Doing calculations with ReSpect

Relativistic calculation of NMR and EPR parameters

Vladimir Malkin

Department of theoretical chemistry, Institute of Inorganic chemistry, Slovak Academy of Sciences, Bratislava, Slovakia

Mariapfarr February 24, 2014

e− e−

Magnetic interactions

coupling

HFS

chemicalshielding

tenzor

J −

σ

g −

A

Magnetic interactions

Relativity

Atomic and molecular properties caused by relativistic effects

Yellow colour of Au[1] Liquid state of Hg[2]

[1] N. Bartlett, Gold Bull. 1998, 31, 22 [2] L. J. Norrby, J. Chem. Edu. 1991, 68, 110

Motivation

F FF F

αα αβ

βα ββ

αβαβ

Dirac equation (4-component scheme)

2-component scheme

0 1 0 1 01 0 0 0 1x y z

ii

σ σ σ−

= = = −

Pauli matrices

1-component scheme

00

FF

αα

ββ

Terminology

nonrelativisticlimit

(n-1)d

ns

np

Relativistic Effects on Atomic Valence Energy LevelsE

+ spin-free relativistic effects

(n-1)d3/2

+ spin-orbit coupling

(n-1)d5/2

ns

np1/2

np3/2

Breit type corrections

P. Pyykko, E. Pajanne, Int. J. Quant. Chem., v. VII, 785-806, (1973), “Hydrogen-like relativistic corrections for electric and magnetic hyperfine integrals.

Comparison of results for 127I Nuclear Quadruple Coupling Constants (in MHz) calculated with DFT (NR + NR and DKH2 + DKH2) method in comparison to

experimental data

I. Malkin, O.L. Malkina, V.G. Malkin, Chem. Phys. Lett., 361 2002, 231

NQCC in I-X series

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-3500-3000-2500-2000-1500-1000-5000

Experimental data

Cal

cula

ted

valu

es

NR

Rel-2

NQCC in I-X series

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-3500-3000-2500-2000-1500-1000-5000

Experimental data

Cal

cula

ted

valu

es

NR+NRDKH2+DKH2

E. Malkin, I. Malkin, O.L. Malkina, V.G. Malkin, M. Kaupp, Phys. Chem. Chem. Phys., 2006, 8, 4079 – 4085.

Finite size of nucleus

Charge distribution Magnetic moment distribution

Point nucleus

D. Andrae, Phys. Rep., 2000 , 336, 413-525

0

5000

10000

15000

20000

25000

30000

0 5000 10000 15000 20000 25000 30000

Experimental data

Cal

cula

ted

valu

es

NonrelativisticPoint nucleusFinite nucleus

The solid line corresponds to ideal agreement with experiment.

HgH

HgCN

HgF

HgAg

Calculated and experimental isotropic 199Hg HFCs

Spin-Orbit interaction

� 0

0,1

0,2

0,3

0,4

0,5

0,6

L S

Spin-orbit interactions

Spin-orbit correction to chemical shift (SO-CS)

Spin-orbit corrections to NMR chemical shift

Spin-orbit corrections to NMR chemical shift

A Karplus-Type Relation for Spin-Orbit Shifts in Iodoethane

1H "SO shift"

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15SO

con

trib

utio

n to

1 H sh

ield

ing

(ppm

)

0 20 40 60 80 100 120 140 160 180

12.0

10.5

9.0

7.5

6.0

4.5

3.0

1.5

0.0

-1.5

-3.0

-4.5

3KFC(H,I)

3KFC (E

,I) (10 19NA

-2m-3)

H-C-C-I dihedral angle (deg)

Chem. Eur. J. 1998, 4, 118.

H

I

Available approaches

Calculations of the EPR g-tensor

1-component unrestricted 2-component restricted 2-componnet unrestricted 4-component unrestricted

There are specific problems associated with any of listed above approaches

1-component or 2-component ?

-40 -30 -20 -10 0

-40

-35

-30

-25

-20

-15

-10

-5

0

5

BP 1-comp. (unrestricted)BP 1-comp. (this work, unrestricted)ZORA 2-comp. (restricted)DKH 2-comp. (this work, unrestricted)

∆g||,expt / in ppt

∆g ||

,cal

c/ i

n pp

tPerformance for ∆g|| in 2Σ Radicals

PdH HgAgHgHCdH

LaO RhC

Restricted or unrestricted ?

2-component approaches for calculations of g-tensor

Note: in a spin-orbit coupled spin restricted relativistic ZORA calculation and the ESR block key, ADF will also calculate and print the nuclear magnetic dipole hyperfine interaction, but the terms due to the spin-polarization density at the nucleus are absent. Furthermore, if there is more than one unpaired electron, the computed results will simply be incorrect, without any warning from the program.

Expression based on Kramer’s pair formalism

3-SCF calculations

Scaling the speed of the light …

I. Malkin, O.L. Malkina, V.G. Malkin, and M. Kaupp, J. Chem. Phys., 123 (2005) 244103

Scaling the speed of the light !

