An Ionic Bonding Model - Introducing Crystal Field Theory

Crystal field theory for transition metal complexes simplifies the complex species to one featuring point charges involved in purely ionic bonds. The theory focuses on the usually partly filled valence level d sub-shell, with a key recognition being that the fivefold energy degeneracy of the d subset present in the 'bare' metal will be lost in a ligand environment, leading to nonequivalence of energies amidst the nd orbitals. This then demands consid- eration of how the electrons occupy these levels, since variation in this occupancy can be associated with variation in properties. Reducing the inherently spherical metal ion to a point positive charge appears less of an approximation than reducing ligand donor groups each to a point negative charge that represents the electron pair. Ignoring ligand bulk and shape aspects would seem a big leap, but as it turns out the model does yield useful outcomes in terms of interpreting physical properties such as colour and magnetic properties in metal complexes. Bonding is considered to arise dominantly through electrostatic forces between cation and anion point charges located in the ionic array. Unfortunately, while responsible for a stable assembly, these primary electrostatic interactions have little direct influence on properties. Rather, it the effect of ionic interactions on the set of valence electrons that is the key. For elements of the main group this includes p orbitals; for most transition metal ions encountered, these are purely the set of d electrons; in the lanthanoids, we would be dealing with the f-electron set in a similar way.

The CFT developed as the earliest theory from Bethe's work published in 1929, based on a group theory approach to the influence on the energy levels of an ion or atom upon lowering symmetry in a ligand environment. First developed to interpret paramagnetism, it was subsequently applied more widely in the development of the field of coordination chemistry in the 1950s. This led to identification of shortcomings that were addressed by the development of the more versatile ligand field theory (LFT), which includes recognition that both σ and π bonds can occur in complexes as in pure organic compounds. The two are sufficiently closely related in terms of their core operations involving the d orbitals for them to be often used (albeit inappropriately) interchangeably. While deficient in some aspects, the CFT remains a useful theory for qualitative and limited quantitative interpretation. What is perhaps most remarkable about this theory is that it works at all, given the simplicity and level of assumptions - but it does. Further, it has stood the test of time to remain adequate despite the vast changes in the field over the decades since its evolution.

What we are doing in taking this approach to developing a model is mixing a purely ionic model with an atomic orbital model. The valence orbitals of the central atom are assumed to be influenced by the close approach of the ligands acting simply as points of negative charge. We can start considering the way the model operates by employing for illustrative purposes a set of p orbitals, since here we have a simple case where each p orbital lies along one axis of an imposed three-dimensional coordinate system (Figure 3.8). What we know from the simple atomic orbital model is that we can represent the three empty p orbitals as equal in energy. If we surround these bare p orbitals with a symmetrical 'atmosphere' of negative charge associated with the presence of ligand donors, there is no obvious change because our p orbitals carry no electrons yet. Now, consider what happens if we insert an electron into the p-orbital set, and allow it to occupy any orbital. A coulombic repulsion will occur between the inserted electron and the surrounding 'atmosphere' of negative charge that is identical regardless of the orbital it occupies, raising the energy of the set of p orbitals equally. This is the so-called spherical field situation (very occasionally called a steric field). The next step is to introduce some directionality into the interaction, by restricting the negative charge of the ligand to localities along one specific direction, say equidistant from the metal in each direction along the z axis. If we place our p electron in the p orbital, the electrostatic interaction will be stronger than if we were to place it in either the p, or p, orbital, because of the greater distance between the orbital lobes and the spatially restricted negative charge in the latter cases. The consequence is that an electron in the p orbital will feel a stronger interaction than one in the p, and p, orbitals, resulting in loss of degeneracy, the latter two orbitals becoming lower in energy that the former orbital; moreover, the latter two are also of equal energy because they are spatially equivalent relative to the fixed negative charge location. The outcome is an energy diagram as shown in Figure 3.8. The p. orbital has been raised in energy relative to the spherical field case (commonly taken as the zero reference point), whereas the p, and p, orbitals are lowered in energy relative to this reference point. Moreover, the model actually leads to the p orbital being raised twice as much as the two other orbitals are lowered, so that the overall effect is energy-neutral, in the absence of insertion of electrons into the assembly. The spatially-defined negative charge field introduced has removed or lifted the degeneracy of the p orbitals that existed in a pure spherical field. The situation we have described is not met in reality since the central atom in a coordination compound does not normally

Figure 3.8 The concept of crystal field influences applied for purely illustrative purposes to a set of p orbitals. The directional field here results from imposing a specific interaction along the z axis alone.

employ only a set of p orbitals as its valence orbital set. Usually, we are dealing with central atoms with a set of d orbitals as the highest occupied energy levels employed.

