1. Inorganic Chemistry II CHEM 251 Transition Metals and Coordination Chemistry
Dr. Ahmad Hamaed

2. Chapter 1: 1.1 Guideline and Introduction:
In this course we discuss the coordination chemistry of the d-block elements.
The term transition metals is also widely used. However the group 12 metals (Zn, Cd, and Hg), which have completely filled d-orbitals are not classified as transition metals.
Throughout our discussions, we shall use the terms d-block and f-block metals.

3. Position of d-block elements in the Periodic Table

4. Uses of Transition Metals
Transition metals have many uses in industry:
Iron is used for steel
Copper is used for electrical wiring and water pipes
Titanium for paint
Silver for photographic paper
Manganese, chromium, and cobalt as additive to steel
Platinum for industrial and automotive catalysts.
All these metals play a vital role in the world economy and high technology, and electronics.
Therefore, these metals are very strategic and critical minerals.

5. Biological roles of TM ions:
Besides their roles in industry, TM ions play a vital roles in living organisms:
Complexes of iron provide for the transport and storage of oxygen.
Molybdenum and iron compounds are catalysts in nitrogen fixation.
Zinc is found in more than 150 biomolecules in humans.
Copper and iron play a crucial role in the respiratory cycle.
Cobalt is found in vitamin B12

6. General properties of TM
Whereas the chemistry of the representative elements changes across a period as the number of valence electrons changes.
In contrast, the TMs show great similarities within a given period as well as within a given vertical group.
This is due to that fact that the last electrons added for TMs are inner electrons that cannot easily participate in bonding as can the s and p electrons.
Thus the chemistry of TMs is not affected by the gradual change in the number of electrons as is the chemistry of the representative elements.

7. General properties of TM
TM, as a class, behave like as typical metals, possessing metallic luster, high electrical and thermal conductivities.
Despite their similarities, TMs do vary considerably in certain properties. For example, tungsten has a melting point of 3400 ºC; Mercury is a liquid at 25 ºC. Some TMs such as Fe, and Ti are strong, other such as Cu, Au, and Ag are relatively soft.
Some react readily with O2 to form oxide, others do not readily form oxides.
In forming ionic compounds with nonmetals, TMs exhibit the following characteristics:

8. General properties of TM
More than one oxidation state is often found. For example, Fe combines with Cl to form FeCl2 and FeCl3.
The cations are often complex ions, species where the transition metal is surrounded by a certain number of ligands (molecules or ions that behave as Lewis bases).
Most TM-compounds are colored, because the TM- complex ions absorb visible light of specific wavelengths.
We will concentrate on the first row TMs (Sc to Zn) because of their great practical significance.

9. Electron Configurations of First-Row TMs
The electron configurations of first-row TMs are obtained by adding electrons to the five 3d orbitals. The configuration of the first TM, scandium, is Sc: [Ar] 4s2 3d1 (only 1 electron in the d orbital) That of Titanium is Ti: [Ar] 4s2 3d2(has 2 electrons in the d orbital) And that of Vanadium is V:[Ar] 4s2 3d3 (has 3 electrons in the d orbital) Chromium is the next element. The expected configuration is Cr:[Ar] 4s2 3d4 , we expect the Cr to have 4 electrons in the d orbital. However, the observed configuration is Cr:[Ar] 4s1 3d5( half-filled 4s orbital and half-filled 3d orbital).

10. Electron Configurations of First-Row TMs
The TMs from manganese through nickel have the expected configuration:
Mn: [Ar] 4s2 3d5 ; Fe: [Ar] 4s2 3d6 ; Co: [Ar] 4s2 3d7 ; Ni: [Ar] 4s2 3d8
The configuration for copper is expected to be Cu: [Ar] 4s2 3d9. However, the observed configuration is Cu: [Ar] 4s1 3d10 (half filled s and a completely filled d).
Zinc has the expected configuration: Zn: [Ar] 4s2 3d10

11. Justification for the Unexpected Electron Configuration of Chromium
Basically, The Cr electron configuration occurs because the energies of the 3d and 4s orbitals are very similar for the first- row transition elements. When electrons are placed in a set of degenerate orbitals (orbitals of same energy level), they occupy each orbital singly to minimize electron repulsions. Since the 4s and 3d orbitals are virtually degenerate in the Cr atom, we would expect the configuration Since the second arrangement has greater electron-electron repulsions and thus a higher energy

12. Electronic Configuration of Mn+ ions
In transition metal ions, the 3d orbitals are lower in energy than the 4 s orbitals.
In contrast to the neutral transition metals, where the 3d and 4s have very similar energies.
This means that the electrons remaining after the ion is formed occupy the 3d orbitals, since they are lower in energy.
Therefore, first-row transition metal ions do not have 4s electrons. For example the manganese has the configuration [Ar] 4s23d5, while that of Mn2+ is [Ar] 3d5.
The neutral Titanium has the configuration [Ar] 4s23d2, while that of Ti3+ is [Ar] 3d1.

