are specialized e.g.: • CHARMM – biomolecules • OPLS – mostly proteins and organic liquids • AMBER – proteins and DNA • GROMOS – biomolecular systems

4. Molecular force field • A molecular force field is a potential function • Geometric representation of a system • Born-Oppenheimer approximation makes it possible to use nuclei as coordinates • Formulas based on QM and experimental data • Calculates the total energy of a system and minimizes it with respect to the atomic coordinates.

5. Additive force fields • Total energy is a sum of: • Intramolecular: • Bond lengths • Angle bending • Bond rotation (torsion) • Intermolecular • Non-bonded interactions

6. Additive force fields • Bond stretching energy:

7. Additive force fields • Intramolecular standard terms:

8. Additive force fields • Intermolecular terms

9. Additive force fields • Different force fields uses different additional terms • CHARMm uses an improper torsion term: • AMBER uses an explicit terms for hydrogen bonds

10. Polarizable force fields • Additive force fields use only point charges • The electron distribution changes however as a function of the surrounding electrostatic field • Compensation by enhancing atomic charges • Works well in most cases • Most critical in active sites

11. Polarizable force fields • Polarizable force fields are still under development • Methods to include electronic polarization in force fields • Self-consistent field calculation and Matrix diagonalization mostly gives a too high computational demand • Fluctuating charge • Induced dipoles

12. Polarizable force fields • Fluctuating charge model • Based on the movement of charge between bonded atoms in response to the surrounding electrostatic field Electronegativities Hardness of bonded atom

13. Polarizable force fields • Induced Dipole Model • Apoint dipole is induced at each contributing center in response to the total electric field: Ei0 is the field due to the permanent atomic charges Eiinduced is the field due to the (other) induced dipoles αiis the polarizability of atom

14. Optimization parameters • The parameters of a force field are the constants of the used formulas that must be optimized whenever a new molecule is introduced. • The intermolecular and intramolecular parameters are coupled • An iterative approach is required to obtain self-consistent parameters • Optimization of intramolecular parameters • ->Optimization of intermolecular parameters • ->Intramolecular parameters rechecked • Typically, this only requires one or two iterations, but it may be more with highly flexible molecules.

15. Optimization parameters

16. Optimization parameters • Using analogy or experimental values to optimize parameters • Structure analogy • Identify internal parameters to be optimized • Optimize only new parameters!

17. Optimization parameters • Optimization of intermolecular parameters using experimental or QM values: • Local/Small Molecule • Interaction enthalpies (MassSpec) • Interaction geometries (microwave, crystal) • Dipole moments • QM • Global/condensed phase • Pure solvents (heats of vaporization, density, heat capacity, isocompressibility) • Aqueous solution (heats/free energies of solution, partial molar volumes) • Crystals (heats of sublimation, lattice parameters, interaction geometries)

18. Optimization parameters • Optimization of intramolecular parameters: • For most drug molecules the amount of experimental data is minimal, requiring the use of QM data • Geometries (equilibrium values) • Microwave, electron diffraction, ab initio, small molecule x-ray crystallography (CSD), crystal surveys of geometries • Vibrational spectra (force constants) • Infrared, raman, ab initio • Conformational energies (force constants) • Microwave, ab initio