Transcript CMx Charges for SCC-DFTB and Some GaN Vignettes

CMx Charges for SCC-DFTB
and Some GaN Vignettes
Christopher J. Cramer
University of Minnesota
DFTB Energy Functional
E  0 r 
occupied

i r
hiKS
i
 Exc  0 r 
 hKS
1
0 ri r  2

 0 r1 0 r2 
r1  r2
dr1dr2
 Vxc 0 r0 rdr  EN

 ,   

  
 T  veff  0, A r    0, B r   ,   A,   B


Erep  0 r 
atoms
atoms
A
AB
 Erep  0, A r 
2  r , r
E
 rep  0, A  0, B 
SCC-DFTB Energy Functional
E  0 r   r  E  0 r 
1

2




2
 Exc
 1
 r  r dr dr

1
2  1 2
 r  r



r


r


1
2 
 1 2
0 

r 
atoms
 qAr  rA 
A
1
2




atoms
2
1

E
1

xc
 r  r dr dr 

qAqB AB
2  1 2
 r1  r2  r1 r2   1
2 A, B




0


 AB

 2A, A  B
 

aa bb, A  B
Class II Partial Charges (Population Analysis)
occ
P  2 cic i
S 
   dr
i

N  trPS  trSP  tr S1/ 2PS1/ 2



qk  Z k  N k

N k  PS

k
Mulliken

N k   S1/ 2 PS1/ 2
k
Löwdin


Class IV Partial Charges (CM2 and CM3)
qkCMx  q(II)
k 
 BkkCkkBkk  Dkk
k k
Bkk' 
  PS PS
  k   k' 


Ckk  Ckk ,
Dkk 
Mayer
bond
order
empirical
Dkk 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
Training Set and Error Functions
• Training set roughly 400 neutral and 25 ionic
molecules
• Compare point-charge derived dipole moments to
experimental values
2
2
2 1/ 2

 
 


   qk y k    qk z k  
   
q
x
k
k
 
 
 

  k
  k
 
 k



• 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
CH3Cl
H2O
HCN
O
S
H
NH3
H
H
CH3CO2H
O
O
O
Me
Me
Me
O
Me2O
MeNH2
MeOH
H
MeCN
H
O
O
O
O
H
Me
NH2
CH3F
CH3SiH3
H2S
CH3SH
NH2
NCNH2
Performance Example 2
Accurate, Density, and CM3 Dipole Moments
nitramide
N N
H
H
O
O
H
H
N N
O
O
O
N N
H
H
O
O
H
H
N N
O
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!
Accurate, Density, and CM3 Dipole Moments
dimethylnitramine
N N
Me
Me
4.81
4.21
4.67
O
O
Me
Me
N N
5.04
4.43
4.87
O
O
O
N N
Me
Me
O
3.43
2.99
3.33
MUE  mean unsigned error:
MUE (density) = 0.49 debyes
MUE (CM3) = 0.12 debyes
Accurate: mPW0/MG3S density dipole
Me
Me
O
N N
O
3.69
3.38
3.77
Accurate, Density, and CM3 Dipole Moments
NO2
N
N
O2N
N
: RDX
NO2
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, and CM3 Dipole Moments
O2N
NO2
N
O2N
N
N
N
N
NO2
O2N

1.56
1.32
1.80
: HNIW; CL-20
NO2
N
[hexa-nitrohexaaza-iso-wurtzitane]

0.31
0.42
0.79
MUE  mean unsigned error:
MUE (density) = 0.32 debyes
MUE (CM3) = 0.29 debyes
Accurate: mPW1PW91/MG3S density dipole

