Force-field parameterisation, synthesis and crystal structure of a novel tricarbonylchromium arene complex

Article abstract of DOI:10.1016/S0022-328X(99)00372-1

We construct a force field for organochromium poly(benzyl phenyl ether) dendrimers from reported experimental data and experimental data measured by us. Potential function terms are principally optimised through the use of crystal structure data of a novel [Cr(CO)₃(C₆H₅CH₂OCH ₂C₆H₅)Cr(CO)₃] complex. We report the synthesis and the crystal structure data of the chromium complex. In addition the important benzyl ether linkage torsion angle parameter is optimized by comparison with ab initio torsional data of a model compound. With this information, a force field suitable for molecular mechanics and dynamics calculations of organochromium poly(benzyl phenyl ether) dendrimers is constructed. The force field is tested by mapping the energy surface and simulating the crystal structure of [Cr(CO)₃(C₆H₅CH₂OCH ₂C₆H₅)Cr(CO)₃].

Full text of DOI:10.1016/S0022-328X(99)00372-1

www.elsevier.nl/locate/jorganchem
Journal of Organometallic Chemistry 588 (1999) 176–185
Force-field parameterisation, synthesis and crystal structure of a
novel tricarbonylchromium arene complex
Samantha J. Hughes a, John R. Moss a,1, Kevin J. Naidoo a,*, Janet F. Kelly b,
Andrei S. Batsanov b
a Department of Chemistry, Uni6ersity of Cape Town, Rondebosch 7701, South Africa
b Department of Chemistry, Uni6ersity of Durham, Durham, UK
Received 1 January 1999; received in revised form 1 June 1999
Abstract
We construct a force field for organochromium poly(benzyl phenyl ether) dendrimers from reported experimental data and
experimental data measured by us. Potential function terms are principally optimised through the use of crystal structure data of
a novel [Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3] complex. We report the synthesis and the crystal structure data of the chromium
complex. In addition the important benzyl ether linkage torsion angle parameter is optimized by comparison with ab initio
torsional data of a model compound. With this information, a force field suitable for molecular mechanics and dynamics
calculations of organochromium poly(benzyl phenyl ether) dendrimers is constructed. The force field is tested by mapping the
energy surface and simulating the crystal structure of [Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3]. © 1999 Elsevier Science S.A. All
rights reserved.
Keywords: Dendrimers; Tricarbonylchromium arene complexes; Parameterisation; Force field; Molecular mechanics; Ab initio; Crystal structure
eration dendrimers. Computational techniques have
been used to study these complex macromolecules [11–
16]. While most of these calculations involved coarse-
1. Introduction
Incorporation of metals into a dendritic architecture
has resulted in the preparation of dendrimers with a
wide range of properties, enabling their use as liquid
crystals [1], catalysts [2,3] and inorganic sensors [3].
Recently, an increasing amount of interest has been
focused on the synthesis of novel organometallic den-
drimers [1–8]. Previous work done in our laboratories
has led to the synthesis of new iron and ruthenium
dendrimers, based on the poly(benzyl phenyl ether)
class of dendrimer [9]. We have also examined the
functionalisation of the peripheral aromatic rings as
(arene)tricarbonylchromium(0) complexes (Fig. 1) as
has been done for polysilane dendrimers [10].
grained methods, only
a
limited number of
comprehensive investigations using force-field methods
on dendrimers have been reported [17,18]. Further-
more, no computational studies of any organometallic
dendrimers have been reported. However, we have re-
cently completed an exhaustive study on the structure
of organic dendrimers and the corresponding
organochromium poly(benzyl phenyl ether) dendrimers,
by molecular mechanics and dynamics techniques [19],
using the program CHARMM [20]. These calculations
were only possible through the development of a force
field for these dendrimers, which we report here. The
development of the force field rests largely on the
extension of an existing CHARMM force field [21,22] to
include parameters for the treatment of the
organometallic moieties.
The fractal nature of these macromolecules leads to
difficulties in obtaining suitable crystals, thus preclud-
ing the use of X-ray methods for all but the lowest-gen-
Two necessary parts of the force field were absent
from existing data and required development. First
all parameters related to the (arene)tricarbonyl-
* Corresponding author. Fax: +27-21-6897499.
E-mail address: knaidoo@psipsy.uct.ac.za (K.J. Naidoo)
1 Also corresponding author.
0022-328X/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.
PII: S0022-328X(99)00372-1

S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
177
C6H5)Cr(CO)3] (2) in Section 2 and the crystal structure
of this compound in Section 3. We then discuss the
parameterization procedure in Section 4. We compare
the results of a conformational energy surface, which
we constructed, to experimental crystal structure con-
formations in Section 5.1. In Section 5.2 we report two
test calculations where we have simulated crystal struc-
tures of the chromium complex using (a) the experimen-
tal and (b) the computer-predicted low-energy
conformations.
