Structural classification of metal complexes with three-coordinate centres

Article abstract of DOI:10.1039/c5dt02773j

Attempts to describe the geometry about three-coordinate silver(i) complexes have proven difficult because interatomic angles generally vary wildly and there is no adequate or readily available classification system found in the literature. A search of the Cambridge Structural Database shows that complexes formed between any metal centre and three non-metal donors (18001 examples) usually adopt geometries that are quite different than ideal 'textbook' extremes of either trigonal planar (～4% with α = β = γ = 120 ± 2°), T-shaped (～0.05% with α = 180 ± 2°, β = γ = 90 ± 2°), or trigonal pyramidal (～0.3% with α = β = γ = 110 ± 2°). Moreover, there are multiple variations of "Y-type" and "other" shapes that require elaboration. Thus, to assist in future structural descriptions, we developed a classification system that spans all known and yet-to-be-discovered three-coordinate geometries. A spreadsheet has also been constructed that utilizes the "shape-space" approach to extract the structural description from a user input of three angles about a tri-coordinate centre and the number of atoms in a plane. The structures of two silver(i) complexes of new N-donor ligands p-NH₂C₆H₄C₆H₄CH(pz = pyrazol-1-yl)₂, L1, and 2-ferrocenyl-4,5-di(2-pyridyl)imidazole, L2, illustrate the utility of this classification system.

Full text of DOI:10.1039/c5dt02773j

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Structural Classification of Metal Complexes with Three-
Coordinate Centres.
Timothy L. Davis,a Joshua L. Watts,a Kenneth J. Brown,*a Jeewantha S. Hewage,b Alexander R.
Treleven,b Sergey V. Lindemanb and James R. Gardinier,*b
Received 00th January 20xx,
Accepted 00th January 20xx
DOI: 10.1039/x0xx00000x
www.rsc.org/
Attempts to describe the geometry about three-coordinate silver(I) 2D or 3D space).1 It is common that the observed structure of
complexes have proven difficult because interatomic angles generally vary a metal complex has a geometry that lies somewhere between
wildly and there is no adequate or readily available classification system the “high-symmetry” limits. For this reason,
a host of
found in the literature. A search of the Cambridge Structural Database structural parameters or indices have been developed in
shows that complexes formed between any metal centre and three non- attempts to describe how distorted an actual complex is
metal donors (18,001 examples) usually adopt geometries that are quite relative to the limiting geometries for a given coordination
different than ideal ‘textbook’ extremes of either trigonal planar (~4 % number. For example, the twist angle,
with α=β=γ=120 ±2o), T-shaped (~0.05 % with α=180±2o, β=γ=90 ±2o), or trigonal faces in six-coordinate structures can be manipulated
trigonal pyramidal (~ 0.3 % with α=β=γ=110 ±2o). Moreover, there are to give a “
6” parameter = /60 that varies between 1 for an
multiple variations of “Y-type” and “other” shapes that require octahedron and 0 for a trigonal prism.2 Similarly, Addison’s
elaboration. Thus, to assist in future structural descriptions, we developed five-coordinate index, τ5 = ( α)/60 ( and are the two
a classification system that spans all known and yet-to-be-discovered largest basal angles) gives a value of 1 for a trigonal bipyramid
θ, between opposing
τ
θ
β
-
β
α
three-coordinate geometries. A spreadsheet has also been constructed
that utilizes the “shape-space” approach to extract the structural =180). 3 In 2007, Houser offered a four-coordinate index τ4
description from a user input of three angles about a tri-coordinate centre [360 – ( )]/141 ( and
and the number of atoms in a plane. The structures of two silver(I) gives a value of 1 for tetrahedron and of 0 for a square planar
complexes of new N-donor ligands p-NH2C6H4C6H4CH(pz=pyrazol-1-yl)2, L1, geometry.4 Recently,
4 was modified by Kubiak and coworkers
and 2-ferrocenyl-4,5-di(2-pyridyl)imidazole, L2, illustrate the utility of this with an asymmetry parameter τδ τ4 to better
(
β
= 180,
α
= 120) and a value of 0 for a square pyramid (
β
=
α
=
α
+
β
α
β are the two largest angles) that
τ
=
(β/α)
classification system.
