Empirical model for the molar rotations of syn-2,2-dimethyl-1,3-dioxanes.

Article abstract of DOI:10.1021/ol0263550

[structure: see text] A useful method for the prediction of molar rotation ([Phi]) of syn-2,2-dimethyl-1,3-dioxanes (acetonides) is described. A series of acetonides were prepared by standard methods. A simple additive relationship between the substituent

Full text of DOI:10.1021/ol0263550

ORGANIC
LETTERS
2002
Vol. 4, No. 18
3075-3078
Empirical Model for the Molar Rotations
of syn-2,2-Dimethyl-1,3-dioxanes
Christopher D. Anderson and Scott D. Rychnovsky*
Department of Chemistry, 516 Rowland Hall, UniVersity of California-IrVine,
IrVine, California 92697-2025
srychnoV@uci.edu
Received June 12, 2002
ABSTRACT
A useful method for the prediction of molar rotation ([Φ]) of syn-2,2-dimethyl-1,3-dioxanes (acetonides) is described. A series of acetonides
were prepared by standard methods. A simple additive relationship between the substituents (R, R′) and molar rotation was realized.
Historically, the assignment of absolute configuration to
natural products has been an arduous task. Most common
methods have limitations. X-ray crystallography requires a
crystalline compound or derivative. Circular dichroism
requires a thorough understanding of conformation and often
requires the synthesis of derivatives.1 Mosher ester analysis
requires derivatization of a suitable functional group in the
compound of interest.2 Kishi’s recently introduced NMR
method for the determination of absolute configuration is
currently limited to a narrow set of compounds.3 Optical
rotation (polarimetry) is one of the simplest physical methods
for assaying chirality, but traditionally it has required direct
comparison with a synthetic sample (or known compound)
to assign absolute configuration.4 Recently, Wipf and Beratan
have demonstrated that optical rotations can be predicted with
reasonable accuracy using modern computational methods.5
This strategy holds great promise but is still limited by the
size of the molecule and the number of low-lying conforma-
tions. We describe herein an empirical strategy for predicting
the optical rotation of substituted syn-2,2-dimethyl-1,3-
dioxanes.
Various empirical models have been developed to predict
the sign and magnitude of optical rotation.6 The primary goal
of these methods has been to use the sign of the experimen-
tally determined optical rotation at a single wavelength to
assign the absolute stereochemistry of a molecule. Most
methods are based on van’t Hoff’s principle of optical
superposition. This principle states that the optical rotation
of a molecule is equal to the sum of the rotation of the
individual noninteracting asymmetric carbon atoms contained
in a molecule.7,8 Thus each isolated segment of the molecule
(5) (a) Kondru, R. K.; Wipf, P.; Beratan, D. N. Science 1998, 282, 2247-
2250. (b) Kondru, R. K.; Wipf, P.; Beratan, D. N. J. Phys. Chem. A 1999,
103, 6603-6611.
(6) (a) Walden, P. Z. Phys. Chem. 1894, 15, 196-208. (b) Marker, R.
E. J. Am. Chem. Soc. 1936, 58, 976-978. (c) Wiffen, D. H. Chem. Ind.
1956, 964-968. (d) Brewster, J. H. J. Am. Chem. Soc. 1959, 81, 5475-
5483. (e) Brewster, J. H. J. Am. Chem. Soc. 1959, 81, 5483-5493. (f)
Brewster, J. H. J. Am. Chem. Soc. 1959, 81, 5493-5500. (g) Brewster, J.
H. Tetrahedron 1961, 13, 106-122. (h) Brewster, J. H. Top. Stereochem.
1967, 2, 1-72. (i) Brewster, J. H. Tetrahedron 1974, 30, 1807-1818. (j)
Kauzmann, W.; Clough, F. B.; Tobias, I. Tetrahedron 1961, 13, 57-105.
(k) Snatzke, G. In Methodicum Chimicum; Korte, F., Ed.; Academic Press:
New York, 1974; Vol. 1A, pp 415-429 and references therein.