The situation in the case of d orbitals is somewhat greater in complexity because there are now five orbitals involved, and these orbitals have distinctly different characteristics. Whereas all p orbitals look the same and have orbitals directed in an identical manner along an axis, this is not the case with d orbitals. There are a set of 'triplets': the day, d and dy orbitals, that each look like a four-leaf clover and whose lobes point between axes of a three-dimensional coordinate set centred on the metal ion. Another orbital (d,2,2) looks identical, but locates its orbital lobes along the x and y axes. The final member (d) is unique in appearance, and locates its major lobes along the z axis. Despite these differences, they form, in the absence of any field, a degenerate set - or put simply, they are all of equal energy. In a symmetrical spherical field of charge density the outcome is no different from the initial behaviour for the p orbits; simply, all orbitals are raised in energy equally, remaining degenerate. However, when point charges are introduced in specific locations, this degeneracy is removed. In a situation where six point charges are introduced symmetrically along the x, y and z axes, each equidistant from the central ion at the vertices of an octahedral array (perhaps the most common shape met in coordination chemistry), an entirely different outcome to the spherical field situation results. Because the d and d orbitals have lobes pointing along the axes, they interact most strongly with the ligand point charges, and their energy is raised as a result of this. The interaction for the other three is significantly less - less, in fact, than they felt in a spherical field since there is no charge density close now - so that they effectively drop in energy versus the spherical field. The three orbitals that point their lobes between axes, day, dye and dyz, are shaped identically and oriented in the same manner relative to a different pair of axes; consequently, it is hardly surprising that they experience identical effects and remain degenerate in the octahedral field. However, it is notable (Figure 3.9) that the d, and d orbitals also end up as degenerate despite their apparent differences in shape. How can this be? While it could be said, simply, that it just works out that way, this is hardly a satisfying outcome. The answer lies deep within the mathematical derivation of the atomic model and orbital functions, and mathematical detail is something we are doing our best to avoid here. However, there is a certain simplicity and logic here that we can inspect without recourse to mathematics. It

Figure 3.9

Crystal field influences for a set of d orbitals in an octahedral field.

turns out that the d orbital is in reality a linear combination of two orbital functions d_z²_-y² and d_z²_-y² that are shaped just like the separate d_x²_-y² orbital, but oriented differently. It is then less surprising that the composite we see as the d orbital is energetically identical to the d orbital. But if you're now wondering why these orbital functions need to be combined in the first place - well, that's a story you simply won't find here.

The outcome of the introduction of a defined spatial arrangement of point charges, here an octahedral field, is that the degeneracy of the five d orbitals is removed, and the orbitals arrange themselves in new sets of differing energy. The d orbitals pointing directly towards the ligands (d_x²_-y² and d_z2) and thus along what are the M-L bonds, can be considered to be involved in a traditional σ bond; they sometimes are referred to as d orbitals. The three remaining and more stable orbitals (dxy. dyz and dxz) point away from the M-L bond direction, but may possibly be capable of involving themselves in π-type bonding, and as a consequence are sometimes called d orbitals. However, this view is mixing conventional covalent bonding thinking with a purely ionic model, and thus is problematical, and we shall largely avoid it.

The formation of doubly and triply degenerate sets of orbitals is a characteristic of the octahedral field. Because it is the spatial location of the set of point charges that is significant in generating this outcome, it will hardly come as a surprise to find that every different shape arrangement of point charges will lead to a different characteristic outcome - but more on that later. At present, focusing on the octahedral field, the outcome shown in Figure 3.9 applies. The lower energy set of three orbitals (dxy. dyz and dxz) is called the diagonal set (or, applying mathematical group theory, which we shall not develop here also called t2g where t stands for triplet degeneracy) and the higher energy set of two orbitals (d_x²_-y² and d_z2) is called the axial set (or from group theory eg a doublet level), the names relating to where the orbitals point versus imposed axes. The energy difference between these levels is, compared with the differences between atomic orbital levels generally, relatively small, in line with the influence of the ligand set being a relatively modest one. This energy difference is called the crystal field splitting, represented by a parameter termed A. (where the subscript 'o' is an abbreviation for 'octahedral'). An energy balance between the two sets of orbitals is struck, so that the three lower levels are -0.4 Δ_O lower and the upper two levels +0.6 Δ_O higher than the spherical field position set as the zero reference point. The language of chemistry contains several dialects, and you will find some texts refer to the energy gap Δ_O  as 10Dq (with the diagonal and axial sets lowered 4D or raised 6D respectively); don't be confused as the same conceptual model is being applied. Using the A symbolism is more appropriate, since it carries some additional information that defines the type of field operating in the subscript.

