Studies on the configuration of nitrogenous stereogenic centres in adducts of rhodium(II) tetraacylates with chiral amines: the application of 1H and 13C NMR spectroscopy

Article abstract of DOI:10.1016/j.tetasy.2009.09.021

The ¹H and ¹³C NMR spectra of enantiomerically pure amines (S)-N,N-dimethyl-1-phenylethylamine, (S)-N-methyl-1-phenylethylamine, (S)-N-ethyl-1-phenylethylamine and (S)-N-ethyl-N-methyl-1-phenylethylamine in the presence of a twofold molar excess of dirhodium(II) tetratrifluoroacetate and dirhodium(II) Mosher's acid derivatives [(4S) and (4R)] were measured in CDCl₃ as a solvent. The amines having various substituents at the nitrogen atom (H, CH₃ and CH₂CH₃) formed in such conditions as an equilibrium mixture of C_SN_R and C_SN_S 1:1 adducts. The signals of both diastereoisomers were observed in NMR spectra at either room temperature (303 K) or moderately decreased temperatures (263-273 K). The rates of mutual diastereoisomer conversion were estimated by selective inversion recovery experiments and varied from less than 0.1 to ca. 10 s^-1, depending on the ligand and temperature. Analysis of ¹³C NMR data and NOE experimental data resulted in the unambiguous determination of the configuration at the nitrogen atom with respect to the carbon stereogenic centre. Modelling of adduct structures and calculations of molecular energy and NMR parameters (GIAO) using Density Functional Theory (DFT) were performed in order to support the experimental findings. The calculations were carried out using 3-21G//B3LYP (structure optimizing) and 311G(2d,p)/LanL2DZ//B3LYP theory levels (molecular energy and NMR shielding).

Full text of DOI:10.1016/j.tetasy.2009.09.021

Tetrahedron: Asymmetry 20 (2009) 2331–2343
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Tetrahedron: Asymmetry
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Studies on the configuration of nitrogenous stereogenic centres in adducts
1
of rhodium(II) tetraacylates with chiral amines: the application of H and 13C
NMR spectroscopy
*
´
´
Jarosław Jazwinski , Agnieszka Sadlej
Institute of Organic Chemistry, Polish Academy of Sciences, 01-224 Warszawa, ul. Kasprzaka 44/52, Poland
a r t i c l e i n f o
a b s t r a c t
The 1H and 13C NMR spectra of enantiomerically pure amines (S)-N,N-dimethyl-1-phenylethylamine, (S)-
N-methyl-1-phenylethylamine, (S)-N-ethyl-1-phenylethylamine and (S)-N-ethyl-N-methyl-1-phenyleth-
ylamine in the presence of a twofold molar excess of dirhodium(II) tetratrifluoroacetate and dirho-
dium(II) Mosher’s acid derivatives [(4S) and (4R)] were measured in CDCl3 as a solvent. The amines
having various substituents at the nitrogen atom (H, CH3 and CH2CH3) formed in such conditions as an
equilibrium mixture of CSNR and CSNS 1:1 adducts. The signals of both diastereoisomers were observed
in NMR spectra at either room temperature (303 K) or moderately decreased temperatures (263–
273 K). The rates of mutual diastereoisomer conversion were estimated by selective inversion recovery
experiments and varied from less than 0.1 to ca. 10 sꢀ1, depending on the ligand and temperature. Anal-
ysis of 13C NMR data and NOE experimental data resulted in the unambiguous determination of the con-
figuration at the nitrogen atom with respect to the carbon stereogenic centre.
Article history:
Received 28 July 2009
Accepted 10 September 2009
Available online 29 October 2009
Modelling of adduct structures and calculations of molecular energy and NMR parameters (GIAO) using
Density Functional Theory (DFT) were performed in order to support the experimental findings. The cal-
culations were carried out using 3-21G//B3LYP (structure optimizing) and 311G(2d,p)/LanL2DZ//B3LYP
theory levels (molecular energy and NMR shielding).
Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
used in NMR spectroscopy as chiral recognition agent allowing to
determine the enantiomeric purity of chiral compounds.19
Rhodium(II) dimeric salts (Fig. 1) are known to form adducts
with a large number of organic compounds.1 Two complexation
modes of a ligand, at the axial and/or equatorial positions of the
metal–metal unit, and various adduct stoichiometries yield, poten-
tially, a large family of species.
Dirhodium methods are based on adduct formation in situ, di-
rectly in a solution. The methods work correctly if a well-defined,
stable adduct was formed. The solution instability caused by the
slow adduct rearrangement and formation of an equilibrium mix-
ture of a few species were the frequently occurring complications
of dirhodium methods.11,12 The spectra of such mixtures are
usually time- and temperature-dependent. In these cases, the
knowledge of the mixture composition is very helpful in the
comprehension of spectral results.
Due to complexation properties, rhodium(II) dimeric salts have
been applied in the fields of chemistry, biology and medicine. Rho-
dium(II) tetraacetate acting as the carbene-stabilizing agent has
been used as a catalyst in organic synthesis.2 Enantiomerically pure
chiral rhodium(II) carboxylates and carboxamidates are widely used
as chiral catalysts.3,4 Some rhodium(II) salts have been able to
inhibit DNA replication by binding to nucleobases; this feature
has allowed the testing of these salts in medicine, as anticancer
agents.5–10 So-called dirhodium methods concern the applica-
tion of rhodium(II) tetraacylates in the spectroscopy of organic
compounds Due to absorption in the visible range, rhodium(II)
tetraacetate and tetratrifluoroacetate have been used as the auxil-
iary reagents in CD spectroscopy, as sources of chromophoric
groups.11–18 Enantiomerically pure Mosher’s acid salt has been
Our previous investigations have included 1H, 13C and 15N NMR
studies on adducts of rhodium(II) tetraacylates with some amines
in the CDCl3 solution and in the solid state.11,12,20–22 The formation
of a relatively stable (in the NMR time scale) nitrogenous stereo-
genic centre in complexes due to the slow down of the amine
inversion turned out to be the most interesting result of the work.
Thus, a chiral, enantiomerically pure dirhodium salt, for example,
(4S)-Rh2MTPA4 formed a mixture of two 1:1 diastereoisomers with
the amine NR1R2R3 in CDCl3 solution, whereas racemic N-methyl-
1-phenylethylamine produced four 1:1 adducts. The number of
isomers in the case of 1:2 adducts (Rh2MTPA4L2) ranged from three
to ten, depending on the amine. The signals of all species could be
observed in NMR experiments.21 According to Boltzmann’s law, the
* Corresponding author. Tel.: +48 22 3432009; fax: +48 22 6326681.
E-mail address: jarjazw@icho.edu.pl (J. Jaz´win´ ski).
0957-4166/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tetasy.2009.09.021