2. Synthesis of (C6H5CH2OCH2C6H5)[Cr(CO)3]2
The peripheral groups of the organochromium den-
drimers are (benzyl ether) tricarbonylchromium com-
plexes. The structures of simple benzylic ether
tricarbonylchromium complexes could be used in the
parameterisation of the force field, however the Cam-
bridge Structural Database [23] contained no such ex-
amples. It was therefore necessary, as part of the
parameterisation effort, to synthesise and solve the
structure of a model (arene)tricarbonylchromium com-
plex. We prepared the novel compound [Cr(CO)3-
(C6H5CH2OCH2C6H5)Cr(CO)3] (2) by direct complexa-
tion of dibenzyl ether with chromium hexacarbonyl
(Scheme 1). The desired product was obtained in 49%
yield, along with the intermediate monometallic species
[Cr(CO)3(C6H5CH2OCH2C6H5)] (3) in 34% yield. This
intermediate 3 is a known compound, previously syn-
thesised via a different route [24].
Fig. 1. A first-generation organochromium dendrimer.
chromium(0) complex were needed. For this purpose
we synthesised, crystallised and solved the crystal struc-
ture of a model compound [Cr(CO)3(C6H5CH2OCH2-
C6H5)Cr(CO)3] (2). We then used the data to build a
parameter set. Secondly the CHARMM polymer force
field [22] under development in our laboratory lacked
rotational ether linkage dihedral angle parameters. The
ether linkage is central to the structure and conforma-
tion of the poly(benzyl phenyl ether) class of den-
drimers. We used data generated from ab initio
calculations to develop these CHARMM parameters.
We report the synthesis of [Cr(CO)3(C6H5CH2OCH2-
2.1. General synthesis data
All manipulations were carried out under a nitrogen
atmosphere by using standard Schlenk techniques. Re-
Scheme 1.

178
S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
actions involving chromium carbonyl derivatives were
protected from light. Dibenzyl ether and THF were
dried over sodium–benzophenone and distilled prior to
use. Chromium hexacarbonyl was purchased from
Strem Chemicals and used without further purification.
Column chromatography was conducted with Merck
Kieselgel (230–400) mesh.
Found: C, 51.1; H, 2.95%. M+ 470. C20H14Cr2O7. Calc.
C, 51.1; H, 3.0%. M 470. IR (CH2Cl2) w(CO) 1970 (vs)
1
and 1890 (vs) cm−1. H-NMR (CDCl3) l(ppm): 4.36
(4H, s, ArCH2O), 5.26–5.44 (10H, m, ArH). 13C-NMR
l(ppm): 70.4 (CH2O), 93.7 (p-C), 93.8, 94.8 (o- and
m-C), 111.0 (ipso-C), 191.1 (CO).
IR spectra were recorded in solution on a Perkin–
Elmer Paragon 1000 FT-IR spectrometer. 1H-NMR
spectra were recorded on a Varian Unity Spectrometer
(400 MHz). 13C-NMR spectra were recorded on the
same instrument at 100 MHz. Tetramethylsilane was
used as a reference standard in both cases. Melting
points were measured using a Reichert Thermovar hot-
stage microscope and are uncorrected. Microanalyses
were determined at the University of Cape Town, using
a Fisons EA 1108 CHNS-O instrument. Mass spectra
were recorded on a VG micromass 16F spectrometer
operating at 70 eV with an accelerating voltage of 4 kV
and a variable source temperature.
3. Crystal structure
A crystal of [Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3]
suitable for single-crystal diffraction data collection,
was grown by slow evaporation from CH2Cl2–hexane.
The crystal appeared to be a pseudo-merohedral twin
with the twinning law −h, −k, l; the contribution of
the second component was refined to 0.073(1). All the
measurements were performed at 150 K on a 3-circle
Bruker axs SMART diffractometer, with a CCD area
detector, using graphite monochromated MoꢀKa radia-
tion. A total of 17 533 reflections (4315 unique) with
qB27.5 were measured, of which 3340 were observed
[I\2|(I)]. The crystal was shaped as a platelet with
approximate dimensions 0.4×0.3×0.02 mm3 and re-
quired an empirical absorption correction carried out
with the SADABS program [25]. The minimum and
maximum corrections were 0.73 and 1.00, respectively.
Crystal decay was monitored by repeating the initial 50
frames at the end of the data collection and analyzing
the 205 duplicate reflections.
