NMR Spin-Spin Coupling Constants for Heavy Atom Systems A ZORA Density Functional Approach Jochen...
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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: [email protected]
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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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