COORDINATION CHEMISTRY
Coordination Compounds
Compounds form when elements combine in stoichiometric amounts, resulting in a new, stable substance with unique properties. They are essential for life as we know it.
For example:
KCl + MgCl2 + 6H2O → KCl.MgCl2.6H2O - carnallite
From the valence bond perspective, a complex is formed when Lewis bases (ligands) react with a Lewis acid (metal or metal ion), creating coordinate covalent (or dative) bonds between them. To account for the observed structures and magnetic properties of these complexes, the model utilizes hybridization of metals, p and d valence orbitals. For instance, Pd(II) and Pt(III) complexes are usually four-coordinate, square planar, and diamagnetic. This arrangement is often found for Ni(I) complexes as well since the free ion in the ground state in each case is paramagnetic (d F), so the bonding picture tested has to include the pairing of electrons as well as ligand-metal-ligand bond angles of 90. Pauling suggests that this occurs via hybridization of one (n-1)d, ns, and two np orbitals to form four equivalent hybrids directed toward the corners of a square. For example, in PIC1, 5d combines with 6s 6d, and 6p orbitals to form a dsp3 hybrid. These orbitals then participate in covalent bonds with the ligands, and the bonding electron pairs are provided by the ligands. The eight d electrons in the free one are assigned as pairs to the four hybridized metal d orbitals.
The Electroneutrality Principle and Back Bonding
One of the challenges with the VB assumption of electron donation from ligands to metal ions is that it can lead to a formal negative charge buildup on the metal. This issue arises in all complete treatments of coordination compounds. For instance, let's consider a complex of Co(ll) such as [Co(I)]. The six ligands share twelve electrons with the metal atom, which contributes to the formal charge on the metal a total of -6. However, this is only partially cancelled out by the metal's ionic charge of 2. From a formal charge perspective, the cobalt acquires a net 4 charge. But, Pauling pointed out that metals would not exist with such unfavourable negative charges.
The first step is to identify the metal orbitals and the combinations of pσ orbitals of the ligand which are best suited to permit o overlaps in the + X, + Y, and + Z directions. It can be easily shown with the help of the Group theory that the combinations of pσ orbitals of the ligand and the orbitals of the metal ion which combine with such combinations of pσ orbitals of the ligand to form molecular orbitals, must have the a1g, eg and t1u symmetries. In the octahedral environment, the s orbital of the metal has a1g symmetry, the two dz2, and dx2- y2 orbitals have eg symmetry while the three p orbitals of the metal ion have t1u Symmetry. Hence the s orbital of the metal with a1g symmetry would combine with pσ ligand orbital combinations of a1g symmetry to form a1g bonding molecular orbitals (BMOs) and a*1g antibonding molecular orbitals (ABMOs). The ligand orbitals have such orientations in bonding molecular orbitals that they give maximum positive overlap with the metal ion orbitals.
(Other t1u and t*1u molecular orbitals can be easily drawn similarly). Likewise, dz2 and dx2- y2 orbitals of the metal ion with eg, symmetry combine with pσ ligand-orbital combinations of eg symmetry to form bonding molecular orbitals and e*g antibonding molecular orbitals. A qualitative diagram representing the relative energies of these molecular orbitals in the case of an octahedral complex is given below
The six filled pσ orbitals of the ligands contribute 6 x 2 = 12 electrons to the molecular orbitals. These may be considered filling the bonding molecular orbitals, ag, t1g, and eg. The electrons are previously present in the d orbitals of the free metal ion and may thus be considered to be distributed between t2g non-bonding and eg antibonding molecular orbitals of the complex. The energy gap between t2g and e*g is, thus, equivalent to the crystal field splitting parameter Δo, of the crystal field theory. However, in the crystal field theory, both the t2g and eg sets of orbitals are composed of pure d orbitals of the metal ion whereas according to molecular orbital theory, eg molecular orbitals of the octahedral complex containing only sigma bonds between the metal ion and the ligand, have some ligand orbital character also. Out of the two sets of orbitals, t2g non-bonding orbitals are pure metal d orbitals (i.e., dxy, dyz, and dzx orbitals) whereas e*g antibonding molecular orbitals have a major contribution from eg orbitals of the metal ion (i.e., dz2 and dx2- y2 orbitals) and only minor contribution from the ligand orbitals. Therefore, it can be said that the electrons previously belonging to the free metal ion are accommodated in those molecular orbitals of the octahedral complex which are the pure d orbitals or which have a major contribution from the d orbitals of the metal ion.
