Experimental and theoretical electron density study of estrone.
ABSTRACT The electron density and the electrostatic potential (ESP) distributions of estrone have been determined using X-ray diffraction analysis and compared with theoretical calculations in the solid and gas phases. X-ray diffraction measurements are performed with a Rigaku Rapid rotating anode diffractometer at 20 K. The electron density in the estrone crystal has been described with the multipole model, which allowed extensive topological analysis and calculation of the ESP. From DFT calculations in the solid state a theoretical X-ray diffraction data set has been produced and treated in the same way as the experimental data. Two sets of single molecule DFT calculations were performed: (a) An electron density distribution was obtained via a single-point calculation with a large basis set at the experimental geometry and subsequently analyzed according to the quantum theory of atoms in molecules (AIM) to obtain the bond and most atomic properties, and (b) another electron density distribution was obtained with a smaller basis set, but at a geometry optimized using the same basis set for the analysis of atomic energies. An interesting locally stabilizing hydrogen-hydrogen bond path linking H(1) and H(11B) is found which represents the first characterization of such bonding in a steroid molecule. AIM delocalization indices were shown to be well correlated to the experimental electron density at the bond critical points through an exponential relationship. The aromaticity of ring A, chemical bonding, the O(1)...O(2) distance necessary for estrogenic activity, and the electrostatic potential features are also discussed.
- SourceAvailable from: ncbi.nlm.nih.gov[show abstract] [hide abstract]
ABSTRACT: Model systems have been studied using density functional theory to assess the contributions of π-resonance and through-space effects on electrostatic potentials of substituted arenes. The results contradict the widespread assumption that changes in molecular ESPs reflect only local changes in the electron density. Substituent effects on the ESP above the molecular plane are commonly attributed to changes in the aryl π-system. We show that ESP changes for a collection of substituted benzenes and more complex aromatic systems can be accounted for mostly by through-space effects, with no change in the aryl π-electron density. Only when π-resonance effects are substantial do they influence changes in the ESP above the aromatic ring to any extent. Examples of substituted arenes studied here are taken from the fields of drug design, host-guest chemistry, and crystal engineering. These findings emphasize the potential pitfalls of assuming ESP changes reflect changes in the local electron density. Since ESP changes are frequently used to rationalize and predict intermolecular interactions, these findings have profound implications for our understanding of substituent effects in countless areas of chemistry and molecular biology. Specifically, in many non-covalent interactions there are significant, often neglected, through-space interactions with the substituents. Finally, the present results explain the perhaps unexpectedly good performance of many molecular mechanics force-fields applied to supramolecular assembly phenomena and π-π interactions in biological systems despite the neglect of the polarization of the aryl π-system by substituents.Journal of Chemical Theory and Computation 09/2009; 5(9):2301-2312. · 5.39 Impact Factor
- Natural Product Reports 06/2010; 27(6):887-99. · 10.18 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: ELMAM2 is a generalized and improved library of experimentally derived multipolar atom types. The previously published ELMAM database is restricted mostly to protein atoms. The current database is extended to common functional groups encountered in organic molecules and is based on optimized local axes systems taking into account the local pseudosymmetry of the molecular fragment. In this approach, the symmetry-restricted multipoles have zero populations, while others take generally significant values. The various applications of the database are described. The deformation electron densities, electrostatic potentials and interaction energies calculated for several tripeptides and aromatic molecules are calculated using ELMAM2 electron-density parameters and compared with the former ELMAM database and density functional theory calculations.Acta crystallographica. Section A, Foundations of crystallography 05/2012; 68(Pt 3):337-51. · 49.93 Impact Factor
Experimental and Theoretical Electron Density Study of