distinguish between distorted sawhorse and pinched
tetrahedral geometries.5 Our recent foray into silver(I)
complexes of heteroditopic ligands6 has resulted in the
structural characterization of numerous derivatives with three-
coordinate (3C) metal centers for which we wanted to
accurately describe by using a structural index. To our dismay,
The classification of structures is fundamental to general and
inorganic chemistry. Since the number of ligand atoms bound
to (and their symmetry about) a metal centre governs the
properties of metal complexes, structures are generally first
sorted according to the coordination number of the metal. For
each coordination number there are limiting geometries
whereby the ligating atoms occupy vertex positions in a
polygon or a regular polyhedron (“high-symmetry” points in
we could not find reference in the literature to any such “τ3
”
parameter or related structural index despite the propensity of
silver(I) (or, for that matter, of other main group, d-block, or f-
block complexes), to exhibit 3C metal centers. In attempts to
develop such a parameter it immediately became evident that
this is not a trivial problem. First, the limiting structures of 3C
complexes are not well defined. Textbooks most often cite 3C
structures as being either trigonal planar, T-shape, or trigonal
pyramidal.7 Less frequently, there is reference to a “Y-shape”.8
While the angles for the first two structure types are well
defined, the angles of a trigonal pyramid (≤109.5o) or a “Y-
shape” are not. For the latter, multiple types of Y-shapes seem
to be prevalent (vide infra). Second, it is noted that the
complexity of the various τn formula increases with decreasing
n because there are fewer interatomic angles to use as a
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previously unrecognized shape of relevance to ClF3 are Arrows.
Arrows are identified by the angular relation, 180o >
α
= β + γ.
If one starts from a T-shape and moves both arms “down” 45o
then a “Normal Arrow” (90/45/45) with a quadrilateral
projection is produced. In between the T-shape and the
Normal Arrow are “Expanded” Arrows while between the
Normal and Closed Arrows are “Compressed” Arrows. It is
noted that the top row of Fig. 1 represents a series of highest-
symmetry planar structures with three (trigonal) or two
Chart 1. New heteroditopic ligands used in this work.
reference and, since there is more space around the metal,
structures can adopt a larger number of limiting structures of
both planar and nonplanar varieties, as noted above. Third, it
is extremely difficult to use only angular values and develop a
single τ3 parameter that describes both planar and nonplanar
structures, in part, because of the convention of reporting
obtuse rather than reflex angles (even in planar structures).
Especially problematic are planar structures like that of ClF3,9
(monoclinic) identical angles. Since the
have a continuous range from 180 to 0o, these (or the ratio
/180) could comprise a “YTA index” to describe the “Y-”, “T-”,
β-values of this series
β
or “Arrow-” character of planar (trigonal and) monoclinic
systems. Most systems, however, are triclinic with three
different angles. If one starts with a T-shape and moves the
‘right’ arm up 30o then a triclinic “Orthogonal Y” shape (with
angles 150/120/90) is produced (bottom right, Fig 1). The
Orthogonal Y shape (but wholly rotated 120o) could also be
produced by moving one arm of a trigonal plane 30o. Thus, the
150/120/90 shape is halfway between a T-shape and a trigonal
plane, and is a “high symmetry” point in the 2D, 3C shape-
space. There are other types of triclinic Y-shapes that are
derived from the T-shape, but by moving the vertical leg “left”
or “right”. Thus, the structure on the bottom left of Fig 1
(180/150/30) is an Oblique Y and can be derived from either a
Closed Y or a T-shape. Figure S6 and its accompanying text in
the Supporting information details how the obliqueness of a
triclinic system is measured. As can be seen in Fig 1 or Fig S4,
there are numerous other special shapes that are produced by
simple “one-arm” or “two-arm” distortions of ideal shapes and
all of these, as well as the above examples, provide the basis
for the “ideal structures” found in the planar classification
scheme that is embedded in the Supporting spreadsheet, as
discussed later.
