Transcript NMR spin spin couplings for heavy elements

NMR Spin-Spin Coupling
Constants for Heavy
Atom Systems
A ZORA Density Functional
Approach
Jochen Autschbach & Tom Ziegler,
The University of Calgary, Dept. of Chemistry
University Drive 2500, Calgary, Canada, T2N-1N4
Email: [email protected]
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Heavy Atom Compounds

Relativistic theoretical treatment
 Estimated absolute relativistic effects of
>100% for 6th row elements for NMR spinspin coupling constants
 Bonding changes qualitatively due to relativity
 scaling of nonrelativistic orbital coupling
contributions might be misleading
Therefore a full relativistic
treatment for the spin-spin coupling
constants is needed
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Methodology
Spin-spin coupling constants
Indirect interaction K(A,B)

A
Electrons with
orbital- and spinmagnetic moments

B
Direct interaction Nucleus B

Spin magnetic moment  B
Nucleus A

creates magnetic field
Spin magnetic moment 
A
creates magnetic field
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 E
K ( A, B )    with E   Hˆ 
 A B
2
Reduced coupling tensor
K iso  ( K11  K 22  K 33 ) / 3
Reduced
coupling
constant
 
ˆ
we need to know H ( A ,  B )
including relativity
h
J ( A, B )  2  A  B K iso ( A, B )
4
Coupling constants in Hz from the NMR spectrum
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The ZORA one-electron Hamiltonian
2


1
2
c
Hˆ  V  pˆ pˆ ;   2
2
2c  V
Molecular
effective
Kohn-Sham
potential
if used in DFT
Tnrel +
relativistic corrections
of T and V + spin-orbit
effects
1
pˆ  pˆ  A with A  2 
c N
Variationally
stable two-component relativistic
Hamiltonian
Magnetic field due to
nuclear magnetic
moments
N  rN
3
rN
Replacement to account for magnetic fields
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The ZORA Hyperfine Terms




r
1
r
 
 A  

 A 
FC  SD 




j  3 
j 3 
2
2c2
r
2c
 A 
  rA   Requires solution


of 1st-order pertur1  
 
PSO 
(r


)


(r


)

bation equations
j
A
j 3 
2  3 A
1
2c i  rA
rA  
occ
FCSDPSO
(0) ˆ FCSDPSO (1)
Kjk
(A, B)  2  Re i Hj;A
 i;k;B
i
  jk (rA  rB )  rAk rBj
DSO  4
c
rA3rB3
Nuclei A and B,
DSO
DSO
(0)
ˆ
Kjk (A,B)  Hjk;A,B 
directions j and k
of magnetic
moments
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Description 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, Xa approximation for 1st order exchange
potential
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Results I : scalar ZORA
One-bond
metal ligand
couplings
Hg-C
Pt-P
W-C , W-H,
W-P, W-F
Pb-H ,Pb-C, Pb-Cl
FC + PSO + DSO
terms included
J.A., T. Ziegler, JCP 113 (2000), in press
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Tungsten compounds
Lead compounds
**
*
W(CO)6
W(CO)5PF3
W(CO)5PCl3
W(CO)5WI3
cp-W(CO)3H
WF6
PbH4 *
Pb(CH3)2H2
Pb(CH3)3H
Pb(CH3)4
PbCl4 **
* exp. extrapolated from Pb(CH3)xHy ** not directly measured
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Platinum compounds
Mercury compounds
Pt(PF3)4
Hg(CN)2
[Hg(CN)4]2-
(CH3)Hg-X
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
Hg(CH3)2
CH3HgCl
CH3HgBr
CH3HgI
Hg(CN)2
[Hg(CN)4]2-
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Results II : spin-orbit coupling
2 contributions:
a) spin-orbit coupling for 0th order orbitals
b) ZORA spin-dipole (SD) operator
System *)
Hg(CN)2
HgMeBr
cis-PtH2(PMe3)2
*)
K / 1020 kg/m-2C-2
nrel scalar
SO Expt.
227
443
455
578
129
189
203
256
91
102
114
179
VWN functional, Hg-C and Pt-P coupling constants, SO = spin-orbit
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Results III : solvent effects
Experimental
couplings
obtained in
solution

Coordination
of the heavy
atom by
solvent
molecules
important ?
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K / 1020 kg/m-2C-2
*)
Hg(CN)2 +2MeOH +4MeOH
Expt. +4THF
Expt.
443
(450)
542
(549)
578
558
HgMeCl
+3CHCl3 +4CHCl3
Expt. +3DMSO Expt.
203
234
263
HgMeBr
127
HgMeI
+2CHCl3 +3CHCl3
224
234
+2CHCl3 +3CHCl3
Expt. +3DMSO Expt.
263
295
308
Expt. +3DMSO Expt.
125
HgMe2
193
241
+2CHCl3 +3CHCl3
239
295
283
Expt. +3DMSO Expt.
75
108
127
574
(585)
278
122
*)
582
295
131
308
133
Hg-C coupling, VWN functional, scalar ZORA
(numbers in brackets: ZORA spin-orbit) 13
cis-PtH2(PMe3)2
trans-PtH2(PMe3)2
*)
K / 1020 kg/m2C2
Pt-P coupling,
VWN functional.
scalar ZORA
(in brackets:
ZORA spin-orbit)
no solvent *)
+1 acetone
+2 acetone
Expt.
102 (114)
154
170
155
169 (184)
179
277
247
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Summary





NMR shieldings and spin-spin couplings with
ADF now available for light and heavy atom
systems
Based on the variationally stable twocomponent 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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