13. Common Oxidation Stations In TMs
The transition metals can form a variety of ions by losing one or more electrons.
For the first five metals the maximum oxidation state of Cr ([Ar] 4s13d5)is +6 .
Toward the right end of the period, the maximum oxidation states are not observed; in fact, the +2 ions are the most common. The higher oxidation states are not seen for these metals because the 3d orbitals become lower in energy as the nuclear charge increases (as we move from left to right across a period), and the electrons become increasingly difficult to remove.

14. Ionization Energies in TMs
The ionization energy increases gradually as we go from left to right across a period.
However, the third ionization energy (when an electron is removed from the 3d orbital) increases faster than the first ionization energy. This is a clear evidence of the significant decrease in the energy of the 3d orbitals as we move across a period (from left to right)

15. Selected properties of First-Row Transition Metals

16. Coordination Compounds
A complex ion is a charged species consisting of a metal surrounded by ligands.
A ligand is simply a Lewis base. A molecule or ion having a lone pair that can be donated to an empty orbital on the metal ion to form a covalent compound.
Some common ligands are H2O, NH3, Cl-, and CN-.
The number of ligands attached to a metal ion is called the coordination number.
The most common coordination number are 6, for example in Co(H2O)62+ , and Ni(NH3)62+ ; 4 for example in CoCl42- , and Cu(NH3)42+ ; and 2 for example, in Ag(NH3)2+ ; but others are known.

17. Coordination Compounds
A coordination compound typically consists of a complex ion (a transition metal ion with its attached ligands), and counterions ( anions or cations as needed to produce a compound with no net charge).
The substance [Co(NH3)5Cl]Cl2 is a typical coordination compound. The brackets indicate the composition of the complex ion, in this case Co(NH3)5Cl2+, and the two Cl- counterions as shown outside the brackets.
Note that in the above compound one Cl- acts as a ligand along with the five NH3 molecules.
When dissolved in water, the solid behaves like any ionic solid; the cations and anions are assumed to separate and move out independently:
[Co(NH3)5Cl]Cl → Co(NH3)5Cl2+ +2Cl-

18. Common TM ions and Their Typical Coordination Numbers

19. Ligands
A ligand is a neutral molecule or ion having a lone pair that can be used to form a bond to a metal ion.
The formation of a metal-ligand bond therefore can be described as the interaction between a Lewis base (the ligand) and a Lewis acid (the metal center).
The resulting bond is often called a coordinate covalent bond.
A ligand that can form one bond to a metal center is called a monodentate ligand.
In the Figure (b) the ammonia
is a monodentate ligand

20. Ligands
Some ligands have more than one atom with lone pair that can be used to form a bond to a metal ion. Such ligands are called chelating ligands or simply chelates.
A ligand that can form two bonds to a metal center is called a bidentate ligand. A very common bidentate ligand is ethylenediamine ( abbreviated en). Oxalate is another typical bidentate Ligand.
Fig (a): The bidentate ligand ethylenediamine can bond to the metal ion through the lone pair on each nitrogen atom, thus forming two coordinate covalent bonds

21. Ligands
Ligands that can form more than two bonds to a metal ion are called polydentate ligands. Some ligands can form as many as six bonds to a metal ion.
The best know example is ethylenediaminetetraacetic acid (EDTA). This ligand surrounds the metal center, coordinating through six atoms (a hexadentate ligand).

22. Common Mono-dentate, Bi-dentate, and Poly-dentate Ligands

23. Nomenclature: Rules for Naming Coordination Compounds
As with any ionic compound, the cation is named before the anion.
In naming a complex ion, the ligands are named before the metal ion.
In naming ligands, an o is added to the root name of an anion. For example, the halides as ligands are called fluoro, chloro, bromo, and iodo; hydroxide is called hydoxo; cyanide is cyano; and so on. For a neutral ligand the name of the molecule is used, with the exception of H2O, NH3, CO, and NO, as illustrated in Table on the following page.
The oxidation state of the central metal ion is designated by a Roman numeral in parentheses.

