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

qq

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