Coordination compounds refer to chemical compounds that have a central metal atom in non-metal atoms or groups of atoms. These non-metal atoms, ions, or molecules that surround the central metal atom are called ligands and they donate electrons to the metal. The bonding between the ligands and the central metal atom occurs through coordinate or covalent bonds.
Coordination compounds can be either neutral or charged. When charged, the complex is stabilized by nearby counter-ions. Coordination compounds form as a result of a Lewis acid-base reaction.
Examples of ligands include:
- Negative ligands: Cyanide ion, Halide ion, peroxide ion, sulfide ion
- Positive ligands: Hydrazinium ion, Nitrosonium ion, Nitronium ion
- Neutral ligands: Methylamine, Ammonia, Water
Coordination compounds include most metal complexes or compounds, except for alloys.
DOUBLE SALTS AND COORDINATION COMPOUNDS
Compounds form when elements combine in stoichiometric amounts, resulting in a new, stable substance with unique properties. They are essential for life as we know it.
For example:
KCl + MgCl2 + 6H2O → KCl.MgCl2.6H2O - carnallite
K2SO4 + Al2(SO4)3+ 24H2O →Al2(SO4)3.K2SO4.24H2O - potassium alum
CuSO4 + 4NH3 + H2O → CuSO4.4NH3.H2O - tetramine copper(II)sulphate monohydrate
Fe(CN)2 + 4KCN→ K4[Fe(CN)6] - potassium ferrocyanide
Fe(CN)2 + 4KCN→ K4[Fe(CN)6] - potassium ferrocyanide
Addition compounds are of two types.
1. Those that lose their identity in solution (double salts).
When crystals of carnallite are dissolved in water, the solution shows the properties of K+. Mg2+ and Cl-, ions. Similarly, a solution of potassium alum shows the properties of K+. Al3+ and SO42-; ions. These are both examples of double salts that exist only in the crystalline state. Still, instead When the other two examples of coordination compounds dissolve they do not form simple ions - Cu2+, or Fe2+ and CN- their complex ions remain intact. Thus the cuproammonium on [Cu(H2O)2(NH3)4]2+ and the ferrocyanide ion [Fe(CN)6]4-, custa distinct entities both in the solid and in solution. Complex ions are shown by the use of square brackets. Compounds containing these ions are called coordination compounds. The chemistry of metal ions in solution is the chemistry of their complexes. Transition metal ions, in particular form many stable complexes. In solution 'free' metal ions are coordinated either to water or to other ligands Thus Cu2+ exists as the pale blue complex ion [Cu(H2O)6]2+ in aqueous solution (and also in hydrated crystalline salts). If aqueous ammonia is added to this solution, the familiar deep blue cuproammonium ion is formed:2. Those which retain their identity in solution (complexes)
[Cu(H2O)6]2+ + 4NH3 → [Cu(H2O)2(NH3)4]2+ + 4H2O
*Note that this reaction is a substitution reaction, and the NH3 replaces water in the complex ionsummary
- Coordination compounds are chemical compounds that have a central metal atom surrounded by non-metal atoms or groups of atoms called ligands.
- Ligands donate electrons to the metal and are bound to it by coordinate or covalent bonds.
- These compounds can be neutral or charged and are the product of a Lewis acid-base reaction.
- Examples of ligands include negative, positive, and neutral ligands.
- Coordination compounds include most metal complexes or compounds except alloys.