´
´
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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
R
R
O
Rh
O
O
Rh
O
O
O
Ph
R1
R2
O
R
O
C
N
H3C
H
R
1
2
3
1
2
R = R = CH
1
2
Rh2AcO4
R = CH3
R = CF3
R = (S)- or (R)-C(CF3)OCH3)(Ph)
R = H, R = CH3
3 R1 = H, R2 = C2H6
Rh2TFA4
4 R1 = CH3, R2 = C2H6
Rh2MTPA4
Figure 1. Dimeric rhodium(II) tetraacylates and amines used as ligands (MTPA-H ꢁ
a-methoxy-a-(trifluoromethyl)-phenylacetic acid = Mosher’s acid).
constitution of such an equilibrium mixture was expected to be
temperature-dependent.
ducts; and the exchange between the 1:2 adduct and free amine
in the presence of an excess of ligand. Simultaneously, the mutual
exchange of two non-equivalent N(CH3)2 groups was expected.
Such exchanges (pro-R to pro-S and vice versa) occurred either
by the attack of the rhodium salt to the nitrogen atom in the ad-
duct and structure inversion (SN2-like mechanism) or via adduct
dissociation, ligand inversion and adduct recombination.19 The rate
of pro-R/pro-S exchange of NCH3 indicated the stability of the par-
ticular configuration at the nitrogen atom. The question arose as to
whether the lifetime of a structure was sufficiently long enough to
identify the N-methyl groups (i.e., which one is pro-R, and which
one is pro-S), or establish the configuration of the nitrogenous ste-
reogenic centre by NMR methods. The answer was not obvious; it
should be noted that 1 in an Rh2AcO4 solution, regardless of tem-
perature and stoichiometry, shows one singlet originating from
both N(CH3)2 groups.20
*
*
Adducts of some chiral amines R -NR1R2 (R denotes a group
having a carbon stereogenic centre) with rhodium(II) tetraacylates
were the subject of the present investigations. This included
the application of 1H NMR and 13C NMR techniques to establish
the configuration at the nitrogen atom in relation to the carbon
stereogenic centre. Enantiomerically pure amines (S)-N,N-di-
methyl-1-phenylethylamine 1, (S)-N-methyl-1-phenylethylamine
2, (S)-N-ethyl-1-phenylethylamine 3 and (S)-N-ethyl-N-methyl-1-
phenylethylamine 4 were selected as ligands; three rhodium(II)
salts, Rh2TFA4, (4S)- and (4R)-Rh2MTPA4 were used as substrates.
2. Results and discussion
2.1. Adducts of (S)-N,N-dimethyl-1-phenylethylamine 1
Herein, exchange processes were examined by a method based
on the selective inversion of one signal and observation of signals
evolution with time.23,24 The inspection of a non-perturbed signal
was the most convenient means for the detection of an exchange.
Theoretically, if no exchange takes place, the intensity of this signal
should be independent of time. In practice, some signal enhance-
ment was possible due to NOE between two groups attached to
the same atom. The evolution of N-methyl signals in Rh2TFA4 and
1 solution at various temperatures was shown in Figure 3. For
the 1:1 adduct (Fig. 3a and b), the curves corresponding to the
non-inverted signal revealed the decrease of the pro-R/pro-S ex-
change rate with temperature reduction, up to very low value at
273 K. In case of the 1:1.33 mixture, containing two adducts, the
inversion of one signal in the 1:2 adduct (Fig. 3c) caused two differ-
ent responses of two N-methyl signals in the 1:1 adduct. This
asymmetry became obvious if one considered the fact that the
polarization of N-methyl groups was retained when the 1:2 adduct
lost the ligand producing a 1:1 adduct. The curve, corresponding to
the pro-R/pro-S mutual exchange in the 1:2 adduct, can be seen be-
tween these two lines arising from ligand exchanges. Finally, for
the 1:4 mixture, containing the 1:2 adduct and non-bonded (free)
ligand 1 (Fig. 3d), the inversion of the NCH3 signal in 1 resulted in
the equal response of both NCH3 signals in the adduct.
(S)-N,N-Dimethyl-1-phenylethylamine 1 was the first ligand
under consideration used in the present work as a model in order
to test our research methods. Some NMR data concerning adducts
of 1 have been reported previously.20 Rhodium(II) tetratrifluoroac-
etate formed with 1 the 1:1 or/and 1:2 adducts, depending on the
components’ molar ratio in solution. 1H NMR spectra showed up
four groups of signals (Table 1); from them N(CH3)2 peaks were
the most interesting. N-Methyl groups produced two signals in
the 1H NMR spectrum, since these groups were chemically non-
equivalent in the adduct. The appearance of N(CH3)2 signals de-
pended on the molar ratio of Rh2TFA4 to 1 in the solution and
the sample temperature (Fig. 2). The 1:0.5 mixture assured the
presence of a 1:1 adduct in the solution (and an excess of Rh2TFA4).
Consequently two N-methyl signals appeared in the 1H NMR spec-
trum. This was the only sample that exhibited narrow signals over
the whole temperature range, from 268 to 318 K. The 1:1.33 mix-
ture showed up to four NCH3 signals (268 K), approximately of the
same intensity, derived from the 1:1 and 1:2 adducts. The 1:2 mix-
ture contained solely the 1:2 adduct and provided two NCH3 sig-
nals. Finally, the 1:4 mixture showed two NCH3 signals
originating from the 1:2 adduct and one peak produced by non-
complexed amine.
For an equally populated, two-site exchange system, an ex-
change rate k may be calculated by curve fitting, by the application
of either Eq. (2) to the inverted signal or Eq. (3) to non-perturbed
signal. Depending on the experiment and signals used for the
A few exchange processes were potentially possible in the solu-
tions: the exchange of 1 between the 1:1 adduct and dirhodium
salt in the 1:0.5 solution; the exchange involving 1:1 and 1:2 ad-

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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2333
Table 1
1H and 13C NMR chemical shifts for adducts of some amines with dirhodium saltsa
Adduct
T (K)
CH
CCH3
NH
—
NCH3
NCH2CH3
NCH2CH3
Rh2TFA4-1
303
4.80(67.0)
1.69(17.9)
2.84(38.8)b
2.62(48.5)c
2.82, 2.59
268
268d
263
4.79
1.66
—
—
4.86d
1.68d
2.88d, 2.70d
Rh2TFA4-2
NR
4.97(59.5)
4.60(63.8)
1.80(14.2)
1.66(22.3)
5.41
5.19
2.86(30.7)
2.67(38.0)
NS
NR
(4S)-Rh2MTPA4-2
(4S)-Rh2MTPA4-3
(4R)-Rh2MTPA4-3
Rh2TFA4-4
303
273
273
273
303
303
5.16(58.8)
4.67(63.7)
1.84(13.2)
1.74(23.2)
5.29
5.02
2.90(29.8)
2.68(37.8)
—
NS
NR
5.05(58.1)
4.71(61.5)
1.84(13.9)
1.67(23.2)
4.90
4.86
3.47, 3.25(39.8)
3.19, 3.02(44.8)e
1.07(15.1)
1.15(14.2)
NS
NR
—
—
5.01(58.4)
4.65(61.6)
4.71e(69.3)
1.97(14.0)
1.70(23.0)
1.72(18.6)
4.88
4.85
—
3.45, 3.24(39.9)
3.30, 3.15(44.7)e
3.78, 3.00(47.7)
1.08(15.1)
1.12(14.4)
1.13(9.9)
NS
NR
NS
—
2.59(43.8)
—
4.75(68.3)
4.92(69.1)
1.60(18.4)
1.73(19.4)
2.87(35.5)
2.65(44.0)
3.00e(35.3)
2.71(43.8)
3.36, 2.69(55.6)
0.95(10.4)
1.21(10.6)
(4S)-Rh2MTPA4-4
(4R)-Rh2MTPA4-4
NR
NS
—
—
3.81e, 3.28e(48.0)
4.92(68.5)
4.86e(69.2)
4.88e(68.2)
1.73(19.4)
1.74(19.2)
3.48, 2.83(55.6)
3.78, 3.10e(48.0)
3.50, 3.00e(55.2)
0.89(10.9)
1.17(10.3)
NR
NS
—
—
1.70(19.4)
3.02(35.4)
0.86(10.5)
a
All measurements were performed in CDCl3 solutions containing dirhodium salt and ligand in a molar ratio of 1:0.5 (if not marked otherwise); 1H (13C) chemical shifts
(ppm) are given with respect to the CHCl3 residual signal (1H, 7.26 ppm,) or CDCl3 central peak (13C, 77.0 ppm). Chemical shifts of the main adduct in each mixture are
underlined. Chemical shifts of Ph groups, if assigned and identified, are as follows (Ph ipso, ortho, meta and para protons are denoted as Ci o, m and p, respectively): Rh2TFA4-1;
303 K: (147.1)Ci, 7.60(130.2)o, 7.51(128.3)m, 7.48(126.3)p; 268 K: 7.61o; 268 K. Adduct 1:2: 7.52o; Rh2TFA4-2, CSNR: 7.61(126.9)o, 7.53(128.3)m, 7.44(127.9)p; CSNS adduct
shows practically the same chemical shifts; (4S)-Rh2MTPA4-2, CSNR: 7.58o, 3.11 OCH3; CSNS: 7.53o, 3.12 OCH3; (4S)-Rh2MTPA4-3, CSNR: 7.57(127.4)o, 7.46(129.2)p,
7.40(127.9)m, 3.08 OCH3; CSNS: 3.10 OCH3; (4R)-Rh2MTPA4-3, CSNR: 7.52(127.4)o, 7.44(129.1)m, 7.40(128.0)p, 3.08 OCH3; CSNS: 3.10 OCH3; Rh2TFA4-4, (4S)-Rh2MTPA4-4 and
(4S)-Rh2MTPA4-4: not assigned. The reference data of free ligands are as follow: 1:7a 1.38(20.1) CCH3; 2.20(43.1) NCH3; 3.25(65.9) CH; 7.30 (127.4, 128.1)o,m, 7.23(126.8)p,
(144.0)Ci .2:7a 1.33(23.8) CCH3; 2.31(34.5) NCH3; 3.64(60.2) CH; 7.31(128.4, 126.5)o,m; 7.24(126.8)p; (145.4)Ci; NH not observed. 3: 1.11(15.2) CH2CH3; 1.39(24.1) CCH3; 2.52,
2.57(41.8) CH2CH3; 3.81(58.1) CH; 7.06–7.24(126.3, 126.6, 128.2)o,m,p; 145.7Ci; 4: 1.09(12.0)
mCH2CH3; 1.42(19.0) CCH3; 2.25(37.9) NCH3; 2.40, 2.56(48.1) CH2CH3; 3.60(63.1)
CH; 7.25–7.41(126.6, 127.5, 128.0)o,m,p; 144.1Ci.
b
Pro-R methyl group.
Pro-S methyl group.
1:2 Adduct.
c
d
e
Signals were identified by means of 2D 1H, 1H COSY or 13C, 1H gHSQC spectra.
Figure 2. The 1H NMR signals of N-methyl groups in various Rh2TFA4 and 1 mixtures (CDCl3 solutions), at 303 K (upper traces) and 268 K (lower traces). The spectra represent
the Rh2TFA4 and 1 solution in molar ratio of 1:0.5 (a), 1:1.33 (b), 1:2 (c) and 1:4 (d). Diamonds Ç and squares j indicate the signals of the 1:1 and 1:2 adducts, respectively;
and asterisks (*) indicate the signals of impurity or water. Vertical scales were adjusted arbitrarily.
calculations, one can obtain two quantities: the rate of the mutual
exchange of the two N-methyl groups (pro-R/pro-S exchange) or
the rates of ligand exchange between species. Thus, for a 1:0.5
sample (i.e., for a sample containing the 1:1 adduct only) curve fit-
tings provided the rate of pro-R/pro-S exchange from 0.6 to 1.0 sꢀ1
(318 K) and from 0.1 to 0.3 sꢀ1 (303 K), depending on which signal
was inverted and which data set was used for the calculations. For
low temperature experiments (288 K and below) the calculations
failed; nevertheless a rough estimation suggested the rate k to be
much less than 0.1 sꢀ1. Similar procedures when applied to the
1:2 sample (268 K) provided the rates from 0.8 to 2.3 sꢀ1 for the
1:2 adduct.
The 1:4 mixture contains equimolar quantities of bonded and
free amine 1; thus the signals of CCH3 groups form an equally

