example:  [Mn(OH₂)₆]SO₄ :  coordination #=6, and sulfate is outer sphere.
                [Mn(OH₂)₅SO₄] :  coordination # = 6, and sulfate is inner sphere.

    Coordination numbers can range from 2 up to 12, with 4 and 6 quite common for the upper transition metals.  The following factors influence the coordination number of the complex.

1. The size of the central atom or ion:  Larger atoms (periods 5 & 6) on the left side of the periodic table are larger, and can accommodate more ligands.
2. Steric interactions between the ligands:  Bulky ligands (such as PPh₃) will result in lower coordination numbers.
3. The electronic structure of the metal:  If the oxidation number is high, the metal can accept more electrons from the Lewis bases.  Metals with many d electrons, especially those on the right side of the periodic table, will have lower coordination numbers.

Coordination Number	Typical Examples	Structure or Shape
2	[CuCl2]-, Ag(NH3)+	linear
3 (rare)	[Cu(CN)2]-	trigonal planar
4	CrO42-, NiBr42- favored when metal is small and ligands are large	tetrahedral
4	[PtCl2(NH3)2], [Ni(CN)4]2-  typical for d8 metals and complexes with p bonding ligands	square planar
5	iron porphyrin complexes (square pyramid due to planar porphyrin rings)	distorted square pyramids or trigonal bipyramids
6	common for d0-d9, most 3d M3+ complexes are octahedral. distortions include trigonal prism, especially for chelating ligands with a small bite angle
7	more common for f-block elements.  Structures include pentagonal bipyramid, capped octahedron and capped trigonal prism

    Certain coordination numbers, specifically 5 and 7, have several shapes which are similar in energy, with low energy barriers for inter conversion.  An example of the fluctuating nature of these shapes can be seen in Berry pseudoratation of trigonal bipyramidal structures.  The structure distorts in such a way that the axial groups become equatorial, with a square pyramidal structure as an intermediate.

    The system of naming inorganic complexes incorporates prefixes (mono, di, tri, etc.), to indicate the number of ligands of each type coordinated to the metal.  The ligands have special names (and abbreviations).  Typically, ligands which are negatively charged end in o.  A list of common ligands is provided in the text on page 220.  A common ligand which was omitted are phosphines, and specifically triphenylphosphine, P(C₆H₅)₃.  This ligand is often abbreviated as PPh₃ or Pf₃.  It is important to note that ligands such as this which have prefixes such as di, tri, etc. in their names are enumerated using the prefixes bis, tris and tetrakis when more than one of them is coordinated to a metal.
    The format of naming the complexes is as follows.  Ligands are listed first in alphabetical order (not including prefixes).  This is followed by the name of the metal, and the oxidation state of the metal in roman numerals in parenthesis.

    An alternative system includes the charge on the complex (in arabic numerals) in parenthesis instead of the oxidation state of the metal.  In addition, metal complexes which are negative in charge often use the latin root for the metal, and end in the suffix ate.  The formula of the complex is always written in square brackets, with the metal appearing first, then negatively charged ions, and then neutral ligands.  Ions which are outer sphere are written outside of the square brackets.

• Name the following compounds: trans-[PtCl₂(NH₃)₄]²⁺,  [Ni(CO)₃(py)], [Cr(edta)]^1-
• Write formulas for the following compounds: cis-diaquadichloroplatinum(II), diamminetetra(isothiocyanato)chromium(III), and tris(ethylenediamine)rhodium(III)

    Many ligands have more than one site which can coordinate with a metal atom or ion.  These are referred to as ambidentate ligands.  Small ligands with two sites, such as NO₂^- (N or O)  or SCN^- (S or N) can undergo linkage isomerism.  The name of the ligand indicates which site is bound to the metal.  For NO₂^-, the nitrogen linkage has the name nitro, and the oxygen linkage has the name nitrito.  For thiocyanate ion, the sulfur linkage is named thiocyanato, and the nitrogen linkage is named isothiocyanato.
    Larger ligands with multiple bonding sites can bond to a single metal atom or ion at several sites, forming rings.  These ligands are referred to as polydentate, and form chelate complexes. In the most stable situations, the chelating agent will form 5 or 6 membered rings with the metal.  This produces the proper bite angle to produce octahedral symmetry around the metal.  In ligands with small bite angles, octahedrons will distort to trigonal prismatic geometry.

