CMx Charges for SCC-DFTB and Some GaN Vignettes

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CMx Charges for SCC-DFTB and Some GaN Vignettes

• Christopher J. Cramer
• University of Minnesota

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DFTB Energy Functional
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SCC-DFTB Energy Functional
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Class II Partial Charges (Population Analysis)
Löwdin
Mulliken
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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
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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
  lt???gt (MP2/cc-pVTZ, center of mass) and compare
  partial atomic charges to those determined from
  CHELPG fit to MP2/cc-pVTZ electrostatic potential

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Performance Example
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Performance Example 2
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Accurate, Density, and CM3 Dipole Moments
nitramide
Cs C2v
Cs C2v
3.94 3.59 3.84
4.31 3.93 4.19
2.97 2.71 2.89
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!
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Accurate, Density, and CM3 Dipole 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
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Accurate, Density, and CM3 Dipole 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
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Accurate, Density, and CM3 Dipole 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
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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
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SCC-DFTB Results Before
Signed errors O(0.4 D), RMSE O(0.7 D)
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Optimized Parameters (Mulliken mapping)
Linear (in B.O.) parameters
quadratic parameters
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SCC-DFTB Results After
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CM3 Improvement
Mulliken o CM3
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Gallium Nitride from Cyclotrigallazane
NH3
HGaNHn
GaN
150 C
substantial cubic form in addition to wurtzite
Kormos et al. JACS, 2005, 127, 1493
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What is Nature of HGaNHn?
Kormos et al. JPC A, 2006, 110, 494
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What is Nature of HGaNHn?
Kormos et al. JPC A, 2006, 110, 494
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HGaNHn Is a Mixture of Nanorods
Dipole moment (D)
n GaN GeC
1 2.7 1.0
2 9.0 1.1
3 15.5 0.9
4 23.0 0.5
5 31.3 0.1
6 40.3 -0.4
7 49.7 -0.9
8 59.4 -1.5
9 69.3 -2.1
Kormos et al. JACS, 2005, 127, 1493
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Error compared to DFT and MP2

• Data set included small molecules containing Ga,
  N, and H atoms
• B3LYP and MP2 with 6-311G(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

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H2GaNH23 Binding Energy and Rod Growth
Dimer A
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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

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