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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2334
Figure 3. Selective inversion recovery experiments: evolution with time of N-methyl signals in Rh2TFA4-1 adducts: (a) 1:0.5 mixture, 318 K; blue and red curves represent
the evolution of inverted and non-perturbed signals, respectively; points represent fitted lines; (b) 1:0.5 mixture, the evolution of non-perturbed signal at 318 K (red), 303 K
(green) and 273 K (blue line). Note different vertical scale in plot (a) and (b); (c) 1:1.33 mixture, 268 K; the evolution of non-perturbed signals of the 1:1 adduct (blue and
black curves) and one signal of the 1:2 adduct (red) while the second signal was inverted; (d) 1:4 mixture, 268 K; the evolution of two signals of the 1:2 adduct (red line and
blue points) while the signal of non-bonded amine was inverted; the signals perfectly overlapped.
two-site populated system, meaning Eqs. (2) and (3) could be ap-
plied. The exchange rate of 1 between an adduct and a solution
was found to be from 2.2 to 3.2 sꢀ1. Unfortunately, a similar proce-
dure was not useful in case of 1:1.33 solution (containing the 1:1
and 1:2 adducts), due to CCH3 signals overlapping.
This led us to the following conclusions: (i) N-methyl groups in
the adducts underwent mutual exchange (pro-R/pro-S exchange)
with rates varying from 0.1 sꢀ1 to ca. 2 sꢀ1, depending on the tem-
perature and on Rh2TFA4 to ligand molar ratio; (ii) pro-R/pro-S
exchange in the 1:1 adduct was very slow at the reduced temper-
ature (k ꢂ 0.1 sꢀ1 below 288 K); (iii) consequently, the lifetime 1/k
of a particular configuration varied from 0.5 to a few seconds, and
was long in comparison to the 1H spin-lattice relaxation time T1
(Table 2). It is important to note the following: the aforementioned
pro-R/pro-S exchange rate probably did not describe a single pro-
cess, but it was the outcome of several factors. The slow pro-R/
pro-S exchange did not imply the long lifetime of the particular
conformer. Finally, the ligand exchange rate and pro-R/pro-S ex-
change rate concerned two different processes. This differentiation
is important in the next parts of the work. The measurements of
the exchange rates in CSNR/CSNS adduct mixture (e.g., adducts of
2, 3 and 4, see below) provided the diastereomerization rate, which
is generally different to the ligand exchange rate.
In the next stage of work, DFT calculations were performed. The
structures of three Rh2TFA4-1 conformers (Fig. 5) were optimized
and the corresponding energies and NMR parameters were calcu-
lated. The energies were calculated assuming either a single mole-
cule in vacuum or solvation (CHCl3, IEFPCM model). Both
approaches unambiguously indicated that the conformer I is priv-
ileged (>99% at 303 K). 1H NMR NOE experiments (DPFGSE-NOE)
agreed with the theoretical findings (Fig. 6). Inversion of low shift
NCH3 signal resulted in the enhancement of Phortho and CH signals;
and inversion of the second NCH3 enhanced the Phortho and CCH3
signals. The remaining experiments confirmed these interactions,
since instant inversion of the Phortho signal resulted in the answer
of both N-methyl peaks. The different behaviour of the NCH3 sig-
nals at various temperatures was an interesting result of the exper-
2D EXSY technique was expected to give an insight into the
overall exchange pattern. The EXSY spectrum of the 1:0.5 solution
taken at room temperature (303 K) contained positive off-diagonal
peaks corresponding to the pro-R/pro-S exchange of the N-methyl
groups. These peaks vanished at 288 K due to an exchange slow
down and became negative at 268 K because of dominance of the
NOE enhancement over exchange effects. The sum of rates
k + k estimated on the basis of peak integrations24 was found
ꢀ1
to be 0.3 sꢀ1 at 303 K. Similar experiments performed for the 1:2
adduct provided the k + k value of 2.1 sꢀ1 at 268 K. This means
ꢀ1
that the exchange is faster than that in the 1:1 adduct (k ꢂ 0.1 sꢀ1
at 273 K).
The remaining samples (1:1.33 and 1:4) showed up more com-
plicated spectra (Fig. 4). The on-diagonal N-methyl signal in the 1:2
adduct (1:1.33 mixture) (Fig. 4a) correlated with the second NCH3
peak (pro-R/pro-S exchange), and with two NCH3 signals of the 1:1
adduct (ligand exchange). The various intensities of these signals
were caused by three different exchange rates. The lack of a peak
attributed to the pro-R/pro-S exchange in the 1:1 adduct was an
interesting feature of this spectrum. The same effect appeared in
the spectrum of the 1:4 sample (Fig. 4b); a peak corresponding
to the pro-R/pro-S exchange was weak in comparison to the other
signals. Such a pattern suggested that the mechanism of this ex-
change was not the direct NCH3 exchange in an adduct but an ex-
change via adduct—free ligand—adduct. The ligand exchange rate,
calculated on the basis of CCH3 signals, was found to be 5.1 sꢀ1
(k + kꢀ1); similar value (5.2 sꢀ1) provided CH signals.

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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2335
Figure 4. EXSY spectra of Rh2TFA4: 1 solution (268 K): (a) 1:1.33 sample (NCH3 region); (b) 1:4 solution (aliphatic region). Diamonds (Ç) indicate the signals of the 1:1
adduct; squares (j) denote the signals of the 1:2 adduct, and circles (d) indicate the signals of non-complexed ligand 1. Off-diagonal signals corresponding to the pro-R/pro-S
exchange are indicated by red asterisks; and the signals related to the ligand exchange are indicated by blue asterisks.
The calculated 1H and 13C chemical shifts for three conformers
are shown in Table 3. The calculations were performed both for a
single molecule and assuming solvation (CHCl3, IEFPCM solvation
Table 2
Non-selective and bi-selective (in parentheses) 1H longitudinal relaxation times T1 (s)
in Rh2TFA4-1 at various temperaturesa
T (K)
Phortho
0.669
CH
CCH3
0.399
NH
NCH3
model). Generally, it is known that calculated chemical shifts differ
from experimental data; the differences depend on the method
and basis set used for the calculations.25 On the other hand,
theoretical and experimental data sets should satisfy the equation
dcalc = adexp + b. Herein, a correlation coefficient and standard
errors were used as criteria of correctness of the structure identifi-
cation. The best correlation between the observed and calculated
shifts was found for conformer I, although the differences were
rather small (Table 3). Standard errors associated with linear
regression, measuring how closely data points spread about the
regression line, were more diversified, and unambiguously indi-
cated to conformer I. No significant differences between solvated
and non-solvated molecules occurred.
273
0.566
0.235 (0.217)
0.226 (0.213)
0.285 (0.299)
0.263 (0.275)
0.362 (0.382)
0.329 (0.340)
0.447 (0.466)
0.408 (0.415)
288
303
318
0.817
1.006
1.189
0.771
0.924
1.067
0.771
0.924
1.067
a
All samples contained a CDCl3 solution of Rh2TFA4 and 1 in a molar ratio of
1:0.5. The measurements were performed using either non-selective or selective
inversion recovery sequence.
Finally, we attempted to estimate the distances between the
hydrogen atoms in the adduct by the use of NOE build-up mea-
surements. It is known that this technique provides rather inaccu-
rate results for flexible molecules.26 On the other hand, in the case
iment. At low temperature, while one NCH3 signal was inverted,
the second one was positive because of an NOE enhancement.
However, at room temperature this signal was negative, due to
the domination of exchange (i.e., saturation transfer) over the NOE.
Ph
H
Me
Me
Me
H
Me
Ph
Me
Me
H
Me
Ph
N
N
N
Me
Me
72º
77º
39º
44º
51º
77º
Rh
Rh
Rh
0.0 (0.0)
I
6.1 (6.6)
III
kcal/mol
5.6 (5.4)
II
Figure 5. Three conformers of the 1:1 Rh2TFA4-1 adduct were used as input for structure optimizations (for the sake of clarity, one Rh atom was shown), relative molecular
energies and some structural parameters (dihedral angles Rh–N–C–CH3, Rh–N–C–H, Rh–N–C–Ci). Energy calculations were performed for optimized structures applying
either single molecule in vacuum or assuming the IEFPCM (CHCl3) solvation model (in parentheses). The energy of I was assumed to be 0.0 kcal/mol.