0,0 0,2 0,4 0,6 0,8 1,0 1,2

2,00

2,05

2,10

2,15

2,20

0,0 0,2 0,4 0,6 0,8 1,0

1,95

2,00

2,05

2,10

2,15

2,20

2,25

Br2- I2

-

g⊥

g||

g⊥

g||

scaling factorSO integrals

scaling factorSO integrals

g-va

lue

g-va

lue

y = -0,113x2 + 0,3279x + 2,0024R2 = 1,0000

y = -0,0584x2 - 0,0128x + 2,0024R2 = 0,9997

y = -0,0293x2 + 0,1884x + 2,0023R2 = 1,0000

y = -0,0184x2 - 0,0014x + 2,0023R2 = 1,0000

quadratic spin-orbit contributions dominate g|| for both systemsand become very important also for g⊥ of I2

- !

Using 2-Component Treatment to Evaluate Importance of Higher-Order Terms

DKH-BP86 results with Hirao basis set

Benchmark calculations …

Radical 1-comp. 2-comp. Exp.O2 2.7 2.3 2.9SO 4.8 3.9 3.6S2 13.3 11.2 14.5SeO 15.3 2.2 32.7NF 1.8 1.6 2.0NCl 5.4 5.0 5.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

-4

-2

0

2

4∆g⊥

∆g||

scaling factor SO integrals

∆g-v

alue

Figure 5

y = -13.377x2 + 15.773xR2 = 0.9999

y = -0.6794x2 + 0.0035xR2 = 1

"We have found a number of lines in the field region expected for SeO but have not yet carried out accurate measurements. Two series of experiments have been terminated by violent explosions in the liquid nitrogen trap, with the subsequent release of hydrogen selenide into the laboratory atmosphere ; accurate measurements will require some degree of patience! " (Alan Carrington and Donald H. Levy, J. Phys. Chem, 71 (1967) 2-12)

Comparison of different approaches for the calculation of Δg in triplet radicals (in ppt)

⊥

MOC

OC CO

CO

H

CO

R3P MPR3

PR3

H

CO

MP

P P

P

H

LR R R R

R R R R

M

OC

OC CO

CO

H

M

OC

OC CO

H

N

NR

R

M HM H

MR3P

Cl PR3

H

[HM(CO)5]q

M = Cr, Mo, W (q=-1)M = Mn, Tc, Re (q=0)

[HMCp(CO)3]M = Cr, Mo, W

[HM(CO)4]M = Co, Rh, Ir

MOC

OC CO

H

H

CO

[H2M(CO)4]M = Fe, Ru, Os

[HM(CO)(PR3)3] M = Co, Rh, Ir

[HM(L)(dhpe)2] M = Fe, Ru, Os L = Cl, CN

[HMCl(PR3)2]M = Ni, Pd, Pt

M

R3P

Cl PR3

Cl

H

[HMCl2(PR3)2] M = Co, Rh, Ir

[HM(NHC)]M = Cu, Ag, Au

[HMPh]M = Zn, Cd, Hg

Dramatic spin- orbit effectson hydride 1H shifts

[HIrCl2(PMe3)2]

[HHgPh]

P. Hrobárik, V. Hrobáriková, F. Meier, M. Repiský, S. Komorovský, M. Kaupp J. Phys. Chem. A 2011, 115, 5654.

MS

S S

S

O

EPR Parameters in Tungsten(V) Complexes

The important role of higher-order spin-orbit contributions.Calculation of ∆g-tensors (in ppt) at 1-, 2- and 4-comp. level of theory using BP86 functional. (2-comp.: SO-ECP on metal/IGLO-II/CGO; 4-comp.: all electron DKS)

Complex Method ∆g11∆g22 ∆g33 ∆giso

[WO(bdt)2]-

1-comp.a 53 -32 -51 -10

2-comp.a 46 -48 -65 -22

4-comp. 46 -58 -79 -30

Exp. 42 -71 -91 -40

a P. Hrobárik, O. L. Malkina, V. G. Malkin, and M. Kaupp Chem. Phys. 356, 229 (2009).

MethodΔg11

[ppt]

⊗g22

[ppt]

⊗g33

[ppt]

⊗gis

o [ppt]

1-c DKH -32 -10 -8 -17

4-c mDKS -60 -19 -16 -31

Exp. -82 -20 -20 -41

Demonstration of 4-c calculations for larger, biologically relevant models

-surprisingly large higher-order SO effects for a 3d system!-revising estimates of performance of different functionals

BP86 results.

P. Hrobárik, M. Repiský, V. Hrobáriková, M. Kaupp Theor. Chem. Acc. 2011, 129, 715.

SOS2SeOSeSSe2TeOTeSTeSeTe2

J. Chem. Phys. 125, 054110 (2006)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.98 1.99 2 2.01 2.02 2.03 2.04 2.05 2.06

Calculated g⊥ = 2.023

D v

alue

s

g value

Evaluation of g-tensor and Zero-Field-Splitting (D) for GdH3

HGd

H

H

zS = 7/2

Ms=+7/2

Ms=-7/2

Ms=+5/2

Ms=+3/2

Ms=+1/2

Ms=-1/2

Ms=-3/2

Ms=-5/2

In cm-1; 2-component calculations (DFT with B3PW91).

2-Component Calculations of ZFS in GdH3

D 1/6[E(7/2) – E(5/2)] 1/4[E(5/2) – E(3/2)] 1/2[E(3/2) – E(1/2)]

All-electron 0.22 0.22 0.22

ECP 0.23 0.23 0.23

REHE-2014 conference"Relativistic effects in heavy element

chemistry and physics”Smolenice congress centrum, Slovakia,

September 20-25, 2014

Thank you!