534 Inorganic Chemistry, Vol. 40, No. 3, 2001
Koch and Bargon
The Spin Density Matrix and the Product Operator
Formalism
A theoretical interpretation of the PHIP phenomenon based
on the product operator formalism8 allows us to forecast or
interpret PHIP spectra. In this description, the spin density
matrix of parahydrogen is represented by σparahydrogen ) I1I2. On
transferring the parahydrogen molecule into an AX spin system
during hydrogenation, its spin density matrix is propagated,
governed by the Hamiltonian for weakly coupled systems.
Averaging over the duration of the hydrogenation, the spin
density matrix of the former two parahydrogen atoms in the
resulting AX spin system of the hydrogenation product simpli-
fies to σPASADENA ) I1zI2z. The subscript z denotes the orientation
in a Cartesian coordinate system, whereby z coincides with the
direction of the external magnetic field, and the numbers mark
the respective protons. By contrast, the spin density matrix of
two hydrogen nuclei at thermal equilibrium, i.e., long after the
reaction, is described by σthermal ) I1z + I2z.
Figure 1. The apparatus used to carry out the hydrogenation inside of
the NMR magnet. The device is installed on top of the magnet. Before
the hydrogenation starts, the sled can be lowered by about 10 cm by
means of the pulleys. Thereby a glass capillary connected to the
parahydrogen source by means of a Teflon tube can be lowered into
the NMR probe actuated by an electromagnet, which is electrically
controlled by the computer of the NMR spectrometer.
Application of a radio frequency pulse corresponding to the
flip angle â and the phase y to the initial magnetization
σPASADENA ) I1zI2z generates three operator terms according to
âIy
98
I1zI2z
cos2 â I1zI2z + cos â sin â (I1zI2x + I1xI2z) + sin2 â I1xI2x
from parahydrogen cause in-phase splittings in the PHIP
resonances, just as is the case in regular (“thermal”) NMR
spectra.
The first and the last term thereof represent zero and double
quantum coherences, respectively, which cannot be detected
under these conditions. However, the term in the middle
corresponds to an observable single quantum coherence, which
is maximized if the flip angle â equals π/4. Therefore, when
recording PHIP spectra, â is set to half the conventional value
used in ordinary NMR spectroscopy, where π/2 represents the
optimal value.
This fact can be taken advantage of in order to eliminate
interfering resonances stemming from unpolarized systems, i.e.,
from molecules which do not participate in the hydrogenation
sequence. This includes the resonances stemming from the
solvent, from unpolarized starting material, or from previously
formed product molecules that have since reached thermal
equilibrium. For this purpose, individual scans are accumulated,
whereby the flip angles are alternated between -π/4 and 3π/4,
consecutively. As a consequence of this change of the flip angle
by 180° between two consecutive pulses, the amplitudes of
regular, i.e., of “thermal”, NMR resonances alternate in signs,
whereas the signs of the PHIP signals remain the same,
irrespectively. Accordingly, upon accumulating the correspond-
ing signals, the “unpolarized” resonances are suppressed and
eliminated, whereas the “polarized” PHIP resonances add up
and become accumulated to yield a better signal-to-noise ratio.
In Situ PHIP NMR Spectroscopy of Homogeneous
Hydrogenations
This paper describes the use of PHIP to detect some new
dihydride products at low concentrations which can otherwise
not be seen using conventional NMR methods. For this purpose,
the hydrogenation with parahydrogen is carried out in situ using
the apparatus in Figure 1, which allows us to monitor the
reaction and thereby determine its kinetic constants.
Results and Discussion
Reactions of [RhCl(NBD)]2 with Parahydrogen in the
Presence of Tertiary Phosphines. The binuclear precursor (di-
µ-chlorobis[η4-2,5-norbornadiene]rhodium(I) ) [(Rh(NBD)Cl]2)
is well suited for the in situ preparation of a variety of
homogeneous hydrogenation catalysts, if tertiary phosphines
(here PMe3, PMe2Ph, PMePh2, PEt3, PEt2Ph, PEtPh2, or P(n-
butyl)3) are added to the solution of this precursor. Upon the
addition of dihydrogen to these mixtures, NBD is hydrogenated
off, and the mononuclear dihydride species Rh(H)2ClL3 is
generated, most likely via the complex RhClL3 as an intermedi-
ate. This dihydride complex plays a key role as an intermediate
in any subsequent catalytic hydrogenation.
The single quantum coherence I1zI2x + I1xI2z develops under
the Hamiltonian for weakly coupled systems into the term
sin(πJ12t)(I1y + I2y). The sine modulation of the term (I1y + I2y),
corresponding to the coupling between the transferred parahy-
drogen protons, is responsible for the observed antiphase
splitting in the resonances of the PHIP spectra. By contrast,
the regular “thermal” resonances of species, which are chemi-
cally uninvolved in the hydrogenation reactions, experience a
cosine modulation governed by their respective couplings,
resulting in in-phase splittings of the resonances in the PHIP
NMR spectra. Likewise, couplings to protons which do not stem
As a characteristic example, Figure 2a shows the results
obtained upon the addition of parahydrogen to a solution of 10
mg [Rh(NBD)Cl]2 and 19 µL PMePh2 in acetone-d6 (Rh: P )
1:3). The strong polarized resonances of the dihydride protons
of the complex Rh(H)2Cl(PMePh2)3 are observed in the 1H NMR
spectrum, whereby the hydride trans to a PMePh2 ligand occurs
at δΗ ) -9.4 ppm, whereas the hydride trans to the chloride
has a higher chemical shift and appears at δH_ ) -17.6 ppm.
The latter is characteristic for hydride protons in the trans
position to such an electronegative ligand. The hydride reso-
nance at lower field shows a large coupling to one trans
phosphorus (JHP(trans) ) 178.6 Hz), an additional coupling to
two equivalent cis phosphorus nuclei (JHP(cis) ) 14.1 Hz), a
(8) Sørensen, O. W. Prog. NMR Spectrosc. 1989, 21, 503-569.