´
´
2336
J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
Ph
Me
Me
H
N
Me
Rh
Figure 6. 1H NMR (DPFGSE-NOE) spectra of the 1:1 Rh2TFA4-1 adduct, at 268 K. The inset shows NCH3 signals in the spectrum taken at 303 K, while high-frequency NCH3
signal is inverted. Dominance of the NOE enhancement over exchange effects at low temperature is clearly visible.
of Rh2TFA4-1, the lifetime of the adduct was long, and one con-
cating that the experimental error was comparable with the mea-
sured values.
former was privileged. Averaged distances (hdꢀ3iꢀ1/3 26
)
between
CH, Phortho and CH3 groups for optimized structures I–III, NOE
build-up rates and some estimated H–H distances were collected
in Table 4 (see Section 4 for the details). The measurements pro-
vided reasonable, but rather qualitative results. For example, ex-
pected Phortho–NCH3 (pro-S) and Phortho–NCH3 (pro-R) distances
were 3.61 and 3.41 Å, while the values of 3.64 and 3.35 Å were ob-
tained from an NOE build-up using Phortho–CCH3 distance as a
reference.
The NULL technique is another approach to H–H distance deter-
mination.27 The method is based on the measurements of two
relaxation times: total T1, by conventional inversion recovery tech-
nique, and selective T1sel, with inversion of all signals, except one.
The differences 1/T1sel ꢀ 1/T1 are proportional to H–H distances to
an atom in question. However, this method failed in the case of
Rh2TFA4-1 adduct, probably due to the short 1H relaxation time
T1. The experiment was repeated twice and the linear correlation
between two sets of (1/T1sel ꢀ 1/T1) values was expected. In fact
the correlation was very poor (correlation coefficient of 0.6) indi-
2.2. Adducts of (S)-N-methyl-1-phenylethylamine 2
Some 1H, 13C and 15N NMR chemical shifts of Rh2TFA4 and
Rh2MTPA4 adducts with 2 were reported previously.20,21 The mea-
surements taken at reduced temperature revealed that 2 forms two
1:1 adducts with each of the above dirhodium salts. However, the
configuration of the nitrogenous stereogenic centre in these ad-
ducts was not determined.
The Rh2TFA4-2 adduct appeared to be unstable and decomposes
in the CDCl3 solution within 1–2 h, despite the low temperature of
measurement (263 K). The application of advanced, time consum-
ing NMR techniques was difficult in this case. Nevertheless, the
determination of configuration at the nitrogen atom on the basis
of experimental 1H and 13C chemical shifts and some results of the-
oretical computations was attempted. At first, six possible struc-
tures of Rh2TFA4-2 were optimized and their molecular energies
were computed (Fig. 7). The calculations unambiguously pointed

´
´
J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2337
Table 3
Calculated 1H and 13C NMR chemical shifts for three hypothetical conformers of 1:1 Rh2TFA4-1 and two diastereoisomers of Rh2TFA4-2a
Ph(Ci)
Phortho
Phmeta
Phpara
CH
CCH3
NCH3
Rc
rmsc
b
I
(146.1)
7.78(134.5)
7.72(133.7)
7.70(134.1)
5.12(75.9)
1.62(20.7)
0.999(0.998)
0.13(3.6)
3.14(41.1)
2.71(50.9)
I (CHCl3)
II
(145.9)
(146.1)
(146.9)
(145.0)
(145.7)
7.93(134.7)
7.98(135.4)
8.09(135.7)
7.79(135.3)
7.87(135.5)
7.92(134.0)
7.52(133.3)
7.64(133.2)
7.48(133.7)
7.62(133.6)
7.90(134.5)
7.55(133.7)
7.71(133.6)
7.52(133.7)
7.68(133.6)
5.13(76.1)
4.18(85.8)
4.51(84.6)
5.60(71.1)
5.58(71.4)
1.62(20.4)
1.97(19.0)
1.95(19.1)
1.80(18.1)
1.87(17.9)
0.999(0.998)
0.991(0.992)
0.995(0.993)
0.994(0.994)
0.996(0.994)
0.12(3.7)
0.38(6.8)
0.30(6.2)
0.30(5.8)
0.25(5.8)
3.17(41.2)
2.72(50.8)
2.62(51.9)
3.27(52.4)
II (CHCl3)
III
2.64(51.6)
3.31(52.0)
3.31(51.3)
2.90(44.4)
III (CHCl3)
3.35(51.3)
2.94(44.1)
3.11(30.7)
2.83(39.3)
IV (CHCl3)
VII (CHCl3)
(147.2)
(149.1)
7.93(132.8)
7.89(132.8)
7.98(134.7)
7.90(134.3)
7.93(134.4)
7.86(134.1)
5.32(66.8)
4.87(71.0)
1.63(13.6)
1.56(24.7)
0.999(0.999)d,e
1.000(0.999)f,e
0.15(2.4)d,e
0.10(1.8)f,e
1H and 13C chemical shifts are given in ppm. Calculations were performed for both single molecule in the vacuum and molecule in CHCl3 (IEF PCM solvation model). All
a
data concerning 13C are given in parentheses.
b
Signals arising from pro-R N-methyl group were underlined.
Correlation coefficients R and rms were obtained from the least-square linear regression performed for each set of calculated and experimental (303 K, CDCl3, Rh2TFA4 and
c
1 with molar ratio of 1: 0.5, Table 1) data.
d
The correlation between calculated data for IV and experimental data for the isomer identified as CSNR (Table 1). Reverse correlation (IV and CSNS provided R of
0.999(0.997) and rms of 0.25(2.7).
e
The correlation between all calculated (IV and VII) and experimental (CSNR and CSNS) data assuming the assignments like those in Table 1 provided R and rms of
0.999(0.999) and 0.12(2.0); opposite assignment resulted in the values of 0.996(0.993) and 0.25(6.3).
f
The correlation between calculated data for VII and experimental data for the isomer identified as CSNS (Table 1). Reverse correlation (VII and CSNR provided R of
0.999(1.000) and rms of 0.12(1.5).
Table 4
Averaged distances (Å) between CH, Phortho and CH3 groups for three hypothetical conformers I–III and NOE build-up rates
Averaged distancea
I
II
III
NOE build-up rateb
Calculated distances (Å)c
CH–NCH3
CH–NCH3
CH–CCH3
3.00
3.86
2.61
2.96
2.72
2.63
3.85
3.09
2.64
8.1 NCH3(CH); 6.4 CH(NCH3)
0.8 NCH3(CH); n.o. CH(NCH3)
6.9 CCH3(CH); 8.9 CH(CCH3)
2.65
3.74
2.61
H–Ph
2.69
3.61
3.41
3.26
2.67
4.87
3.62
3.33
2.77
3.32
4.9
7.1 Ph(CH); 9.3 CH(Ph)
Ph–NCH3
Ph–NCH3
Ph–CCH3
4.8 NCH3(Ph); 4.6 Ph (NCH3)
7.3 NCH3(Ph); 8.2 Ph (NCH3)
9.4 CCH3(Ph); 8.6 Ph (CCH3)
3.63
3.34
3.19
3.26
CCH3–NCH3
CCH3–NCH3
NCH3–NCH3
4.76
3.17
3.08
3.26
4.74
3.06
3.05
3.68
3.08
0.8 NCH3(CCH3); n.o.CCH3(NCH3)
10.7 NCH3(CCH3); 11.5CCH3(NCH3)
13.8 NCH3(NCH3); 14.5 NCH3(NCH3)
4.95
3.21
3.08
a
Averaged distances (Å) between hydrogens in CH, Ph and CH3 groups calculated on the basis of optimized structures according to the formula (hdꢀ3iꢀ1/3
)
11; see Section 4
for the details. Only ortho-hydrogens of Ph group were considered. Pro-R N-methyl signals are given in italics. n.o. means ‘not observed’.
b
The pair of interacted groups are given in each row; the observed and inverted (in parentheses) signals were indicated next to each values.
Reference distance is double-underlined.
c
to the diastereoisomers IV and VII as the structures with the low-
est energy. However, the theoretical calculations did not decide
which isomer (IV or VII) was preferred, since their minimal molec-
ular energy depended on which model (isolated or solvated mole-
cule) was applied. In the next step the calculations of 1H and 13C
chemical shifts for IV and VII were performed (Table 3). The corre-
lations between the theoretical and experimental data sets for a
single compound did not solve the problem, since all combinations
of data (i.e., CSNR Rh2TFA4-2 vs IV, or CSNR vs VII, etc.) did not pro-
vide decisive differences with regard to the coefficients R and rms.
Overall regression using the data of both diastereoisomers at once
(IV and VII vs CSNR and CSNS) appeared to be more diagnostic (Ta-
ble 3). The analysis of C13 chemical shifts provided subsequent evi-
dence: the chemical shift differences between major and minor
components of Rh2TFA4-2 (ꢀ4.3, ꢀ8.1 and ꢀ7.3 ppm for CH,
CCH3 and NCH3, respectively) followed the corresponding differ-
ences between IV and VII (ꢀ4.2, ꢀ11.1 and ꢀ8.6 ppm). Hence,
these findings showed that isomer IV (CSNR) as the major compo-
nent and VII (CSNS) as the minor component of the Rh2TFA4-2
mixture.
The 1H NMR spectrum of the (4S)-Rh2MTPA4 and 2 1:0.5 mix-
ture showed the signals of two adducts, in the molar ratio of 1–
5.3 (Fig. 8). Although the optimizations of (4S)-Rh2MTPA4-2 struc-
tures were not performed due to large molecule and computing
limitations, it was tentatively assumed that the previous findings
(i.e., for Rh2TFA4-2) were valid in this case too. Hence, (4S)-
Rh2MTPA4-2 adducts were expected to adopt the structures IV
and VII. Diastereomerization rates of 0.2 and 0.8 sꢀ1 (at 303 K)
for forward and reverse processes were estimated on the basis of
selective inversion recovery experiments; hence diastereoisomer
lifetimes came to seconds.
Vicinal 3J(CH–NH) coupling constants provided a preliminary
argument indicating the configuration at the nitrogen atom.21
The CH and NH signals of the major adduct appeared as quartets,
split by coupling with CH3 groups. Vicinal NH–CH coupling, of ca.
1.5 Hz, appeared as line broadening only: half-widths of the line
in NCH3 and NCH3 doublets came to 2.5 Hz, whereas for CH and
NH quartets this value reached 4 Hz. In contrast, the NH and CH
signals of the minor adduct were more complicated due to the
large vicinal coupling, of ca. 10 Hz (Fig. 8). According to Karplus’

