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

DFTB Energy Functional

SCC-DFTB Energy Functional

Class II Partial Charges (Population Analysis) Mulliken Löwdin

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, x = 3, Winget et al. J. Phys. Chem. A 2002, 106, Thompson et al. J. Comput. Chem. 2003, 24, 1291

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

Performance Example

Performance Example 2

Accurate, Density, and CM3 Dipole Moments 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

Accurate, Density, and CM3 Dipole Moments dimethylnitramine MUE (density) = 0.49 debyes MUE (CM3) = 0.12 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error:

Accurate, Density, and CM3 Dipole Moments : RDX MUE (density) = 0.86 debyes MUE (CM3) = 0.19 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error;

Accurate, Density, and CM3 Dipole Moments : HNIW; CL-20 MUE (density) = 0.32 debyes MUE (CM3) = 0.29 debyes Accurate: mPW1PW91/MG3S density dipole  MUE  mean unsigned error: [hexa-nitrohexaaza-iso-wurtzitane]

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

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

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

SCC-DFTB Results — After

CM3 Improvement + Mulliken o CM3

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

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

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

[HGaNH] n Is a Mixture of Nanorods Kormos et al. JACS, 2005, 127, 1493 nGaNGeC Dipole moment (D)

Error compared to DFT and MP2 Data set included small molecules containing Ga, N, and H atoms B3LYP and MP2 with 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

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

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