1. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 1 East Carolina University Density Functional Theory In Chemistry An alternate formulation of Schrödinger’s Theory http://www.ecu.edu/cacs/lectures/uncw_2006.ppt

2. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 2 East Carolina University In Density Functional Theory, the electron density is the quantity of interest. In Wavefunction Functional Theory, the wave function is the quantity of interest. Very Good Reference: R.G. Parr and W. Yang, Density-Functional Theory, (Oxford Press, 1989).

3. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 3 East Carolina University Density Functional Theory (Hohenberg-Kohn 1964) The ground state energy E of an N-electron system is a functional of the electronic density  and it is a minimum when evaluated with the exact ground state density. Minimize E[ , ] with respect to variations in  subject to the constraint of charge conservation, N=   d   { E[ , ] -    d  } = 0 The resulting Euler-Lagrange equation is  E /   = 

4. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 4 East Carolina University

5. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 5 East Carolina University

6. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 6 East Carolina University

7. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 7 East Carolina University

8. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 8 East Carolina University Fukui Function as finite difference

9. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 9 East Carolina University

10. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 10 East Carolina University

11. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 11 East Carolina University

12. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 12 East Carolina University

13. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 13 East Carolina University

14. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 14 East Carolina University Electron Localization Function

15. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 15 East Carolina University

16. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 16 East Carolina University ELF for CH 3 CH 3

17. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 17 East Carolina University ELF for H 2 CO

18. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 18 East Carolina University Fate of atmospheric toulene

19. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 19 East Carolina University

20. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 20 East Carolina University

21. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 21 East Carolina University

22. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 22 East Carolina University Climbing-Image Nudged Elastic Band

23. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 23 East Carolina University

24. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 24 East Carolina University

25. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 25 East Carolina University

26. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 26 East Carolina University

27. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 27 East Carolina University

28. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 28 East Carolina University Interior Exterior

29. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 29 East Carolina University Low-energy electron emission from condensed-phase targets induced by fast protons, SF 6 absorbed on copper surface

30. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 30 East Carolina University SF 6 on a copper surface

31. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 31 East Carolina University

32. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 32 East Carolina University W 2 (hpp) 4, hpp is the anion of 1,3,4,6,7,8- hexahydro-2H-pyrimido[1,2-a]pyrimidine.

33. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 33 East Carolina University

34. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 34 East Carolina University Biological sulfate

35. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 35 East Carolina University

36. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 36 East Carolina University Scorpion toxin from the Brazilian scorpion, Tityus serrulatus KEGYLMDHEGCKLSCFIRPSGYCGRECGIKKG SSGYCAWPACYCYGLPNWVKVWDRATNKC

37. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 37 East Carolina University

38. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 38 East Carolina University

39. Computational Chemistry at ECU Lee Bartolotti bartolotttil@ecu.edu 39 East Carolina University www.ecu.edu/cacs