´
´
J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2338
Ph
H
Me
Me
H
Me
Ph
H
Me
H
H
N
N
N
H
Me
Ph
Me
74º
77º
39o
42º
51º
77o
Rh
Rh
Rh
0.0 (1.0)
4.7 (5.8)
kcal/mol
4.2 (4.1)
V
H
VI
IV
Ph
Me
H
Me
H
H
Me
H
H
Me
Ph
N
N
N
Me
Me
Ph
73º
72º
33º
44º
57º
84º
Rh
0.2 (0.0)
VII
Rh
Rh
4.6 (5.8)
IX
kcal/mol
4.5 (5.2)
VIII
Figure 7. Six conformers (CSNR and CSNS) of the 1:1 Rh2TFA4-2 adduct used as input for structure optimizations (for the sake of clarity, one Rh atom was shown), relative
molecular energies and some structural parameters (dihedral angles Rh–N–C–CH3, Rh–N–C–H, Rh–N–C–Ci). Energy calculations were performed for optimized structures
applying either single molecule in vacuum or assuming the IEFPCM (CHCl3) solvation model (in parentheses). Energies of the CSNR conformer IV (isolated molecule) or CSNS
VII (solvated molecule) were assumed to be 0.0 kcal/mol.
Figure 8. 1H NMR spectrum of the 1:1 (4S)-Rh2MTPA4-2 adduct (CDCl3, 303 K). Insets show (a) the expansions of NH/CH and (b) Ph regions.
relationship, the large and small coupling constants were expected
to correspond to anti-periplanar and gauche arrangements of the
CH and NH bonds. The calculations performed for the two con-
formers of 2 (GIAO, B3LYP//6-311G++(2d,p)) provided the 3J values
of 8.8 and 1.1 Hz. In conclusion, structures IV and VII were tenta-
tively identified as the major and minor adducts, respectively.
The NOE experiments provided independent and unambiguous
evidence. For the major adduct the inversion of the CCH3 signal
caused the enhancement of the CH, Phortho and NCH3 signals; inver-
sion of the CH signal enhanced the CCH3, Phortho and NH signals.
These last three signals are perturbed also during NCH3 inversion.
Finally, inversion of the NH enhanced the CH, Phortho and NCH3
peaks. Such interaction patterns unambiguously identified the ma-
jor adduct Rh2MTPA4-2 as IV, with the CSNR configuration. For the
minor component, the inversion of CCH3 caused an increase of CH,
Phortho and NH signals, whereas inversion of the CH perturbed the
intensities of CCH3, Phortho and NCH3 peaks. The inversion of the
NCH3 signal resulted in one NOE interaction, with the NH signal;
inversion of the CH resulted in two interactions with the CCH3
and NCH3. However, all lacking interactions were found in a NOESY
2D spectrum. These NOE interactions identified the minor compo-
nent as VII, having the CRNS configuration.

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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2339
2.3. Adducts of (S)-N-ethyl-1-phenylethylamine 3
salt [(4S) and (4R)] behaved similarly and formed the same mixture
of adducts; there were no significant differences in 1H and 13C
chemical shifts between the (4R)- and (4S)-diastereoisomers (Table
1). The signals of the minor components, due to low intensities and
overlapping were difficult to detect, and only careful inspection of
the 2D spectra (1H,1H COSY and 13C,1H gHSQC) allowed signal iden-
tifications and assignments. The same reasons made it difficult to
estimate the diastereomerization rate in the mixture, and to apply
NOE techniques to the minor adduct. In contrast, NOE experiments
(truncated driven NOE, at 303 K) were successful in case of the
main adduct. Apart from irrelevant NOE interactions between sub-
stituents attached to the same carbon atom (e.g., between CCH3,
Phortho and CH groups, or between NH and Et), some diagnostic
enhancements were noted. Namely, saturation of the NH signal re-
sulted in answers of Phortho and CH signals; saturation of the low-
frequency signal of the CH2 group (at 3.25 ppm) enhanced the sig-
nal of CCH3 and Phortho groups. It is noteworthy that there was no
reaction of the Phortho signal during irradiation of the high-fre-
quency CH2 peak (at 3.47 ppm); this suggests that only one hydro-
gen atom from CH2 group was close to Ph. Hence, the rotation
around CH–CH2 bond was hindered and the particular arrange-
ment of the ethyl group was fixed. Irradiation of CCH3 resulted in
the answer of both CH2 signals; irradiation of the Ph enhanced
Since the mixture of rhodium tetratrifluoroacetate and
3
decomposed rapidly, the Rh2TFA4-3 adduct was not studied by ad-
vanced NMR techniques. Nevertheless, this adduct was used as a
model molecule for computations. Two configurations at the nitro-
gen atom and all the arrangements around N–C and N–CH2 bonds
resulted in 18 structures of the adduct (two diastereoisomers, nine
conformers of each). Structure optimizations and molecular energy
calculations were performed for all of these structures (Fig. 9). The
results led us to the conclusion that molecular energy depended
mainly on the arrangement of the substituents around the N–CH
bond. Anti-periplanar conformations with Ph and Rh groups oppo-
site to each other exhibited the lowest energy (Fig. 9, structures X,
XI and XII). The arrangement of the ethyl group (rotation around
CH–CH2 bond) provided the smallest contribution to the energy
(cf. structures X, XIII and XIV). Finally, two diastereoisomers, CSNR
XIV and CSNS XV, were expected to exist in the mixture of dirho-
dium salt and 3.
Although the calculations were performed for Rh2TFA4-3, we as-
sumed that the results applied also to Rh2MTPA4-3. In fact, the
spectrum of Rh2MTPA4 and 3 (1:0.5 mixture) contained the signals
of two adducts, with molar ratio of ca. 1:10. Each of the dirhodium
a
Ph
N
Me
H
Me
H
Me
Me
H
H
H
H
H
H
H
H
H
N
N
H
Ph
Me
Me
Ph
83º
50º
83º
32º
80º
53º
Rh
0.3
Rh
Rh
5.2
XII
Ph
kcal/mol
4.2
XI
X
H
Ph
Ph
H
H
H
H
H
H
Me
H
H
Me
Me
Me
N
N
N
H
H
H
Me
Me
70º
75o
65º
46º
41º
52º
Rh
1.9
Rh
0.0
Rh
1.2
kcal/mol
XIV
Ph
XV
XIII
Ph
Me
Me
H
Ph
N
H
b
Me
Me
H
Me
H
H
H
H
H
H
N
N
Me
Me
Me
Me
73º
73º
78º
43º
41º
38º
Rh
Rh
Rh
1.4
0.0
XVI
0.3
kcal/mol
XVII
XVIII
Figure 9. Selected conformers of (a) 1:1 Rh2TFA4-3 (X–XV) and (b) Rh2TFA4-4 (XVI–XVIII) used as input for structure optimizations, relative molecular energies and some
structural parameters (dihedral angles Rh–N–C–CH3, Rh–N–C–CH2, Rh–N–C–H, Rh–N–C–Ci). Energies of XIV (Rh2TFA4-3 set) and XVI (Rh2TFA4-4 set) were adjusted to 0 kcal/
mol. For the sake of clarity, one Rh atom is shown. All calculations were performed for single molecule in vacuum. The figure represents the structures exhibiting the lowest
molecular energy.

