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CM x 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). L öwdin. Mulliken. Class IV Partial Charges (CM2 and CM3). Mayer bond order. empirical
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CMx Charges for SCC-DFTB and Some GaN Vignettes Christopher J. Cramer University of Minnesota
Class II Partial Charges (Population Analysis) Löwdin Mulliken
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. A2002, 106, 10707 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
Accurate, Density, andCM3Dipole Moments nitramide Cs C2v Cs C2v 3.94 3.59 3.84 4.31 3.93 4.19 2.97 2.712.89 3.28 3.07 3.27 Accurate: mPW0/MG3S density dipole Approximate dipoles MUE mean unsigned error: MUE (density) = 0.30 debyes MUE (CM3) = 0.08 debyes from mPW0/MIDI!
Accurate, Density, andCM3Dipole Moments dimethylnitramine 4.81 4.21 4.67 5.04 4.43 4.87 3.43 2.99 3.33 3.69 3.38 3.77 MUE mean unsigned error: MUE (density) = 0.49 debyes MUE (CM3) = 0.12 debyes Accurate: mPW0/MG3S density dipole
Accurate, Density, andCM3Dipole Moments : RDX 5.97 5.22 6.20 7.19 6.22 7.34 MUE mean unsigned error; MUE (density) = 0.86 debyes MUE (CM3) = 0.19 debyes Accurate: mPW0/MG3S density dipole
Accurate, Density, andCM3Dipole Moments : HNIW; CL-20 [hexa-nitrohexaaza-iso-wurtzitane] 1.56 1.32 1.80 0.31 0.42 0.79 2.56 1.95 2.41 MUE mean unsigned error: MUE (density) = 0.32 debyes MUE (CM3) = 0.29 debyes Accurate: mPW1PW91/MG3S density dipole
All 14 nitramines (0.2) (2.8) (2.9) MUD (CM3) = 0.1 MUD (ChElPG) = 5.7 MUD (Löwdin) = 5.9 CM3 Delivers Consistent Partial Atomic Charges Polarization energies (in nitromethane) calculated using different charge schemes by wave function (kcal/mole): electrostatic fitting MUD mean unsigned deviation: 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
CM3 Improvement + Mulliken o CM3
Gallium Nitride from Cyclotrigallazane NH3 [HGaNH]n GaN 150° C substantial cubic form in addition to wurtzite Kormos et al. JACS, 2005, 127, 1493
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 Dipole moment (D) Kormos et al. JACS, 2005, 127, 1493
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
Future Plans • Reparameterize SCC-DFTB to get better agreement with higher levels of theory • Hardness was not found to have sufficient influence • Reoptimize Erep to B3LYP data • Add empirical dispersion term to get better binding energies and distances