NMR Spin-Spin Coupling NMR Spin-Spin Coupling Constants for Heavy Atom Constants for Heavy Atom

SystemsSystems

A ZORA Density Functional A ZORA Density Functional ApproachApproach

Jochen Autschbach & Tom Ziegler, The University of Calgary, Dept. of Chemistry University Drive 2500, Calgary, Canada, T2N-1N4Email: jochen@cobalt78.chem.ucalgary.ca

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Heavy Atom CompoundsHeavy Atom Compounds

Relativistic theoretical treatment Estimated absolute relativistic effects of

>100% for 6th row elements for NMR spin-spin coupling constants

Bonding changes qualitatively due to relativity scaling of nonrelativistic orbital coupling contributions might be misleading

Therefore a full relativistic Therefore a full relativistic treatment for the spin-spin coupling treatment for the spin-spin coupling constants is neededconstants is needed

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Spin-spin coupling constantsSpin-spin coupling constants

Nucleus ASpin magnetic momentcreates magnetic field

Direct interaction Nucleus BSpin magnetic momentcreates magnetic field

Aμr Bμ

r

Electrons withorbital- and spin-magnetic moments

Indirect interactionIndirect interaction K(A,B)

MethodologyMethodology

Aμr Bμ

r

3

ΨΨ=μƒμƒ

ƒ= HE

EBAK

BA

ˆ),( withrr2

),(),( iso BAKh

BAJ BAγγπ

= 24

we need to knowwe need to know including relativityincluding relativity

),(ˆ BAH μμrr

Reduced coupling tensor

Coupling constants in Hz from the NMR spectrum

3332211 /)( KKKK iso ++=

Reducedcoupling constant

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The ZORA one-electron Hamiltonian The ZORA one-electron Hamiltonian

Vc

cppVH

−=ΛσΛσ+= 2

2

22

21

;ˆˆˆ rr

ˆ p → ˆ p +r A with

r A =

1

c2

r μ N ×

r r N

rN3

N∑

Replacement to account for magnetic fields

Tnrel + relativistic corrections of T and V + spin-orbit effects

Magnetic field due tonuclear magnetic moments

MoleculareffectiveKohn-Shampotentialif used in DFT

Variationallystable two-com-ponent relativistic Hamiltonian

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FC+SD=1

2c2 σjr ∇ Λ

r r ArA3

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ −

1

2c2r σ ∇j Λ

r r ArA3

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

PSO=1

2c2i

Λ

rA3 (

r r A ×

r ∇ )j +(

r r A ×

r ∇ )j

Λ

rA3

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

DSO=

Λ

c4

δjk(r r A ⋅

r r B)−rAkrBj

rA3rB

3Nuclei A and B,directions j and kof magnetic moments

The ZORA Hyperfine TermsThe ZORA Hyperfine Terms

KjkFC+SD+PSO(A,B)=2 Re ϕi

(0) ˆ H j;AFC+SD+PSOϕi;k;B

(1)

i

occ∑

KjkDSO(A,B)= ˆ H jk;A,B

DSO ρ(0)

Requires solutionof 1st-order pertur-bation equations

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Description of the programDescription of the program Auxiliary program for ADF (Amsterdam Density

Functional V. 99 and 2.3, see www.scm.com) Based on nonrelativistic, ZORA scalar or ZORA

spinorbit 0th order Kohn-Sham orbitals Solution of the coupled 1st order Kohn- Sham

equations due to FC-, SD-, and PSO term (instead of finite perturbation)

Accelerated convergence for scalar relativistic calculations (< 10 iterations)

Spin-dipole term available Currently no current-density dependence

in V, X approximation for 1st order exchange potential 7

Results I : scalar ZORAResults I : scalar ZORAOne-bond One-bond metal ligand metal ligand couplingscouplings

Hg-CPt-PW-C , W-H, W-P, W-FPb-H ,Pb-C, Pb-Cl

FC + PSO + DSOterms included

J.A., T. Ziegler, JCP 113 (2000), in press8

Tungsten compoundsTungsten compounds

W(CO)6

W(CO)5PF3

W(CO)5PCl3W(CO)5WI3

cp-W(CO)3HWF6

Lead compoundsLead compounds

PbH4 *

Pb(CH3)2H2

Pb(CH3)3HPb(CH3)4

PbCl4 **

* exp. extrapolated from Pb(CH3)xHy ** not directly measured

*

**

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Platinum compoundsPlatinum compounds

Pt(PF3)4

PtX2(P(CH3)2)

cis-PtCl2(P(CH3)3)2

trans-PtCl2(P(CH3)3)2

cis-PtH2(P(CH3)3)2

trans-PtH2(P(CH3)3)2

Pt(P(CH3)3)4

Pt(PF3)4

Hg(CH3)2

CH3HgClCH3HgBrCH3HgIHg(CN)2

[Hg(CN)4]2-

Hg(CH3)2

(CH3)Hg-X

[Hg(CN)4]2-Hg(CN)2

Mercury compoundsMercury compounds

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Results II : spin-orbit couplingResults II : spin-orbit coupling

2 contributions:a) spin-orbit coupling for 0th order orbitalsb) ZORA spin-dipole (SD) operator

System *)

K / 1020 kg/m-2C-2

nrel scalar SO Expt.

Hg(CN)2 227 443 455 578

HgMeBr 129 189 203 256

cis-PtH2(PMe3)2 91 102 114 179

*) VWN functional, Hg-C and Pt-P coupling constants, SO = spin-orbit 11

Results III : solvent effectsResults III : solvent effects

Experimentalcouplingsobtained in solutionCoordinationof the heavyatom by solvent moleculesimportant ?

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K / 1020 kg/m-2C-2 *)

Hg(CN)2 +2MeOH +4MeOH Expt. +4THF Expt.

443

(450)

542

(549)

574

(585)

578 582 558

HgMeCl +3CHCl3 +4CHCl3 Expt. +3DMSO Expt.

203 234 278 263 295 308

HgMeBr +2CHCl3 +3CHCl3 Expt. +3DMSO Expt.

127 224 234 263 295 308

HgMeI +2CHCl3 +3CHCl3 Expt. +3DMSO Expt.

125 193 241 239 295 283

HgMe2 +2CHCl3 +3CHCl3 Expt. +3DMSO Expt.

75 108 122 127 131 133*) Hg-C coupling, VWN functional, scalar ZORA (numbers in brackets: ZORA spin-orbit) 13

*) K / 1020 kg/m2C2

Pt-P coupling, VWN functional.scalar ZORA(in brackets:ZORA spin-orbit)

cis-PtH2(PMe3)2 trans-PtH2(PMe3)2

no solvent *) 102 (114) 170

+1 acetone 154 155

+2 acetone 169 (184) 277

Expt. 179 247 14

SummarySummary NMR shieldings and spin-spin couplings with

ADF now available for light and heavy atom systems

Based on the variationally stable two-component ZORA method

Relativistic effects on spin-spin couplings are substantial and recovered by ZORA

Spin-orbit effects are rather small for the investigated cases

Coordination by solvent molecules has to be explicitly taken into account for coordinatively unsaturated systems

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