Elizabeth A. Zhurova,†Che ´rif F. Matta,‡Nan Wu,†,§Vladimir V. Zhurov,†and
A. Alan Pinkerton*,†
Contribution from the Department of Chemistry, UniVersity of Toledo, Toledo, Ohio 43606,
Department of Chemistry, Dalhousie UniVersity, Halifax, NoVa Scotia, Canada B3H 4J3, and
Department of Biochemistry, Case Western ReserVe UniVersity, CleVeland, Ohio 44106
Received February 14, 2006; E-mail: firstname.lastname@example.org
Abstract: The electron density and the electrostatic potential (ESP) distributions of estrone have been
determined using X-ray diffraction analysis and compared with theoretical calculations in the solid and gas
phases. X-ray diffraction measurements are performed with a Rigaku Rapid rotating anode diffractometer
at 20 K. The electron density in the estrone crystal has been described with the multipole model, which
allowed extensive topological analysis and calculation of the ESP. From DFT calculations in the solid state
a theoretical X-ray diffraction data set has been produced and treated in the same way as the experimental
data. Two sets of single molecule DFT calculations were performed: (a) An electron density distribution
was obtained via a single-point calculation with a large basis set at the experimental geometry and
subsequently analyzed according to the quantum theory of atoms in molecules (AIM) to obtain the bond
and most atomic properties, and (b) another electron density distribution was obtained with a smaller basis
set, but at a geometry optimized using the same basis set for the analysis of atomic energies. An interesting
locally stabilizing hydrogen-hydrogen bond path linking H(1) and H(11B) is found which represents the
first characterization of such bonding in a steroid molecule. AIM delocalization indices were shown to be
well correlated to the experimental electron density at the bond critical points through an exponential
relationship. The aromaticity of ring A, chemical bonding, the O(1)‚‚‚O(2) distance necessary for estrogenic
activity, and the electrostatic potential features are also discussed.
Estrogens are known to be responsible for the development
of secondary sexual characteristics, as well as effecting growth,
differentiation, and function of a wide range of tissues. They
have been extensively investigated since the role of estradiol
in promoting breast cancer was determined.1,2Estrogens and
related compounds bind as ligands to the estrogen receptor (ER)
forming an activated complex. A series of events are initiated
by the ER complex resulting in the activation or repression of
selective genes and subsequent induction or suppression of the
production of characteristic proteins. To better understand the
role of the ligand in ER-mediated processes, extensive research
into the influence of different estrogen derivatives on the
regulation of hormone responsive genes has been carried out
(see, for example, refs 2-8). Even though most changes in the
estrogen ligand affect its affinity for the receptor, this does not
necessarily correlate with the ligand’s ability to stimulate the
transcription of estrogen responsive genes. The mechanism by
which these structurally altered ligands regulate the differential
induction of gene expression is currently unknown. However,
it has been suggested that the differences in the electrostatic
potential generated by the lone pair electrons of the phenolic
oxygen and π-electrons of the aromatic ring can be responsible
for the variation in the regulation of hormone dependent genes.6
It is obvious that the binding ability of the ligand to the receptor
is not the only important factor in the biological activity of an
estrogen or of a potential drug; secondary interactions and
several domains of the receptor are involved. However, the
initial driving force toward binding to a receptor must be due
to the match between the topography of the electrostatic potential
(ESP) of the estrogen or of a pharmacologically active molecule
and that of the binding site.
Here we present a detailed electron density and electrostatic
potential study of a natural estrogen, Estrone (3-hydroxy-1,3,5-
†University of Toledo.
§Case Western Reserve University.
(1) Wakeling, A. E.; Bowler, J. J. Endocrinol. 1987, 112, R7-R10.
(2) Parl F. F. Estrogens, Estrone Receptor and Breast Cancer. Amsterdam:
IOS Press: 2000.
(3) Davis, M. D.; Butler, W. B.; Brooks, S. C. J. Steroid Biochem. Mol. Biol.
1995, 52, 421-430.
(4) Vander Kuur, J. A.; Wiese, T.; Brooks, S. C., Biochemistry 1993, 32, 7002-
(5) Pilat, M. J.; Hafner, M. S.; Kral, L. G.; Brooks, S. C. Biochemistry 1993,
(6) Vander Kuur, J. A.; Hafner, M. S.; Christman, J. K.; Brooks, S. C.