The structure was solved by direct methods, followed
by Fourier difference syntheses. Full matrix least-
squares refinement was carried out against F2 of all
data using the SHELXTL software [26]. PLUTO was used
for the molecular plotting [27]. The hydrogen atoms
were located using the geometrical method of AFIX
instruction in the SHELXL-93 program [26] and then
allowed to refine freely.
2.2. Preparation of [Cr(CO)3(C6H5CH2OCH2C6H5)-
Cr(CO)3] (2)
Chromium hexacarbonyl (2.43 g, 11.0 mmol) was
added to a stirred solution of dibenzyl ether 1 (1 cm3,
5.26 mmol) in a mixture of dibutyl ether (45 cm3) and
THF (4 cm3) and the resulting yellow solution was
refluxed for 29 h. A further portion of chromium
hexacarbonyl (0.50 g, 2.3 mmol) was then added, and
the mixture was refluxed for 3 h in an attempt to force
the reaction to completion, but the reaction was
stopped when signs of decomposition were observed.
The solution was allowed to cool and the solvent was
removed under reduced pressure. The resulting residue
was dissolved in CH2Cl2 and filtered through Celite® to
give a clear yellow solution. The solvent was evapo-
rated under reduced pressure to give a yellow solid
along with some decomposition products (2.251 g).
This mixture was flash chromatographed on silica gel
(80 g) eluting with toluene–hexane (9:1) to give (diben-
zyl ether)tricarbonylchromium(0) [24] (3) as a yellow oil
(216 mg), followed by mixed fractions. The mixed
fractions were flash chromatographed on silica gel (150
g), eluting with toluene–hexane (9:1) to afford a further
portion of 3 (374 mg, 34% combined). IR (hexane)
w(CO) 1981 (vs) and 1913 (vs) cm−1. MS: m/z 334
[M+]. 1H-NMR (CDCl3) l(ppm): 4.17 (2H, s,
ArCH2O), 4.55 (2H, s, ArCH2O), 5.15–5.30 (5H, m,
ArH), 7.15–7.30 (5H, m, ArH). 13C-NMR (CDCl3)
l(ppm): 70.2 (ArCH2O), 73.0 (ArCH2O), 91.5 (p-C),
92.0, 92.8 (o- and m-C), 107.9 (ipso-C), 127.9 (p-C),
127.7, 128.5 (o- and m-C), 137.4 (ipso-C), 232.6 (CO).
Further elution afforded the product 2 (1.199 g,
48.5%). M.p. 126–127°C (CH2Cl2/hexane). Anal.
The weighting scheme employed was of the form
w=1/[l2Fo2 +(0.0393P)2+7.6327P] where P=(F2o+
2F2c)/3. The crystallographic data together with data
collection details are given in Table 1.
3.1. Structural analysis of [Cr(CO)3(C6H5CH2OCH2-
C6H5)Cr(CO)3] (2)
The structure of [Cr(CO)3(C6H5CH2OCH2C6H5)-
Cr(CO)3] (2) was established by single-crystal X-ray
diffraction analysis. The molecular structure is shown
in Fig. 2 and selected bond lengths and angles are given
in Table 2. The complex displays the classic piano-stool
structure [28]. The aromatic rings are planar, with the
Cr atoms situated directly beneath the ring centroids, at
,
distances of 1.72 and 1.71 A. In monosubstituted
chromium arene complexes, the tricarbonyl tripod usu-
ally adopts one of two conformations in relation to the
ring: anti eclipsed or syn eclipsed, depending

S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
179
Table 1
atoms making up a molecule are defined as spheres of
varying sizes and charges in an attempt to adequately
describe their electronic states. The van der Waals and
Coulombic terms (non-bonded terms) describe these
atomic physical properties. The parameters for the non-
bonded terms are taken from existing CHARMM force
fields [21].