10
11
PhICl2, or CF3ICl2 whose sum of angles about the central
halide are less than 360o (349.2o , 353.7 o, and 343.2o
respectively). Herein, the possible limiting structures of 3C
metal complexes are identified and the methodology used to
classify three-coordinate structures is outlined.
The
classification scheme is then used to describe the geometry
about three-coordinate silver(I) centres in two complexes of
the new N-donor ligands, H2NC6H4C6H4CHpz2 (pz = pyrazol-1-
yl), L1, and 2-ferrocenyl-4,5-di(2-pyridyl)imidazole, L2 (left and
right of Chart 1). Results of a search of three-coordinate metal
complexes in the Cambridge Structural Database (CSD) are also
examined to ascertain the frequency of occurrence of the most
common and of limiting “high symmetry” structures.
When four atoms reside in a plane, the planar projections will
adopt either triangular or quadrilateral shapes between two
hypothetical (chemically impossible) linear extremes (Closed Y
or Closed Arrow), exemplified in Figure
1 and, more
completely, in Figures S4-S6. The three angles about the
centre atom in 3C structures will be given from largest to
If the centre atom of a trigonal plane is pulled “upward” and
smallest angle (when possible) by
α
/β
/
γ
.
The T-shape
normal to the plane, then right trigonal pyramids (α = β = γ <
(180/90/90, top row centre Fig 1) and Trigonal plane
(120/120/120) are well known. In between the T-shape and
120o) are formed where the apex of the pyramid lies directly
above the middle of the base triangle (Fig. 2). The relative
positions of the incircle and circumcircle of a base triangle
defines the type and aids in finding metrics of different
pyramids. The origin of an incircle, Oic, is found at the point of
intersection of three lines that bisect each internal angle. The
Trigonal plane are “Compressed Y’s” (120<
structure, bottom row, Fig 1) or, -dominant Y’s”, if
monoclinic ( γ). Similarly between the Trigonal plane and
Closed Y (180/180/0) are “Extended Y” shapes (0<
<120, 2nd
structure, bottom row, Fig 1) or “ -dominant Y’s” if . A
α
<180, 3rd
“
α
β
=
γ
γ
α = β
origin of
a circumcircle, Occ, is the point where three
perpendicular bisectors of the base edges meet. The radii of
Figure 2. Left: Perspective drawing of a trigonal pyramid of height h, slant height s1,
side edge length, e. Right: Projection of the base triangle (right) of edge length b1 and
internal angle Α’. The circumcircle of the base triangle with radius rcc is green, the
incircle with radius ric is black.
Figure 1. Representative arrangements of atoms in planar 3C structures. The numbers
are interatomic angles. Projections of atoms on plane give grey polygons (or just lines)
with red dashed lines.
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Figure 3. Perspective (top) and side (bottom) views showing “acute” (left), “normal”
(center), and “obtuse” (right) pyramids. The red dashed lines are the base triangle. b1
is the length of a base triangle edge that is also opposite of apex angle α (b2 is opposite
of apex angle β). Blue line h is the height of the pyramid. Occ is the origin of the base
triangle’s circumcircle. φ1incl is the incline of the side triangle (with α apex angle) with
respect to base triangle. x1 = perpendicular distance from b1 to Occ.
Figure 4. Various views of the structures of the cations in [Ag2(ꢀ-L1)2](BF4)2, 1, and
[Ag2(ꢀ-L2)2](SbF6)2, 2. Thermal ellipsoids at the 50% probability level.
the incircle and circumcircle are ric and rcc. The origins Occ and
Oic coincide in a right trigonal pyramid but do not coincide in
other pyramids (vide infra). The projection of the sides, e, on
the base triangle coincides with the three lines drawn from Occ
to each vertex of any base triangle. If the edges of the side
triangles, e, are of unit length then the pyramid height, h, and
by their relation to planar structures.