24. Nomenclature: Rules for Naming Coordination Compounds (Cont’d)
When more than one type of ligand is present, they are named alphabetically. Prefixes do not affect the order.
If the complex ion has a negative charge, the suffix –ate is added to the name of the metal. Sometimes the Latin name is used to identify the metal (see table 21.15)

25. Example 1: Naming Coordination Compounds
Give the systematic name for each of the following coordination compounds:
a) [Co(NH3)5Cl]Cl2
Ans: The oxidation state of Co is determined by examining the charges of all ligands. NH3 is neutral, each Cl has one -1 charge. Thus the cobalt has the oxidation state of +3, and we use cobalt (III) in the name.
The ligand include: ONE Cl- ion and FIVE NH3 molecules. The chloride ion is designated as chloro, and each NH3 molecule is designated as ammine. The prefix penta- indicates that there are five NH3 ligands present.
The name is: Pentaamminechlorocobalt (III) chloride
Cation Anion

26. Example 1: Naming Coordination Compounds
The name of K3Fe(CN)6 ?
K = has a charge of +1, CN has a charge of -1
Therefore Fe must carry 3+ charge. Therefore it is Fe(III).
The complex ion present is Fe(CN)63- . The CN- lignad is designated cyano, and the prefix hexa indicates that there are 6 of them present. Since the complex ion is an anion, we use the Latin name ferrate. The oxidation state is indicated by (III) at the end of the name. The anion name is therefore hexacyanoferrate(III). The cations are K+ ions, which are simply named potassium.
Then the compound name is: Potassium hexacyanoferrate(III)

27. Example 1: Naming Coordination Compounds
C. What is the name of [Fe(en)2(NO2)2]2SO4?
First determine the oxidation state of the metal center by examining the charges of the ligands: ethylenediamine is neutral, NO2 has a -1 charge, SO4 has a -2 charge. Each Fe then must have +3 charge.
Since the name ethylenediamine already contains di, we use bis instead of di to indicate the presence of two en ligands.
The name for NO2- as a ligand is nitro, and the prefix di indicates the presence of two NO2- ligands.
Since the anion is sulfate, the compound’s name is:
Bis(ethylenediamine)dinitroiron(III) sulfate
Cation Anion,
Since the complex ion is a cation, the Latin name for iron (Ferrate) is NOT used.

28. Example 2: Naming Coordination Compounds
Given the following systematic names, give the formula of each coordination compound.
Triamminebromoplatinum(II) chloride
Triammine = 3 NH3, bromo = 1 Br-, the oxidation state of platinum is II.
Thus the complex ion is [Pt(NH3)3Br]+. One Cl- is needed to balance the 1+ charge of the cation.
Therefore, the formula of the compound is [Pt(NH3)3Br]Cl.

29. Example 2: Naming Coordination Compounds
b. Potassium hexafluorocobaltate(III)
The complex contains six fluoride ion F- ligands attached to a Co3+ ion to give CoF63-.
Note that the -ate ending indicates that the complex ion is an anion.
The cations are K+ ions, and three of them are required to balance the 3- charge on the complex ion.
Thus the formula is K3[CoF6].

30. Common Shapes for 2, 3, and 4-coordinate complexes

31. Common Shapes for 5-coordinate complexes

32. Shapes for 6, 7, and 8-coordinate complexes

33. Isomerism
Isomers are species that have the same formula but different properties.
Isomers contain exactly the same types and numbers of atoms but the arrangements of the atoms differ, and this leads to different properties.
We will consider two main types of isomers: structural isomerism, where the isomers contain the same atoms but one or more bonds differ, and stereoisomerism, where all the bonds in the isomers are the same but the spatial arrangements of the atoms are different.
Each of these classes also has subclasses which we will now consider.

34. Classes of Isomers

35. 1- Structural Isomerism: coordination Isomerism
We consider here the first type of structural isomerism,
the coordination isomerism.
Coordination isomers are possible only for salts in which both
cation and anion are complex ions. The isomers arise from the
interchange of ligands between the two metal centers.
Examples of coordination isomers are:
1- [Co(en)3][Cr(ox)3] and [Cr(en)3][Co(ox)3] pair,
where ox represents the oxalate ion, a bidentate ligand.
2- [Co(NH3)6][Co(NO2)6] and [Co(NH3)4(NO2)2][Co(NH3)2(NO2)4]
3- [PtII (NH3)4][PtIV (Cl6)] and [PtIV (NH3)4 Cl2][PtII Cl4]

36. 2- Structural Isomerism: Ionization Isomerism
Ionization isomerism result from the interchange of an anionic ligand within the coordination sphere with an anion outside the coordination sphere (counterion).
Violet [Cr(NH3)5SO4]Br and red [Cr(NH3)5Br]SO4 are ionization isomers. In the first case SO42- is coordinated to Cr3+ and Br- is the counterion; in the second case, the roles of these ions are reversed.
These two isomers can be readily distinguished by appropriate qualitative tests for ionic sulfate and bromide.
These isomers are also easily distinguished by IR spectroscopy

37. 3- Structural Isomerism: Hydration Isomerism
Hydration isomers result from the interchange of H2O and another ligand between the first coordination sphere and the ligands outside it.
A classical example of hydration isomerism is that of green crystals [Cr(OH2)4Cl2].2H2O and blue crystals of [Cr(OH2)5Cl]Cl2. H2O and finally the violet [Cr(OH2)6]Cl3
The complexes can be distinguished by precipitation of the free chloride ion using aqueous silver nitrate as per the equation:
AgNO3 (aq) + Cl- (aq) → AgCl(s) NO3- (aq)
(white precipitate)