´
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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2340
the NH peak. However, saturation of the CH peak provided only
non-diagnostic interactions, with Phortho and CCH3 protons. The
above NOE interactions, although incomplete, unambiguously
identified the main isomer of Rh2MTPA4-3 as CSNR (X or XIV).
Despite the lack of NOE data, two arguments suggested CSNS
configuration of the minor adduct, there were a COSY experiment
and 13C NMR data. The minor adduct produced a cross peak be-
tween the CH and NH hydrogens in the COSY spectrum; lack of
the corresponding cross peak in the case of the main adduct. This
finding indicated a larger 3J(CH,NH) value in the minor adduct
and are smaller in the main one. By analogy to Rh2TFA4-2, one
can conclude that the minor and major adducts contain anti-peri-
planar and gauche arrangements of CH and NH bonds, respectively
(structures XV and XIV). On the other side, differences in 13C chem-
ical shifts between CSNR and CSNS diastereoisomers exhibited sim-
ilar features for all pairs of 2 and 3 adducts. The signals of CCH3 and
NCH3 (or NCH2) groups were especially diagnostic. For instance,
the pair of (4S)-Rh2MTPA4-2 diastereoisomers exhibited negative
d(CSNR)–d(CSNS) values of ꢀ10.0 ppm for CCH3 and ꢀ8.0 ppm for
the NCH3 methyl groups. Analogous differences between major
and minor (4S)-Rh2MTPA4-3 adducts were ꢀ9.3 ppm (CCH3) and
ꢀ5.0 ppm (NCH2). Finally, the best linear correlation between the
calculated and experimental 13C data was found assuming a CSNR
configuration for the main adduct and a CSNS configuration for
the secondary adduct.
experimental 13C chemical shifts provided additional evidence.
The correlation was better assuming the assignment shown in Ta-
ble 1 than in the opposite case.
2.5. The application of experimental and calculated 13C NMR
chemical shifts
The carbon chemical shifts of adducts studied in the present work
exhibited interesting features which appeared to be very helpful for
structure determination. These subjects are worthy of re-capitula-
tion. To begin with, in order to verify the configuration assignments,
the computation of 13C chemical shifts and the linear regression be-
tween theoretical and experimental data were performed (Tables 1
and 5). Only the signals of CH, CH3, NCH3 and NCH2CH3 groups were
considered; the signals of Ph groups were omitted as troublesome
for identification and not diagnostic. For the sake of simplification,
the calculations were performed for Rh2TFA4 adducts only; these
theoretical data were correlated with the chemical shifts of both
Rh2TFA4 and Rh2MTPA4 adducts. The regressions were checked for
each pair of diastereoisomers, that is, experimental data for CSNR
and CSNS diastereoisomers together as one set were correlated with
the corresponding theoretical values assuming configuration
assignment either like that in Table 1 or opposite. Despite such sim-
plifications, the results were unambiguous. Standard errors associ-
ated with linear regression (rms), measuring how closely data
points spread about regression, line appeared to be especially signif-
icant. Depending on the rhodium salt (Rh2TFA4 or Rh2MTPA4), the
best correlations (rms from 0.6 to 2.1; R from 0.997 to 1.000) were
found if the configurations at the nitrogen atom, such as those in
the Table 1 were assumed. Opposite assignments provided poor re-
sults (rms from 5.9 to 10.7, R 0.909 to 0.974). Hence, theoretical find-
ings supported the experimental conclusions (however, one should
bear in mind that some structures were identified by 13C chemical
shift only, e.g., adducts of 4).
2.4. Adducts of (S)-N-ethyl-N-methyl-1-phenylethylamine 4
Each of the investigated dirhodium salts Rh2TFA4 and
Rh4MTPA4 [(4S) and (4R)] formed two adducts in the solution in
the molar ratio of 1:1.5 (Rh2TFA4-4) and 1:1.8 (Rh2MTPA4-4). The
diastereomerization rate was evaluated by selective inversion
recovery experiments and came to ca. 1 s ꢀ1 for Rh2TFA4-4 (at
270 K) and less than 1 sꢀ1 for Rh2MTPA4-4 (263 K). However, the
rate of Rh2TFA4-4 increased up to ca. 10 sꢀ1 at 303 K. Structure
optimization and molecular energy calculations performed for all
18 conformers/diastereoisomers allowed us to select the structures
XVI and XVII as the most likely adducts in the mixture (Fig. 9).
Both diastereoisomers were expected to appear in ca. 1:1 molar ra-
tio (energy difference of 0.3 kcal/mol).
Unfortunately, NOE experiments failed in the case of these
adducts. Only unimportant NOE interactions were detected for
Rh2TFA4-4 (303 K), namely, some interactions between CCH3 and
Phortho or CH hydrogen atoms. Negative results may be caused
either by the fast ligand exchange or/and by fast rotation around
the N–C bond. Some signal overlapping was another impediment
to the measurements. On the other hand, a temperature decrease
resulted in signal broadening. In the case of Rh4MTPA4-4, difficul-
ties arose from signal proximity and overlapping. Although
inspection of 2D spectra allowed the identifications of all 1H
and 13C signals, the application of any selective experiment was
impossible.
Carbon chemical shifts were the only mean of structure identi-
fication. The conformer XVI with a CSNS configuration was an ana-
logue of (CSNR)-Rh2MTPA4-2 as far as the methyl group was
considered, or of (CSNS)-Rh2MTPA4-3 with regard to the CH2 group.
Diastereomeric dispersion was calculated as a chemical shift differ-
ence between NR and NS adducts which was negative for both the
NCH3 group in Rh2MTPA4-2 (ꢀ8 ppm) and the CH2 group in
Rh2MTPA4-3 (ꢀ5 ppm). Thus, the chemical shift difference be-
tween XVI (CSNS) and XVII (CSNR) was expected to be the same
(i.e., negative) similar to Rh2MTPA4-2 for the NCH3 group and
opposite (positive) than in Rh2MTPA4-3 for the CH2 group. These
conditions were satisfied if the major Rh2MTPA4-4 adduct was as-
signed to XVI and minor one to XVII (Table 1). The same applied to
Rh2TFA4-4 adducts. Correlations of theoretically calculated and
Two parameters related to NMR were commonly used for
describing the complexation: complex (or adduct) formation shift
D
d (ppm) defined as chemical shift difference of a signal in the
adduct and free ligand, and diastereomeric dispersion (Hz)
D
m
specified as chemical shift difference of a signal in the two
diastereoisomers.19 These two parameters concerning the 13C
data of dirhodium adducts are shown in Table 6. Assuming the
same convention for all adducts,
= d(CSNR) ꢀ d(CSNS), one could attribute a sign to each of
and . For the sake of comparison, was expressed in ppm.
D
d = dcomplex ꢀ dfree ligand and
D
m
Dd
D
m
Dm
Rh2TFA4-1 contains two N-methyl groups, one pro-R (38.8 ppm),
anti-periplanar to the CH hydrogen, and pro-S (48.5 ppm), gauche
to CH. The corresponding
Dd values are negative and positive,
of ꢀ4.3 and 5.4 ppm. The chemical shift difference dpro-R–dpro-S
,
which can be regarded as dispersion, is negative (ꢀ9.7 ppm).
All adducts of 2 and 3, with CSNR configurations and NCH3 (NCH2)
groups anti-periplanar to CH hydrogen, exhibit negative
for these groups, from ꢀ1.9 to ꢀ4.7 ppm, whereas CSNs adducts
display positive d, from 2.9 to 3.5 ppm. The diastereoiso-
meric dispersion of NCH3 (NCH2) is negative and varied from ꢀ4.8
to ꢀ8.0 ppm. CCH3 groups exhibit large negative , of ca. ꢀ10 ppm,
although d values for both diastereoisomers are negative. One
Dd
D
Dm
D
can also find some trends in
(Table 6).
Dd and Dm for CH carbon atom
The adducts of 4 require some comment. Due to the two alkyl
groups at the nitrogen atom, CH3 and CH2CH3, CSNR adducts of 4
correspond to the CSNS adducts of 2 with regard to the N-methyl
group, but to CSNR adducts of 3 if one considers N-ethyl group. Con-
sequently, the adducts of 4 exhibit positive
Dm for NCH3, and neg-
ative for NCH2, that is, with the opposite and the same sign than
D
m
the remaining adducts, respectively. The
Dd of CH and CCH3 groups
is not diagnostic in the case of 4.