Crystal data and structure refinement for 2
Empirical formula
Formula weight
Temperature (K)
Wavelength (A)
Crystal system
Space group
C20H14Cr2O7
470.31
150(2)
0.71073
Monoclinic
P121/n1
,
A standard harmonic potential function is employed
to describe the bond stretching motion:
Unit cell dimensions
,
a (A)
7.6250(5)
10.5321
23.562(2)
90
90.613(4)
90
1892.1(2)
4
,
b (A)
Eb=S kb(r−r0)2
(1)
,
c (A)
h (°)
i (°)
k (°)
,
where r0 is the equilibrium value of the bond length (A)
and kb is in kcal mol−1
is also described using a harmonic approximation:
A
−2. The bond angle bending
,
3
,
V (A )
Z
Dcalc (g cm−3
)
1.651
1.189
952
Absorption coefficient (mm−1
F(000)
)
Crystal size (mm3)
q range for data collection
Index ranges
0.4×0.3×0.02
0.86°BqB27.49°
−95h59, −135k513,
−305l527
17533
Reflections collected
Independent reflections
Observed reflections [I\2|(I)]
Absorption correction
Max. and min. transmission
Refinement method
4315 [Rint=0.0674]
3340
Multi-scan (SADABS
1.00 and 0.73
)
Full-matrix least-squares on
F2
Data/restraints/parameters
Goodness-of-fit on F2
Final R indices [I\2|(I)]
R indices (all data)
4311/0/319
1.072
R1=0.0528 wR2=0.1190
R1=0.0795 wR2=0.1386
Largest shift/estimated S.D. ratio −0.001
Largest difference peak and hole 0.593, −0.611
−3
,
(e A
)
on whether the substituent is electron withdrawing or
donating, respectively [28]. In this present structure, only
one of the rings (C11–C16) adopts the expected anti
eclipsed conformation, the other ring (C21–C26) being
staggered. There is precedent for monosubstituted arene
complexes adopting the staggered conformation due to
strong steric effects [28], but it is not clear whether steric
reasons are the cause in this instance. Fig. 2(a) and (b)
illustrates the conformation of the two aromatic rings in
the dibenzyl ether bis-complex (view down centroid–Cr
axis). The staggered ring displays significant bond length
variation, with the carbon–carbon bonds situated above
the carbonyl ligands, lengthened by an average value of
,
0.023 A. The anti eclipsed complexed ring shows no
significant bond length variation.
4. Force-field parameterisation
Fig.
2.
(a)
The
crystal
structure
of
[Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3] (2), (view down Cr1-cen-
troid axis). (b) [Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3] (2), (view
down Cr2-centroid axis).
Molecular mechanics is based on a classical mechanics
force-field description of a molecule. In general the

180
S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
Table 2
No improper torsion angles were included in the
description of the organometallic species. We used
parameters from existing CHARMM force fields [22,21]
for bonds, angles and dihedrals not directly related to
the chromium ion.
,
Selected bond lengths (A) and angles (°) for 2
,
Bond lengths (A)
Cr(1)ꢀC(1)
Cr(1)ꢀC(2)
Cr(1)ꢀC(12)
Cr(1)ꢀC(15)
Cr(1)ꢀC(11)
Cr(2)ꢀC(6)
Cr(2)ꢀC(22)
Cr(2)ꢀC(23)
Cr(2)ꢀC(26)
1.843(5)
1.854(5)
2.222(5)
2.227(5)
2.239(4)
1.856(5)
2.205(5)
2.213(5)
2.239(5)
Cr(1)ꢀC(3)
Cr(1)ꢀC(16)
Cr(1)ꢀC(13)
Cr(1)ꢀC(14)
Cr(2)ꢀC(5)
Cr(2)ꢀC(4)
Cr(2)ꢀC(21)
Cr(2)ꢀC(24)
Cr(2)ꢀC(25)
1.850(5)
2.202(4)
2.225(5)
2.228(5)
1.845(5)
1.856(5)
2.209(5)
2.236(5)
2.240(5)
4.1. De6elopment of (arene)tricarbonylchromium
parameters
The program CHARMM is designed for molecular
mechanics and dynamics calculations of macro-
molecules [20]. CHARMM has an extensive parameter set
for the treatment of organic monomers, but does not
contain many parameters for metallic species. It was
therefore necessary to extend the existing force field to
include the tricarbonylchromium(arene) moiety. First,
we define the topology of the arene complex. The
Cr(CO)3 group was bonded to the benzyl via a dummy
atom located at the centre of the benzene ring. We used
a scheme similar to that of Doman et al. [29] when
treating forces on the dummy atom. By placing the
dummy atom at the centroid and ‘bonding’ it to the
ring atoms, the forces on the dummy atom were equally
distributed onto the ring carbons.