38. 4- Structural Isomerism: Linkage Isomerism
Linkage isomers may arise when one or more of the ligands can coordinate to the metal ion in more than one way, example in [SCN]-, both the N and S atoms are potential donor sites. Such a ligand is called ambidentate.
Because [SCN]- is ambidentate, the complex
[Co(NH3)5 (NCS)]2+ has two isomers which are distinguished by using the following nomenclature:
[Co(NH3)5 (NCS-N)]2+, the thiocyanate ligand coordinates through the nitrogen donor atom.
[Co(NH3)5 (NCS-S)]2+, the thiocyanate ion is bonded to the metal center through the sulfur atom.

39. 4- Structural Isomerism: Linkage Isomerism (cont’d)
Also NO2- ligand can coordinate to the metal center through the N atom or through the O atome in the following ways:
As a ligand NO2- can bond to the metal ion (a) through a lone pair on the nitrogen atom or (b) through a lone pair on one of the oxygen atoms.

40. Stereoisomerism: Geometric, cis-tans Isomerism
Stereoisomers have the same bonds but different spatial arrangements of the atoms.
One type of stereoisomers is called geometric isomerism, or cis-tans isomerism.
Geometric isomerism, or cis-tans isomerism occurs when atoms or groups of atoms assume different positions around a rigid ring or bond (No rotation allowed).
An important example is the compound Pt(NH3)2Cl2, which has a square planar structure. Which has two possible arrangements of ligands.

41. Stereoisomerism: Geometric, cis-tans Isomerism (cont.)
In the trans isomer, the ammonia molecules are cross (trans) from each other.
In the cis isomer, the ammonia molecules are next (cis) to each other.
Square planar species of the general form EX2Y2 or EX2YZ may possess cis- and trans-isomers

42. The Importance of Being cis
In 1964, a group of scientists were using a platinum electrodes to apply an electric field to a colony of E-coli bacteria noticed that the bacteria failed to divide but continue to grow, forming long fibrous cells.
Further study revealed that cell division was inhibited by small concentrations of cis-Pt(NH3)2Cl2 and cis-Pt(NH3)2Cl2 formed electrolytically in the solution.
Thus these and similar platinum complexes were evaluated as antitumor agents, which inhibit the division of cancer cells.
The results showed that cis-Pt(NH3)2Cl2 was active against a wide variety of tumors, which are very resistant to treatment by more traditional methods.

43. The Importance of Being Cis (cont.)
However, although the cis complex showed significant antitumor activity, the corresponding trans complex had no effect on tumors. This shows the importance of isomerism in biological systems. When drug was synthesized great care must be taken to obtain the correct isomer.
Promising antitumor candidates are shown below. Note that all are cis complexes.

44. Stereoisomerism: Geometric cis-tans Isomerism (cont.)
Geometric isomerism also occurs in octahedral complex ions of the general form EX2Y4 (of two identical groups).
For example, the compound [Co(NH3)4Cl2]Cl has cis (Violet) and trans (Green) isomers.

45. Stereoisomerism: Geometric, fac-mer Isomerism
An octahedral species containing three identical groups, of the general type EX3Y3 may possess fac- and mer-isomers.
If an octahedral species has the general formula EX3Y3, then the X groups (and also the Y groups) may be arranged so as to define one face of the octahedron or may lie in a plane that also contain the central atom E. These stereoisomers are labeled fac (facial) and mer (meridional) respectively.

46. Stereoisomerism: In Trigonal Bipyramidal Species
In trigonal bipyramidal species of the general form EX5, there are 2 types of X atom: axial and equatorial. This leads to the possibility of stereoisomerism when more than one type of substituent is attached to the central atom. Iron pentacarbonyl, Fe(CO)5, is trigonal pyramidal and if one CO is exchanged for PPh3, two stereoisomers are possible depending on whether the PPh3 ligand is axially or equatorially sited.
For trigonal bipyramidal EX2Y3, three stereoisomers are possible depending on the relative positions of the X atoms.
Axial Equatorial

47. Stereoisomerism: Enantiomerism optical Isomerism
Enantiomers are a pair of stereoisomers that are non- superimposable mirror images.
Diastereomers are a pair of stereoisomers that are not enantiomers.
(+) and (-) prefixes
d and l prefixes
R and S prefixes
∆ and Lambda

48. Stereoisomerism: Enantiomerism or optical Isomerism

49. Stereoisomerism: Optical Isomerism

50. Chirality = handedness

51. Example

52. Optical activity is exhibited by molecules that have nonsuperimposable mirror images (Enantiomers)

53. Enantiomerism = Optical Isomerism; d, l isomers
The isomer that rotates the plane of the light to the right (when viewed down the beam of oncoming light) is said to be dextrorotary; designated by d.
The isomer that rotates the plane of the light to the left is said to be levorotary (l).
An equal mixture of the d and l forms in solution, called racemic mixture, does not rotate the plane of the polarized light at all because the two opposite effects cancel each other.