In order to identify 3C structure types from angular values, a
method loosely based on Alvarez’s12 “shape-space” approach
(for four- to nine-coordinate structures) is used. Basically, the
three input angles are compared to those of a host of ideal
shapes (planar or pyramidal) and those angular values that
deviate the least from ideal are called a match. The
the incline angle of the side relative to the base,
calculated from the apex angles via the slant height, s1 =
cos( /2) and the base length, b1 = 2sin( /2) as fully detailed in
1incl
φ1incl, can be
α
α
minimization function follows the form of Equation 1. Here,
, and are the angles to be tested, whereas αid βid id are the
Min(o) = (3)-½([( id)2 + ( id)2 + (γ − γid)2]1/2 (1)
α,
the Supporting Information. For a right trigonal pyramid,
φ
is less than 90o. Other types of trigonal-pyramids can be
characterized by the number of identical angles about the
β
γ
,
, γ
α
–
α
β – β
ideal angles of the “high-symmetry” shapes to which the input
angles are compared. The constant (3)-½ is a normalization
factor. The Supporting Information includes a spreadsheet
that allows users to input angular values and the number of
atoms in a plane. The resulting output provides the name and
various metrics of the ideal shape that most closely matches
the input values.
apex. Thus, cases where
α
pyramids whereas those with
=
β
α
≠
γ
≠
or
α
≠
β
=
γ
are monoclinic
β ≠ γ are triclinic pyramids.
Monoclinic pyramids have Occ separated from Oic in the base
triangle plane in only one direction, perpendicular to the base
triangle edge that is opposite of the unique angle. Triclinic
pyramids have Occ separated from Oic in two directions, both
parallel and perpendicular to the base triangle edge that is
During the course of studies on the coordination chemistry of
redox active heteroditopic ligands, we prepared silver(I)
opposite of the side triangle with
α as an apex angle. As
illustrated in Figure 3, monoclinic or triclinic pyramids can
further be classified as either “acute”, “normal”, or “obtuse” if
Occ resides, respectively, either inside, directly on, or outside
of the base triangle edges (Fig 3). As such, the incline angles
are less than, equal to, and greater than 90o for an acute, a
normal, and an obtuse pyramid, respectively. Similar to right
trigonal pyramids, other pyramids can be created by taking the
centre atom of a monoclinic or triclinic planar structure and
pulling “upward” thereby decreasing apex angles
proportionally, according to the Law of Sines, until a linear
limit 0/0/0 (Closed Arrow) is reached. Alternatively, some
pyramids can be formed by taking a planar structure and
pulling two of the ‘arms’ together until a planar folded limit is
complexes [Ag(L1)](BF4),
1, and [Ag(L2)](SbF6)·CH2Cl2, 2. Both
1
and 2 crystallized as solvates with complex cations that were
cyclic dimers in the solid state. In these dimers, the
κ2N,κ1N- ligands spanned two three-coordinate silver centres
(top of Fig. 4) where the respective long Ag···Ag separations of
ꢀ-
10.845 and 4.997
interactions. Importantly, the silver centres in
with sum of angles either exactly or very nearly 360o
’s(Ag1), 359o; (Ag2), 360o) whereas the symmetry-
equivalent silver(I) centres in were decidedly pyramidal
’s(Ag1): 340o) and none were ideal T-shape, trigonal
Å
precluded any direct intermetallic
1
were planar
(Σ∡
2
(Σ∡
planar, nor trigonal pyramidal (with three identical angles). So,
these complexes provide reasonable examples of the need for
reached (αfold,lim = β-γ, see Fig S7 and accompanying text). For
example, if the two horizontal arms of a T-shape (180/90/90)
an advanced classification system. For
1, Ag2 is planar with
angular values 164/112/84, most closely matching a “1/3
β
-
are pulled out of the plane while maintaining two angles at
1
90o, the third angle
α
would decrease from 180o to 90o until a