Appropriate equilibrium bond and angle values for
the dummy atom were obtained from the crystal struc-
ture values listed in Table 2. The dummy atom was
treated as an aromatic carbon atom, thus carbon-like
force constants were applied to it. The mass of the
dummy atom was assigned to be the same as that of
carbon, but the van der Waals radius of the dummy
atom was set to zero, to avoid the introduction of
O(1)ꢀC(1)
O(3)ꢀC(3)
O(5)ꢀC(5)
1.161(6)
1.153(6)
1.155(6)
O(2)ꢀC(2)
O(4)ꢀC(4)
O(6)ꢀC(6)
1.155(6)
1.151(6)
1.154(6)
Centroid–Cr(1)
1.72 a
Centroid–Cr(2)
1.71 a
O(7)ꢀC(7)
1.413(6)
1.499(7)
1.412(7)
1.413(7)
1.402(7)
1.417(7)
1.412(8)
1.427(8)
O(7)ꢀC(8)
1.429(6)
1.515(6)
1.419(7)
1.389(8)
1.416(6)
1.427(6)
1.401(8)
1.379(7)
C(8)ꢀC(21)
C(11)ꢀC(12)
C(12)ꢀC(13)
C(14)ꢀC(15)
C(21)ꢀC(22)
C(22)ꢀC(23)
C(24)ꢀC(25)
C(7)ꢀC(11)
C(11)ꢀC(16)
C(13)ꢀC(14)
C(15)ꢀC(16)
C(21)ꢀC(26)
C(23)ꢀC(24)
C(25)ꢀC(26)
Bond angles (°)
C(1)ꢀCr(1)ꢀC(3)
C(3)ꢀCr(1)ꢀC(2)
C(5)ꢀCr(2)ꢀC(4)
91.0(2)
86.1(2)
90.0(2)
C(1)ꢀCr(1)ꢀC(2)
C(5)ꢀCr(2)ꢀC(6)
C(6)ꢀCr(2)ꢀC(4)
88.5(2)
84.5(2)
89.2(2)
C(7)ꢀO(7)ꢀC(8)
111.3(4)
178.1(4)
178.6(5)
177.0(4)
109.6(4)
121.3(4)
120.5(5)
120.5(5)
119.8(4)
120.2(4)
119.8(5)
118.9(5)
120.4(5)
O(1)ꢀC(1)ꢀCr(1)
O(3)ꢀC(3)ꢀCr(1)
O(5)ꢀC(5)ꢀCr(2)
O(7)ꢀC(8)ꢀC(21)
C(12)ꢀC(11)ꢀC(16)
C(16)ꢀC(11)ꢀC(7)
C(14)ꢀC(13)ꢀC(12)
C(14)ꢀC(15)ꢀC(16)
C(22)ꢀC(21)ꢀC(26)
C(26)ꢀC(21)ꢀC(8)
C(24)ꢀC(23)ꢀC(22)
C(26)ꢀC(25)ꢀC(24)
177.0(4)
178.5(4)
176.7(5)
107.7(4)
119.0(4)
119.6(4)
120.1(5)
120.1(5)
119.1(4)
120.6(5)
120.9(5)
120.9(5)
O(2)ꢀC(2)ꢀCr(1)
O(4)ꢀC(4)ꢀCr(2)
O(6)ꢀC(6)ꢀCr(2)
O(7)ꢀC(7)ꢀC(11)
C(12)ꢀC(11)ꢀC(7)
C(11)ꢀC(12)ꢀC(13)
C(13)ꢀC(14)ꢀC(15)
C(15)ꢀC(16)ꢀC(11)
C(22)ꢀC(21)ꢀC(8)
C(23)ꢀC(22)ꢀC(21)
C(23)ꢀC(24)ꢀC(25)
C(25)ꢀC(26)ꢀC(21)
Table 3
CHARMM atom classification
C
ring–Centroid–Cr(2) 90.2,
Name
Description
89.8 a,b
Cring–Centroid–Cr(2) 90.0,
90.0 a,b
DUM
CA
Dummy atom for centroid
Aromatic carbon
CA1
MCR
CM
Alternate aromatic carbon
Chromium metal atom
Carbonyl carbon
a Errors are not available for these measurements.
b Two values are indicated because there are two average values for
that parameter due to bond length alternation in the aromatic ring.
OM
Carbonyl oxygen
DUM
Dummy atom for centroid
Eq=S kq(q−q0)2
(2)
where q0 is the value of the angle at equilibrium and kq
Table 4
is in kcal mol−1 rad−2
.
Selected force-field bond parameters for Eq. (1)
A Fourier term (Eq. (3)) approximates the energy
associated with torsional rotation (n is the periodicity
and can take on values of 1–6):
Bond
kb
r0
MCR-CM
MCR–DUM
OM–CM
CA1–DUM
CA–DUM
300.0
1.84
1.73
1.14
1.41
1.41
210.0
1115.0
305.0
E =S ꢀk ꢀ−k cos(nƒ)
(3)
ƒ
ƒ
ƒ
The force constant k is in kcal mol−1 rad−2 and the
305.0
ƒ
dihedral angle ƒ is in degrees.

S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
181
Table 5
Selected force-field angle parameters for Eq. (2)
kq (kcal mol−1 rad−2
)
q0 (°)
kq (kcal mol−1 rad−2
)
q0 (°)
CM–MCR–CM
MCR–CM–OM
CM–MCR–DUM
CA–DUM–MCR
5.00
25.00
5.00
90.0
179.0
126.2
90.0
CA1–DUM–MCR
CA1–DUM–CA1
CA1–DUM–CA
CA–DUM–CA
50.00
40.00
40.00
40.00
89.4
120.0
60.0
50.00
120.0
non-existent interactions with the carbon atoms of the
aromatic ring. Dihedral force constants for torsions
involving the dummy atom were set to zero to allow
free rotation of the chromium tricarbonyl group. The
force constants for the metal dummy stretch and bend
were assigned by analogy to similar metal dummy
parameters already present in the force field [21].