54. Geometric Isomerism Vs. Optical Isomerism
Geometric isomers are not necessarily optical isomers. For instance, the trans isomer of [Co(en)2Cl2]+ shown in Fig is identical to its mirror image. Since this isomer is superimposable on its mirror image, it does not exhibit optical isomerism and is not chiral.
On the other hand, cis-[Co(en)2Cl2]+ is not superimposable on its mirror image: a pair of enantiomers exists for this complex (the cis isomer is therefore chiral)

55. Chirality in Terms of Symmetry
Chiral molecules (Greek, kheir, hand) have a degree of asymmetry that makes their mirror images nonsuperimposable. This condition can be expressed in terms of symmetry elements.
A molecule can be chiral only if it has no rotation-reflection (Sn) axes. This means that chiral molecules either have no symmetry elements or have only axes of proper rotation (Cn).
Tetrahedral molecules with four different ligands or with unsymmetrical chelating ligands can be chiral, as can octahedral molecules with bidentate or higher chelating ligands or with [Ma2b2c2], [Mabc2d2], [Mabcd3], [Mabcde2], or [Mabcdef] structures (M = metal, a, b, c, d, e, f = momodentate ligands. Not all isomers for such molecules are chiral, but the possibility must be considered for each.

56. Finding the Isomers by Systematical Listing the Possible Structures
One approach to tabulating isomers
is shown in table 9-5 and Fig
The notation <ab˃ indicated that
a and b are trans to each other,
with M the metal ion and
a, b, c, d, e, and f are the monodentate
ligands. The six octahedral
positions are commoly numbered
as in the figure, with positions
1 and 6 in the axial positions and
With 2 though 5 in counterclockwise
order as viewed from the 1 position.

57. Example 1

58. Example 2

59. Number of Possible Isomers for Specific Complexes

60. Delta or Lambda?

61. Delta or Lambda?

62. Delta or Lambda?

63. Delta or Lambda?

64. Delta or Lambda?

65. Delta or Lambda?

67. Delta or Lambda?

68. Delta or Lambda?

69. Chapter 3: Bonding in Coordination Complexes
In this chapter we consider the bonding theories of the d- block metal complexes, electronic spectra and magnetic properties.
We focus on first row d-block metals, for which theories of bonding are most successful.
d-orbitals
A d-orbital is characterized by having a value of the quantum number of I = 2.
For l= 2, there are only 5 real solutions to the Schrodinger equation, ml =+2, +1, 0, -1, -2.
Therefore we have a set of 5 degenerate (same energy level) d-orbital which are shown in the next page.

70. The Set of d-orbitals

71. The Set of d-orbitals (cont.)
The lobes of the dyz, dxy, and dxz point between the axes and each orbital lies in one of the three planes defined by the axes.
The dx2-y2 is related to dxy, but the lobes of the dx2-y2 orbital point along (rather then between) the x and y axes.
dz2 is a linear combination of dz2-x2 and dz2-y2 orbitals.
The fact that 3 of the 5 d-orbitals have their lobes directed between the Cartesian axes, while the other 2 are directed along these axes is a key point in the understanding of bonding models for d-block metal complexes and their physical properties.

72. The Set of d-orbitals (cont.)
As a consequence of there being a distinction in their directionalities, the d orbitals in the presence of ligands are split into groups of different energies.
The type of splitting and the magnitude of the energy differences depending on the arrangement and the nature of the ligands.
The magnetic properties and the electronic absorption spectra, both of which are observable properties reflect the splitting of d-orbitals.

73. Various Bonding Methods

74. The Valence Bond Theory (VBT)
VBT: This method is based on the localized electron model.
The localized electron model is a very useful model for describing the bonding in molecules.
Recall that a central feature of this method is the formation of hybrid atomic orbitals that are used to share electron pairs to form sigma bonds between atoms.
Although this theory is seldom used today, the hybrid notation is still common in discussing bonding (especially in organic compounds, hydrocarbons).

75. The Valence Bond Theory (VBT)
In VBT an empty hybrid orbital on the metal center can accept a pair of electrons from a ligand to form a σ-bond. The choice of a particular p or d atomic orbitals may depend on the definition of the axes with respect to the molecular framework.
Example in linear ML2, the M-L vectors are usually defined to lie along the z axis.

