Transcript NMR spin spin couplings for heavy elements

Theoretical Studies of
Heavy-Atom NMR Spinspin Coupling Constants
With Applications to Solvent
Effects in Heavy Atom NMR
Jochen Autschbach & Tom Ziegler,
University of Calgary, Dept. of Chemistry
University Drive 2500, Calgary, Canada, T2N-1N4
Email: [email protected]
1
What is interesting about
Heavy Metal Compounds ?
Spin-orbit
coupling, scalar relativistic effects
Relativistic theoretical treatment: sizeable
effects on bonding for 6th row elements
(bond contractions, De,ne,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 constants
Coordination by solvent molecules possible
2
Methodology
Spin-spin coupling constants
Indirect coupling K(A,B)

A
Electrons with
orbital- and spinmagnetic moments
Direct coupling
(vanishes for rapidly
rotating molecules)
Nucleus A

Spin magnetic moment  A
creates magnetic field

B
Nucleus B

Spin magnetic moment  B
creates magnetic field
3
 2E
K( A, B) 
wit h E   Hˆ 
AB
Reduced spin-spin coupling tensor
K iso  ( K11  K 22  K 33 ) / 3
Reduced
coupling
constant
we need to know
including relativity


ˆ ( ,  )
H
A
B
h
J(A, B)  2  A B Kiso(A, B)
4
Coupling constants in Hz from the NMR spectrum
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The ZORA one-electron Hamiltonian
2
1
2c
ˆ
H  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
coupling
Variationally
stable two-component relativistic
Hamiltonian
Magnetic field due to
nuclear magnetic
moments
1
N  rN
pˆ  pˆ  A w ith A  2 
3
c N
rN
Replacement to account for magnetic fields
5
The ZORA Hyperfine Terms
 rA  1
 rA 
1
FC  SD  2  j  3  2  j  3 
2c
 rA  2c
 rA  Requires solution
st-order perturof
1
1 
 
PSO  2  3 (rA  ) j  (rA  ) j 3 
bation equations
2c i rA
K
FC  SD  PSO
jk
rA 
oc c
(A, B)  2  Re 
(0)
i
FC  SD PSO
(1)
ˆ
H j; A
 i; k; B
i
  jk (rA rB )  rAkrBj
DSO  4
3 3
c
rA rB
ˆ DSO  (0)
K DSO
(A,
B)

H
jk
jk ; A, B
Nuclei A and B,
directions j and k,
point-like magnetic
dipoles
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Description 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, Xa or VWN 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
JCP 113 (2000), 936.
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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 : spinorbit coupling
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
System *)
Spin-orbit (SO) coupling causes cross terms between the spin-dependent operators (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.
*)
VWN + Becke86 + Perdew 88 functional, Tl-X coupling constants
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Results III : solvent effects
Experimental results on pages 9 and 10 obtained from
solution. The cases where results are unsatisfactory are
marked red (linear Hg and square planar Pt complexes)
SO coupling yields only minor
corrections in all these cases!
Is coordination of the heavy
atoms by solvent molecules
important?
Some structures that
were optimized,
explicitly including a
number of solvent
molecules
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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
*)
JACS 123 (2001), 3341.
Hg-C coupling, VWN functional, scalar ZORA
(numbers in parentheses: ZORA spin-orbit) 13
Pt complexes
cis-PtH2(PMe3)2
trans-PtH2(PMe3)2
*)
K / 1020 kg/m2C2
Pt-P coupling,
VWN functional.
scalar ZORA
(in parentheses:
ZORA spin-orbit)
no solvent *)
107 (97)
170
+1 acetone
154
155
257
+2 acetone
N/A
169 (158)
277
Expt.
179
247
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Results III : more solvent effects
Two heavy nuclei:
A Pt-Tl cyano complex
Complex I
N
Two-bond coupling much larger
than one-bond coupling
N
C
N
C
2.55 (2.60)
C
Pt
Tl
1.93 (2.01)
C
C
2.15 (2.13) *)
C
N
Experiment: **)
1J(Tl-Pt) : 57 kHz
1J(Tl-CB) : 2.4 kHz
2J(Tl-CA) : 9.7 kHz
2J(Tl-CC) : 0.5 kHz
Four water molecules can coordinate to
Tl in aqueous solution (exp. confirmed)
*) Optimized bond distances, experimental bond lengths in parentheses (in Å)
**) J. Glaser et al., JACS 117 (1995), 7550.
N
N
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Results III : more solvent effects
Spin-spin couplings complex I, J / kHz
Coupling
nrel
scalar
Scalar SO
Exp.
+ 4H2O + 4H2O (in H2O)
19.0
43.1
40.3
57.0
Pt-Tl
5.4
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 structure
and 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 effects
free
complex: both couplings
are comparably large in magnitude but of opposite sign
inclusion of solvent molecules
shifts both couplings. The onebond coupling is – as expected –
influenced much stronger.
As a result, the two-bond coupling is much larger than the onebond coupling
Delocalized bonds along the
C-Pt-Tl-C axis are responsible
for the large magnitude of the
two-bond Tl-C coupling in the
free complex
JACS 123 (2001), in press.
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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 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 bars
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