Computation and computational thinking in Chemistry

1. Computation and computational thinkingin Chemistry Paul Madden School of Chemistry

2. The “plan” • My interest – atomistic, predictive calculations of the properties of materials • Energy minimization – optimization ideas • Cutting out the computer – application of optimization strategies in synthesis

3. numerous technologies benefit from the capability to model thermodynamic and transport properties accurately & reliably - +

4. Pyroprocessing of Nuclear Waste LiCl/KCl “solvent” – now fluorides More principles: Are the (continuum) models of transport adequate representations of reality?

5. Why simulate?: interpretation/visualization provide data not obtainable by experiment answer problems of principle, test theory

6. Molecular Dynamics simulation: Follow trajectory of interacting atoms r Newton’s Laws of Motion

8. Molecular Dynamics simulation: Follow trajectory of interacting atoms r Newton’s Laws of Motion Need a “Law of Force” – sometimes “pairwise additive” (like gravitation F ∞ 1/ r 2)

9. Electron Densities and the “Force Laws” - + Ionic, Non-bonding Covalent Overlap of two spherical, non-bonding charge densities

10. Electron Densities and the “Force Laws” - + Ionic, Non-bonding Covalent Overlap of two spherical, non-bonding charge densities A stiff spring between bonded atoms Can model the dependence on interatomic separation

11. because of the simplicity of these force laws can model (atomistically) molecular materials of great complexity Phospholipid Cell membrane Can visualise (qualitatively)

12. Ion permeation through α-haemolysin "These movies were made by Dr. Aleksei Aksimentiev using VMD and are owned by the Theoretical and Computational Biophysics Group, NIH Resource for Macromolecular Modeling and Bioinformatics, at the Beckman Institute, University of Illinois at Urbana-Champaign."

13. Electron Densities and the “Force Laws” - + Ionic, Non-bonding Covalent Overlap of two spherical, non-bonding charge densities Now “easily” manipulated by chemistry (200 years) Control the “liaisons” affected by thermal motion

14. Inhibition of Cyclin Dependent Kinases (CDKs) CDK2 is involved in DNA replication It is overexpressed in cancer cells, => Find inhibitors CDK2 ATP binding pocket

15. Inhibition of Cyclin Dependent Kinases (CDKs) NU2058 NU6102 9d-NU6027 NU6027 ATP Staurosporine SU9516

16. Inhibition of Cyclin Dependent Kinases (CDKs) CDK2 is involved in DNA replication It is overexpressed in cancer cells, => Find inhibitors CDK2 ATP binding pocket

17. MD simulation: Follow trajectory of interacting atoms r Newton’s Laws of Motion Need a “Law of Force” – sometimes pairwise additive – and this makes large-scale possible But, this only works if the electrons are moving “trivially” with nucleii

18. Interatomic interactions mediated by local electron density generally, this depends on instantaneous coordination environment Electron density for a self-interstitial in Aluminium

19. Interatomic interactions mediated by local electron density generally, this depends on instantaneous coordination environment Electron density for a self-interstitial in Aluminium Can obtain the forces direct from an electronic structure calculation “First-Principles” Such calculations can give accurate binding energies (v.i.)

20. Interatomic interactions mediated by local electron density generally, this depends on instantaneous coordination environment Electron density for a self-interstitial in Aluminium Can obtain the forces direct from an electronic structure calculation (on-the-fly) Additional benefit: obtain the electronic structure

21. E.g: mechanism of oxidation of a silicon surface (M. Payne)

23. The ab initio MD methods are general and particularly useful when covalent bonds are broken and formed But they are very expensive, meaning that many issues, requiring large simulations or long runs, are out of reach

24. Why simulate?: interpretation/visualization provide data not obtainable by experiment answer problems of principle, test theory i.e. quantitative, realistic modelling

25. Properties of materials under extreme conditions

26. Mineralogy of the earth’s interior

27. Phase diagram of H2O -- or is it?? 1 GPa = 10,000 atmospheres!!

28. Direct coexistence simulation – to obtain melting temperature Determine T & P at which equilibrated solid and liquid

29. Size Matters: Gillan, Alfè

30. The ab initio MD methods are general and particularly useful when covalent bonds are broken and formed But they are very expensive, meaning that many issues are out of reach Maybe we can use simpler representation of electronic structure in some cases

31. The ab initio MD methods are general and particularly useful when covalent bonds are broken and formed But they are very expensive, meaning that many issues are out of reach Maybe we can use simpler representation of electronic structure in some cases e.g. in ionic materials simple force laws do not work quantitatively

32. Maybe in “ionic” materials: Electron density in an AlF3 crystal Ions are not spherical – they are deformed in this environment Incorporate such ideas into interaction potential and parameterize A-I Multiscale modelling

33. Direct coexistence simulation to determine the melting temperature of MgO Determine T & P at which equilibration occurs

34. Melting curve of MgO ab initio model

36. Many problems may be regarded as optimization e.g. lowest energy structures of a cluster or a crystal = = + +

37. Finding a global minimum may be easy, or hard Energy Landscape concept

38. = + + For “hard” problems non-minimization strategies, such as “genetic algorithms” have been adopted

39. Structures of virus capsids Hard for minimization

40. Genetic algorithm Parents 110001101001001001110 00110110101101011100 Crossover 1100011010010 1001110 1011100 0011011010110 Offspring mutation “fitness” Start with a population of “parents” and evolve successive generations, by stochastically selecting moves, to improve fitness

41. Representation of problems within GA paradigm

42. Folding a protein, which should be “hard”, must actually be easy (for nature – simulated annealing works!).

43. Primary Structure: Sequence • The primary structure of a protein is the amino acid sequence Typical protein will contain ~ 200 links

44. Tertiary Structure: A Protein Fold Proteins only work when properly folded

45. Primary Structure: Sequence • Twenty different amino acids have distinct shapes and properties

46. Secondary Structure: , , & loops •  helices and  sheets are stabilized by hydrogen bonds between backbone oxygen and hydrogen atoms

47. Tertiary Structure: A Protein Fold

48. Levinthal paradox, 1968 • A polypeptide chain of 100 residues (amino acids) • Each residue has only 2 possible configurations • 2^100~10^30 configurations • 10^-11 second is required to convert one to another • 10^19 seconds ~10^11years! • Doubling time for a bacteria is <30 minutes • Molten globule (microsecond ~ millisecond) • Native state (millisecond ~ seconds)

49. Idea of a folding “funnel”

50. “Foldability” must be encoded in the amino acid sequence