76. Hybrid Orbitals for Octahedral Complex Ions
For octahedral complexes, d2sp3 hybrids of the metal orbitals are required

77. Formation of Hybrid Orbitals (VBT)

78. Applications of VBT Consider the octahedral complexes of Cr(III) (d3):
The atomic orbitals required for hybridization in an octahedral complex of a first row d-block metal are: 3dz2, 3dx2-y2, 4s, 4px, 4py, and 4pz. These orbitals must be unoccupied to be available to accept six pairs of electrons from the six ligands.
The Cr3+ (d3) ion has three unpaired electrons and these are accommodated in the 3dxy, 3dxz, and 3dyz orbitals:

79. Applications and Limitations of VBT
With the electrons from the six ligands included and a hybridization scheme applied for an octahedral complex, the diagram becomes:
This diagram is appropriate for all octahedral Cr(III) complexes because the three 3d electrons always singly occupy different orbitals.

80. Applications and Limitations of VBT
For octahedral Fe(III) complexes (d5), we must account for the existence of both high- and low-spin complexes.
The electronic configuration of the free Fe3+ ion is:
For a low-spin octahedral complex such as [Fe(CN)6]3-, we can represent the electronic configuration by means of the following diagram where the electrons shown in red are donated by the ligands:

81. Applications and Limitations of VBT
For a high-spin octahedral complex such as [FeF6]3-, the five 3d electrons occupy the five 3d orbitals and the two d orbitals required for the sp3d2 hybridization scheme must come from the 4d set.
With the ligand electrons included, valence bond theory describes the bonding as follows, leaving three empty 4d atomic orbitals (not shown):
However, this scheme is unrealistic because the 4d orbitals are at a significantly higher energy than the 3d atomic orbitals.

82. Applications and Limitations of VBT
Nickel (II) (d8) forms paramagnetic tetrahedral and octahedral complexes, and diamagnetic square planar complexes.
Bonding in a tetrahedral complex can be represented as follows (electrons donated by the four ligands are shown in red):
An octahedral nickel(II) complex can be described by the diagram:
in which the three empty 4d orbitals are not shown.

83. Applications and Limitations of VBT
For a diamagnetic square planar nickel (II) complexes, valence bond theory gives the following picture:

84. VBT for Complex Ions
VBT can be used to account for the bonding in complex ions, but there are two important points to keep in mind:
The VSEPR model for predicting structure generally does not work for complex ions. However, we can safely assume that a complex ion with a coordination number of 6 will have an octahedral arrangement of ligands, and complexes with two ligands will be linear. Complex ions with a coordination number of 4 can be either tetrahedral or square planar, and there is no completely reliable way to predict which will occur in a particular case.
The interaction between a metal ion and a ligand can be viewed as a Lewis acid-base reaction (electron-donating and electron withdrawing) with the ligand donating a lone pair of electrons to an empty orbital of the metal ion to form a coordinate covalent bond:

85. VBT for Complex Ions (cont.)
The hybrid orbitals used by the metal ion depend on the number and arrangement of the ligands.
For example, accommodating the lone pairs from six ammonia molecules in the octahedral Co(NH3)63+ ion requires a set of six empty hybrid atomic orbitals in an octahedral arrangement.
An octahedral set of orbitals is formed by the hybridization of two d, one s, and three p orbitals to give a set of six d2sp3 orbitals.

86. VBT: Hybridization (Tetrahedral and Square Planar)

87. Hybrid Orbitals for Tetrahedral, Square Planar and Linear Complex Ions

88. Hybridization Schemes of Different Geometric Configurations

89. The Crystal Field Theory (Ionic M-L Bonding)

90. The Crystal Field Theory in Octahedral Complexes

91. The Crystal Field Theory in Octahedral Complexes

92. The Crystal Field Theory in Octahedral Complexes

93. The Crystal Field Theory in Octahedral Complexes

94. The Crystal Field Theory in Octahedral Complexes
The energy separation between the 2 sets of d orbitals (t2g and eg) is ∆oct (‘delta oct’) or 10Dq
The overall stabilization of the t2g orbitals equals the overall destabilization of the eg set.
Thus the two orbitals in the eg set are raised by 0.6∆oct with respect to the barycenter while the three orbitals in the t2g set are lowered by 0.4∆oct . The magnitude of ∆oct is determined by the strength of the crystal field, the two extremes being called weak field and strong field

95. The Crystal Field Theory in Octahedral Complexes

96. Example1:

97. The Crystal Field Theory in Octahedral Complexes

98. CFT: Ligands Spectrochemical Series

99. Trends in the Values of ∆oct
∆oct is an experimental quantity.
Factors governing the magnitude of ∆oct are the identity and the oxidation state of the metal ion and the nature of the ligand.
For a given ligand and a given metal ∆oct increases with increasing oxidation state.
For a series of Mn+ metal ions (constant n) given in a triad, ∆oct increases significantly down the triad (Fig 20.5).
For a given ligand and a given oxidation state, ∆oct varies irregularly across the first row of the d-block.