Biochemistry 1993, 32, 7016-7021.
(7) Adams, J.; Garcia, M.; Rochefort, H. Cancer Res. 1981, 41, 4720-4726.
(8) Brueggemeier, R. W.; Miller, D. D.; Dalton, J. T. In Foye’s Principles of
Medicinal Chemistry, 5th ed.; Williams, D.A., Lemke, T. L., Eds.;
Lippincott Williams and Wilkins: Philadelphia, PA, 2002; pp 685-717.
Published on Web 06/16/2006
10.1021/ja061080v CCC: $33.50 © 2006 American Chemical Society
J. AM. CHEM. SOC. 2006, 128, 8849-8861 9 8849
The estrone crystal exists in three different forms depending
on the crystallization method.9We have performed both
experimental and theoretical studies on form II (orthorhombic)
of this crystal which can be easily crystallized, to give a better
description of the properties of the compound as a whole, as
well as its functional groups.
Experimental and Computational Details
A regularly shaped crystal (Table 1), crystallized from an ethanol/
ethyl acetate solvent system, was mounted on the top of a glass capillary
and slowly cooled to 20 K. The X-ray diffraction measurements were
performed with a Rigaku R-Axis Rapid diffractometer with a high
power Mo rotating anode generator (18 kW), graphite monochromator,
and a curved image plate detector, with cooling provided by an open
flow helium cryostat.10-12Low temperature significantly increased the
atomic scattering power in the high angle area, and relatively strong
spots were observed even at the edge of the detector at 2θ ∼140°. To
obtain high redundancy of data, six runs covering 0°-180° in ω were
collected at different ? and ? settings, two at ? ) 0° (? ) 0°, 180°)
and four at ? ) 45° (? ) 90°, 180°, 270°, 0°). The last run with ? )
0° and ? ) 45° was then eliminated due to temperature instability. For
the first five runs the temperature varied by no more than 2°. To avoid
significant overlap of reflections in any one image, a 4° ω-scan range
was chosen. Oscillation ranges for adjacent images overlapped by 2°
to provide precise scaling between them. Thus, each run consisted of
a total of 89 images. An exposure time of 150 s per image was chosen
to maximize scattering power and avoid saturation of the strongest
reflections. The measurement was completed in ∼44 h.
The collected data were indexed with the program HKL2000,13and
the predicted reflection positions were used for data integration with
the program VIIPP.14,15Oval integration boxes oriented along radial
directions with variable size depending on the R1-R2 splitting were
used. Since ∼13% of the Bragg reflections from the estrone crystal
have very low intensities (and were essentially unobserved), reflections
below 4σ(I) were rejected during the integration, as well as partial and
overlapped reflections. Data have been corrected for the floodfield
distribution and the Lorentz-polarization effect. We considered the
effects of absorption (µ ) 0.08 mm-1) and thermal diffuse scattering
at 20 K to be negligible. Data were scaled and then averaged in the
222 point group with the program SORTAV.16Most of the scaling factors
for different images in the same run were very close to unity (usually
within 1%, however, in one case a difference of 2.6% was observed).
Scales between runs did not differ more then 1.2% from unity. Extreme
outliers (5.7% of the total data) were rejected during averaging, and
reflections measured no more than twice were also discarded from the
final data set. Other experimental details are listed in Table 1. A number
of statistical measures of data quality obtained from the program
SORTAV16are deposited. The values for Rintand the average I/σ(I) in
the various resolution shells suggest good data quality.
The estrone(II) crystal structure was first solved by Busetta et al.9
The estrone molecule and crystal packing diagram showing a zigzag
hydrogen bonding scheme similar to the one reported by Busetta et al.
are shown in Figure 1. From our experimental data, the crystal structure
was resolved by direct methods, and a preliminary least-squares
refinement was carried out with the SHELXTL program suite.17The
positions of hydrogen atoms at this stage were determined from the
difference Fourier peaks. Anisotropic thermal motion was considered
for all non-hydrogen atoms, and the latter were refined isotropically.