    One of the highly useful synthetic uses of chelating agents and metal ions involves the template effect, in which a group of ligands can be assembled by coordination to a central metal ion.  A large variety of macrocyclic compounds can be synthesized in this way.

    There are several types of isomerism exhibited in transition metal complexes.  In considering only complexes with octahedral geometry around the metal, the following types of isomerism are seen.

1. Geometric Isomerism - The existence of cis and trans isomers in compounds with the general formula [MX₂Y₄].  In the trans isomer, the two X groups are on opposite sides of the compound (on the same axis).  In the cis isomer, the two X groups occupy adjacent sites.  The symmetry of the molecules vary, and the isomers can be easily detected using infrared and Raman spectroscopy.  Complexes with the general formula [MX₃Y₃] can exist as two different isomers.  The three like ligands can either occupy a triangular face of the octahedral structure or three sites in one plane while the other ligands occupy three sites in a perpendicular plane.  The isomers are designated as fac (for facial) or mer  (for meridional).
2. Chirality and Optical Isomerism - Octahedral complexes can contain chiral centers, and thus exhibit optical isomerism.  The optical isomers, which are non superimposable mirror images of each other, will bend the plane of polarized light in different directions.  The pair of isomers are known as enantiomers or an enantiomeric pair.  Molecules which are chiral have the absence of an improper axis of rotation.  Non-chiral molecules have a mirror plane through the central atom or a center of inversion.  An example of the formation of many isomers can be seen in the reaction of cobalt (III) chloride with ethylenediamine, a bidentate ligand.  The products of the reaction include a violet colored product, a green product, and a yellow product.

    The violet product(s) are the isomers (a) and (b) above.  They are mirror images of each other, and constitute an enantiomeric pair, cis - [CoCl₂(en)₂]⁺.  The green product is isomer (c), trans-[CoCl₂(en)₂]⁺ which lacks optical activity.  The yellow product, [Co(en)₃]⁺, also exists as an enantiomeric pair.  The three bidentate ligands can connect to the octahedral sites of the metal in a right handed or left handed fashion, similar to the blades on a propeller or the threads on a screw.

 

Return to Class Schedule

Bonding and Electronic Structure of d-Metal Complexes
Crystal Field Theory

 

Octahedral Complexes

I^-<Br^-<S^2-<Cl^-<NO₃¹<N₃^-<F^-<OH^-<C₂O₄^2-<H₂O<NCS^-<CH₃CN
<pyridine<NH₃<en<bipy<phen<NO₂^-<PPh₃<CN^-<CO

1.  D_o  increases with increasing oxidation number of the metal.  This is due to the smaller size of the ion, resulting in smaller metal to ligand distances, and hence, a greater ligand field.
2.  D_o increases as you go down a group.  This is due to the better bonding ability of expanded shells using the 4d or 5d orbitals.

Mn²⁺<Ni²⁺<Co²⁺<Fe²⁺<V²⁺<Fe³⁺<Co³⁺<Mn⁴⁺<Mo³⁺<Rh³⁺<Ru³⁺<Pd⁴⁺<Ir³⁺<Pt⁴⁺

Return to Class Schedule

Calculating the Ligand Field Stabilization Energy

• For 3d metals (d⁴-d⁷):  In general, low spin complexes occur with very strong ligands, such as cyanide.  High spin complexes are common with ligands which are low in the spectrochemical series, such as the halogen ions.
• For 4d and 5d metals (d⁴-d⁷):  In general, the size of D_o is greater than for 3d metals.  As a result, complexes are typically low spin.  Even a ligand such as chloride (quite weak) produces a large enough value of D_o  in the complex RuCl₆^2- to produce a low spin, t_2g⁴ configuration.