(7) van’t Hoff, J. H. Die Lagerung der Atome im Raume; 2nd ed.;
Vieweg: Brunswick, Germany, 1894.
(1) Berova, N.; Nakanishi, K. In Circular Dichroism: Principles and
Applications; 2nd ed.; Berova, N., Nakanishi, K., Woody, R. W., Eds.;
Wiley-VCH: New York, 2000; pp 337-382.
(2) (a) Dale, J. A.; Mosher, H. S. J. Am. Chem. Soc. 1973, 95, 512-
519. (b) Ohtani, I.; Kusumi, T.; Kashman, Y.; Kakisawa, H. J. Am. Chem.
Soc. 1991, 113, 4092-4096. (c) For limitations of Mosher’s ester, see: Seco,
J. M.; Quin˜oa´, Riguera, R. Tetrahedron: Asymmetry 2000, 11, 2781-2791.
(3) Kobayashi, Y.; Hayashi, N.; Tan, C.-H.; Kishi, Y. Org. Lett. 2001,
3, 2245-2248.
(4) Eliel, E. L.; Wilen, S. H.; Mander, L. N. Stereochemistry of Organic
Compounds; John Wiley & Sons: New York, 1994; pp 1071-1093.
(8) Kondru, R. K.; Lim, S.; Wipf, P.; Beratan, D. N. Chirality 1997, 9,
469-477.
10.1021/ol0263550 CCC: $22.00 © 2002 American Chemical Society
Published on Web 08/09/2002

can be treated independently and summed to give the
predicted rotation for the complete molecule. Brewster’s
empirical model has been one of the most successful.6d-i In
the Brewster model, the contribution of each carbon-carbon
bond is calculated and the components are summed. Since
each conformation contributes to the observed rotation,
application of Brewster’s model to conformationally flexible
molecules requires the contribution of each conformer in a
Boltzmann-weighted average to be summed, which can be
tedious. A general analysis of additivity schemes for more
complex frameworks has been developed by Ruch.9 This
analysis has been applied to allenes10 and stereogenic
carbons11 with some success. Ruch’s analysis underlies our
own work with syn-2,2-dimethyl-1,3-dioxanes.
cyanohydrin acetonide 6 in 71% yield in a standard three-
step sequence.16 The lithium anion of 6 was alkylated with
several electrophiles in good yield (steps d-g, Scheme 1),
Scheme 1. Preparation of syn-2,2-Dimethyl-1,3-dioxanes 8
and 10a
The 2,2-dimethyl-1,3-dioxane (e.g. acetonide 4) structure
is one of the most widely used protecting groups for 1,3-
diols and has been used to assign relative configurations to
diols as the syn and anti isomers are easily distinguished by
13C NMR analysis.12 The conformation of the syn- and anti-
2,6-dialkyl-1,3-dioxanes are well defined, with the former
adopting a chair conformation and the latter adopting a 2,5-
twist-boat conformation.12,13 Furthermore, the two substitu-
ents on a syn acetonide ring are remote in space and unlikely
to interact with each other. Thus we postulate that the specific
conformation of R1 will not depend on the identity or
conformation of R2. The syn isomer 4 is a “category a”
molecular framework as defined by Ruch, in that it has only
two substituents (ligands) and these ligands are exchanged
by a mirror plane.9 Ruch has shown that the optical rotation
of category a skeletons can be predicted with “chirality
functions” in which each ligand has an empirically derived
λ-parameter.10,11 The range of ligands is restricted by the
requirement that a molecule with exclusively identical ligands
must have the symmetry of the skeleton. In the case of
skeleton 4, this restriction excludes the use of R1 or R2 that
contain stereogenic centers. It is obvious on inspection that
4 will be achiral when R1 is identical to R2 and when R1
and R2 do not contain stereogenic centers. We set out to
develop a simple, empirical additivity scheme to predict the
molar rotations of syn acetonide structures.