A multipole model refinement18using the XD program package19was
performed for both experimental and solid state theoretical (see below)
data. The atomic standard local coordinate systems used to describe
the electron density in estrogens have been previously reported.20To
reduce correlations in the least-squares process, carbon atoms have been
refined only up to the octapole level, while the oxygen atoms were
refined up to hexadecapoles. To account for the hydrogen bonding in
the crystal and the H-H intramolecular bonding (see below), all dipole
and quadrupole parameters were refined for H(1A), H(1) (constrained
to H(2, 4)), and H(11B) (constrained to H(11A)) atoms, while only
the dipoles and one P20quadrupole parameter were refined for all other
hydrogens. Chemical constraints for similar carbon and hydrogen atoms
were applied at the initial stages of refinements. Then, these constraints
were gradually released, and the final model was refined unconstrained
for the non-hydrogen atoms. The H(1, 2, 4), H(8, 9, 14), all H(A, B),
and H(18(A, B, C)) were constrained to group values for the
experimental data; however, no constraints were retained for the
theoretical data. The molecular electroneutrality requirement has also
been applied in each case. A total of nine expansion-contraction
parameters, κ and κ′, were utilized in order to allow the necessary
(9) Busetta, B.; Courseille, C.; Hospital, M. Acta Crystallogr. 1973, B29, 298-
(10) Hardie, M. J.; Kirschbaum, K.; Martin, A.; Pinkerton, A. A. J. Appl.
Crystallogr. 1998, 31, 815-817.
(11) Kirschbaum, K.; Martin, A.; Parrish, D.; Pinkerton, A. A. J. Phys. Condens.
Mater. 1999, 11, 4483-4490.
(12) Ribaud, L.; Wu, G.; Zhang, Y.; Coppens, P. J. Appl. Crystallogr. 2001,
(13) Otwinowski, Z.; Minor, W. Methods Enzymol. 1997, 276; 307-326.
(14) Zhurov, V. V.; Zhurova, E. A.; Chen, Y.-S.; Pinkerton, A. A. J. Appl.
Crystallogr. 2005, 38, 827-829.
(15) Zhurova, E. A.; Zhurov, V. V.; Tanaka, K. Acta Crystallogr. 1999, B55,
(16) Blessing, R. H. Cryst. ReV. 1987, 1, 3-58.
(17) Sheldrick, G. M. SHELXTL, Vers.6.14. An Integrated System for SolVing,
Refining and Displaying Crystal Structures from Diffraction Data; Uni-
versity of Go ¨ttingen: Germany, 2000.
(18) Hansen, N.; Coppens, P. Acta Crystallogr. 1978, A34, 909-921.
(19) Koritsanszky, T.; Richter, T.; Macchi, P.; Gatti, C.; Howard, S.; Mallinson,
P. R.; Farrugia, L.; Su, Z. W.; Hansen, N. K. XD - A Computer Program
Package for Multipole Refinement and Analysis of Electron Densities from
Diffraction Data; Tech. Rep.; Freie Universita ¨t Berlin: Berlin, Germany,
(20) Kirschbaum, K.; Kumaradhas, P.; Parrish, D.; Pinkerton, A. A.; Zhurova,
E. A. J. Appl. Crystallogr. 2003, 36, 1464-1466.
Table 1. Experimental Details
crystal size (mm3)
unit cell dimensions (Å)
0.20 × 0.20 × 0.10
a ) 7.7358(1)
b ) 9.9137(1)
c ) 18.3572(2)
V (Å3), Z
Rinta/average data multiplicity
reflections used (I > 4σ, measured
more than 2 times)
refinement based on
total number of parameters
final R(F2) indices:
spherical atom refinement
aspherical atom refinement
goodness of fit
aRint) ∑?n/(n-1)∑|I - I h|/∑∑|I|.