Bonding in Coordination Compounds
There has been much work done in attempting to formulate theories to describe the bonding coordination compounds and so rationalize and predict their properties. The first success along these lines was the (VB) theory that Linus Pauling and others applied in the 1930s and following years. In the 1950s and 1960s the crystal field (CF) theory and its modifications, generally known under the label ligand field (LF) theory, gained preeminence and in turn gradually gave way to the molecular orbital (MO) theory. Although both the valence bond and crystal field theories have been largely displaced as working models for the practising inorganic chemist, they continue to contribute to current discussions of coordination compoundsValence Bond Theory
From the valence bond perspective, a complex is formed when Lewis bases (ligands) react with a Lewis acid (metal or metal ion), creating coordinate covalent (or dative) bonds between them. To account for the observed structures and magnetic properties of these complexes, the model utilizes hybridization of metals, p and d valence orbitals. For instance, Pd(II) and Pt(III) complexes are usually four-coordinate, square planar, and diamagnetic. This arrangement is often found for Ni(I) complexes as well since the free ion in the ground state in each case is paramagnetic (d F), so the bonding picture tested has to include the pairing of electrons as well as ligand-metal-ligand bond angles of 90. Pauling suggests that this occurs via hybridization of one (n-1)d, ns, and two np orbitals to form four equivalent hybrids directed toward the corners of a square. For example, in PIC1, 5d combines with 6s 6d, and 6p orbitals to form a dsp3 hybrid. These orbitals then participate in covalent bonds with the ligands, and the bonding electron pairs are provided by the ligands. The eight d electrons in the free one are assigned as pairs to the four hybridized metal d orbitals.
In some cases, such as with Cl-, Ni(II) forms four-coordinate complexes that are paramagnetic and tetrahedral. For these instances, VB theory assumes that the d orbital occupation of the complex is the same as that of the free ion, which eliminates the possibility that valence-level d orbitals can accept electron pairs from the ligands. Hybrid orbitals of either the sp or pd type (involving 4p or 4d orbitals) or a combination of the two provide the proper symmetry for the bonds as well as allow for the magnetic properties due to two unpaired electrons. The presented examples illustrate a useful rule, originally called "the magnetic criterion of bond type," which allows prediction of the geometry of a four-coordinated complex if its magnetic properties are known: diamagnetic-square planar, paramagnetic tetrahedral.
The valence bond picture for six-coordinate octahedral complexes involves d2sp3 hybridization of the metal. The specific d orbitals that meet the symmetry requirements for the metal-ligand o bonds are the and da. As with the four-coordinated complexes discussed above, the presence of unpaired electrons in some octahedral compounds renders the valence level (n-1)d orbitals unavailable for bonding. This is true, for instance, for paramagnetic [COF6] the VB model invokes the participation of 4s, 4p, and 4d orbitals in the hybridization. However, for diamagnetic [Co(NH3)], the 3dz2 and 3dx2- y2 are vacant and participate in hybridization with 4s and 4p orbitals.
The valence bond picture for six-coordinate octahedral complexes involves d2sp3 hybridization of the metal. The specific d orbitals that meet the symmetry requirements for the metal-ligand o bonds are the and da. As with the four-coordinated complexes discussed above, the presence of unpaired electrons in some octahedral compounds renders the valence level (n-1)d orbitals unavailable for bonding. This is true, for instance, for paramagnetic [COF6] the VB model invokes the participation of 4s, 4p, and 4d orbitals in the hybridization. However, for diamagnetic [Co(NH3)], the 3dz2 and 3dx2- y2 are vacant and participate in hybridization with 4s and 4p orbitals.
The Electroneutrality Principle and Back Bonding
One of the challenges with the VB assumption of electron donation from ligands to metal ions is that it can lead to a formal negative charge buildup on the metal. This issue arises in all complete treatments of coordination compounds. For instance, let's consider a complex of Co(ll) such as [Co(I)]. The six ligands share twelve electrons with the metal atom, which contributes to the formal charge on the metal a total of -6. However, this is only partially cancelled out by the metal's ionic charge of 2. From a formal charge perspective, the cobalt acquires a net 4 charge. But, Pauling pointed out that metals would not exist with such unfavourable negative charges.
Donor atoms on ligands are highly electronegative in general (e.g., N, O, and the halogens). Therefore, bonding electrons will not be shared equally between the metal and ligands. Pauling suggested that complexes would be most stable when the electronegativity of the ligand was such that the metal achieved a condition of essentially zero net electrical charge. This tendency for zero or low electrical charges on atoms is known as the electroneutrality principle. It is a rule-of-thumb used to make predictions regarding electronic structure in many types of compounds, not only complexes.
Pauling has made semiquantitative calculations correlating the stability of complexes with the charges on the central metal atom. For example, it was shown that [Be(H2O)6] and [AI(H2O)6] are stable, but [Be(H2O)4] and [Al(NH3)4] are not. Four water molecules effectively neutralize the ionic charge of beryllium, but six water molecules donate too many electrons.