a The R substituent is defined in Table 1. (a) TMS‚NEt2; (b)
DIBALH, Et2O, -78 °C; (c) (i) TMSCN, 18-crown-6/KCN, (ii)
acetone, 2,2-DMP, CSA; (71%); (d) 2-(tert-butyldimethylsilyloxy)-
ethyl bromide, LDA, THF, -40 °C (73%); (e) LHMDS then allyl
chloride, THF, -78 to -20 °C; (48%); (f) n-BuBr, LDA, THF,
-40 °C (50%); (g) 1-bromo-3-butene, LDA, THF, -40 °C (68%);
(h) Li, NH3, -78 °C, THF or Et2O; (i) 2-phenethylbromide, LDA,
THF, -40 °C (60%); (j) see Supporting Information.
and the cyano group was removed in a stereoselective
reduction.15 Nitrile 9 was alkylated with 2-phenethylbromide
and then treated under dissolving metal conditions to generate
acetonide (6S)-8l in 42% yield over two steps. The 2,2-
dimethyl-1,3-dioxanes (6R)-8a and (6S)-8l were converted
to compounds (6R)-8e-k and (6S)-8m-s by standard
methods.17 Acetonide (6R)-8t (R ) H) was prepared by
DIBALH reduction of 5 and acetonide formation.
MW[R]
100
[Φ] )
(1)
Synthesis of the desired substrates began with â-hydroxy
ester 5 (98% ee)14 and with cyanohydrin 9, which was
derived from L-malic acid.15 Ester 5 was converted to
Optical rotation data was collected for each of the
acetonides, and the molar rotation was calculated according
to eq 1, where MW is molecular weight.18 Molar rotation is
(9) Ruch, E. Acc. Chem. Res. 1972, 5, 49-56.
(10) Ruch, E.; Runge, W.; Kresze, G. Angew. Chem., Int. Ed. Engl. 1973,
12, 20-25.
(15) Rychnovsky, S. D.; Zeller, S.; Skalitzky, D. J.; Griesgraber, G. J.
Org. Chem. 1990, 55, 5550-5551.
(16) Rychnovsky, S. D.; Griesgraber, G. J. Org. Chem. 1992, 57, 1559-
1563.
(11) Richter, W. J.; Richter, B.; Ruch, E. Angew. Chem., Int. Ed. Engl.
1973, 12, 30-36.
(12) Rychnovsky, S. D.; Rogers, B. N.; Richardson, T. I. Acc. Chem.
Res. 1998, 31, 9-17.
(17) Details are provided in Supporting Information.
(18) Rotations were measured at 23-25 °C in CHCl3 (c 0.80-1.40).
Uncertainties in molar rotation derive from errors in mass, volume and
rotation measurements. Estimated uncertainties for the molar rotations in
Table 1 are approximately 10%.
(13) Eliel, E. L.; Knoeber, M. C., Sr. J. Am. Chem. Soc. 1968, 90, 3444-
3458.
(14) Rychnovsky, S. D.; Sinz, C. J. Tetrahedron Lett. 1998, 39, 6811-
6814.
3076
Org. Lett., Vol. 4, No. 18, 2002

Table 1. Acetonide Molar Rotations and Refined λ-values
R
molar rotationa
λ-valued
R
molar rotationa
λ-valued
8a
8b
8c
8d
8e
8f
8g
8h
8i
CH2CH2OTBDMSc
CH2CHdCH2
+23.4
+43.5
+41.6
+59.1
+28.6
+20.9
+15.1
+19.9
-18.2
-27.7
-39.3
-79.5
-51.6
-55.6
-36.0
-56.5
-74.2
-73.1
-75.2
-113.5
-124.7
-134.4
8l
CH2OTIPSb
CH2OHb
+67.5
+36.3
+25.4
+31.4
+58.7
+77.3
+70.1
+71.8
+95.1
0.0
-18.3
-61.0
-69.7
-63.7
-36.4
-18.4
-25.0
-34.5
0.0
c
8m
8n
8o
8p
8q
8r
8s
8t
8u
nBuc
CH2CH2CHdCH2
CH2OAcb
CH2OPivb
CH2OTBDPSb
CH2OTBDMSb
CH2OBnb
CH2Clb
c
CH2CH2OHc
CH2CH2OAcc
CH2CH2OPivc
CH2CH2OBnc
CH2CH2Clc
CH2CH2Brc
CH2CH2Ic
H
8j
8k
CH2Bn
-95.1
a Molar rotations for the (6R) acetonides are shown. Molar rotations measured in CHCl3 at concentrations of 0.80-1.40 at the sodium D line. b (S,S)
enantiomer (6S)-8 was prepared. c Molar rotations corrected to 100% ee. d The λ-value for H was arbitrarily set to zero.