A R T I C L E S
Zhurova et al.
8850 J. AM. CHEM. SOC.9VOL. 128, NO. 27, 2006
flexibility while attempting to maintain a minimum number of
parameters (see Table 2). For the theoretical data, all κ and κ′ values
were freely refined including those for the hydrogen atoms. For the
experimental data, the κ′ set refined from the theoretical data was used,
while κ values for all hydrogen atoms were fixed to 1.2. The O-H
and C-H bond lengths were fixed to the tabulated values21according
to their hybridization state. Highly correlated parameters were refined
in separate groups; with the existing constraints (experimental data)
the refinement procedure was stable, and full convergence of all
parameters has been reached in each case.
From the experimental data, the rigid-bond test22showed that the
differences of mean-square displacement amplitudes along the inter-
atomic vectors were less than 7 × 10-4Å2. Averaged ratios of observed
and calculated structure factors23,14were very close to unity indicating
a correct scale factor for all data,24as well as good model fitting for
the whole sin θ/λ range. The residual electron density (the difference
between observed and calculated multipole electron densities: δFresid
) Fexper - Fmult) showed no peaks above or below 0.11/-0.09 eÅ-3
for the experimental data and 0.07/-0.07 eÅ-3for the theoretical data
(Figure 2). For the electron density analysis the program packages
XDPROP,19TOPXD,25and WinXPRO26,27have been used.
The density functional theory (DFT) B3LYP periodic theoretical
calculation was performed with the program CRYSTAL98.28The 6-31G-
(d,p) basis set and a molecular geometry fixed at that observed
experimentally29were used. The theoretical structure factors have been
calculated for all possible hkl indices up to sin θ/λ ) 1.0 Å-1and used
for refinements in the same manner as that for the experimental data.
DFT molecular calculations were performed by obtaining the electron
density of a single estrone molecule, frozen at the experimental
geometry, at the B3LYP/6-311++G(d,p) level of theory. The resulting
electron density was integrated using PROAIM,30,31and bond critical
point data and the molecular graph were obtained by the use of AIM
2000.32,33AIMDELOC34was used to calculate the delocalization indices
δ(A,B) between bonded atoms.35All AIM36atomic properties were
obtained at the B3LYP/6-311++G(d,p)//(experimental geometry) level
of theory except atomic energies to avoid the complications due to
nonvanishing virials of the forces on the nuclei in a nonequilibrium
geometry (vide infra).
To validate our discussion of atomic energies, we have also
performed a careful full geometry optimization followed by a vibrational
frequencies calculation all at the B3LYP/6-31G(d,p) level starting from
the experimental geometry as an initial guess (the final maximum force
and RMS force were as small as 0.000 006 and 0.000 001 hartrees/
bohr, respectively). The absence of any negative frequencies was
confirmed. A wave function at the same level of theory used in the
(21) Allen, F. H.; Kennard, O.; Watson, D. G.; Brammer, L.; Orpen, A. G.;
Taylor, R. J. Chem. Soc., Perkin Trans. 2, 1987, S1-S19.
(22) Hirshfeld, F. L. Acta Crystallogr. 1976, A32, 239-244.
(23) Calculated with the program XDRKplot (courtesy of Dr. Stash, 2004).
(24) In the case of experimental data.
(25) Volkov, A.; Gatti, C.; Abramov, Yu.; Coppens, P. Acta Crystallogr. 2000,
(26) Stash, A. I.; Tsirelson, V. G. J. Appl. Crystallogr. 2002, 35, 371-373.
(27) Stash, A. I.; Tsirelson, V. G. Crystallogr. Rep. 2005, 50, 202-209.
(28) Saunders, V. R.; Dovesi, R.; Roetti, C.; Causa `, M.; Harrison, N. M.;
Orlando, R.; Sicovich-Wilson, C. M. CRYSTAL98 User’s Manual; Uni-
versity of Torino: Torino, 1998.