Alternating carbons in the aromatic ring were by
necessity assigned to different atom types (CA and
CA1) for the purposes of construction; however, the
force constants for the interactions involving CA were
identical to those involving CA1, only the equilibrium
angle values differing in a manner consistent with the
crystal structure.
The carbonyl carbon and oxygen parameters were
already present in the CHARMM force field [21]; these
were used after checking to ensure that they did not
deviate significantly from the crystal structure values.
Force constants for bond stretch, angle bend and dihe-
dral interactions involving the metal and the carbonyl
group were obtained by analogy to other metal car-
bonyls present in the force field, or from the literature
[29,30]. The non-bonded parameters were already
present in the force field, with the exception of those of
the dummy atom. A listing of CHARMM atom classifica-
tions is shown in Table 3. The newly added parameters
are reported in Tables 4–7. A complete list of the
CHARMM parameters has been published by MacKerell
et al. [21] We found that torsion parameters involving
the metal complex had small effect on the energy of the
system as is often the case with this potential function.
A free rotation about the dummy–chromium bond,
unhindered by the potential form represented in Eq.
(3), appeared to give qualitatively better results in the
case of our conformational energy surface calculations.
Fig. 3. (a) The ether linkage torsion angle c as found in the
poly(benzyl phenyl ether) dendrimer. (b) Benzyl phenyl ether model
compound used in parameterisation of the ether linkage.
4.2. Parameterisation of ether linkage
In addition to the chromium parameters, a second
area of force-field parameterisation was crucial to the
accurate simulation of dendrimers. The ether linkage
torsion angle c, illustrated in Fig. 3(a), is present where
surface groups are connected to the interior monomers,
as well as in the links between internal monomers, and
monomers to the central core molecule. It therefore has
a significant effect on the topology of the macro-
molecule. Thus it is crucial that this torsion angle be
parameterised properly in order for the simulation re-
sults to have any validity. The parameters for this
torsion angle were adapted from the CHARMM polymer
Table 6
Table 7
Dihedral parameters for metal-centred torsion angle rotations
Selected non-bonded parameters for chromium complex 2
Dihedral angle
k (kcal mol−1 rad−2
)
n
Phase a
Polarizability
E
van der Waals radius
ƒ
CA–DUM–MCR–CM
CA1–DUM–MCR–CM 0.155
X–MCR–CM–X 0.05
0.155
6
6
4
180.0
180.0
0.000
MCR 0.01
−0.020
−0.0262
−0.1591
1.465
2.
1.540
CM
OM
1.650000
0.84000
DUM 0.000000
−0.000000 0.000000
a The phase is the minimum geometry of the dihedral.

182
S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
Table 9
Selected torsion angles from the two conformations
Torsion angle
XRAY
GMIN
b (°)
c (°)
T1 (°)
T2 (°)
−179.8
175.6
−25.2
92.1
−180
180
11.6
−85.9
Single-point ab initio energy calculations were carried
out on each set of minimised coordinates resulting from
the molecular mechanics calculations described above
for the dihedral angle c. We used GAUSSIAN94 [31] for
all our ab initio calculations, which were performed at
the Hartree–Fock level with the 6-31G(d) basis set.
This produced the ab initio rotational potential for c,
which is shown with the molecular mechanics rotational
potential for comparison in Fig. 4. The topology about
the dihedral has three energy barriers as the carbon–
carbon bond is rotated from −180° to 180°. The local
maxima (−120° and 120°) occur where a hydrogen
atom and a phenyl ring eclipse each other, while the
global maximum (0°) occurs where two phenyl rings are
eclipsed.
Fig. 4. The modified CHARMM and ab initio energy scans as a
function of c.
Table 8
Trial k values with differences in barrier ratios and global maxima
ƒ
ratios from force field calculations and ab initio results
k
Barrier ratio dif- Global maxima difference
ference
ƒ
(kcal mol−1 rad−2
)
(kcal mol−1
)
0.27
0.25
0.23
0.20
0.17
0.15
0.41
0.40
0.16
0.25
0.16
0.11
1.40
1.80
1.78
1.75
1.69
1.60
To parameterise the ether linkage torsion angle, the
CHARMM data were fitted to the ab initio data, by
changing the value of the coefficient k in the torsional
ƒ
energy term of the force field, on a trial-and-error basis,
starting with the initial value k =0.27 kcal mol−1
ƒ
rad−2. The energy scans were compared using two
criteria: the difference in the barrier height ratio, and
the difference between the values of the global maxima.
force field [22]. To ensure that this torsion is treated
correctly, parameterisation was carried out by trial-
and-error fitting of torsional rotation data to ab initio
quantum mechanical data for a simple model com-
pound, benzyl phenyl ether (Fig. 3(b)).