triorthogonal pyramid (90/90/90) is reached. Then further
compressed Orthogonal Y” (160/110/90;
an Orthogonal Y to a T-shape) but with 4, 2, and 6o deviations
in , and
for a Min = 4.32o. The geometry about Ag1 in
/ of the way from
3
α
,
β
γ
2
reduction to αfold,lim = 0, would cause the original T-shape
= β-γ
(146/121/73) is an acute triclinic pyramid. The pyramid is
to be completely folded into two dimensions 90/90/0. Thus,
guaranteed to be acute since the sum of any combination of
pyramids can be classified both according to their metrics and
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two apex angles is greater than 180o. This pyramid most Since most metal complexes have coordination numbers
closely matches that derived by taking a -Compressed Semi- between 4 and 6, there have been extensive studies regarding
Orthogonal Y (165/120/75) and folding the two arms that flank their structural classification. The CSD search performed here
angle
by 20o (7%), effectively lifting the centre atom 0.226 revealed that 3C metal complexes are relatively rare, but
units out of the plane of ligand atoms, leaving only 1, 1, and 2o significant, accounting for ~5% (18,001/372,280) of all MEn (n =
γ
α
deviations in α, β, and γ, respectively, from the experimental 2-6) complexes. Of these, most structures are not adequately
described by ideal trigonal planar, pyramidal, or T- shape
angles, thereby giving a Min = 1.41o.
The non-ideal angles about silver in
1
and
2
prompted a query geometries. So, to address issues with structural description
into the frequency of occurrence of various geometries in 3C of three coordinate complexes, we developed a system for
silver or other metal complexes. The CSD search results (see their classification based on angular values and knowledge of
Supporting Information) identified 18,001 instances where any the number of atoms in the plane (available from modern
metal was (only) bound to three non-metals, cases referred to crystallographic software). This classification system was
as ME3. Of these, nearly 15% (2,751) were 3C silver implemented into a spreadsheet found in the supporting
complexes. If one allows a 2o variation in
rounding errors (some
’s = 361o) or possible experimental names and metrics of the planar triangle or pyramid. Since
uncertainties then a
’s ≥ 354o would represent a “planar” most ME3 complexes are those with metals from groups 11-13
α, β, γ to account for information whereby users can input angular data to extract
Σ
∡
Σ
∡
complex. Under these criteria, 63% of all 3C metal complexes (56 %, 10,000/18,001), it is expected that this new
and 82% of 3C silver complexes are planar (Fig 5). Thus, classification system will be most helpful for describing the
compound
2 represents a rather rare example of pyramidal 3C coordination geometries in complexes of these groups,
silver. Contrary to expectations based on general and especially the highly variable ones of three-coordinate silver(I).
inorganic chemistry texts, very few 3C complexes actually
exhibit ideal structures. While the most common 3C ME3
Notes and references
geometry is indeed trigonal planar
constitutes only about 3.8 % (679/18,001) of all 3C structures.
Similarly, only ~0.05 3C ME3 complexes are T-shape
=180±2o, =90 ±2o). The most common angles for
pyramidal 3C ME3 complexes are
= 96±2o, = 95±2o,
(α=β=γ
=120±2o), this
‡
JRG thanks Prof Q. Timerghazin for helpful discussions, the NSF (CHE-0848515)
and Marquette University for funding. KJB thanks the U.S. Dept. of
Transportation's Dwight David Eisenhower Transportation Fellowship Program
(DDETFP) and the WSSU Research Initiation Program (RIP) for funding
%
(α
β=γ
α
β
γ =
94±2o, (549/18,001, 3.0%) corresponding to a 13.6% closed
1
2
3
R. B. King, Coord. Chem. Rev., 2000, 197, 141; R. B. King
Inorg. Chem. 1981, 20, 363.
