Doing calculations with ReSpect Relativistic calculation of NMR and - - PowerPoint PPT Presentation

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 chemical shielding 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 F F F

αα αβ βα ββ

     

α β α β Dirac equation (4-component scheme) 2-component scheme

1 1 1 1

x y z

i i σ σ σ −       = = =       −      

Pauli matrices 1-component scheme

F F

αα ββ

     

Terminology

nonrelativistic limit

(n-1)d ns np Relativistic Effects on Atomic Valence Energy Levels

E

+ spin-free relativistic effects

(n-1)d

3/2

+ spin-orbit coupling

(n-1)d

5/2

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
• 3500
• 3000
• 2500
• 2000
• 1500
• 1000
• 500

Experimental data Calculated values NR Rel-2

NQCC in I-X series

• 3500
• 3000
• 2500
• 2000
• 1500
• 1000
• 500
• 3500
• 3000
• 2500
• 2000
• 1500
• 1000
• 500

Experimental data Calculated values NR+NR DKH2+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

5000 10000 15000 20000 25000 30000 5000 10000 15000 20000 25000 30000

Experimental data Calculated values

Nonrelativistic Point nucleus Finite nucleus

The solid line corresponds to ideal agreement with experiment. HgH HgCN HgF HgAg

Calculated and experimental isotropic 199Hg HFCs

Spin-Orbit interaction

฀ 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 0.15

SO contribution to 1H shielding (ppm)

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
• 40
• 35
• 30
• 25
• 20
• 15
• 10
• 5

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||,calc / in ppt Performance for ∆g|| in 2Σ Radicals

PdH HgAg HgH CdH 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

• ne 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 factor SO integrals scaling factor SO integrals g-value g-value

y = -0,113x2 + 0,3279x + 2,0024 R2 = 1,0000 y = -0,0584x2 - 0,0128x + 2,0024 R2 = 0,9997 y = -0,0293x2 + 0,1884x + 2,0023 R2 = 1,0000 y = -0,0184x2 - 0,0014x + 2,0023 R2 = 1,0000

quadratic spin-orbit contributions dominate g|| for both systems and 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 2.9 SO 4.8 3.9 3.6 S2 13.3 11.2 14.5 SeO 15.3 2.2 32.7 NF 1.8 1.6 2.0 NCl 5.4 5.0 5.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

• 4
• 2

2 4

∆g⊥ ∆g||

scaling factor SO integrals ∆g-value

Figure 5 y = -13.377x2 + 15.773x R2 = 0.9999 y = -0.6794x2 + 0.0035x R2 = 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)

⊥

M OC OC CO CO H CO R3P M PR3 PR3 H CO M P P P P H L R R R R R R R R M OC OC CO CO H M OC OC CO H N N R R M H M H M R3P 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

M OC 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 ic s spin in- orbit e t effe ffects ts

• n h

hydr dride de 1H s shifts fts

[HIrCl2(PMe3)2] [HHgPh]

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

2011, 115, 5654.

M S 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).

Method Δg11 [ppt] ⊗g22 [ppt] ⊗g33 [ppt] ⊗gis

• [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.

SO S2 SeO SeS Se2 TeO TeS TeSe Te2

• J. Chem. Phys. 125, 054110 (2006)

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

H Gd H H

z S = 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!