An Introduction to Computational Chemistry

1. Computational Chemistry CHM 425/525 Fall 2010 Dr. Martin An Introduction to Computational Chemistry

2. What is Computational Chemistry? • Use of computers to aid chemical inquiry, including, but not limited to: • Molecular Mechanics (Classical Newtonian Physics) • Semi-Empirical Molecular Orbital Theory • Ab Initio Molecular Orbital Theory • Density Functional Theory • Molecular Dynamics • Quantitative Structure-Activity Relationships • Graphical Representation of Structures/Properties

3. Levels of Calculation • Molecular mechanics...quick, simple; accuracy depends on parameterization. • Semi-empirical molecular orbital methods...computationally more demanding, but possible for moderate sized molecules, and generally more accurate. • Ab initio molecular orbital methods...much more demanding computationally, generally more accurate.

4. Levels of Calculation... • Density functional theory…more efficient and often more accurate than ab initio calc. • Molecular dynamics…solves Newton’s laws of motion for atoms on a potential energy surface; temperature dependent; can locate minimum energy conformations. • QSAR…used to predict properties of new structures or predict structures that should have certain properties (e.g., drugs)

5. Relative Computational “Cost” • Molecular mechanics...cpu time scales as square of the number of atoms... • Calculations can be performed on a compound of ~MW 300 in a minute on a pc, or in a few seconds on a parallel computer. • This means that larger molecules (even large peptides) and be modeled by MM methods.

6. Relative Computation “Cost” • Semi-empirical and ab initio molecular orbital methods...cpu time scales as the third or fourth power of the number of atomicorbitals (basis functions) in the basis set. • Semi-empirical calculations on ~MW 300 compound take a few minutes on a pc, seconds on a parallel computer (cluster).

7. Molecular Mechanics • Employs classical (Newtonian) physics • Assumes Hooke’s Law forces between atoms (like a spring between two masses) Estretch = ks (l - lo)2 graph: C-C; C=O

8. Molecular Mechanics... • Similar calculations for other deviations from “normal” geometry (bond angles, dihedral angles) • Based on simple, empirically derived relationships between energy and bond angles, dihedral angles, and distances • Ignores electrons and effect of p systems! • Very simple, yet gives quite reasonable, though limited results, all things considered.

9. Properties calculated by MM: • “Steric” or Total energy = sum of various artificial energy components, depending on the program...not a “real” measurable energy. • Enthalpy of Formation (sometimes) • Dipole Moment • Geometry (bond lengths, bond angles, dihedral angles) of lowest energy conformation.

10. Molecular Mechanics Forcefields • MM2, MM3 (Allinger) • MMX (Gilbert, in PCModel) • MM+ (HyperChem’s version of MM2) • MMFF (Merck Pharm.) • Amber (Kollman) • OPLS (Jorgensen) • BIO+ (Karplus, part of CHARMm) • (others)

11. Semi-Empirical Molecular Orbital Theory • Uses simplifications of the Schrödinger equation to estimate the energy of a system (molecule) as a function of the geometry and electronic distribution. • The simplifications require empirically derived (not theoretical) parameters (or fudge factors) to allow calculated values to agree with observed values.

12. Properties calculated by molecular orbital methods: • Energy (enthalpy of formation) • Dipole moment • Orbital energy levels (HOMO, LUMO, others) • Electron distribution (electron density) • Electrostatic potential • Vibrational frequencies (IR spectra)

13. Properties calculated by molecular orbital methods... • HOMO energy (Ionization energy) • LUMO energy (electron affinity) • UV-Vis spectra (HOMO-LUMO gap) • Acidity & Basicity (proton affinity) • NMR chemical shifts and coupling constants • others

14. Semi-Empirical MO Theory Types • Hückel (treats p electrons only) • CNDO, INDO, ZINDO • MINDO/3 • MNDO • AM1, PM3 (currently most widely used) Collections of these are found in AMPAC, MOPAC, HyperChem, Spartan, Titan, etc.

15. Ab Initio Molecular Orbital Theory • Uses essentially the same (Schrödinger) equation as semi-empirical MO calculation • Introduces fewer approximations, therefore needs fewer parameters (“fudge factors”) • Is more “pure” in relation to theory; if theory is correct, should give more accurate result. • Takes more cpu time because there are fewer approximations.

16. Variations of Ab Initio Theory • HF (Hartree-Fock) • electron experiences a ‘sea’ of other electrons • Moller-Plesset perturbation theory • includes some electron correlation; MP2, MP3 • Configuration Interaction • QCISD, QCSID(T) • All of the above involve choices of basis sets: • STO-3G, 3-21G, 6-31+G, 6-311G**, etc. (many)

17. Basis Sets • STO-3G (Slater-type orbitals approximated by 3 Gaussian functions)

18. Split Basis Sets... Use two sizes of Gaussian functions to approximate orbitals: • 3-21, 6-31, 6-311 (large and small orbitals) • additional features which can be added to any basis set: • polarization functions (mixes d,p with p,s orbitals) • e.g., 6-31G** [= 6-31G(d,p)] • diffuse functions + (allows for distant interactions)

19. Molecular Geometry • Molecular geometry can be described by three measurements: • bond length (l) • bond angle (a) • dihedral angle (q)

20. Bond length • Distance between nuclei of adjacent atoms that are covalently bonded (can also describe distance between non-covalently bonded, or non-bonded atoms) • But atoms are in constant motion, even at absolute zero! How do we define the “distance” between them?

21. Measurements of bond length • X-ray crystallography • distances in crystalline solid; only ‘heavy’ atoms • geometry may differ from solution phase • Gas Phase electron diffraction • weighted average distances in gas phase • not a single conformation; solvent effects ignored • Neutron diffraction • only heavy atoms included

22. Equilibrium bond length • Molecules exist in an ensemble of energy states which depends on T. • Several vibrational and rotational states are populated for each electronic state. • Geometry optimization computations determine the equilibrium bond length.

23. Units of Measurement • Bond lengths are usually reported in Angstroms (1Å = 10-10 m = 100 pm); this is not an SI unit, but it is convenient because most bond lengths are of 1 to 2 Å. • Angles are measured in degrees. • Potential energy is usually measured in kcal/mol (1 kcal/mol = 4.184 kJ/mol).

24. Some Applications... • Calculation of reaction pathways & energies • Determination of reaction intermediates and transition structures • Visualization of orbital interactions (forming and breaking bonds as a reaction proceeds) • Shapes of molecules, including large biomolecules • Prediction of molecular properties

25. …more Applications • QSAR (Quantitative Structure-Activity Relationships) • Remote interactions (those beyond normal covalent bonding distance) • Docking (interaction of molecules, such as pharmaceuticals with biomolecules) • NMR chemical shift prediction

26. Modeling Charge-Transfer Complexation of Amines with Singlet Oxygen N-O “bond” distance = 1.55 Å DqN = +0.35esu DqOdistal = -0.33 esu

27. Modeling Aggregation Effects on NMR Spectra • N-Phenylpyrrole has a concentration-dependent NMR spectrum, in which the protons are shifted upfield (shielded) at higher concentrations. • We hypothesized that aggregation was responsible.

28. Modeling Aggregation Effects on NMR Spectra... Two monomers were modeled in different positions parallel to one another, and the energy was plotted vs. X and Y. The NMR of the minimum complex was calculated.

29. Orbital Perturbations • Proximity of orbitals results in perturbation. • This shows methane with one H 2.0Å above the middle of the p bond of ethene • This leads to alterations in the magnetic field, which affects the NMR chemical shift

30. Magnetic Shielding Surfaces