A. Avdeef; J. P. Fackler, Jr., Inorg. Chem. 1975, 14, 2002; D. L.
Kepert, Inorg. Chem. 1972, 11, 1561; A
A. W. Addison, T. N. Rao, J. Reedijk, J. van Rijn; G. C.
Verschoor, J. Chem. Soc. Dalton Trans. 1984, 1349.
L. Yang, D. R. Powell, R. P. Houser, Dalton Trans. 2007, 955.
M. H. Reineke, M. D. Sampson, A. L. Rheingold; C. P. Kubiak,
Inorg. Chem. 2015, 54, 3211.
trigonal pyramid (or near triorthogonal pyramid); only 0.3 %
are “ideal” trigonal pyramidal (α=β=γ
=110 ±2o). A large
majority of 3C structures are Y- shape. For instance, there are
(4,946/18,001) 27.5% of cases that fit under the general
category of ‘Extended Y’ shapes (120±2o <
120±2o;
obliqueness) while another (4,481/18,001) 24.9% are
‘Compressed Y’ shapes (
> 120o ±2 ; 90± 2o < γ β < 120± 2o;
’s ≥ 354o, again ignoring asymmetry). There are also 46
examples or 0.3% of ME3 cases with arrowhead distortions
’s < 360o, and h ~ 0), a geometry that has not been
α & γ <
β < 180±2o,
4
5
Σ∡
’s ≥ 354o; i.e., not considering asymmetry or
6
7
J. R. Gardinier, J. S. Hewage, S. V. Lindeman, Inorg. Chem.
2014, 53, 12108.
α
&
Σ
∡
G. A. Lawrance Introduction to Coordination Chemistry, John
Wiley & Sons Ltd: West Sussex, UK; 2010; Chapter 4.; T. L.
Brown, H. E. Lemay, Jr., B. E. Bursten, C. J. Murphy
Chemistry: The Central Science, 10th Ed.; Pearson Education
Inc: Upper Saddle River, NJ; 2006; Chapter 9.
J. R. Gispert Coordination Chemistry, Wiley-VCH Verlag
GmbH & Co.: Weinheim; 2008; Chapter 3.
(α=β+γ, Σ∡
well recognized in texts previously but is important in
hypervalent halide compounds.13
8
9
D. F. Smith, J. Chem. Phys. 1953, 21, 609.
10 J. V. Carey, P. A. Chaloner, P. B. Hitchcock, T. Neugebauer, K.
R. Seddon, J. Chem. Res. 1996, 358, 2031. (b) E. M. Archer, T.
G. D. van Schalkwyk Acta Crystallogr. 1953, 6,88.
11 R.Minkwitz, M.Berkei Inorg. Chem. 1999, 38, 5041.
12 D. Casanova, J. Cirera, M. Llunell, P. Alemany, D. Avnir, S.
Alvarez, J. Am. Chem. Soc. 2004, 126, 1755; S. Alvarez, P.
Alemany, D. Casanova, J. Cirera, M. Llunell, D. Avnir, Coord.
Chem. Rev. 2005, 249, 1693.
13 This ME3 search did not include iodine as the central atom,
M, an element for which the arrowhead geometry
(restricting h < 0.06 Å) is most prevalent with 147 of 277 (or
53%) of occurrences.
Figure 5. Histograms showing the ln(frequency of occurrence) of the Σ∡’s in 3C ME3
complexes (blue, 18001 total) or 3C Ag (yellow, 1812 total) in the CSD. Single instances
were scaled to 0.1 on the ln scale.
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TOC Graphic
A classification system was developed to account for all
known and yet-to-be-discovered three-coordinate
geometries.
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TOC Abstract
The varieties of known and yet-to-be-discovered three-coordinate geometries are now defined.
TOC Graphic