Ligand Field Theory

The world of transition metal chemistry is a visually spectacular and functionally critical domain, populated by compounds whose vibrant colors, fascinating magnetic properties, and diverse structures have long intrigued scientists. Explaining this rich variety of behaviors requires a powerful theoretical framework that goes beyond simple bonding models. Ligand Field Theory (LFT) stands as that cornerstone theory, providing a quantum mechanical lens to understand and predict the properties of these ubiquitous compounds. It addresses the fundamental question of how the interaction between a central metal ion and its surrounding ligands dictates nearly every aspect of a complex's identity.

This article will guide you through the core concepts of Ligand Field Theory in two main chapters. First, in "Principles and Mechanisms," we will explore how the interaction between metals and ligands splits the d-orbitals, covering the foundational ideas from Crystal Field Theory to the more robust molecular orbital approach of LFT. We will examine how metal identity and ligand properties, especially π-bonding, fine-tune this splitting and dictate properties like color and magnetism. Then, in "Applications and Interdisciplinary Connections," we will see the theory in action, illustrating how LFT explains chemical reactivity, the function of metalloproteins in biology, and the properties of advanced materials, revealing its power as a unifying principle across scientific disciplines.

Imagine you are a tiny observer standing on a central metal ion. All around you, in a beautifully symmetric octahedral arrangement, six ligands are approaching. What do you feel? You feel a force, a field of influence. This field is the heart of the matter, and understanding its nature is our journey. It’s a journey that will take us from a simple, intuitive picture to a remarkably powerful theory that explains the vibrant colors, fascinating magnetic properties, and intricate structures of a vast world of chemical compounds.

Let's start with the simplest possible picture, an idea so useful it has its own name: ​​Crystal Field Theory (CFT)​​. Let’s pretend the approaching ligands are nothing more than six negative point charges, and our metal ion is a positive center holding its precious $d$-electrons. These electrons reside in five orbitals, each with a distinct shape and orientation in space.

Now, a fundamental principle of physics is that like charges repel. An electron in a $d$-orbital will be repelled by the negative charge of the ligands. But here's the crucial part: not all $d$-orbitals will feel this repulsion equally. Two of these orbitals, collectively called the ​​$e_g$ set​​ ($d_{z^2}$ and $d_{x^2-y^2}$), have their lobes pointing directly at the incoming ligands along the Cartesian axes. Imagine trying to push the north poles of two magnets together—the repulsion is intense. Electrons in these $e_g$ orbitals are in a high-energy, uncomfortable situation.

The other three orbitals, known as the ​​$t_{2g}$ set​​ ($d_{xy}$, $d_{xz}$, and $d_{yz}$), are more fortunate. Their lobes are nestled between the axes, pointing away from the direct line of fire of the approaching ligands. The repulsion they feel is much weaker.

The result? The once-degenerate (equal-energy) set of five $d$-orbitals is split by the octahedral "crystal field." The $e_g$ set is pushed up to a higher energy, and the $t_{2g}$ set is lowered to a stable, lower energy. The energy difference between them is the single most important parameter in our story: the ​​ligand field splitting energy​​, denoted as $\Delta_o$ for an octahedral field. This simple electrostatic model correctly predicts the fundamental splitting of the d-orbitals.

The point-charge model is a wonderful starting point, but nature is more subtle and interconnected. Ligands aren't just points of charge; they are molecules or ions with their own orbitals and electrons. The bond between a metal and a ligand has covalent character—they share electrons. To embrace this reality, we graduate from Crystal Field Theory to the more sophisticated and accurate ​​Ligand Field Theory (LFT)​​, which is essentially the application of Molecular Orbital (MO) theory to these systems.

In LFT, we no longer talk about pure electrostatic repulsion. Instead, we see the metal and ligand orbitals combining to form a new set of molecular orbitals. The interaction that creates the $e_g$ orbitals' high energy is now understood as the formation of ​​sigma ($\sigma$) antibonding orbitals​​, denoted $e_g^*$. These orbitals arise from the head-on overlap of the metal $e_g$ orbitals and the ligand $\sigma$-donor orbitals. As with any bonding/antibonding pair, the antibonding orbital is destabilized and raised in energy.