Summary
- From the valence bond point of view, the formation of a complex involves the reaction between Lewis bases (ligands) and a Lewis acid (metal or metal ion) with the formation of coordinate covalent (or dative) bonds between them The model utilizes hybridization of metals, p., and d valence orbitals to account for the observed structures and magnetic properties of complexes.
- For these cases, VB theory assumes the d orbital occupation of the complex to be the same as that of the free ion, which eliminates the possibility that valence-level d orbitals can accept electron pairs from the ligands.
- One difficulty with the VB assumption of electron donation from ligands to metal ions is the buildup of a formal negative charge on the metal.
- Since this is a problem that arises, in one form or another, in all complete treatments of coordination compounds, the following discussion is appropriate to all current bonding models Consider a complex of Co(ll) such as [Co(I)] The six ligands share twelve electrons with the metal atom, thereby contributing to the formal charge on the metal a total of -6, which is only partially cancelled by the metal's ionic charge of 2 From a formal charge point of view, the cobalt acquires a net 4 charge, However, Pauling pointed out why metals would not, in fact, exist with such unfavourable negative charges Because donor atoms on ligands are in general highly electronegative (eg, N, O, and the halogens), the bonding electrons will not be shared equally between the metal and ligands.
Crystal Field Theory (CFT)
Crystal Field Theory (CFT) is an electrostatic model that explains the bond between a metal ion and ligands in transition metal complexes. The theory assumes that this bond is purely ionic, formed through electrostatic interactions. CFT is a crucial concept in the field of chemistry, as it provides insights into the behaviour of transition metal complexes, including their colours, magnetism, structures, stability, and reactivity. Here are the key points to understand about CFT:Description: CFT explains the net change in crystal energy resulting from the orientation of d orbitals of a transition metal cation inside a coordinating group of anions (ligands).
Complexes: Transition metals form complexes, which consist of a central metal atom or ion surrounded by ligands.
Interaction: CFT considers the interaction between ligands and the central metal atom as a purely electrostatic phenomenon. Ligands are treated as point charges near the atomic orbitals of the central atom.
Geometrical Disposition: Understanding the geometrical disposition of d orbitals is essential to comprehending crystal field interactions.
Degeneracy: In a free gaseous metal ion, d orbitals are fivefold degenerate (i.e., they have the same energy).
Splitting: When transition metals bond with ligands, the d orbitals split apart due to different symmetries and the inductive effect of the ligands on the electrons.
High Spin Complex: Contains more unpaired electrons and is expected with weak field ligands.
Low Spin Complex: Contains fewer unpaired electrons and is associated with strong field ligands.
Crystal Field Stabilization Energy (CFSE): The energy difference resulting from the splitting of d orbitals.
Remember that the central assumption of CFT is that metal-ligand interactions are purely electrostatic in nature. Understanding this theory and its concepts is essential for understanding the chemical behaviour of transition metal complexes.
Crystal Field Stabilization Energy (CFSE)
Crystal Field Stabilization Energy (CFSE) is a term that is used in Crystal Field Theory (CFT) to explain the behaviour of transition metal complexes. CFSE refers to the change in energy that occurs when the d-orbitals of a metal cation split as it interacts with ligands in a complex. The stability of a complex increases with the CFSE value.
In an octahedral complex, the electron configuration is divided into two subsets- t2g and eg. Electrons in the more stable t2g subset contribute to stabilization, while electrons in the higher energy eg subset contribute to destabilization. The overall CFSE is expressed as a multiple of the crystal field splitting parameter Δ.
The CFSE values for different electron configurations (from d₀ to d₁₀) can be used to calculate the Octahedral Site Preference Energies (OSPE), which is the energy difference between the octahedral and tetrahedral configurations. The conversion factor between octahedral and tetrahedral splitting parameters is Δtet = (4/9)Δoct.
To summarize, CFSE explains the energy changes that occur as electrons arrange themselves in d orbitals when ligands are present in a complex. It is an important factor in determining the stability and properties of transition metal complexes.
jahn-Teller distortion
The Jahn-Teller effect, also known as Jahn-Teller distortion, is a phenomenon that explains the distortion of molecules and ions due to certain electron configurations. Sometimes, random movements of bonds prevent the distortion from occurring, or the distortion is so weak that it can be ignored. However, the Jahn-Teller theorem states that any non-linear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy since the distortion reduces the overall energy of the molecule.