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J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2341
Table 5
Calculated 13C chemical shifts (ppm) and diastereomeric dispersions
Dm
(in parentheses, ppm) for the adducts of Rh2TFA4 with amines 1–4a
Adduct
CH
CCH3
Ph(Ci)
NCH3
NCH2CH3
NCH2CH3
Rh2TFA4-1
I
75.9
72.4
20.7
20.7
146.1
147.9
41.1b, 50.7c(ꢀ9.6)d
39.6b, 47.5c
Rh2TFA4-2
Rh2TFA4-3
Rh2TFA4-4
IV
NR
NS
NR
NS
NR
NS
66.6(ꢀ4.2)
13.8(ꢀ11.3)
147.5(ꢀ1.7)
30.5(ꢀ8.9)
29.6
39.4
37.1
—
—
—
—
45.0(8.0)
42.3
37.0
34.8
65.2
14.8
150.3
VIII
XIV
XV
XVII
XVI
70.8
68.8
25.1
24.6
149.2
152.8
67.1(ꢀ4.3)
14.2(ꢀ11.8)
148.0(ꢀ2.9)
45.7(ꢀ4.8)
42.2
50.5
16.4(0.2)
16.0
16.2
16.1
13.0(0.5)
10.5
64.5
15.1
151.5
71.4
68.3
26.0
24.6
150.9
155.6
47.4
74.5(ꢀ0.7)
19.1(ꢀ2.1)
146.8(ꢀ1.9)
54.9(ꢀ6.3)
70.8
19.2
149.5
52.8
75.2
71.7
21.2
21.0
148.7
152.3
61.2
56.1
12.5
9.7
a
Dispersions
D
m
were calculated as difference d(CSNR) ꢀ d(CSNS). The first entry for each structure contains chemical shifts and Dm of an adduct; the second entry concerns
chemical shifts calculated for ligand fragment while dirhodium unit is removed (see explanation in the text). All calculations were performed for a single molecule in vacuum.
b
Pro-R N-methyl signal.
Pro-S N-methyl signal.
The dispersion (ppm) was calculated as dpro-R ꢀ dpro-S.
c
d
Table 6
13C adduct formation shift
D
d and diastereomeric dispersions Dm
(in parenthesis) for some adducts of dirhodium salts with amines 1–4a
Adduct
T (K)
CH
1.1
CCH3
NCH3
NCH2CH3
NCH2CH3
Rh2TFA4-1
Rh2TFA4-2
303
ꢀ2.2
ꢀ4.3b, 5.4c(ꢀ9.7)d
NR
263
303
273
273
273
303
303
ꢀ0.7(ꢀ4.3)
ꢀ9.6(ꢀ8.1)
ꢀ3.8(ꢀ7.3)
NS
NR
3.6
ꢀ1.5
3.5
(4S)-Rh2MTPA4-2
(4S)-Rh2MTPA4-3
(4R)-Rh2MTPA4-3
Rh2TFA4-4
ꢀ1.4(ꢀ4.9)
ꢀ10.6(ꢀ10.0)
ꢀ0.6
ꢀ4.7(ꢀ8.0)
NS
NR
3.5
3.3
—
0.0(ꢀ3.4)
ꢀ10.2(ꢀ9.3)
ꢀ2.0(ꢀ5.0)
ꢀ0.1(0.9)
ꢀ1.0
NS
NR
3.4
ꢀ0.9
—
—
3.0
0.3(ꢀ3.2)
ꢀ10.1(ꢀ9.0)
ꢀ1.1
ꢀ1.9(ꢀ4.8)
ꢀ0.1(0.7)
NS
NR
NS
3.5
—
2.9
ꢀ0.8
6.2(1.0)
ꢀ0.4(0.2)
5.9(8.3)
ꢀ0.4(ꢀ7.9)
7.5
ꢀ2.1(ꢀ0.5)
5.2
6.0(0.6)
ꢀ0.6
ꢀ2.4
ꢀ1.6
(4S)-Rh2MTPA4-4
(4R)-Rh2MTPA4-4
NR
NS
0.4(0.0)
6.1(8.7)
ꢀ0.1(ꢀ7.6)
ꢀ1.4(ꢀ0.3)
7.5
5.4
6.1(1.0)
0.4
0.2(ꢀ0.2)
0.4
ꢀ2.6
ꢀ1.1
NR
NS
5.9(8.4)
ꢀ0.1(ꢀ7.2)
7.1
ꢀ1.7(ꢀ0.2)
ꢀ1.5
5.1
ꢀ2.5
a
The
D
d(13C) and
D
m
(
13C) values (ppm) were calculated for 1:1 adducts on the basis of Table 1, according to formulas
D
d = dadduct ꢀ dfree ligand and
D
m
= d(CSNR) ꢀ d(CSNS).
The values arising from the main isomers are underlined.
b
Pro-R N-methyl signal.
Pro-S N-methyl signal.
The dispersion (ppm) was calculated as dpro-R ꢀ dpro-S.
c
d
As was aforementioned, the calculated chemical shifts corre-
lated well with the experimental data and can be used for struc-
3. Conclusion
ture identification. It is difficult to calculate the
Dd parameter
Each of the enantiomerically pure amines 2–4 forms with rho-
dium(II) salts in CDCl3 solutions two diastereoisomeric adducts,
with CSNR and CSNS configurations. The lifetimes of the diastereoi-
somers are relatively long (in NMR time scale); the signals of all
species can be observed conveniently at room temperature
(303 K) or moderately decreased temperature (263–273 K). Diaste-
reomerization rates, depending on the temperature, vary from ca.
10 to much less than 1 sꢀ1. Apart from slow diastereomerization,
the adducts exist as relatively stable conformers.
Configurations at the nitrogen atom were determined with re-
spect to a carbon centre by NOE experiment, at least in most cases.
NOE build-up measurements provided qualitatively interatomic
distances in molecules. The alternative NULL method failed, prob-
ably due to short relaxation time T1 of protons in adducts.
reasonably because calculated chemical shifts of an adduct con-
cern a particular conformation, whereas reference data of free li-
gand consist of averaged chemical shifts originating from a few
conformers with unknown populations. However, one can calcu-
late easily
findings.
D
m
; these values (Table 6) reproduce well experimental
The last question concerns the origin of
D
d and , that is,
Dm
whether they are caused by the dirhodium unit or by particular
arrangements of the substituents in a ligand. In order to explore
this subject, we performed chemical shift calculations for the mol-
ecules obtained from optimized adduct structure by simple dele-
tion of the dirhodium unit. The structures of such molecules
were far from optimum, but exhibited the same structural features
like those in adducts. Chemical shifts obtained by this way differed
slightly from those in adducts, but were qualitatively similar. Con-
cluding, mainly the arrangement of substituents in the ligand frag-
Carbon-13 data (chemical shift d, adduct formation shift
Dd and
diastereomeric dispersion ) exhibit some features which can be
D
m
very useful in studies on configuration. Computed optimal adduct
ment determined the magnitude of
Dd and Dm.
structures and calculated chemical shifts were in agreement with

´
´
J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2342
the experimental results and provided supporting structural
information.
(32 K) and number of scans either 8 or 16 per FID. Typical VD list
included 0.01, 0.05, 0.1, 0.18, 0.25, 0.5, 0.75, 1.0, 1.5, 2.0, 3.5, 5.0
and 10.0 s delays. Selective 180° pulse (i-SNOB32) from 10 to
80 ms depending on the desired selectivity was applied for the
selective inversion. NOE measurements were performed using
DPFGSE-NOE 1D technique (Bruker’s ‘selnogp.3’ pulse programme)
with the parameters: a relaxation delay of 3 s, number of scans
either 64 or 128 and mixing times from 30 to 250 ms. The remain-
ing parameters were as mentioned above. EXSY 2D spectra were
acquired using a NOESY 2D sequence (Bruker’s ‘noesyst’ pro-
gramme, phase sensitive using States-TPPI method), with the
parameters: a relaxation delay of 1.2 s, sweep width of 8 ppm, an
4. Experimental
4.1. Syntheses
All amines were obtained from commercially available primary
(S)-1-phenylethylamine according to the described procedures.
Tertiary (S)-N,N-dimethyl-1-phenylethylamine
1 was obtained
from the primary amine by the methylation with formic acid and
formic aldehyde.28 Secondary (S)-N-methyl-1-phenylethylamine
2 was obtained by the reaction with methyl chloroformate and
subsequent reduction with LiAlH4.29 (S)-N-Ethyl-1-phenylethyl-
amine 3 was prepared by the acetylation of primary amine and
subsequent reduction with LiAlH4. (S)-N-Ethyl-N-methyl-1-phen-
ylethylamine 4 was obtained from 3 by the reaction with formic
acquisition time of 0.26 s, number of scans of
8 and a
2048 ꢄ 256(2048 ꢄ 2048) data matrix. Mixing times from 100 to
300 ms were applied.
NOE build-up measurements were achieved by means of
DPFGSE-NOE, using five to six mixing times from 25 to 220 ms.
NOE enhancements were referred to intensity of inverted signal
at 0 ms mixing time (Bruker’s ‘lastcal’ command), assuming signal
intensities of 100, 200 and 300 for CH, Phorto and CH3 groups,
respectively. NOE enhancements were plotted against mixing
time; in case of deviation from linearity the points corresponding
to long mixing times were removed. Then NOE build-up rates were
extracted from the plot as a line slope. Atomic distances d(H–H)
were read out from optimized structures I–III. Distances between
CH3, CH and Phortho groups were obtained by averaging of all indi-
acid and formic aldehyde.28 Rhodium(II) tetra-
a-methoxy-a-(tri-
fluoromethyl)-phenylacetate dimer (4R) and (4S) were prepared
from commercially available dirhodium tetraacetate and enantio-
merically pure Mosher’s acid (MTPA).30 Rhodium(II) tetraacetate
and rhodium(II) tetratrifluoroacetate were commercially available
and were purchased from Aldrich.
4.2. Structure optimization and shielding calculations (DFT)
vidual H–H atomic distances d according to the formula (hd
i
ꢀ3 ꢀ1/3) =
GAUSSVIEW 3.0 and GAUSSIAN 03 package31 have been used for the
construction of molecules and all DFT calculations. Structure opti-
mizations of adducts were performed at 3-21G//B3LYP theory le-
vel. Electronic energies and NMR shieldings (GIAO) were
calculated by the B3LYP method using LANL2DZ basis set for rho-
dium atoms and 6-311G(2d,p) basis set for H, C, N, O and F atoms.
Calculations were performed either assuming the single molecule
in vacuum or applying IEFPCM solvation model (CHCl3). Shielding
scales were recalculated to chemical shift scales using reference
shielding incorporated in GAUSSIAN package, of 31.88 ppm for 1H
(0 ppm, TMS) and 182.47 ppm for 13C (0 ppm, TMS). 3J(1H,1H) cou-
pling constants were calculated using B3LYP//6-311G++(2d,p) the-
ory level.
P
(
dꢀi 3)/i)ꢀ1/3 (i.e., three d(H–H) values were averaged in order
to obtain d(CH–CH3), six values for d(Phortho–CH3), etc).26
Experimental distances dx were estimated by the formula
dx = dref
NOE build-up coefficients from Table 4 as
(rref/rx)
1/6, using a theoretical distance as a reference and
r. For simplification,
the calculations were performed for each kind of interaction sepa-
rately; for instance when the Phortho signal was inverted,
d(CCH3–Phortho) = 3.26 Å and NOE build-up rate of CCH3 group
(9.4) were used as reference values. Then NOE build-up rates of
both NCH3 groups (4.8 and 7.3) were used for the calculation of
two NCH3–Phortho distances (3.65 and 3.4 Å). The calculations were
repeated using build-up rates on Phortho signal, obtaining distances
of 3.62 and 3.29 Å. Averaging provided the values of 3.63 and
3.34 Å (Table 4).
4.3. NMR measurements
4.4. Data treatment and estimation of exchange rates
All NMR experiments were run on a BRUKER DRX-500 Avance
spectrometer with XWINNMR acquisition and processing software,
equipped with a 5-mm triple broadband inverse probe (TBI) with
z-gradient coil. The sample temperatures (from 268 to 318 K) were
adjusted using the instrument temperature panel, and tempera-
ture readings were taken without further corrections. Standard
parameter sets were applied for conventional 1H and 13C NMR
spectra. All measurements were taken in CDCl3 (99.8% D atom sta-
bilized by Ag); solvent signals were used as secondary references:
7.26 ppm (1H) and 77.0 ppm (13C). A typical sample contained ca.
10 mg of dirhodium salt and 0.5 equiv of a ligand; such a ratio en-
sured the presence of one adduct (1:1) in the mixture. All samples
for NOE, EXSY and T1 measurements were deoxygenated by four
freeze–pump–thaw cycles, using J. Young valve NMR-tubes.
The measurements of relaxation times T1 were carried out by
standard inversion recovery sequence D1–180°–VD–90°–AQ (Bru-
ker’s ‘irt1’ pulse programme). The NULL experiment (inversion
recovery measurements with all but one signal inverted)27 was
achieved by D1–180ꢃsel–180°–VD–90°–AQ pulse sequence. The
chemical exchange was studied by the use of D1–180ꢃsel–VD–90°–
AQ sequence. Typical parameters for all the above experiments
were as follows: a relaxation delay D1 from 6 to 10 s, an acquisition
time AQ of 2.7 s, sweep width of 12 ppm, a data matrix of 32 K
All data treatments were performed using the Mathcad 2001
Professional programme. Standard procedures were applied for lin-
ear regressions and curves fitting (Matcad’s ‘line’ and ‘MinErr’ pro-
cedures). The quality of a least squares fitting was expressed as the
Pearson correlation coefficient R and standard error rms (Matcad’s
‘corr’ and ‘stderr’ procedures).33
Exchange and diastereomerization rates were estimated using
the general equation describing the evolution of perturbed two-
site, equally populated systems under slow-exchange conditions:23
M1ðtÞ ¼ M1ð1Þ ꢀ 0:5ðeꢀðrþ2kÞt þ eꢀrtÞ½M1ð1Þ ꢀ M1ð0Þꢅ
ꢀ 0:5ðꢀeꢀðrþ2kÞt þ eꢀrtÞ½M2ð1Þ ꢀ M2ð0Þꢅ
where M1(t) denotes the magnetization of site 1 as a function of
time t; M1(1) and M2(1) represent the equilibrium magnetization
of sites 1 and 2, respectively; M1(0) and M2(0) represent the magne-
tization at time 0 (i.e., at the beginning of the experiment, immedi-
ately after selective 180° pulse); k is the exchange rate from site 1 to
2 and r denotes the relaxation rate 1/T1. If both sites were perturbed
equally (bi-selective inversion), the equation was converted to
MðtÞ=Mð1Þ ¼ 1 ꢀ ð1 þ aÞeꢀrt
ð1Þ