proportional to the number of moles of analyte, rather than
the mass of analyte as in the case of specific rotation.
Presenting the data as molar rotations allows for direct
comparison of the optical rotatory power between different
substrates. The unrefined λ-value for each substituent is the
molar rotation for the appropriate compound (6R)-8 minus
that for (6R)-8t (R ) H). This arbitrarily defines hydrogen
as the zero point for λ. The refined λ-values in Table 1 were
calculated by minimizing the RMS deviation between
calculated and experimentally determined molar rotations for
compounds (6R)-8a-u and 28-35 (Table 2).18 Compounds
28-35 were included to add redundancy and to increase the
structural diversity of our dioxanes.
The λ-values from Table 1 can be used to predict the molar
rotations of a range of substituted acetonides. The simple
additivity relationship is defined in Figure 1. The λ-values
Table 2. Predicted Molar Rotations
compound
R1
R2
CH2OBn
CH2CH2OBn
CH2CH2OBn
CH2OAc
calcd
exptl18
deviation
ref
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
CH2CH2OH
CH2OH
CH2CH2CHdCH2
CH2OH
CH2CH2OTBDMS
CH2CH2OTBDMS
CH2OBn
CH2OTBDPS
CH2OTBDPS
CH2CHdCH2
CH2CH2OH
CH2OAc
+31.5
-14.2
-39.2
-8.7
+18.4
+54.5
-48.1
-20.1
-38.8
-4.9
+64.5
-40.9
-48.7
-10.1
+31.1
+69.5
-76.5
-57.4
-65.8
-4.4
-31.5
+11.1
+19.9
-26.5
+48.9
-36.5
-26.1
-6.1
-47.9
-36.7
-53.4
+7.6
+47.2
+34.3
-32.9
-9.9
33.0
26.7
9.5
20a
20b
20c
20d
20a
20a
20a
20a
20a
20e
20f
20g
20h
20i
20h
20h
20j
20i
20k
17
1.4
CH2OH
CH2OBn
12.7
15.0
28.4
37.3
27.0
0.5
13.8
2.4
7.8
CH2CH2OPiv
CH2CH2OH
CH2CH2OBn
CH2CH2OH
CH2CH2OAc
CH2OH
CH2CHdCH2
CH2CH2OBn
CH2CH2OBn
CH2CH2OBn
CH2CH2OTBDMS
CH2CH2OTBDMS
CH2CH2OPiv
nBu
-17.7
+8.7
CH2OPiv
CH2CH2OH
CH2CH2I
+12.1
-18.7
+59.2
-23.6
-22.9
-5.3
-54.8
-37.3
-37.3
+5.4
7.8
10.3
12.9
3.2
0.8
6.9
0.6
16.1
2.2
1.9
0.2
CH2CHdCH2
CH2CH2OH
CH2CH2OAc
CH2OTIPS
CH2OTBDMS
CH2OTIPS
CH2OH
CH2CH2Br
CH2CH2OH
CH2CH2Cl
CH2Cl
nBu
nBu
17
17
17
17
17
17
CH2CH2OTBDMS
CH2CH2OTBDMS
CH2CH2OTBDMS
nBu
+45.3
+34.1
-22.9
-21.1
10.0
11.2
Org. Lett., Vol. 4, No. 18, 2002
3077

Our additivity model was evaluated by calculating the
molar rotation of known compounds 10-27 (Table 2).19,20
A literature search revealed 18 compounds that contained
substituents in our data set. The calculated and experimental
molar rotations are presented in Table 2. Unrefined λ-values
worked well for most substituents but gave poor predictions
for a few compounds. Large substituents are the ones most
likely to violate our assumption that the two R groups will
not interact with each other. Intermolecular aggregation and
hydrogen bonding may also contribute to the deviations
between predicted and experimental values. Our model using
refined λ-values correctly predicts the sign of the molar
rotation for 17 of 17 literature acetonides (14 and 22 are
enantiomers). A graphical representation of the predicted and
experimental values is presented in Figure 2. The data for
the test compounds (10-27) shows a good correlation
(R2 ) 0.90) to the best-fit line.