    Evidence for LFSE can be seen in the enthalpies of hydration of the 3^rd period M²⁺ ions.  Without considering LFSE. the enthalpies should increase linearly as the size of the ion decreases and bond strength increases (the green line).  Instead, the data show two "humps", with the enthalpies for the configurations d⁰, d⁵, and d¹⁰ falling in the straight line. The other metal  ions show greater enthalpies of hydration (the orange line) in keeping with the calculated ligand-field stabilization energy for each configuration. When the calculated LFSE is subtracted from the observed values, they fall on the straight line which ignores LFSE, and only considers ionic size.

Return to Class Schedule

The Electronic Structure of Four-Coordinate Complexes
Tetrahedral and Square Planar Shapes

    The d orbitals of tetrahedral complexes also split into two groups.  Examination of the symmetry tables shows that the d_xy, d_yz, and d_xz have the same symmetry properties as the p_x, p_y, and p_z orbitals.  If the tetrahedron is viewed as ligands occupying the alternating corners of a cube, with the metal atom in the center, these d orbitals point in the direction of the ligands.  As a result, they will be higher in energy than the degenerate orbitals of the free metal atom or ion.  The d_z2 and d_x2_-y2 orbitals point between the ligands (towards the center of each face of the cube), and are lower in energy.

    The splitting pattern has the lower two orbitals (the e_g set) stabilized by 3/5 D_T , and the upper three orbitals (the t₂ set) 2/5 D_T greater in energy, where D_T is the size of the splitting in a tetrahedral field.  The size of D_T is approximately half the size of the octahedral splitting D_o for the same metal and ligands, so virtually all tetrahedral complexes are weak field/high spin.

    Octahedral complexes can undergo tetragonal distortions (the elongation of the z-axis, and shortening of the x and y axes) to become elongated into molecules with square planar (D_4h) symmetry.  This distortion is often observed in Cu²⁺ (d⁹) octahedral complexes.  As the z-axis is elongated, the degeneracy between the d_z2 and d_x2 _{- y}2 orbitals is broken, with the d_z2 orbital lower in energy since the ligands are further away.

        The extreme case of a tetragonal distortion is to form a true square planar complex in which the ligands along the z-axis are completely removed.  In this case, the d_z2 orbital drops even lower in energy, and the molecule has the following orbital splitting diagram.

        As a result of these distortions, there is a net lowering of energy (an increase in the ligand field stabilization energy) for complexes in which the metal has a d⁷, d⁸, or d⁹ configurations, and thus electrons would occupy the upper e_g set if an octahedral complex. In general, the size of the splitting in a square planar complex, D_SP is 1.3 times greater than D_o for complexes with the same metal and ligands.  As a result, the distortion results in square planar complexes with lower energies  than the comparable octahedral complex.  This distortion to square planar complexes is especially prevalent for d⁸ configurations and elements in the 4^th and 5^th periods such as:  Rh (I), Ir (I), Pt(II), Pd(III), and Au (III).  Nickel (II) four-coordinate complexes are usually tetrahedral unless there is a very strong ligand fields such as in [Ni(CN)₄]^2-, which is square planar.

    The tetragonal distortions described above are illustrations of the Jahn-Teller Effect.  The effect can be summarized by a statement which predicts which complexes will undergo distortion.  It does not predict the extent of the distortion.
 
 

The Jahn-Teller Effect      If the ground electronic configuration of a non-linear complex is orbitally degenerate, the complex will distort so as to remove the degeneracy and achieve lower energy.

