1. CMx Charges for SCC-DFTB and Some GaN Vignettes Christopher J. Cramer University of Minnesota

2. DFTB Energy Functional

3. SCC-DFTB Energy Functional

4. Class II Partial Charges (Population Analysis) Mulliken Löwdin

5. Class IV Partial Charges (CM2 and CM3) Mayer bond order empirical linear and quadratic parameters x = 2, Li et al. J. Phys. Chem. A, 1998, 102, 1820. x = 3, Winget et al. J. Phys. Chem. A 2002, 106, 10707 Thompson et al. J. Comput. Chem. 2003, 24, 1291

6. Training Set and Error Functions Training set roughly 400 neutral and 25 ionic molecules Compare point-charge derived dipole moments to experimental values For ions, compare point-charge-derived moments to (MP2/cc-pVTZ, center of mass) and compare partial atomic charges to those determined from CHELPG fit to MP2/cc-pVTZ electrostatic potential

7. Performance Example

8. Performance Example 2

9. Accurate, Density, and CM3 Dipole Moments 3.94 3.59 3.84 4.31 3.93 4.19 2.97 2.71 2.89 3.28 3.07 3.27 nitramide MUE (density) = 0.30 debyes MUE (CM3) = 0.08 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error: C s C 2v from mPW0/MIDI! Approximate dipoles

10. Accurate, Density, and CM3 Dipole Moments 4.81 4.21 4.67 5.04 4.43 4.87 3.43 2.99 3.33 3.69 3.38 3.77 dimethylnitramine MUE (density) = 0.49 debyes MUE (CM3) = 0.12 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error:

11. Accurate, Density, and CM3 Dipole Moments 5.97 5.22 6.20 7.19 6.22 7.34 : RDX MUE (density) = 0.86 debyes MUE (CM3) = 0.19 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error;

12. Accurate, Density, and CM3 Dipole Moments 1.56 1.32 1.80 0.31 0.42 0.79 : HNIW; CL-20 MUE (density) = 0.32 debyes MUE (CM3) = 0.29 debyes Accurate: mPW1PW91/MG3S density dipole 2.56 1.95 2.41  MUE  mean unsigned error: [hexa-nitrohexaaza-iso-wurtzitane]

13. CM3 Delivers Consistent Partial Atomic Charges Polarization energies (in nitromethane) calculated using different charge schemes by wave function (kcal/mole): MUD (CM3) = 0.1 MUD (ChElPG) = 5.7 All 14 nitramines (0.2) (2.8) MUD (Löwdin) = 5.9 (2.9) MUD  mean unsigned deviation: electrostatic fitting population analysis

14. SCC-DFTB Results — Before Signed errors O(0.4 D), RMSE O(0.7 D)

15. Optimized Parameters (Mulliken mapping) Linear (in B.O.) parameters quadratic parameters

16. SCC-DFTB Results — After

17. CM3 Improvement + Mulliken o CM3

18. Gallium Nitride from Cyclotrigallazane Kormos et al. JACS, 2005, 127, 1493 NH 3 150° C [HGaNH] n GaN substantial cubic form in addition to wurtzite

19. What is Nature of [HGaNH] n ? Kormos et al. JPC A, 2006, 110, 494

20. What is Nature of [HGaNH] n ? Kormos et al. JPC A, 2006, 110, 494

21. [HGaNH] n Is a Mixture of Nanorods Kormos et al. JACS, 2005, 127, 1493 nGaNGeC 12.71.0 29.01.1 315.50.9 423.00.5 531.30.1 640.3-0.4 749.7-0.9 859.4-1.5 969.3-2.1 Dipole moment (D)

22. Error compared to DFT and MP2 Data set included small molecules containing Ga, N, and H atoms B3LYP and MP2 with 6-311+G(2df, p) basis set on N and H and CEP-31G ECP and basis set on Ga Data set included six dimers for binding energies and intermolecular distances, seven reaction energies, and nine molecules for bond lengths and angles

23. [H 2 GaNH 2 ] 3 Binding Energy and Rod Growth Dimer A

24. Future Plans Reparameterize SCC-DFTB to get better agreement with higher levels of theory –Hardness was not found to have sufficient influence –Reoptimize E rep to B3LYP data Add empirical dispersion term to get better binding energies and distances