Initially, the metal's $t_{2g}$ orbitals, which don't point at the ligands, are considered largely ​​non-bonding​​. Thus, the splitting energy $\Delta_o$ is now seen as the energy gap between the occupied (or to-be-occupied) non-bonding/bonding $t_{2g}$ orbitals and the empty (or to-be-occupied) antibonding $e_g^*$ orbitals. This makes the $t_{2g}$ set the ​​Highest Occupied Molecular Orbital (HOMO)​​ and the $e_g^*$ set the ​​Lowest Unoccupied Molecular Orbital (LUMO)​​ in many common cases, like a low-spin $d^6$ complex. This MO picture is far more powerful because it can explain phenomena that the simple electrostatic model cannot, such as the subtle variations in the strength of the ligand field.

The magnitude of the splitting, $\Delta_o$, is not a fixed constant; it is "tunable," depending on the specific metal, its oxidation state, and the identity of the ligands. Understanding what tunes this gap is key to predicting a complex's properties.

The Metal's Role

First, the metal ion itself. Imagine two complexes with the same ligands but different metal oxidation states, say $[M(L)_6]^{2+}$ and $[M(L)_6]^{3+}$. The M$^{3+}$ ion has a higher positive charge. This stronger positive core acts like a more powerful gravitational center, pulling the negatively charged (or polarized) ligands closer. The metal-ligand bond distance, $R$, shrinks. Since the interaction strength that causes the splitting is intensely sensitive to distance (theoretically scaling as $1/R^5$), this seemingly small change has a big effect. Closer ligands mean a stronger field and a larger $\Delta_o$. This is a general and very useful rule: for a given metal and ligand, ​​$\Delta_o$ increases with increasing oxidation state​​,.

The Ligand's Symphony: The Spectrochemical Series

Second, and more dramatically, the ligands. Ligands are not created equal. Some produce a huge splitting (strong-field ligands) while others produce a small one (weak-field ligands). The ranking of ligands by their ability to split the d-orbitals is called the ​​spectrochemical series​​. This is where Ligand Field Theory truly shows its explanatory power, particularly through the inclusion of ​​pi ($\pi$) bonding​​.

The $\sigma$-bonds we discussed earlier are just the primary melody. The harmony comes from $\pi$-interactions, which involve the metal's $t_{2g}$ orbitals. There are two main types:

1. ​​$\pi$-Donors:​​ These ligands, like the halide ions ($F^-$, $Cl^-$, $Br^-$, $I^-$), come equipped with filled $p$-orbitals that have the right symmetry to interact with the metal's $t_{2g}$ set. This interaction is like two filled orbitals getting too close; it's a repulsive-like effect that creates a bonding/antibonding pair. The metal's $t_{2g}$ orbitals become antibonding in this $\pi$-interaction, pushing them up in energy. Since $\Delta_o$ is the gap between $t_{2g}$ and $e_g^*$, raising the $t_{2g}$ level decreases the gap. This elegantly explains why the halides are weak-field ligands and resolves a puzzle for CFT. Why is the order $I^- < Br^- < Cl^- < F^-$? Because the p-orbitals of iodine are higher in energy and a better match for the metal's d-orbitals, making $I^-$ a better $\pi$-donor than $F^-$. Better $\pi$-donation means the $t_{2g}$ level is pushed up more, and $\Delta_o$ becomes smaller.

2. ​​$\pi$-Acceptors (or $\pi$-Acids):​​ These are the superstars of the strong-field world, ligands like carbon monoxide (CO), cyanide (CN⁻), and pyridine. These ligands possess empty, accessible $\pi^*$ (pi-antibonding) orbitals. The metal's filled (or partially filled) $t_{2g}$ orbitals can donate electron density back to the ligand into these empty $\pi^*$ orbitals. This process is called ​​back-bonding​​. It's a true covalent sharing that stabilizes the entire complex. For our energy diagram, this interaction pulls the energy of the metal's $t_{2g}$ orbitals down. Lowering the $t_{2g}$ starting point while the $e_g^*$ level remains high dramatically increases the gap $\Delta_o$. This is why ligands capable of back-bonding are at the strong-field end of the spectrochemical series,.

So, the spectrochemical series is not some arbitrary list. It is a beautiful ranking of the electronic dance between metal and ligand, a combination of the foundational $\sigma$-melody and the rich $\pi$-harmonies of donation and acceptance.