(29) After preliminary multipole refinements of the experimental data, the
obtained molecular geometry was used for the theoretical solid state and
(30) Bader, R. F. W. AIMPAC. http://www.chemistry.mcmaster.ca/aimpac/.
(31) Biegler-Ko ¨nig F. W.; Bader R. F. W.; Tang T.-H. J. Comput. Chem. 1982,
(32) Biegler-Ko ¨nig, F. W.; Scho ¨nbohm, J.; Bayles, D. http://gauss.fh-bielefeld.de/
(33) Biegler-Ko ¨nig, F. W.; Scho ¨nbohm, J.; Bayles, D. AIM2000 - A program
to analyze and visualize atoms in molecules. J. Comput. Chem. 2001, 22,
(34) Matta, C. F. AIMDELOC: Program to calculate AIM localization and
delocalization indices (QCPE0802); Quantum Chemistry Program Ex-
change, Indiana University: IN, 2001 (http://qcpe.chem.indiana.edu/).
(35) Fradera, X.; Austen, M. A.; Bader, R. F. W. J. Phys. Chem. 1999, A103,
(36) Atoms in molecules - refers to the Quantum Theory of Atoms in Molecules
Figure 1. The top and side views of the estrone molecule showing 50%
probability ellipsoids at 20 K (a, b) and estrone(II) crystal packing diagram
viewed down the a-axis showing the ribbons formed by the hydrogen
bonding scheme (c).
Table 2. Expansion/Contraction (κ and κ′) Multipole Model
atomsno. theory expmttheoryexpmt
C(1), C(2), C(4)
0.991(1) 1.070(12) 1.070
Electron Density Study of Estrone
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 128, NO. 27, 2006 8851
geometry optimization was then obtained for the analysis of atomic
Results and Discussion
An intramolecular interatomic distance which is important
in preserving biological activity of estrogens is the O(1)‚‚‚O(2)
distance, which should range from ca. 10.3 Å to 12.1 Å for
optimal estrogenic activity.8It has also been remarked that a
distance of ca. 11 Å is very close to two ?-helix turns in a
polypeptide (2 × 5.38 Å) which corresponds to 7.5 amino acid
residues37(at the rate of 3.6 residues per turn). In the present
structure, we find these two oxygen atoms separated by 10.8325-
(4) Å, a value that does not change much upon geometry
optimization at the B3LYP/6-31G(d,p) level at which it assumes
the value of 10.8948 Å. The O‚‚‚O distance we report here
(whether experimental or optimized) is in very close agreement
with those previously reported between the phenolic oxygen
and O(17?) in two crystallographically independent estriol
molecules where it assumes the values 10.952(7) Å and 11.085-
(7) Å,37in 4-bromo-estrone where it is 10.78(4) Å,37and in
the estradiol molecule where it is in the range 10.863-11.226
Multipole and Topological Analysis of the Electron
Density. Static multipole electron density maps are shown in
Figures 2 and 3. There is a very good qualitative agreement
between the experimental and theoretical (solid state calculation
with the multipole model refined) results, except for the lone
pair region of the O(2) atom, which appeared to be more
polarized in the experimental case. All the expected features of
covalent bonding and oxygen lone pair regions are clearly seen,
as well as the polarization of the electron density indicating
the hydrogen H(1A)‚‚‚O(2) bond40(Figure 3).
The hydroxyl H(1A) atom lays almost in the aromatic ring
plane with a deviation of 0.03 Å from the A-ring mean plane
(Figure 1). It could be expected in this case that the hydroxyl
group would be of sp2type geometry having some interaction
with the π-orbitals of the aromatic ring. Although the electron
density of the lone pair regions of both oxygen atoms is
(37) Cooper, A.; Norton, D. A.; Hauptman, H. Acta Crystallogr. 1969, B25,
(38) Kirschbaum, K.; Parrish, D.; Pinkerton, A. A.; Zhurova, E. A. To be
(39) Cambridge Structural Data Base, 2005.