The molecular mechanical torsional potential as a
function of c (C2ꢀC3ꢀO4ꢀC5) was obtained by varying
c through 360°, constraining at 10° intervals. At each
c value two aromatic ring conformations were varied.
(C1ꢀC2ꢀC3ꢀO4) and (C6ꢀC5ꢀO4ꢀC3) were systemati-
cally varied from −180° to 180° at 30° intervals fol-
lowed by steepest descents and conjugate gradients
minimisation. Every permutation of the two ring orien-
tations was explored for each value of c, and the
lowest-energy structure was recorded.
Trial k values appear in Table 8, along with the two
ƒ
fitting criteria.
Overall, the best agreement with the ab initio data
was found with k =0.15 kcal mol−1 rad−2. The bar
ƒ
rier height ratio closely matches the ab initio ratio, and
Fig. 6. The energy surface of chromium complex 2 as a function of b
and c, showing the global minimum near (−180, 180). Contours are
at 2 kcal mol−1 intervals above the minimum.
Fig. 5. The torsion angles b and c for the energy map.

S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
183
5.1. Mapping the energy surface of the dibenzyl ether
bis-complex 2
Using CHARMM, the global minimum conformation
of the dibenzyl ether bis-complex 2 was found by
mapping the energy surface of the molecule as a func-
tion of two torsion angles b (C11ꢀC8ꢀO7ꢀC7) and c
(C21ꢀC7ꢀO7ꢀC8) indicated on Fig. 5. Two additional
torsion angles were taken into account when generat-
ing the energy surface, viz. T1 (C22ꢀC21ꢀC7ꢀO7) and
T2 (C12ꢀC11ꢀC8ꢀO7). The latter torsion angles deter-
mine the orientation of the aromatic rings, for which
several minimum-energy conformations could exist at
each b/c combination. Consequently at each interval,
the lowest-energy local minimum was found by step-
ping through all of the T1 and T2 permutations at 30°
intervals, followed by steepest descents and conjugate
gradients minimisation algorithms.
Inspection of the resulting energy surface (Fig. 6)
reveals the presence of high-energy barriers to rotation
at b=0° and c=0°, and the global minimum at
b= −180°, c=180°, indicating that the molecule
adopts the fully extended conformation in the global
minimum structure. The two phenyl rings (torsion an-
gles T1 and T2) adopt gauche conformations. Table 9
lists the values of these dihedral angles for comparison
with those found in the crystal structure. For simplic-
ity from now on we refer to the global minimum
Fig. 7. (a) Conformation from crystal structure (XRAY) and (b)
global minimum conformation from CHARMM conformational search
(GMIN).
the value of the global maxima are fairly similar. The
original k =0.27 kcal mol−1 rad−2 resulted in a bet-
ƒ
ter match of global maxima values, but a worse match
for the barrier height ratio. The latter is the more
important criterion, as it is a measure of the accuracy
of the torsion angle contribution to the total potential,
whereas the value of the global maxima is an indica-
tion of the accuracy of the entire parameter set.
conformer obtained from the energy surface as GMIN
,
while the conformation of the crystallographic asym-
metric unit is referred to as XRAY.
It is evident that although the GMIN conformer ap-
proximates the XRAY conformer in terms of the pri-
mary dihedral angles b and c, the two structures
differ to quite a large extent in the ring torsion angle
orientations (T1 and T2), with the result that the
molecules adopt very different conformations (Fig. 7).
The orientation of the right-hand-side aromatic rings
in Fig. 7 is determined by the ring torsion angle T1,
whereas the aromatic ring on the left-hand side is
controlled by T2.
The changed sign for T1 in GMIN has little effect on
the overall conformation. However, the value of T2
(−85.9 as compared to +92.1 in XRAY) in the
GMIN structure results in the projection of the tricar-
bonylchromium group on the opposite face to that
found in the XRAY structure. The XRAY conformer
was minimised in vacuo, to relax the structure. Small
adjustments were observed, but the molecule retained
the same conformation, and therefore approximately
the same values of b, c, T1 and T2 (Table 10). GMIN
was found to be lower in energy than the minimised
XRAY structure by 1.4 kcal mol−1. This difference in
energy can be ascribed to the molecule adopting a
5. Testing the force field
The accuracy of the new parameters was investi-
gated by searching the conformational space of the
[Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3] complex for
the lowest-energy conformer and then comparing this
structure with the one found by single-crystal analysis
described in Section 3.1 above. We perform a second
test where we show that the experimental crystal struc-
ture can be accurately reproduced with the newly con-
structed force field.