´
´
J. Jazwinski, A. Sadlej / Tetrahedron: Asymmetry 20 (2009) 2331–2343
2343
where coefficient a denotes a non-ideal inversion (0 < a < 1). If one
signal was inverted, the evolutions of inverted and non-perturbed
signals were described by Eqs. (2) and (3), respectively:
the equation exp(ꢀtm/2k) = (1 ꢀ b)/(1 + b), where tm denotes mixing
time and b states the ratio of the cross peak to diagonal peak
volume.24
M1ðtÞ=M1ð1Þ ¼ 1 ꢀ 0:5ð1 þ aÞðeꢀðrþ2kÞt þ eꢀrt
Þ
ð2Þ
ð3Þ
References
M1ðtÞ=M1ð1Þ ¼ 1 ꢀ 0:5ð1 þ aÞðꢀeꢀðrþ2kÞt þ eꢀrt
Þ
1. Cotton, F. A.; Walton, R. A. Multiple Bonds Between Metal Atoms; Claredon Press:
Oxford, 1993. Chapter 7, pp 431.
The measurement and exchange rate estimation were performed
for 1:0.5, 1:2 and 1:4 mixtures of Rh2TFA4 and 1, that is, for the
solutions containing the 1:1 adduct, 1:2 adduct or equimolar
amounts of the 1:2 adduct and free amine, respectively.Evolutions
of magnetization M(t) as a function of time were obtained from
selective inversion recovery experiment. Either NCH3 signals (first
two samples) or CCH3 signals (1:4 sample) were used. Typically,
both signals of each sample were inverted, one by one; giving to-
tally four data sets for each sample at given temperature. The initial
value of a, essential for MinErr algorithm, was estimated on the ba-
sis of M(t) and M(1), taken from the first experiment (VD delay of
10 ms); guess k value was assumed to be 1 sꢀ1. The parameters a
and k were obtained by curve fitting procedure, using Eq. (2) for in-
verted signal and (3) for non-inverted signal. In the theory, one can
perform a fitting procedure using three parameters, k, a and r simul-
taneously. However, the attempt to do it often resulted in non-real-
istic values, without physical meaning (for instant k < 0 or a
drastically differs than expectation). Finally, the best results were
obtained when r was assumed as a known parameter, taken from
bi-selective inversion recovery experiment using the Eq. (1). Such
simplification did not significantly influence the results.Since both
NCH3 groups are located at the same nitrogen atom, the NOE
enhancement of non-perturbed NCH3 signal was expected during
selective inversion experiment.26 Such effect was noted in some
measurements (Fig. 3). However, the inclusion of the NOE in Eq.
(2) did not improve significantly the data fitting.For two-site system
with unequal populations the following equation was used
2. Clayden, J.; Greeves, N.; Warren, S.; Wothers, P. Organic Chemistry; Oxford
University Press: Oxford, 2001. p. 1057.
3. Doyle, M. J. Org. Chem. 2006, 71, 9253–9260.
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2007, 46, 7494–7502. and references cited therein.
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11. Frelek, J.; Górecki, M.; Jazwinski, J.; Masnyk, M.; Ruskowska, P.; Szmigielski, R.
Tetrahedron: Asymmetry 2005, 16, 3188–3197.
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12. Frelek, J.; Jazwinski, J.; Masnyk, M.; Ruskowska, P.; Szmigielski, R. Tetrahedron:
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13. Frelek, J.; Klimek, A.; Rus´kowska, P. Curr. Org. Chem. 2003, 7, 1081–1104.
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14. Frelek, J.; Jagodzinski, J.; Meyer-Figge, H.; Sheldrick, S.; Wieteska, E.; Szczepek,
J. Chirality 2001, 13, 313–321.
15. Frelek, J. Tetrahedron: Asymmetry 1999, 10, 2809–2816.
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17. Frelek, J. Pol. J. Chem. 1999, 73, 229–239.
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19. Duddeck, H. Chem. Rec. 2005, 5, 396–409. and references cited therein.
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20. Jazwinski, J. J. Mol. Struct. 2005, 750, 7–17.
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22. Jazwinski, J.; Kamienski, B. Solid State NMR 2007, 32, 25–33.
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24. Bain, A. Prog. Nucl. Magn. Reson. Spectrosc. 2003, 43, 63–103.
25. Chesnut, D. Chem. Phys. Lett. 2003, 380, 251–257.
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Conformational Analysis; VCH: New York, 1989.
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29. Pallavicini, M.; Valloti, E.; Villa, L.; Resta, I. Tetrahedron: Asymmetry 1994, 5,
363–370.
M1ðtÞ ¼ M1ð1Þ ꢀ A½M1ð1Þ ꢀ M1ð0Þꢅ ꢀ B½M2ð1Þ ꢀ M2ð0Þꢅ
where A ¼ ½kfeꢀðrþkf þkrÞt þ kreꢀrt ꢅ=½kf þ krꢅ, B ¼ ½krðꢀeꢀðrþkf þkrÞt þ eꢀrt Þꢅ=
½kf þ krꢅ, kf and kr state forward and reverse exchange rates, respec-
tively. By analogy to Eqs. (2) and (3), this equation converted to
(4) and (5) for selectively inverted and non-perturbed signals,
respectively:
30. Wypchlo, K.; Duddeck, H. Tetrahedron: Asymmetry 1994, 5,
31. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.;
Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.;
Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.;
Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao,
O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo,
C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi,
R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.;
Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.;
Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.;
Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.;
Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe,
M.;Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C. J. A. GAUSSIAN
03, Revision B.5, Pople Gaussian: Pittsburgh PA, 2003.
27–30.
M1ðtÞ=M1ð1Þ ¼ 1 ꢀ Að1 þ aÞ
M1ðtÞ=M1ð1Þ ¼ 1 ꢀ Bð1 þ aÞM2ð1Þ=M1ð1Þ
ð4Þ
ð5Þ
The equations contain four parameters to fit, r, kf, kr and a. How-
ever, an attempt to fit all parameters simultaneously resulted in a
large spread of kf and kr values, depending on the signal used for
the calculations. The best results were obtained assuming a and r
as known parameters (estimated from signal integrals and bi-selec-
tive T1 measurement) and fitting only kf and kr.The exchange rate k
(k1 + kꢀ1) estimations from 2D EXSY spectra were achieved using
ˇ
32. Kupce, E.; Boyd, J.; Campbell, I. J. Magn. Reson., Ser. B 1995, 106, 300–303.
33. Mathcad User’s Guide with Reference Manual, MathSoft, Cambridge, 2000, http://
www.mathsoft.com/.