(40) Krijn, M. P. C. M.; Graafsma, H.; Feil, D. Acta Crystallogr. 1988, B44,
Figure 2. Residual electron density (left) and static multipole deformation density (right) in the A (aromatic) ring plane: (a) from the experimental data,
(b) from the solid state theoretical data. Contour interval is 0.05 eÅ-3; red solid lines are positive; blue dot lines are negative; black dash line is a zero
contour. The Fourier series have been truncated at sin θ/λ ) 1.0 Å-1. For clarity, the zero line is omitted from the residual maps.
A R T I C L E S
Zhurova et al.
8852 J. AM. CHEM. SOC.9VOL. 128, NO. 27, 2006
somewhat smeared, both the deformation electron density and
the Laplacian (∇2F(r)) maps (Figure 3) demonstrate two
nonbonding concentrations of electron density for each atom,
i.e., two lone pairs. The existence of two charge concentrations
in the lone pair region is, probably, an indication that the
interaction of the hydroxyl oxygen orbitals with the π-orbitals
of the aromatic ring is not very significant.
Bond critical points in the electron density41associated with
shared (covalent) intramolecular bonding are listed in Table 3.
A very good agreement between experiment and theory is also
observed. Every chemical bond is represented with a (3,-1)
bond critical point with a high electron density value and a
negative Laplacian. The double O(2)-C(17) bond has the
highest electron density but is not significantly elliptical. The
bonds in the aromatic ring have much higher electron density
at the bond critical point (Fb) 2.12 eÅ-3when averaged over
the six bonds in ring A in estrone42) and much higher ellipticities
(? ) 0.21 again, when averaged over the six bonds in ring A in
estrone42) than those of the rest of the C-C bonds in estrone.
These values are not much different than the values of Fb)
2.08 eÅ-3and ? ) 0.20 we calculated for the benzene molecule
at the B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level
of theory. (For comparison, the average value of the electron
density in single C-C bonds in estrone is 1.67 eÅ-3, and the
average ellipticity, 0.05.) The polarization of the C-O, O-H,
and C-H bonds is evident, the C-C bonds being less polarized.
All these values are in the expected range found in the literature
(see, for example, refs 43-49).
The molecular calculation results are generally in excellent
agreement with both the experimental and the periodic calcula-
tion results, as can be seen from Table 3. The largest discrep-
ancies between the three sets of results in Table 3 are in the
values of the Laplacian, ∇2Fb.
(43) Destro, R.; Merati, F. Z. Naturforsch. 1993, 48a, 99-104.
(44) Li, X.; Wu, G.; Abramov, Yu. A.; Volkov, A. V.; Coppens, P. Proc. Natl.
Acad. Sci. U.S.A. 2002, 99, 12132-12137.
(45) Ellena, J.; Goeta, A. E.; Howard, J. A. K.; Punte, G. J. Phys. Chem. 2001,
(46) Hibbs, D. E.; Hanrahan, J. R.; Hursthouse, M. B.; Knight, D. W.; Overgaard,
J.; Turner, P.; Piltz, R. O.; Waller, M. P. Org. Biomol. Chem. 2003, 1,
(41) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford:
Clarendon Press, 1990.
(42) From the experimental data.
Figure 3. Static multipole deformation density (left) and the Laplacian of the total electron density (right) in the O(2)-C(17)‚‚‚O(1) (0.5 - x - 3, -y -
1, 0.5 + x - 1) plane: (a) from the experimental data, (b) from the solid state theoretical data. The deformation density isocontours and the Fourier series
truncation are as those in Figure 2. The Laplacian contour interval is 15 eÅ-5, negative ∇2F(r) contours are red, and positive contours are blue. Numbers
on the maps correspond to the values at the maxima in the negative Laplacian.
Electron Density Study of Estrone
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 128, NO. 27, 2006 8853