2.56
1.95
2.41
CM3 Delivers Consistent Partial Atomic Charges
1 1 
GP       qk qk  kk 
2  k ,k 
Polarization energies (in nitromethane) calculated using
different charge schemes by wave function (kcal/mole):
m PW1PW91/M IDI!
Conform e r
-HNIW
-HNIW
-HNIW
CM 3
-12.6
-13.2
-13.7
ChElPG
-13.4
-13.6
-13.9
HF/M IDI!
CM 3
-12.4
-13.0
-13.7
MUD  mean unsigned deviation:
MUD (CM3) = 0.1
MUD (ChElPG) = 5.7
MUD (Löwdin) = 5.9
All 14 nitramines
(0.2)
(2.8)
(2.9)
ChElPG
-19.1
-19.2
-19.6
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
NH3
150° C
[HGaNH]n
GaN
substantial cubic
form in addition
to wurtzite
Intensity (cps)
2500
2000
1500
1000
500
0
200
300
400
500
Wav elength (nm)
600
Kormos et al. JACS, 2005, 127, 1493
What is Nature of [HGaNH]n?
Y
Y
Y
X
Y
Y
Y
X
Y
Y
X
X
Y
X
Y
Y
X
Y
X
X
Y
X
Y
X
Y
Y
Y
X
Y
X
X
X
Y
Y
X
flat-chair (FC)
X
X
Y
X
X
X
Y
X
X
X
Y
X
Y
X
Y
Y
X X
X X Y Y
Y
Y
Y
X
X
X
Y
Y
Y
X
X
Y
Y
rolling-chair (RC)
flat-boat (FB)
Kormos et al. JPC A, 2006, 110, 494
What is Nature of [HGaNH]n?
RC
FC
FB
Kormos et al. JPC A, 2006, 110, 494
[HGaNH]n Is a Mixture of Nanorods
Dipole moment (D)
+
n
GaN
GeC
etc.
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
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-DFT B
bond lengt hs
angles
int ermolecular dist ances
react ion energy
binding energy
bond lengt hs in 
angles in degrees
energies in kcal/mol
B3LYP
0.049
3.86
0.43
21.21
3.21
MP 2
0.038
4.03
0.43
3.65
[H2GaNH2]3 Binding Energy and Rod Growth
Binding Energies (kcal/mol)
Dimer
A
B
C
D
H3[(HGaNH)3]n–1H3 + H3[(HGaNH)3]H3
MP2//RHF SCC-DFT B
-7.4
-3.08
-3.8
-1.41
-7.8
0.13
-4.1
-1.64
H3[(HGaNH)3]nH3 + 3H2
n
2
3
4
5
6
7
8
9
Dimer A
En(kcal/mol)
SCC-DFT B B3LYP
63.8
2.2
57.6
-4.3
55.3
-3.8
53.8
-5.2
52.6
-6.2
51.8
-7.1
51.1
-7.6
50.6
-8.3
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
Acknowledgments
Biradicals, Diradicals, Ilk
Dr. Benjamin Gherman
Dr. Mark Seierstad
Dr. Willia m T. G. Johnson
Dr. Youngshang Pak
Dr. Michael Sullivan
Dr. Stefan Debbert
Dr. Bethany Kormos
Dr. Chris Kin singer
John Lewin
David Heppner
Gallium Nitride
Dr. Bethany Kormos
Joseph Scanlon
tRNA Dynamics
Dr. Maria Nagan
Dr. Ed Sherer
Stephanie Ker imo
Solvation
Dr. Candee Chambers
Dr. Jiabo Li
Dr. Tianhai Zhu
Dr. David Giesen
Dr. Gregory Hawkins
Dr. Paul Winget
Dr. James Xidos
Dr. Jason Thompson
Casey Kelly
Adam Chamberlin
Senior Collaborators
Prof. Dan Falvey (Maryland)
Prof. Laura Gagliardi (Genève)
Prof. Wayne Gladfelter (Minn)
Prof. Shinobu Itoh (Osaka)
Prof. Jaroslaw Kalinowski
(Warsaw)
Prof. Hilkka Kenttämaa (Purdue)
Prof. Bogdan Lesyng (Warsaw)
Prof. Eric Patterson
(Truman State)
Prof. Piotr Piecuch
(Michigan St.)
Prof. Bill Tolman (Minnesota)
Prof. Don Truhlar (Minnesota)
Dr. Eric Weber (US EPA)
Support from: US ARO, NSF, EPA, Minnesota Supercomputing Institute
AMSOL, SMxPAC, GA MESSPLUS, HONDOPLUS, OMNISOL,
etc. available from various sources
(see http:// comp.chem.umn.e du/mccdir/so ftware.htm)