cmx charges for scc-dftb and some gan vignettes christopher j. cramer university of minnesota
TRANSCRIPT
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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
€
E ρ0 r( )[ ] = ψ i r( )hiKS ρ0 r( )[ ] ψ i r( )
i
occupied
∑ −1
2
ρ0 r1( )ρ0 r2( )
r1 − r2
dr1dr2∫∫
+ Exc ρ0 r( )[ ] − Vxc ρ0 r( )[ ]∫ ρ0 r( )dr + EN
€
μ hKS ν =εμ , μ = ν
μ T + veff ρ0, A r( ) + ρ0, B r( )[ ] ν , μ ∈ A, ν ∈ B
⎧ ⎨ ⎪
⎩ ⎪
€
Erep ρ0 r( )[ ] = Erep ρ0, A r( )[ ]A
atoms
∑ + Erep2( )
A<B
atoms
∑ ρ0, A r( ),ρ0, B r( )[ ]
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SCC-DFTB Energy Functional
€
E ρ0 r( ) + δρ r( )[ ] = E ρ0 r( )[ ]
+1
2
1
r1 − r2
+δ 2Exc
δρ r1( )δρ r2( )ρ0
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟δρ r1( )δρ r2( )
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥∫∫ dr1dr2
€
δρ r( ) = ΔqAδ r − rA( )A
atoms
∑
€
1
2
1
r1 − r2
+δ 2Exc
δρ r1( )δρ r2( )ρ0
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟δρ r1( )δρ r2( )
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥∫∫ dr1dr2 =
1
2ΔqAΔqBγAB
A, B
atoms
∑
€
γAB =2ηA, A = B
aa bb( ), A ≠ B
⎧ ⎨ ⎪
⎩ ⎪
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Class II Partial Charges (Population Analysis)
€
Pμν = 2 cμi
i
occ
∑ cνi
€
Sμν = φμφν∫ dr
€
N = tr PS( ) = tr SP( ) = tr S1/ 2PS1/ 2( )
€
N k = PS( )μμμ∈k
∑€
qk = Zk − N k
€
N k = S1/ 2PS1/ 2( )
μμμ∈k
∑
Mulliken Löwdin
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Class IV Partial Charges (CM2 and CM3)
€
qkCMx = qk
(II) + Bk ′ k Ck ′ k Bk ′ k + Dk ′ k ( )′ k ≠k
∑
€
Bkk' = PS( )μλPS( )λν
λ
∑ν ∈k'
∑μ∈k
∑Mayerbondorder
Ckk ′=−Ck′k, Dkk′ =−Dk′k
empiricallinear 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, 10707Thompson 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 <|μ|> (MP2/cc-pVTZ, center of mass) and compare partial atomic charges to those determined from CHELPG fit to MP2/cc-pVTZ electrostatic potential
€
μ =± qk xk
k
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
+ qk yk
k
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
+ qkzk
k
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2 ⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
1/ 2
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Performance Example
O
OMe
H
O
HH
O
MeMe
OO
O
O
NH2H
O
NH2Me
S
HH
CH3CO2HH2O
MeOH MeNH2Me2O
NH3
NCNH2
HCN
MeCN
CH3F CH3SHCH3SiH3 H2S
CH3Cl
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Performance Example 2
Mode l RMS Erro r (D)
CM2/ any level <0.20
MP2/6 -31G* < | | > 0.21
HF/ 6-31G* < | | > 0.31
HF/ 6-31G* CHELPG 0.33
PM3 < | | > 0.43
AM 1 < | | > 0.44
AM 1 Mullik en 0.89
HF/ 6-31G* Mul liken 0.93
PM3 Mullike n 1.00
HF/ 6-31G* NPA 1.05
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Accurate, Density, and CM3 Dipole Moments
N NO
OH
HN N
H
H
O
ON N
HH
O
ON N
H
H
O
O
3.943.593.84
4.313.93 4.19
2.972.71 2.89
3.283.07 3.27
nitramide
MUE (density) = 0.30 debyes MUE (CM3) = 0.08 debyes
Accurate: mPW0/MG3S density dipole
MUE mean unsigned error:
Cs C2v Cs C2v
from mPW0/MIDI!