One key question that begs an answer at this stage is simply what factors govern the size of Δ_O? Answering this should give us the satisfaction of being able to predict certain spectroscopic properties. Obviously, since we are involving both metal and ligand in our complex, we can anticipate that both have a role to play. If we fix the metal's identity then we can focus on the ligands, and their particular properties that influence A. For octahedral complexes of most first-row transition metal ions at least the presence of colour suggests that somehow part of the visible (white) light spectrum is being removed. This can be envisaged if the energy gap between the diagonal (12g) and axial (eg) levels equates with the visible region, leading to absorption of a selected part of the visible light that occurs to cause the complex to undergo electron promotion from the lower to the higher energy level. Simply by monitoring the change in colour as ligands are changed we can determine the energy gap Δ_O applying for any ligand set. The stronger the crystal field.

the larger Δ_o and hence the more energy required to promote an electron, leading to a higher energy transition, seen experimentally as a shift of the absorbance peak maximum to shorter wavelength. This allows us to rank particular ligands in terms of their capacity to separate the diagonal and axial energy levels. This has been done to produce what is called the spectrochemical series. For some common ligands that bind as monodentates to a single site, this order in terms of ability to split the diagonal and axial energy levels apart is of the form:

I^-<Br^-<SCN^- < C^-< s^2- <NO^- <F^- <HO^- <OH2 <NCS^- <NH₃ <NO^2- < PR3<CN^- <CO.

Notably, this order is just about independent of metal ion in any oxidation state or even adopting any common geometry.

The problem is that this experimentally-based trend does not sit comfortably with the crystal field model. For example, this trend indicates that an ion like Br is far less effective than a neutral molecule like CO at splitting the d-orbital set, which is at odds with a model based on electrostatic repulsions, in which one might expect a charged ligand to be more effective than a neutral one. Of course, electronegativities dipole effects and even size may be invoked as contributing to the difference, but these are hard to see as overriding effects, particularly when the O-donor anion HO turns out to be a weaker ligand than its larger, neutral O-donor parent water (H2O) and ammonia is a stronger ligand than water despite having a smaller dipole moment and larger molar volume. Something is not quite right with the CFT world.

The CFT, while useful, simply suffers most from being based on a concept of point charges. Real ligand donors have size - and along with size comes the strong possibility of the donor group or atom undergoing deformation of its electron density distribution simply as a result of being placed near a positive charge centre. In effect, you can think of this as a shift of electron density towards the region between the metal and the donor, or what we would think of as happening when a covalent bond forms. While the outcome here is far from covalent bond formation, there is an introduction of some covalency into the otherwise purely ionic bonding model - think of it as dark grey, rather than purely black. In fact, if we see black and white as the two extremes of ionic and covalent bonding, rarely is one of the extremes applicable; it seems chemistry, like life, is full of compromise. The outcome of allowing some covalency in the model is a fairly minor perturbation, not a drastic change - except the theory morphs into ligand field theory to distinguish the changes introduced.

اخر الاخبار

اخبار العتبة العباسية المقدسة

أساتذة المجمَع العلمي يشرفون على تحكيم المسابقة القرآنية في جامعة النهرين

قسم الشؤون الدينية ينشر صناديق مخصصة لزكاة الفطرة داخل مرقد أبي الفضل العباس (عليه السلام) وخارجه

شعبة التوجيه الديني النسوي تختتم مجالسها العبادية لإحياء ليالي القدر المباركة

قسم الشؤون الفكرية ينظم ندوة توعوية ثقافية في محافظة ذي قار

المزيد

الآخبار الصحية

تأثير اللياقة البدنية على الدماغ

تجربة سريرية تظهر فوائد اللوز للمصابين بالسمنة

اكتشاف طريقة غير متوقعة لتقليل خطر الإصابة بالسكري

خمسة مؤشرات صحية مهملة قد تنقذ حياتك

المزيد

الآخبار التكنلوجية

علماء الجيولوجيا يفكون لغز الصدع العملاق تحت الماء في المحيط الأطلسي

تحذير جديد: الاحترار العالمي يتسارع وقد نكسر حاجز 1.5 درجة قبل 2030

الصين تكشف عن ألياف كربون تفوق قوة الفولاذ بـ10 مرات

الجهاز المناعي يظهر دورا غير متوقع في صحة العظام

المزيد

مواضيع ذات صلة

A Covalent Bonding Model - Embracing Molecular Orbital Theory

Holding On - The Nature of Bonding in Metal Complexes

Complex Shape - Not Just Any Which Way

The Foundation of Coordination Chemistry

Photo-Oxidative Degradations of Polymers

Oxidation of Step-Growth Polymers

Hydrolytic Degradation of Polymers at Elevated Temperatures

The Termination Reaction

صناعة حمض الكبريتيك

تركيب حامض الكبريتوز

كلوريد الثيونيل Thionyl Chloride

حامض الكبريتوز: Sulphureous Acid