100. Trends in the Values of ∆oct
Trends in the values of ∆oct lead to the conclusion that metal ions can be placed in a spectrochemical series which is independent of the ligands:
Spectrochemical series are empirical generations and simple crystal field theory cannot account for the magnitude of ∆oct values.

101. Example 2:

102. Crystal Field Model for Tetrahedral Complexes

103. Tetrahedral and Octahedral Arrangement of Ligands.

104. Crystal Field Model for Tetrahedral Complexes
In the figure above the crystal field diagrams for octahedral and tetrahedral complexes are shown. The relative energies of the sets of d orbitals are reversed. For a given ligand, the splitting is much larger for the octahedral complex (∆oct ˃ ∆tet ) because in this arrangement the dz2 and dx2-y2 orbitals point their lobes directly at the point charges and thus relatively high in energy. Note that the subscript g is the symmetry labels is not needed in the tetrahedral case.

105. Example: CFT in Tetrahedral Complex

106. Example: CFT in a Square planar and Linear Complexes

107. Example: CFT in a Square planar Complex
The figure above shows a crystal field diagram for a square planar complex oriented in the xy plane with ligands along the x and y axes. The position of the dz2 orbital is higher than those of the dxz and dyz orbitals because of the “doughnut” of electron density in the xy plane. The actual position of dz2 is somewhat uncertain and varies in different square planar complexes.

108. The Square Planar Crystal Field

109. From Octahedral to Square Planar

110. Example

111. Square Planar Vs. Tetrahedral Crystal Field

112. Linear Crystal Field
The above shows the crystal field diagram for a linear complex where the ligands lie along the z axis

113. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
We now consider the effects of different numbers of electrons occupying the d orbitals in an octahedral crystal field.
For a d1 system, the ground state correspond to the electron configuration t2g1. with respect to the barycenter there is a stabilization energy of -0.4∆oct as shown in the diagram 20.2 below: CFSE = -(1× 0.4)∆oct
This is the so-called crystal field stabilization energy, CFSE.
For a d2 ion, the ground state configuration is t2g2 and the CFSE = -0.8 ∆oct

114. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
A d3 ion, the ground state configuration is t2g3 and the
CFSE = -1.2 ∆oct .
For a ground state d4 ion, two arrangements are possible: the four electrons may occupy the t2g set with the configuration t2g4 (diagram 20.3), or may singly occupy four orbitals, t2g3 eg1 (diagram 20.4). Configuration 20.3 corresponds to a low-spin arrangement, and 20.4 corresponds to a high-spin arrangement.
The preferred configuration is that with the lower energy and depends on whether it is energetically preferable to pair the fourth electron or promote it to the eg level.

115. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
Two terms contribute to the electron-pairing energy, P, which is the energy required to transform two electrons with parallel spin in different degenerate orbitals into spin-paired electrons in the same orbital.
The loss in the exchange energy which occurs upon pairing the electrons.
The coulombic repulsion between the spin-paired electrons.
For a given dn configuration, the CFSE is the difference in energy between the d electrons in the octahedral crystal field and the d electrons in a spherical crystal field (see Figure 20.2)

116. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
Consider a d4 configuration:
In a spherical crystal field, the d orbitals are degenerate and each of 4 orbital is singly occupied.
In an octahedral crystal field (eq 20.3) shows how the CFSE is determined for a high-spin d4 configuration:
CFSE = -(3×0.4)∆oct + 0.6∆oct = -0.6∆oct(eq 20.3)
For a low spin d4 configuration , the CFSE consists of two terms: the four electrons in the t2g orbitals give rise to -1.6 ∆oct term, and a pairing energy, P, must be included to account for the spin-pairing of the two electrons.

117. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
Now consider a d6 ion:
In a spherical crystal field, one d orbital contains spin-paired electrons, and each of the four orbitals is singly occupied.
On going to the high-spin d6 configuration in the octahedral field (t2g4, eg2), no change occurs to the number of spin-paired electrons and the CFSE is given by eq 20.4: CFSE= -(4×0.4)∆oct + (2×0.6)∆oct = -0.4 ∆oct
For a low-spin d6 configuration (t2g6, eg0), the six electrons in the t2g orbitals give rise to a -2.4∆oct term. Added to this is a pairing energy term of 2P which accounts for the spin-pairing associated with the two pairs of electrons in excess of the one in the high-spin configuration.

118. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
The requirement for high-spin is ∆oct < P.
The requirement for low-spin is ∆oct ˃ P.
we can now relates types of ligand with a preference for high- or low-spin complexes. Strong field ligands such as [CN]- favor the formation of low-spin complexes, while weak field ligands such as halides tend to favor high-spin complexes.
However, we cannot predict whether high- or low-spin complexes will be formed unless we have accurate values of ∆oct and P. On the other hand, with some experimental knowledge in hand, we can make some comparative predictions.

119. Crystal Field Stabilization Energy (CFSE): High- and Low-spin Octahedral Complexes
For example, if we know from magnetic data that [Co(OH2)6]3+ is low-spin, then from the spectrochemical series we can say that [Co(ox)3]3- and [Co(CN)6]3- will be low-spin. The only high-spin cobalt(III) complex is [CoF6]3-

120. CFSE for various dn configurations

121. d5 Complexes in Weak Field and Strong Field

122. Jahn-Teller distortion

123. Jahn-Teller distortion
Octahedral complexes of d9 and high-spin d4 ions are often distorted. For example, CuF2 the solid state structure of which contains octahedrally sited Cu2+ centers, and [Cr(OH2)6]2+ so that two metals- ligands bonds (axial) are different from the remaining four (equatorial) as shown in the following structures.

125. Structural effects of Jahn-Teller distortion

126. Jahn-Teller Distortion
Jahn-Teller distortion is shown in structures 20.5 (elongated octahedron) and (compressed octahedron).
For a high-spin d4 ion, one of the eg orbitals contains one electron while the other is vacant. If the singly occupied orbital is the dz2, then most of the electron density in this orbital will be concentrated between the cation and the two ligands on the z-axis. Thus, there will be greater electrostatic repulsion associated with these ligands than with the other four, and therefore the complex suffers elongation (20.5). As in the complex [Cr(OH2)6]2+ , where the electronic configuration of the Cr2+ is dxy1 dyz1 dxz1 dz21 .

127. Jahn-Teller Distortion
On the other hand, the occupation of the dx2-y2 orbital would lead to elongation along the x and y axes as in the structure 20.6.
A similar argument can be put forward for the d9 configuration in which the two orbitals in the eg set are occupied by one and two electrons respectively.
The corresponding effect when the t2g set is unequally occupied is expected to be very much smaller because the orbitals are not pointing directly at the ligands.

128. Jahn-Teller Distortion
The observed Jahn-Teller distortion of an octahedral complex is accompanied by a change in symmetry (Oh to D4h) and a splitting of the eg and t2g sets of orbitals. Elongation of the complex is accompanied by the stabilization of each d orbital that has a z component, while the dxy and dx2-y2 orbitals are destabilized (As shown in the diagram below).

132. Jahn-Teller Distortion

133. Crystal Field Splitting Diagram from Octahedral to Tetragonal (distorted Octahedral) to Square Planar

139. Advantages and Limitations of Crystal Field Theory
CFT can bring together structures, magnetic properties and electronic properties.
Trends in CFSEs provide some understanding of thermodynamic and kinetic aspects of d-block metal complexes.
CFT is surprisingly useful when one considers its simplicity.
Disadvantages:
CFT provides no explanation as why particular ligands are placed where they are in the spectro-chemical series.
Also CFT concept of the repulsion of orbitals by the ligands and its lack of any explanation of bonding in coordination complexes.
The purely electrostatic approach does not allow for the lower (bonding) molecular orbitals, and thus fails to provide a complete picture of the electronic structure.

161. Molecular Orbital / Ligand Field Theory:
The electrostatic crystal field and the molecular orbital theory were combined into a complete theory called ligand field theory, described qualitatively by Griffith and Orgel.
The use of the molecular orbital theory is another approach to the bonding in metal complexes.
In contrast to crystal field theory, the molecular orbital /ligand field model considers covalent interactions between the metal center and ligands.
MO/ Ligand Field theory is a more complete description of bonding in terms of the electrostatic energy levels of the frontier orbitals. It uses some of the terminology of the crystal field theory but includes the bonding orbitals. However, most descriptions do not include the energy of these bonding orbitals

162. Molecular Orbitals For Octahedral Complexes
For octahedral complexes, the molecular orbitals can be described as resulting from a combination of a central metal atom accepting a pair of electrons from each of six σ donor ligands. The interaction of these ligands with some of the metal d orbitals is shown in Fig
The dx2-y2 and dz2 orbitals can form bonding orbitals with the ligand orbitals, but the dxy, dxz, and dyz orbitals cannot form bonding orbitals.
Bonding interactions are possible with the s (weak, but uniformly with all the ligands) and the p orbitals of the metal, with one pair of the ligands orbitals interacting with each p orbital.

163. MO = Linear Combination of Atomic Orbitals (LCAO)

164. MO = Linear Combination of Atomic Orbitals (LCAO)
MO = Linear Combination of Atomic Orbitals (LCAO). Metal-Ligands Bonding