Approximate dipoles
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Accurate, Density, and CM3 Dipole Moments
4.814.21 4.67
5.044.43 4.87
3.432.99 3.33
3.693.38 3.77
dimethylnitramine
MUE (density) = 0.49 debyes MUE (CM3) = 0.12 debyes
Accurate: mPW0/MG3S density dipole
N NO
OMe
MeN N
Me
Me
O
ON N
MeMe
O
ON N
Me
Me
O
O
MUE mean unsigned error:
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Accurate, Density, and CM3 Dipole Moments
5.975.22 6.20
7.196.227.34
: RDX
MUE (density) = 0.86 debyes MUE (CM3) = 0.19 debyes
Accurate: mPW0/MG3S density dipole
N N
N
NO2
O2N NO2
MUE mean unsigned error;
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Accurate, Density, and CM3 Dipole Moments
1.561.321.80
0.310.42 0.79
: HNIW; CL-20
MUE (density) = 0.32 debyes MUE (CM3) = 0.29 debyes
Accurate: mPW1PW91/MG3S density dipole
2.561.95 2.41
N N
N N
NNNO2O2N
NO2
NO2O2N
O2N
γ
MUE mean unsigned error:
[hexa-nitrohexaaza-iso-wurtzitane]
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CM3 Delivers Consistent Partial Atomic Charges
Conformer CM3 ChElPG CM3 ChElPGγ-HNIW -12.6 -13.4 -12.4 -19.1-HNIW -13.2 -13.6 -13.0 -19.2-HNIW -13.7 -13.9 -13.7 -19.6
1 91/ !mPW PW MIDI / !HF MIDI
Polarization energies (in nitromethane) calculated using different charge schemes by wave function (kcal/mole):
MUD (CM3) = 0.1MUD (ChElPG) = 5.7
All 14 nitramines(0.2)(2.8)
MUD (Löwdin) = 5.9 (2.9)
MUD mean unsigned deviation:
GP =−12
−1ε
⎛ ⎝ ⎜
⎞ ⎠ ⎟ qkq ′ k γk ′ k k, ′ k ∑
electrostatic fitting
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
quadraticparameters
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SCC-DFTB Results — After
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CM3 Improvement
+ Mullikeno CM3
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Gallium Nitride from Cyclotrigallazane
Kormos et al. JACS, 2005, 127, 1493
NH3
150° C[HGaNH]n GaN
substantial cubicform in addition
to wurtzite
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What is Nature of [HGaNH]n?
Kormos et al. JPC A, 2006, 110, 494
XY
XY
XY
Y
XY
XY
XY
XY
XY
Y
XY
XY
XY
Y
XY
XY
X
Y
XYY
XXYY
XY
X
Y
Y
Y
X
X
XY
X
X
X
X
X
Y
X
Y
Y
Y
X
XYY
YX
X YYX
X Y
flat-chair (FC)
rolling-chair (RC) flat-boat (FB)
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What is Nature of [HGaNH]n?
Kormos et al. JPC A, 2006, 110, 494
FC FB
RC
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[HGaNH]n Is a Mixture of Nanorods
Kormos et al. JACS, 2005, 127, 1493
+etc.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
Dipole moment (D)
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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 6-311+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
mean unsigned error of SCC-DFTB
B3LYP MP2bond lengths 0.049 0.038
angles 3.86 4.03intermolecular distances 0.43 0.43
reaction energy 21.21binding energy 3.21 3.65
bond lengths in Åangles in degreesenergies in kcal/mol
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[H2GaNH2]3 Binding Energy and Rod Growth
Dimer A
ΔEn(kcal/mol)n SCC-DFTB B3LYP2 63.8 2.23 57.6 -4.34 55.3 -3.85 53.8 -5.26 52.6 -6.27 51.8 -7.18 51.1 -7.69 50.6 -8.3
Binding Energies (kcal/mol)
Dimer MP2//RHF SCC-DFTBA -7.4 -3.08B -3.8 -1.41C -7.8 0.13D -4.1 -1.64
H3[(HGaNH)3]n–1H3 + H3[(HGaNH)3]H3
H3[(HGaNH)3]nH3 + 3H2
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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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Acknowledgments Biradicals, Diradicals, Ilk tRNA Dynamics Senior Collaborators
Dr. Benjamin Gherman Dr. Maria Nagan Prof. Dan Falvey (Maryland) Dr. Mark Seierstad Dr. Ed Sherer Prof. Laura Gagliardi (Genève)
Dr. William T. G. Johnson Stephanie Kerimo Prof. Wayne Gladfelter (Minn)
Dr. Youngshang Pak Prof. Shinobu Itoh (Osaka) Dr. Michael Sullivan Solvation Prof. Jaroslaw Kalinowski
Dr. Stefan Debbert Dr. Candee Chambers (Warsaw)
Dr. Bethany Kormos Dr. Jiabo Li Prof. Hilkka Kenttämaa (Purdue) Dr. Chris Kinsinger Dr. Tianhai Zhu Prof. Bogdan Lesyng (Warsaw)
John Lewin Dr. David Giesen Prof. Eric Patterson
David Heppner Dr. Gregory Hawkins (Truman State) Dr. Paul Winget Prof. Piotr Piecuch
Gallium Nitride Dr. James Xidos (Michigan St.)
Dr. Bethany Kormos Dr. Jason Thompson Prof. Bill Tolman (Minnesota) Joseph Scanlon Casey Kelly Prof. Don Truhlar (Minnesota)
Adam Chamberlin Dr. Eric Weber (US EPA)
Support from: US ARO, NSF, EPA, Minnesota Supercomputing Institute
AMSOL, SMxPAC, GAMESSPLUS, HONDOPLUS, OMNISOL, etc. available from various sources (see http://comp.chem.umn.edu/mccdir/software.htm)