Why do we care so much about this energy gap? Because it dictates nearly all of the interesting, observable properties of transition metal complexes.

Color and Electronic Spectra

The vibrant colors of gemstones and chemical solutions are the most direct manifestation of $\Delta_o$. Color arises when a substance absorbs certain wavelengths of visible light and reflects or transmits others. For transition metal complexes, the energy of the absorbed light often corresponds precisely to the energy required to promote an electron from a lower-energy $d$-orbital to a higher-energy one—a ​​$d-d$ transition​​. An electron in a $t_{2g}$ orbital can absorb a photon of energy $h\nu = \Delta_o$ and jump up to an empty spot in an $e_g^*$ orbital.

Ligand field theory allows us to go even further. It helps us predict not just the energy, but the number of absorption bands we expect to see. A single electron configuration, like the $t_{2g}^6 e_{g}^2$ configuration of a $d^8$ ion (e.g., $Ni^{2+}$), doesn't just correspond to one energy state. Due to the different ways electrons can arrange themselves while respecting quantum rules, this configuration gives rise to multiple distinct electronic states, labeled with special identifiers called ​​term symbols​​. For a $d^8$ octahedron, the ground state is called $^3A_{2g}$. There are three other states with the same spin ($^3T_{2g}$, $^3T_{1g}(F)$, and $^3T_{1g}(P)$) to which an electron can jump without violating the spin selection rule ($\Delta S = 0$). As a result, we expect to see three spin-allowed absorption bands in the spectrum of a $d^8$ octahedral complex,. LFT provides the map of allowed energy levels for these electronic journeys.

Magnetism, Structure, and the Jahn-Teller Effect

The magnitude of $\Delta_o$ also competes with another energy: the pairing energy, $P$, which is the energetic cost of forcing two electrons into the same orbital.

• If $\Delta_o < P$ (weak field), it's energetically cheaper for an electron to jump the gap and occupy an $e_g^*$ orbital than to pair up. This leads to a maximum number of unpaired electrons and a ​​high-spin​​ complex.
• If $\Delta_o > P$ (strong field), it's cheaper to pay the pairing energy price and fill the $t_{2g}$ orbitals completely before occupying the high-energy $e_g^*$ set. This leads to a minimum number of unpaired electrons and a ​​low-spin​​ complex.

This competition can lead to a remarkable phenomenon known as ​​spin crossover​​. In some complexes, like certain iron(II) ($d^6$) compounds, $\Delta_o$ and $P$ are delicately balanced. At low temperatures, the complex might be in its low-spin state ($t_{2g}^6 e_g^0$, diamagnetic). But upon heating, thermal energy can provide the kick needed to overcome $\Delta_o$, and the complex switches to a high-spin state ($t_{2g}^4 e_g^2$, paramagnetic)!

This is not just an electronic reshuffling; it has profound structural consequences. Remember that the $e_g^*$ orbitals are $\sigma$-antibonding. The low-spin state has zero electrons in these orbitals. The high-spin state suddenly has two. Populating antibonding orbitals weakens the metal-ligand bonds and causes them to lengthen. The entire complex visibly expands!

But there's more. The high-spin $d^6$ state has an orbital degeneracy (its term symbol is $^5T_{2g}$). Nature, it seems, has a rule for such situations, articulated by the ​​Jahn-Teller theorem​​: any non-linear molecule in an orbitally degenerate electronic state will distort itself to remove that degeneracy and lower its energy. A perfect octahedron in a degenerate state is unstable. It will stretch or compress along one axis, lowering its symmetry from the perfect $O_h$ to something like a tetragonally distorted shape. So, the switch from low-spin to high-spin not only causes the bonds to lengthen but also causes the complex to distort its very shape. The electron configuration dictates the molecular geometry.

Finally, the covalent nature of LFT explains one last subtle point. Because the metal's d-electrons are delocalized over the ligands in MOs, the "cloud" of electron density expands. This ​​nephelauxetic effect​​ (from the Greek for "cloud-expanding") increases the average distance between the d-electrons, reducing their mutual repulsion. This reduction in electron-electron repulsion is measurable and is one more piece of compelling evidence that the true picture of bonding is one of shared electrons, not just static charges,.

From a simple idea of repulsion, we have built a framework that unifies the color, magnetism, and structure of an enormous class of molecules. It is a testament to the power and beauty of quantum mechanics, where the shape of an orbital and the rules of symmetry compose the rich and varied world we see around us.