Table 10
Selected dihedral angles from both crystal structure calculations
Dihedral
XRAY
XRAY
GMIN
(vacuum)
GMIN
(crystal)
(vacuum)
(crystal)
b (°)
c (°)
T1 (°)
T2 (°)
−179.2
173.3
−29.7
96.0
179.9
173.3
−29.7
96.0
−180.0
180.0
11.6
−85.9
−78.7
−152.4
−93.4
−115.4

184
S.J. Hughes et al. / Journal of Organometallic Chemistry 588 (1999) 176–185
6. Conclusions
higher-energy conformation in the crystal struc-
ture due to packing effects, as is demonstrated by the
crystal structure calculations, which we discuss
below.
We have synthesised, characterised and determined
the crystal structure of the novel complex
[Cr(CO)3(C6H5CH2OCH2C6H5)Cr(CO)3] (2). Using this
crystal structure, we have constructed a force field
suitable for molecular mechanics calculations of
organochromium dendrimers. In addition the force field
was further parameterised for the important benzyl
ether linkage, by fitting molecular mechanics torsional
rotation data to ab initio torsional data. By mapping
the energy surface and simulating the crystal structure
of the chromium complex 2, we tested the parameter
set. The structures produced from our molecular me-
chanics calculations compared well with those produced
from single-crystal structure experiments and ab initio
calculations. The force field we report here is suitable
for molecular mechanics and dynamics calculations of
organochromium small molecule complexes and poly(-
benzyl phenyl ether) dendrimers.
5.2. Simulating the crystal structures
We simulated the crystal structure of the chromium
complex 2 using the space group P21/n, the lattice
parameters and the conformation (XRAY) from the
crystal structure determination in two ways: first by
fixing the experimentally determined lattice parameters
and then secondly by optimising the lattice parameters
within the CHARMM force field. Prior to the crystal
structure simulation we minimised the two conformers
in vacuo. This was followed by generating all symme-
try-related images of the asymmetric unit within a
,
cut-off of 999.0 A.
The XRAY conformer is stabilised in the crystal by
11 kcal mol−1, with no significant change in confor-
mation (Table 10) when the lattice parameters are
fixed. When we allowed the lattice parameters to opti-
mise within the CHARMM force-field environment we
observed a further 11 kcal mol−1 stabilisation energy.
The main dihedral angles (T1, T2, b, and c) were
only changed by a few degrees and the cell parameters
7. Supplementary material
Crystallographic data for the structural analysis
have been deposited with the Cambridge Crystallo-
graphic Data Centre, CCDC no. 133310 for com-
pound 2. Copies of this information may be obtained
free of charge from: The Director, CCDC, 12 Union
Road, Cambridge, CB2 1EZ, UK (Fax: +44-1223-
336-033; email: deposit@ccdc.cam.ac.uk or www:
http://www.ccdc.cam.ac.uk).
,
increased by 0.4 A in the case of a and b while the
,
dimension c showed a shift of approximately 0.9 A
,
from 23.562 to 24.458 A. The small deviation of the
CHARMM-simulated crystal structure from the experi-
mentally determined lattice and molecular parameters
is a good measure of the reliability of the force field.
In future the non-bonded terms could possibly be fur-
ther optimised when constructing
a
general
Acknowledgements
organometallic force field to reduce the difference in
CHARMM-simulated lattice parameters and those deter-
mined experimentally.
S.J.H., J.R.M. and K.J.N. wish to thank the Uni-
versity of Cape Town, the Foundation for Research
Development (Pretoria) and AECI Ltd. for financial
support. The authors wish to thank Professor J.A.K.
Howard (University of Durham), for X-ray diffrac-
tometer time and contributions toward the crystal
structure solution.
The GMIN conformation was also simulated in the
crystal structure environment, but does not pack well
into the P21/n space group due to close contacts be-
tween the asymmetric unit and the symmetry-related
molecules. In order to eliminate close contacts but still
pack into the same space group, a severe distortion of
conformation is necessary (Table 10). The conformer
obtained after minimisation in the lattice is thus very
different from the GMIN conformer, and has a molecu-
lar energy much higher (ca. 30 kcal mol−1) than the
corresponding XRAY crystal conformer, which is con-
sistent with our expectation that GMIN should be en-
ergetically disfavoured in this crystal environment.
However, we note that the energy of the XRAY con-
former in the crystal environment is more than 20 kcal
mol−1 lower in energy than either the vacuum or
GMIN or XRAY conformers, which indicates that crys-
tal packing is energetically favourable.
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