The Jahn-Teller effect is usually observed when two axial bonds in octahedral complexes are shorter or longer than the equatorial bonds. The effect can also be seen in tetrahedral compounds, and its strength depends on the electronic state of the system.
The Jahn-Teller effect can be classified as strong or weak, depending on the degree of distortion that occurs in the molecule. The strength of the effect is influenced by the electronic state of the system, the type of metal and ligands, and the degree of overlap between the metal and ligand orbitals.
In general, when the metal-ligand orbital interactions are strong, there is a higher chance of observing a strong Jahn-Teller effect. Conversely, when the t2g orbitals are unevenly occupied, a weak Jahn-Teller effect is expected.
d-orbitals | Jahn-Teller distortion strength |
|---|---|
d1 | - |
d2 | - |
d3 | - |
d4 (large δ) | s |
d4 (small δ) | w |
d5 (large δ) | s |
d5 (small δ) | w |
d6 (large δ) | s |
d6 (small δ) | w |
d7 | - |
d8 | - |
d9 | - |
d10 | - |
Here, s denotes a strong Jahn-Teller effect, w denotes weak Jahn-Teller effect, and - denotes no Jahn-Teller distortion.
[Cu(H2O)6]^2+ is an example of a molecule that shows a strong Jahn-Teller effect. The copper ion in this molecule possesses a d9 electronic configuration, which is a spatially degenerate electronic ground state. The Jahn-Teller effect causes the molecule to undergo a geometrical distortion that removes the degeneracy and lowers the overall energy of the molecule. In this case, the distortion results in an elongation of the two trans-Z-ligands, which eventually leads to the formation of square planar complexes.
Molecular orbital theory
The molecular orbital theory, although more complicated than the valence bond and crystal field theories, explains more satisfactorily the nature of bonding involved in coordination complexes
For a proper understanding of the molecular orbital theory of metal-ligand bond, we are to refresh our knowledge of the group theory and the terminology used therein which have been discussed in Chapter 3 Thus, we are to recall that the symbols a, e, and t stand, respectively, for non-degenerate, doubly degenerate and triply degenerate*(*degenerate orbitals are orbitals of the same energy doubly and triply degenerate orbitals imply two orbitals of the same energy) orbitals. The symmetry symbol for a particular orbital of the metal may differ in different environments. Thus, a set of p orbitals of metal has t1u symmetry in an octahedral environment whereas it has t2 symmetry in a tetrahedral environment We are also to recall that for an effective combination of atomic orbitals to form molecular orbitals, the following requirements are needed to be met within density
1. The symmetry of the combining atomic orbitals must be the same so that the additive combination of atomic orbitals permits the maximum overlap of orbitals
2. The difference in the energies of the combining orbitals is not large
3. If the two atomic orbitals are of unequal energies, then the bonding molecular orbital would have more characteristics of the lower energy atomic orbital and the antibonding molecular orbital would have more characteristics of the higher energy atomic orbital. The greater the difference in the energies of the combining atomic orbitals, the greater would be the incorporation of the character of the lower energy
atomic orbital in the bonding molecular orbital and the greater the incorporation of the character of the higher energy atomic orbital in the antibonding molecular orbital.
We shall now discuss the molecular orbital theory to explain the nature of
bonding in coordination complexes.
3. If the two atomic orbitals are of unequal energies, then the bonding molecular orbital would have more characteristics of the lower energy atomic orbital and the antibonding molecular orbital would have more characteristics of the higher energy atomic orbital. The greater the difference in the energies of the combining atomic orbitals, the greater would be the incorporation of the character of the lower energy
atomic orbital in the bonding molecular orbital and the greater the incorporation of the character of the higher energy atomic orbital in the antibonding molecular orbital.
We shall now discuss the molecular orbital theory to explain the nature of
bonding in coordination complexes.
Sigma Bonding in Octahedral Complexes
Consider a metal ion surrounded octahedrally by six ligands and suppose that each ligand has a filled pσ orbital on it which is capable of forming a σ bond with the metal ion represented as M without charge for the sake of convenience
The first step is to identify the metal orbitals and the combinations of pσ orbitals of the ligand which are best suited to permit o overlaps in the + X, + Y, and + Z directions. It can be easily shown with the help of the Group theory that the combinations of pσ orbitals of the ligand and the orbitals of the metal ion which combine with such combinations of pσ orbitals of the ligand to form molecular orbitals, must have the a1g, eg and t1u symmetries. In the octahedral environment, the s orbital of the metal has a1g symmetry, the two dz2, and dx2- y2 orbitals have eg symmetry while the three p orbitals of the metal ion have t1u Symmetry. Hence the s orbital of the metal with a1g symmetry would combine with pσ ligand orbital combinations of a1g symmetry to form a1g bonding molecular orbitals (BMOs) and a*1g antibonding molecular orbitals (ABMOs). The ligand orbitals have such orientations in bonding molecular orbitals that they give maximum positive overlap with the metal ion orbitals.