In the previous chapter, we dissected the core principles of Ligand Field Theory. We saw how the simple presence of neighboring atoms—the ligands—can break the perfect spherical symmetry around a transition metal ion, splitting its $d$-orbitals into a landscape of hills and valleys. This might seem like a rather abstract piece of quantum bookkeeping. But the truth is far more exciting. This shifting of energy levels is not a subtle academic point; it is the master key that unlocks a vast and spectacular range of phenomena. It dictates the speed of chemical reactions, paints our world with vibrant colors, drives the machinery of life, and empowers the creation of new materials.

Let us now embark on a journey to see this theory in action. We will see that this single, elegant idea provides a unified explanation for seemingly disparate observations across chemistry, biology, and materials science, revealing the profound and beautiful interconnectedness of the natural world.

Every chemical reaction is a dance of breaking old bonds and forming new ones. The speed of this dance—the reaction rate—is governed by the height of the energy barrier that the molecules must climb to transform. Ligand Field Theory gives us a powerful lens to view the electronic part of this barrier. The Ligand Field Stabilization Energy (LFSE) isn't just a measure of ground-state stability; it's a dynamic quantity that changes as a complex contorts itself into a short-lived transition state. The change in LFSE on the way to this transition state can either pave a smooth road or build a steep mountain for the reaction to traverse.

Consider, for example, complexes of the Zinc(II) ion. If you've ever worked with zinc salts in a chemistry lab, you might have noticed how readily they react. Zinc(II) has a completely filled $d$-subshell—a $d^{10}$ configuration. In an octahedral field, this means both the lower-energy $t_{2g}$ and higher-energy $e_g$ orbitals are full. The stabilization from the $t_{2g}$ electrons is perfectly cancelled by the destabilization from the $e_g$ electrons, resulting in an LFSE of exactly zero. Now, imagine a ligand trying to leave. The complex must momentarily twist into a five-coordinate shape. What is the LFSE of that shape? Astonishingly, for a $d^{10}$ ion, it is also zero, regardless of the transition state's exact geometry. Because the LFSE is zero in the beginning and zero at the energetic peak of the reaction, there is no electronic barrier from the ligand field to overcome. The ligands can come and go with remarkable ease, making the complex kinetically labile.

At the other end of the spectrum, we find ions like Chromium(III). The ruby gem owes its deep red color and incredible hardness in part to the nature of Cr(III) ions embedded in an alumina lattice. In solution, the hexaaquachromium(III) ion, $[Cr(H_2O)_6]^{3+}$, is notoriously sluggish, or kinetically inert. Its $d^3$ configuration places three electrons in the three separate $t_{2g}$ orbitals, each contributing to stabilization. This arrangement confers a substantial LFSE. For this complex to react and lose a water ligand, it must contort, destroying some of that precious stabilization energy. This creates a large electronic activation barrier, dramatically slowing down any ligand exchange. We can even make finer predictions. Comparing $[Cr(H_2O)_6]^{3+}$ ($d^3$) with $[V(H_2O)_6]^{2+}$ (also $d^3$), we find the chromium complex is far more inert. Both have the same ideal LFSE in terms of $\Delta_o$, but the higher +3 charge on chromium pulls the ligands in closer and creates a much larger splitting energy, $\Delta_o$, amplifying the stabilization and thus the activation barrier.

The story gets even more fascinating. Sometimes, a complex is labile not because it lacks stabilization, but because its electronic structure makes its very geometry unstable! Consider the high-spin $d^4$ complex, $[Cr(H_2O)_6]^{2+}$. It has one electron in the high-energy $e_g$ orbitals. But there are two $e_g$ orbitals of equal energy—where should the electron go? Nature resolves this dilemma, as we learned from the Jahn-Teller theorem, by distorting the octahedron. Typically, two axial bonds become longer and weaker than the four equatorial ones. This distortion, driven by electronics, provides a "fast track" for substitution. The two weakened axial ligands are already halfway out the door, making the complex far more labile than one would guess from its LFSE alone. This explains why the order of lability for similar aqua ions isn't always simple, with the $d^4$ $[Cr(H_2O)_6]^{2+}$ reacting faster than both the $d^5$ $[Mn(H_2O)_6]^{2+}$ (which has zero LFSE but no Jahn-Teller distortion) and the $d^8$ $[Ni(H_2O)_6]^{2+}$ (which has a large LFSE and no distortion).