This effect is particularly evident in d⁹ configurations.  The configuration in a octahedral complex would be t_2g⁶e_g³, where the configuration has degeneracy because the ninth electron can occupy either orbital in the e_g set.  A tetragonal distortion removes the degeneracy, with the electron of highest energy occupying the non degenerate d_x2_{- y}2 orbital.  Low spin octahedral complexes with d⁸ configurations are also degenerate, with a square planar distortion removing any degeneracy.

    An altnerative approach to understanding the bonding of transition metal complexes is Ligand Field Theory.  Crystal Field Theory is a simple model which explains the spectra, thermochemical and magnetic data of many complexes.  It's main flaw is that it treats the ligands as point charges or dipoles, and fails to consider the orbitals of the ligands.  Ligand Field Theory applies molecular orbital theory and symmetry concerns to transition metal complexes.  In octahedral symmetry, group theory can be used to determine the shapes and orientation of the orbitals on the metal and the ligands.

    Examination of the symmetry table for O_h shows that the orbitals on the metal have the following attributes.
 

    The t_2g set (d_xy, d_yz, d_xz) does not have any electron density along the bond axes, so these orbitals do not participate in sigma bonding, but will be involved with pi bonding.  A molecular orbital diagram which estimates the energies of the bonding (show above) antibonding and non-bonding orbitals is shown below.

    Since there is a large disparity in energy between the ligand orbitals and the metal orbitals, the lower lying molecular orbitals in the diagram are essentially ligand orbitals.  That is, the electrons of the ligand lone pairs fill the lower levels (e_g, t_1u, and a_1g).  The d electrons on the metal will fill the t_2g (non-bonding) and e_g(antibonding) molecular orbitals.  The split between the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) corresponds to the D_o splitting in crystal field theory.  In crystal field theory, the electrons in these orbitals are viewed as entirely on the metal atom or ion, whereas in ligand field theory the electrons are, to some extent, on the ligands, too.

    Pi bonding is not considered by crystal field theory, but is addressed in ligand field theory.  The orbitals on the metal which were not used for sigma bonding (the t_2g set:  d_xy, d_yz, d_xz) have the same symmetry properties as combinations of the p orbitals on the ligands.  If the energy of the metal and ligand orbitals are comparable, the pi bonding orbitals formed will be significantly lower in energy thatn the atomic orbitals on either the metal or ligand.  Likewise, the antibonding pi orbitals will be much higher in energy.  If the orbitals are very different in energy, only slight mixing will occur.  An example of pi overlap is shown below.

 The effect on the molecular orbital diagram is as follows.  The gap between the t_2g and e_g set will change, because the t_2g set is involved in bonding, so there is not a bonding t_2g set, and an antibonding t_2g set of orbitals.  The gap, represented as D_o becomes the gap between the  t_2g set of antibonding orbitals and the e_g set of orbitals.  As a result, the size of D_o dimishes.

    The above molecular orbital diagram is for ligands which have  pi antibonding orbitals too high in energy to interact with the metal orbitals.  The net effect for these pi donor ligands is to decrease the size of D_o compared to ligands which only act as sigma donors.

Ligands may have empty pi antibonding orbitals higher in energy and with the same symmetry as  the t_2g orbitals of the metal.  These ligands orbitals interact with the t_2g orbitals of the metal creating a bonding orbital which is slightly lower in energy than the t_2g set of the metal, and an antibonding set of orbitals which are much greater in energy than the e_g set of the complex.  The net result is that the size of the splitting, D_o, increases, since the energy of the t_2g bonding orbitals drops a bit.

    The net result is that pi acceptor ligands (such as CO and N₂), with empty antibonding orbitals available to accept electrons from the metal, increase the size of D_o.  The spectrochemical series can be reconsidered with the possiblity of pi bonding in mind.  It shows that the order (with some notable exceptions) goes as follows:

Copyright ©1998 Beverly J. Volicer and Steven F. Tello, UMass Lowell.  You may freely edit these pages  for use in a non-profit, educational setting.  Please include this copyright notice on all pages.