Similarly, the three p orbitals of the metal ion with t1u symmetry combine with pσ ligand-orbital combinations of t1u symmetry to form t1u bonding molecular orbitals and t*1u antibonding molecular orbitals. One such bonding is t1u and one such antibonding t*1u molecular orbital, is obtained by combining pz metal orbital with ligand orbital combinations of appropriate symmetries.
(Other t1u and t*1u molecular orbitals can be easily drawn similarly). Likewise, dz2 and dx2- y2 orbitals of the metal ion with eg, symmetry combine with pσ ligand-orbital combinations of eg symmetry to form bonding molecular orbitals and e*g antibonding molecular orbitals. A qualitative diagram representing the relative energies of these molecular orbitals in the case of an octahedral complex is given below
The six filled pσ orbitals of the ligands contribute 6 x 2 = 12 electrons to the molecular orbitals. These may be considered filling the bonding molecular orbitals, ag, t1g, and eg. The electrons are previously present in the d orbitals of the free metal ion and may thus be considered to be distributed between t2g non-bonding and eg antibonding molecular orbitals of the complex. The energy gap between t2g and e*g is, thus, equivalent to the crystal field splitting parameter Δo, of the crystal field theory. However, in the crystal field theory, both the t2g and eg sets of orbitals are composed of pure d orbitals of the metal ion whereas according to molecular orbital theory, eg molecular orbitals of the octahedral complex containing only sigma bonds between the metal ion and the ligand, have some ligand orbital character also. Out of the two sets of orbitals, t2g non-bonding orbitals are pure metal d orbitals (i.e., dxy, dyz, and dzx orbitals) whereas e*g antibonding molecular orbitals have a major contribution from eg orbitals of the metal ion (i.e., dz2 and dx2- y2 orbitals) and only minor contribution from the ligand orbitals. Therefore, it can be said that the electrons previously belonging to the free metal ion are accommodated in those molecular orbitals of the octahedral complex which are the pure d orbitals or which have a major contribution from the d orbitals of the metal ion.
Summary
- The molecular orbital theory provides a more comprehensive and satisfactory explanation of the bonding nature in coordination complexes, although it is more complex than the valence bond and crystal field theories. To understand the molecular orbital theory of metal-ligand bonding, it is necessary to review our knowledge of group theory and the terminology outlined in Chapter 3. Notably, the symbols a, e, and t correspond to non-degenerate, doubly degenerate, and triply degenerate orbitals, respectively. It is noteworthy that degenerate orbitals exist at the same energy level, and doubly and triply degenerate orbitals denote two orbitals of the same energy
- In an octahedral environment, a set of p orbitals of the metal has t1u symmetry, whereas it has t2 symmetry in a tetrahedral environment. To form molecular orbitals, a proper combination of atomic orbitals requires that the symmetry of combining atomic orbitals is the same to maximize orbital overlap. Additionally, the greater the difference in the energies of the combining atomic orbitals, the higher the incorporation of the character of the lowest energy atomic orbital in the bonding molecular orbital and vice versa.
- The molecular orbital theory provides a clear explanation of the nature of bonding in coordination complexes. According to group theory, the combinations of pσ orbitals of the ligand and the orbitals of the metal ion that combine with such combinations of pσ orbitals of the ligand to form molecular orbitals must have the a1g, eg, and t1u symmetries. The ligand orbitals in bonding molecular orbitals have orientations that yield maximum positive overlap with the metal ion orbitals.
- Furthermore, the six filled pσ orbitals of the ligands contribute 12 electrons to the molecular orbitals. The energy gap between t2g and e*g is equivalent to the crystal field splitting parameter Δo of the crystal field theory. However, the molecular orbital theory posits that eg molecular orbitals of the octahedral complex containing only sigma bonds between the metal ion and the ligand have some ligand orbital character as well.