The magnificent colors of transition metal compounds are the most immediate evidence of d-orbital splitting. The energy gaps created by the ligand field often correspond to the energy of photons in the visible spectrum. When a complex absorbs light of a specific color, an electron leaps from a lower d-orbital to a higher one. We see the complementary color that is not absorbed.

But what happens when a complex has no d-electrons to make that jump? The permanganate ion, $[MnO_4]^-$, is famous for its intensely deep purple color. Yet the manganese atom here is in the +7 oxidation state, meaning it is $d^0$. There are no d-electrons to be found! So where does the color come from? Ligand Field Theory, when expanded into the more general framework of Molecular Orbital Theory, provides the answer. The electron that jumps doesn't start on the metal at all. It starts on one of the surrounding oxide ligands and leaps into one of the empty, low-lying d-orbitals on the manganese. This is called a Ligand-to-Metal Charge Transfer (LMCT) transition. The reason it happens so readily is that the Mn(VII) center, being so highly positive, is immensely "electron-hungry." It exerts a powerful pull, making it easy for a nearby ligand electron to make the jump when energized by a photon of light. This type of transition is much more "allowed" than a simple d-d transition, which explains the breathtaking intensity of the color.

This absorption of light is not just a passive event; it can be a trigger for action. Think of a molecule as a machine. Absorbing a photon can be like flipping a switch that turns the machine on. The hexaamminecobalt(III) ion, $[Co(NH_3)_6]^{3+}$, is a perfect example. In the dark, it is kinetically inert, a stable, low-spin $d^6$ complex with all its electrons nestled in the stable $t_{2g}$ orbitals. But shine light of the correct frequency on it, and everything changes. The photon's energy kicks an electron up from the non-bonding $t_{2g}$ set into a strongly $\sigma$-antibonding $e_g^*$ orbital. An antibonding orbital is, in essence, the "enemy" of a chemical bond. Populating it is like injecting instability directly into the Co-N bonds. With its chemical bonds suddenly weakened, the excited complex finds it easy to discard a ligand, becoming photochemically reactive. Light is thus transformed from a mere illuminator into a precise tool for initiating chemical change.

The subtle energies of ligand fields are not confined to the domain of chemists; they are at the very heart of biology. Nature, the ultimate engineer, has spent eons fine-tuning the coordination environments of metal ions to perform the intricate tasks of life.

Take a deep breath. The oxygen you just inhaled is being ferried through your body by hemoglobin. At the core of hemoglobin is an iron(II) ion, Fe(II). In its oxygen-free state, deoxyhemoglobin, this iron center is five-coordinate and high-spin. Why? LFT gives us the answer. The iron is a $d^6$ ion. For it to be high-spin, the energy required to pair up electrons in the same orbital, the pairing energy $P$, must be greater than the energy splitting $\Delta$ caused by the ligands. The specific five-coordinate environment provided by the porphyrin ring and a histidine residue creates a ligand field that is just weak enough to satisfy this condition: $\Delta \lt P$. This precise electronic state is not an accident; it is crucial for hemoglobin's function, priming the iron center to bind oxygen in a reversible way that a low-spin configuration would not allow.

The level of control is breathtaking. In a class of "blue copper proteins," which are vital for electron transfer in plants and bacteria, a copper(II) ion sits in a distorted tetrahedral site. Its intense blue color and unique magnetic signature (measured by a technique called EPR) are fingerprints of its environment. In the protein plastocyanin, the copper is coordinated by two histidine nitrogens, a cysteine sulfur, and a weakly interacting axial methionine sulfur. Now consider another protein, stellacyanin, where that single axial methionine is replaced by a glutamine, which coordinates with an oxygen atom instead of sulfur. This seemingly minor change, far from the main action, has dramatic consequences. The blue color deepens (shifts to a shorter wavelength), and a key feature of its magnetic fingerprint (the hyperfine coupling constant, $A_{\parallel}$) shrinks significantly. What happened? The new axial oxygen ligand is a stronger donor, exerting a stronger push along the z-axis. This causes the coordination sphere to "flatten" electronically, pushing the energy of the highest-energy $d_{x^2-y^2}$ orbital even higher. This increases the energy of the LMCT transition responsible for the color, and it changes the mixing between d-orbitals in a way that reduces the hyperfine coupling. LFT allows us to read these spectroscopic changes like a book, telling a detailed story of how a single atomic substitution can retune a complex biological machine.