Given the small optical rotation for members in this class,
the agreement between the predicted values and the literature
values is very good.21 This method can be extended to a
variety of other substituents and should be useful for
assigning the configuration of syn-acetonides. It is important
to note that concentration and solvent should be held constant
to make use of these refined λ-values.18 This work further
validates Ruch’s analysis and suggests a wider application
of his approach is warranted.
Figure 1. Predictive model for molar rotations. The unrefined
λ-values for substituents a-t were calculated using the formula
shown. The refined λ-values reported in Table 1 were calculated
as described in the text.
Acknowledgment. The National Institutes for General
Medical Science (GM 43854) provided support for this work.
Supporting Information Available: Experimental pro-
cedures and characterization data. This material is available
free of charge via the Internet at http://pubs.acs.org.
OL0263550
(19) Experimental rotations for compounds 10-27 were measured in
CHCl3, where T ) 16-28 °C.
(20) (a) Mohr, P. Tetrahedron Lett. 1992, 18, 2455-2458. (b) Nicolaou,
K. C.; Daines, R. A.; Uenishi, J.; Li, W. S.; Papahatjis, D. P.; Chakraborty,
T. K. J. Am. Chem. Soc. 1988, 110, 4672-2685. (c) Hirama, M.; Uei, M.
J. Am. Chem. Soc. 1982, 104, 4251-4253. (d) Xie, Z.-F.; Suemune, H.;
Sakai, K. Tetrahedron: Asymmetry 1993, 4, 973-980. (e) Achmatowicz,
B.; Wicha, J. Tetrahedron: Asymmetry 1993, 4, 399-410. (f) Bonini, C.;
Racioppi, R.; Righi, G.; Viggiani, L. J. Org. Chem. 1993, 58, 802-803.
(g) Miyazawa, K.; Yoshida, N. Chem. Lett. 1993, 9, 1529-1530. (h) Mori,
Y.; Furukawa, H. Tetrahedron 1995, 51, 6725-6738. (i) McGarvey, G. J.;
Mathys, J. A.; Wilson, K. J.; Overly, K. R.; Buonora, P. T.; Spoors, P. G.
J. Org. Chem. 1995, 60, 7778-7790. (j) Solladie´, G.; Wilb, N.; Bauder,
C.; Bonini, C.; Viggiani, L.; Chiummiento, L. J. Org. Chem. 1999, 64,
5447-5452. (k) Skalitzky, D. J. Ph.D. Thesis, University of Minnesota,
Minneapolis, MN, December 1992.
Figure 2. Graphical representation of predictive model with refined
λ-values: (0) compounds 8a-u and 28-35; (b) test compounds
10-27.
for 21 different side chains that are reported in Table 1 should
be useful for predicting the molar rotations of 210 unique,
chiral acetonides.
(21) The largest [R]D of a 2,2-dimethyl-1,3-dioxane reported in Table 2
is +23.0 (compound 10).
3078
Org. Lett., Vol. 4, No. 18, 2002