Theoretical Studies of Theoretical Studies of Heavy-Atom NMR Spin-Heavy-Atom NMR Spin-spin Coupling Constantsspin Coupling Constants

With Applications to Solvent With Applications to Solvent Effects in Heavy Atom NMREffects in Heavy Atom NMR

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

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What is interesting about What is interesting about Heavy Metal Compounds ?Heavy Metal Compounds ?Spin-orbit coupling, scalar relativistic effectsRelativistic theoretical treatment: sizeable effects on bonding for 6th row elements (bond contractions, De,e,IP, …) are already textbook knowledge (e.g. “Au maximum”)Simple estimates propose absolute (!) scalar relativistic effects of 100% for 6th row elements for NMR spin-spin coupling constantsCoordination by solvent molecules possible

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Spin-spin coupling constantsSpin-spin coupling constants

Nucleus ASpin magnetic momentcreates magnetic field

Direct coupling(vanishes for rapidly rotating molecules)

Nucleus BSpin magnetic momentcreates magnetic field

Aμr Bμ

r

Electrons withorbital- and spin-magnetic moments

Indirect couplingIndirect coupling K(A,B)

MethodologyMethodology

Aμr Bμ

r

3

K(A,B)=

∂2E∂

r μ A∂

r μ B

withE = Ψ ˆ H Ψ

J (A,B) =h

4π2 γAγBKiso(A,B)

we need to knowwe need to know including relativityincluding relativity

),(ˆ BAH μμrr

Reduced spin-spin 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

ˆ H =V +

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r σ ̂ p Λ

r σ ̂ p ; Λ =

2c2

2c2 −V

ˆ p → ˆ p +

r A with

r A =

1c2

r μ N ×

r r N

rN3

N∑

Replacement to account for magnetic fields

Tnrel + relativistic corrections of T and V , spin-orbit coupling

Magnetic field due tonuclear magnetic moments

MoleculareffectiveKohn-Shampotentialif used in DFT

Variationallystable two-com-ponent relativistic Hamiltonian

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FC +SD=

12c2 σ j

r ∇ Λ

r r ArA

3

⎛

⎝ ⎜ ⎞

⎠ ⎟ −

12c2

r σ ∇ j Λ

r r ArA

3

⎛

⎝ ⎜ ⎞

⎠ ⎟

PSO=

12c2i

ΛrA

3 (r r A ×

r ∇ )j +(

r r A ×

r ∇ )j

ΛrA

3

⎡

⎣ ⎢ ⎤

⎦ ⎥

DSO=

Λc4

δ jk(r r A ⋅

r r B)−rAkrBj

rA3rB

3Nuclei A and B,directions j and k,point-like magnetic dipoles

The ZORA Hyperfine TermsThe ZORA Hyperfine Terms

K jkFC+SD+PSO(A,B) =2 Reϕi

(0) ˆ H j;AFC+SD+PSOϕi;k;B

(1)

i

occ

∑

K jkDSO(A,B) = ˆ H jk;A,B

DSO ρ(0)

Requires solutionof 1st-order pertur-bation equations

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Description of the codeDescription of the code Auxiliary program “CPL” for the program ADF

(Amsterdam Density Functional, see www.scm.com) Based on nonrelativistic, ZORA scalar or ZORA

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

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

Accelerated convergence for scalar relativistic calculations (< 10 iterations)

Spin-dipole term implemented Currently no current-density dependence

in V, X or VWN approximation for 1st order exchange potential

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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

JCP 113 (2000), 936.8

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 : spinorbit couplingResults II : spinorbit coupling

System *)

K / 1020 kg/m-2C-2

Nrel Scalar SO Expt.

Tl-F 120 139 203 202

Tl-Cl 133 129 219 224

Tl-Br 217 132 315 361

Tl-I 288 115 382 474

*) VWN + Becke86 + Perdew 88 functional, Tl-X coupling constants

Spin-orbit (SO) coupling causes cross terms between the spin-dependent ope-

rators (FC,SD) and the orbital dependent ones (here: PSO). The differences

between Scalar and SO in the table above is mainly caused by these cross terms,

and by the SO effects on the PSO contribution itself. Tl-I is the first example where

SO coupling was demonstrated to cause the major contributions to heavy atom

spin-spin couplings. JCP 113 (2000), 9410.11

Results III : solvent effectsResults III : solvent effects

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Experimental results on pages 9 and 10 obtained fromsolution. The cases where results are unsatisfactory aremarked red (linear Hg and square planar Pt complexes)

SO coupling yields only minorcorrections in all these cases!

Is coordination of the heavy atoms by solvent moleculesimportant?

Some structures that were optimized, explicitly including a number of solvent molecules

Mercury compounds with solvents: K / 1020 kg/m-2C-2 *)

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

443

(426)

542 576

(561)

578 582 558

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

203 234 278 263 295 308

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

185 224 234 263 295 308

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

177 193 241 239 295 283

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

75 108 122 127 131 133

*) Hg-C coupling, VWN functional, scalar ZORA (numbers in parentheses: ZORA spin-orbit) 13

JACS 123 (2001), 3341.

*) K / 1020 kg/m2C2

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

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

no solvent *) 107 (97) 170

+1 acetone 154 155 257

+2 acetone N/A 169 (158) 277

Expt. 179 247 14

Pt complexes

15*) Optimized bond distances, experimental bond lengths in parentheses (in Å)**) J. Glaser et al., JACS 117 (1995), 7550.

Experiment: **)

1J(Tl-Pt) : 57 kHz1J(Tl-CB) : 2.4 kHz2J(Tl-CA) : 9.7 kHz2J(Tl-CC) : 0.5 kHz

N

N

C

C

NC

Pt

Tl

C

C

CN

N

N

2.55 (2.60)

2.15 (2.13) *)

1.93 (2.01)

Two heavy nuclei:A Pt-Tl cyano complex

Results III : more solvent effectsResults III : more solvent effects

Two-bond coupling much larger than one-bond coupling

Four water molecules can coordinate toTl in aqueous solution (exp. confirmed)

Complex I

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Results III : more solvent effectsResults III : more solvent effects

Spin-spin couplings complex I, J / kHzCoupling nrel scalar Scalar

+ 4H2OSO+ 4H2O

Exp.(in H2O)

Pt-Tl 5.4 19.0 43.1 40.3 57.0

Tl-CB 1.2 5.7 3.1 3.0 2.4

Tl-CA 3.4 5.7 8.0 7.5 9.7

Tl-CC 0.2 0.5 0.4 0.4 0.5

The unintuitive experimental result 2J(Tl-CA) >> 1J(Tl-CB) questions the proposed structure with a direct Tl-Pt bond(page 15). However, our computations confirm the structureand the unusual coupling pattern. The solvent coordination effect on J(Pt-Tl) and the Tl-C cpouplings is remarkably large.

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Results III : more solvent effectsResults III : more solvent effects

JACS 123 (2001), in press.

free complex: both couplingsare comparably large in magni-tude but of opposite signinclusion of solvent moleculesshifts both couplings. The one-bond coupling is – as expected –influenced much stronger.As a result, the two-bond coup-ling is much larger than the one-bond couplingDelocalized bonds along theC-Pt-Tl-C axis are responsiblefor the large magnitude of thetwo-bond Tl-C coupling in thefree complex

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 the ZORA method Spin-orbit effects are rather small for many cases, but

dominant for Tl-X Coordination by solvent molecules has to be explicitly

taken into account for coordinatively unsaturated systems. Saturating the first coordination shell yields satisfactory results in these cases.

Further solvent contributions within the DFT error bars18