The power to understand and manipulate d-orbital energies is not just an academic exercise; it's a cornerstone of modern technology. From industrial manufacturing to the design of next-generation electronics, Ligand Field Theory provides the rules of the game.

Many of the plastics, pharmaceuticals, and fuels we use are made using catalysts, often based on transition metals. The Monsanto process, for example, produces acetic acid (the main component of vinegar) on a massive scale using a rhodium catalyst. The crucial, rate-limiting step of this process is the attack of the square-planar rhodium catalyst, $[Rh(CO)_2I_2]^-$, on a molecule of methyl iodide. This attack is nucleophilic; electron density from the rhodium's highest occupied d-orbital, the $d_{z^2}$, reaches out to form a new bond. Now, imagine we are catalyst designers. We can ask a very LFT-style question: what if we tweak the ligands? Let's conduct a thought experiment and replace one of the carbon monoxide (CO) ligands with a linear nitrosyl (NO⁺) ligand. NO⁺ is isoelectronic with CO, but it is a much better $\pi$-acceptor, meaning it's better at pulling electron density from the metal into its own empty orbitals. This withdrawal of electron density from the rhodium center stabilizes all the d-orbitals, including the crucial $d_{z^2}$ orbital. A lower-energy, more stable $d_{z^2}$ orbital is less "eager" to donate its electrons. The result? The nucleophilic attack slows down. By choosing our ligands wisely, we can tune the electronic structure of the metal center to speed up or slow down a reaction, a fundamental principle in catalyst design.

The reach of LFT extends beyond discrete molecules into the realm of the solid state. Consider the material Molybdenum disulfide, MoS₂, a layered material with exciting applications in electronics and catalysis. It overwhelmingly prefers a structure where each Molybdenum atom ($Mo^{4+}$, $d^2$) is surrounded by six sulfur atoms in a trigonal prismatic arrangement. Why not a more common octahedral one? The answer lies in the unique d-orbital splitting diagram of the trigonal prism, which features a single, low-lying $a_1'$ ($d_{z^2}$) orbital. The $d^2$ configuration of Mo can place both its electrons in this single, stable orbital, creating a filled sub-level and a large energy gap to the next available orbitals. This special stabilization is the "sweet spot" for a $d^2$ ion, making the trigonal prismatic structure incredibly favorable and giving rise to the material's valuable semiconducting properties. A different material like Tantalum disulfide, TaS₂ ($Ta^{4+}$, $d^1$), doesn't get this special benefit. For its single d-electron, the standard stabilization in an octahedral field is perfectly adequate, and so it can happily adopt an octahedral structure, leading to completely different, metallic properties. The very structure and function of a material can be dictated by how one or two electrons settle into the landscape carved out by the ligand field.

Finally, let's revisit magnetism. An orbital contribution to the magnetic moment arises when an electron can, in a sense, circulate from one d-orbital to another equivalent one, creating an electric current and its associated magnetic field. This is possible when the ground electronic state is orbitally degenerate (a $T$ term in an octahedral field). Now, consider a system with two metal centers, one high-spin $d^6$ and the other high-spin $d^7$. If they are far apart, they act independently. Both have orbitally degenerate $T$ ground states, and both would contribute a first-order orbital moment to the total magnetism. But what happens if we bring them close enough that the electrons become completely delocalized, shared equally between the two centers? The system now acts as a single entity. The individual orbital degeneracies are "quenched" by the strong electronic coupling between the sites. The new ground state for the pair is typically non-degenerate. With no orbital degeneracy, the first-order orbital contribution to the magnetism vanishes. By moving from a valence-trapped to a delocalized state, we fundamentally alter the magnetic properties of the material, a change that LFT allows us to predict and understand.

From the bustling dance of labile complexes to the quiet inertness of a ruby, from the trigger of photosynthesis to the hum of an industrial reactor, we see the same principles at play. The simple, elegant idea of d-orbitals responding to their electric environment provides a unifying thread, weaving together a rich tapestry of scientific phenomena. That is the true power and beauty of Ligand Field Theory.