Satyender Goel†‡ and Artëm E. Masunov†‡*
Derivation and implementation of the pairwise spin-contamination correction and application to study potential energy curves for 3d
transition metal hydrides from BS-DFT† Nanoscience Technology Center, ‡ Department of Chemistry, * Department of Physics,
University of Central Florida, Orlando, FL – 32826
+ -+=S
1H1 1H1
σ
σ*
Mot ivat ion
Spin-contaminat ion correct ion based on Natura l Occupat ions (NO)
Summary and Conc lus ions
TS
ppqpBS
22
2211
2211
11
1
2
121
TBSS EEE
4
2
4
22
1
2
1
10
12 bn
Tbb
bbBS
bbS E
nn
nnE
nnE
442
24
442
42
2
20
-110
-90
-70
-50
-30
-10
10
0 1 2 3 4 5
E(k
ca
l/m
ol)
z(A)
HH
CCSD
Eq - Yamaguchi
BMK-uncorr
BMK-corr
HH
-50
-40
-30
-20
-10
0
10
20
1 1.5 2 2.5 3 3.5
z(A)
BST
TDFT
BSDFT
SS
EEJ
22
TS EEJ 2
Val idat ion
…by Yamaguchi et. al.
…new approach
,
Basis set used: aug-cc-pVQZ
Fig - Spin contamination correction with one correlated pair : Example -
H2
Calculations were done on remote cluster I2lab at UCF.
18 MH systems
(neutral + cations) studied with all
possible/reported multiplicities.
DFT functionals• BMK
• TPSSSoftware• Gaussian 03• Molden
Calculated bond
dissociation energies, bond lengths and Ionization potentials. Performed NBO analysis for electronic structure and populated NOs for spin correction.
TM diatomics : 3d-Metal Hydrides (Sc – Cu)
0 1 2 3 4 5 6-60
-50
-40
-30
-20
-10
0
10
20
z(Å)
E(k
ca
l/m
ol)
MnH
__ 5X, BMK
__ ____________________ 7X, TPSS
________________ 5Σ+, MCSCF+FOCI
__ 7Σ+, MCSCF+FOCI
__ _______ 7X, BMK
__ 5X, TPSS
M BMK TPSSS**2 S**2 S**2
Sc H 1 0.000 0.000 0.762Ti H 4 3.750 3.756 3.758V H 5 6.000 6.015 6.017Cr H 6 8.750 8.794 8.794Mn H 7 12.000 12.002 12.004
5 6.000 6.706 6.199Fe H 4 3.750 4.049 3.778
6 8.750 8.753 8.752Co H 3 2.000 2.141 2.019Ni H 2 0.750 0.763 0.761Cu H 1 0.000 0.000 0.000
Systems
0 1 2 3 4 5 6-70
-60
-50
-40
-30
-20
-10
0
10
20 Spin Correction - MnH
z(Å)
E(k
cal/m
ol)
5X, TPSS: Spin-corrected
5Σ+, MCSCF+FOCI 7Σ+, MCSCF+FOCI
5X, BMK: Spin-corrected
5X, TPSS: Spin-uncorrected
5X, BMK: Spin-uncorrected
Experimental Data available is for lowest multiplicity (M=5).
Corrected values are closer to experimental and differ by 3kcal/mol from uncorrected curve at equilibrium interatomic distance
• BMK is found to outperform all other DFT functionals and ab- initio methods for diatomic TM
hydrides.
• Spin correction approach is good for one correlated pair, needs further validation with
two or more correlated pairs.Spin corrected ‘PEC’
<Ŝ2> is Sz(Sz+1) where, Sz is ½ of the difference in total numbers of α and β electrons.
Spin-Contamination in Unrestricted Density Functional Theory (DFT) CalculationsFor systems with a multiplicity other than one, it is not possible to use the RHF method as is. Often an unrestricted SCF
calculation (UHF/UKS) is performed. The advantage of unrestricted calculations is that they can be performed very efficiently. A disadvantage of UKS approach is that spin-polarized Slater determinant is no longer an eigenfunction of the spin operator. Hence, the average value of <Ŝ2> is not, generally equal to the correct value of Sz(Sz+1). This situation is known as spin contamination and <Ŝ2> is often used as its measure. The common rule is to neglect spin contamination if <Ŝ2> differs from Sz(Sz+1) by less than 10%. As a result of spin contamination, molecular geometry may be distorted toward the high-spin state one, spin density often becomes incorrect, and electron energy differs from the pure spin state ones.
Gaussian 03
• Output Natural Orbitals – ‘NO’
NO2MO
• Spin-Polarized Molecular Orbitals – ‘MO’
ECORR
• Pure Spin State Energy
1. CCSD(T) calculations
2. Spin correction by Eq. :
3. Spin correction based on natural occupation
Potent ia l Energy Curves for 3d-Trans i t ion Meta l Hydr ides
ScH TiH VH CrH MnH FeH CoH NiH CuH-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
MH System
Dev
iati
on
in
Bin
din
g E
ner
gy
(kca
l/m
ol)
MCPF
SA-BLYP
BS-TPSS:DKH
BS-TPSS
SA-B3LYP
BS-BMK:DKH
BS-B3LYP
MCSCF+SOCI
BS-BMK
BS-TPSSh
Fig – Deviation in bond energies from experimental data for
neutral MH with various DFT and WFT methods.
(*)-Barone et. al. 1996, (*)-Furche et. al. 2006 , (*)-Koseki et. al., 2002-2006, (*)-Harrison 2000, (*)-kant moon_1985 ScH, (*)-Chen_1991 TiH, (*)-Chen_1993 CrH VH, (*)-Sunderlin_1990 MnH, (*)Schultz_1990 FeH, (*)-Fisher_1989 Co Ni Cu,kant moon_1989 NiH, (*)-Harrison 2000, (*)-Gray_1991 FeH R, (*)-Beaton 1994 CoH, (*)-Ram_1985 CuH , (*)-NIST Database and Transition netal hydrides by A. Dedieu , (*)-Riley et. al., 2007 JPC
References
0 1 2 3 4 5 6-70
-60
-50
-40
-30
-20
-10
0
10
20DFT - BMK
z(Å)
E(k
ca
l/mo
l)
__________ 1X, CuH
_________4X, FeH
_______________ 4X, TiH__ 2X, NiH
__ 3X, CoH
Potent ia l Energy Curves
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