Is the hybridization of nickel pentacarbonyl possible?

Coordination Chemistry (AC3)

when and where?

2 SWS, Fri 9–11, (initially) as an online course, (later perhaps Willstätter lecture hall,)
Start: April 16, 2021, end: July 16, 2021
next date: SS 2022.

The lecture will start as an online course again this time. To participate, please register in the LSF. This gives me access to your email address. Before the first lecture, you will receive a link via email that will enable you to participate.

I use zoom, you can hear me, but I mute you and turn off your video too. You will see the pdf version of the script. While I'm telling the story, I scroll through the script and attach what I would otherwise have written on the board as a note in the pdf. If you want, you can download the pdf file without notes and add your own text. Unfortunately, there is no expression concerned by the student council this semester. I also put the pdf file with my notes online (see below).

The lecture period is 45 minutes twice, so we take a break from 10:00 to 10:15. During this break, the circuit simply continues, so that you can then use the chat function to ask questions. I'll try to answer these questions immediately. The second option is from 11:00 to 11:15 after the end of the lecture; I then leave the connection open for a quarter of an hour for chats that will be addressed at the next appointment. If there is something afterwards: as always by email.

There are two options for printing out the script for the SS2021. On the one hand, you can download the unedited version (last changed: April 15, 2021), or you can download an annotated version with an added "blackboard picture".

Please note a legal notice for all questions relating to the storage and dissemination of the presented content.

for whom and why?

a) Bachelor's degree Chemistry and Biochemistry: Students in the 4th semester.

b) Chemistry teacher training course: students in their 6th semester.

The lecture teaches the basics of coordination chemistry and prepares students for lectures in bioinorganic chemistry and organometallic chemistry in the bachelor's / master’s degree. For student teachers, the lecture is preparation for the research internship. The previous education of bachelor's and teacher training students is largely equivalent in relation to this lecture, except that the theory of symmetry has not yet appeared in the teaching curriculum. That is why there is a double lesson for higher educators in which the necessary information about the common point groups and how to use character tables is given - usually shortly before the MO scheme of an octahedral complex. There is some teaching material for this double period.


The 1st exam for the summer semester 2021 will take place on Thursday, July 22, 2021, 10:15 am - 11:45 am, in the Liebig, Buchner and other lecture halls.

The 2nd exam for the summer semester 2021 will take place on Friday, October 1, 2021, 8: 15–9: 45 am in the Liebig and Buchner lecture hall.

Please note the rules for registration: (1) Only students who have previously registered via LSF are allowed to take notes. If there are any problems with the registration, please contact the examination office, but not the lecturers of this lecture, as we do not have access to your LSF data. Please bring your student ID with you to the exam. (2) Anyone who has registered and does not appear for the exam receives the rating “failed”. (3) Please do not come to the exam just to see what is being asked, so that you can hand in an empty paper after a quarter of an hour. The exam will appear online soon after the date. All previous exams are already there, so that you can see what is typically asked.

For the exam you should have the main and subgroups of the periodic table in mind; you do not need to memorize the lanthanides and actinides for this lecture.

Old exams:


In the lecture Coordination chemistry the basic principles of complex chemistry are dealt with, with the emphasis on transition metals.


You can find many introductory things in the book Coordination Chemistry - Basics and Current Trends by Birgit Weber (Springer, 2014, ISBN 978-3-642-41684-2), which you can also download as a pdf with your e-media access to the Munich University Library (click on the link, then your e-media Download the bookmarklet, or via e-media to OPAC, search for and download the book).


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Computational chemical calculations are usually carried out with Orca. If coordination compounds or ions are calculated that are actually present in aqueous solution, the CPCM model implemented in Orca is used with standard parameters, and van der Waals interactions are also taken into account using Grimmes' method. Paramagnetic complexes are calculated “unrestricted” in DFT calculations (α and β spins with different energies). In the case of the individual figures, the method and basic sentence are given in the usual notation; For example, bp / def2-tzvp stands for the pure (not hybrid) density functional BP86, def2-tzvp is one of the Ahlrichs basic sets. A typical input file for Orca, with which a structure optimization of the hexaammine iron (II) ion is triggered, can be used for recalculation (details of the calculation: 1st line: uks [unrestricted Kohn-Sham], bp [BP86 method], ri [technical detail], d3 [Grimmes van der Waals correction], def2-tzvp [basic set], def2 / j [auxiliary basic set for ri], tightscf [technical detail], opt [structure optimization, computer chemists say "geometry optimization"] , cpcm (water) [structure of a water-like environment]. The next four lines take care of the transfer of all necessary information to the output file in order to be able to view orbitals. The input of the molecule begins with "* xyz 2 5": xyz means Cartesian coordinates on, 2 is the charge, 5 is the multiplicity).

Gabedit is recommended as a graphical tool for operating Orca, with which the images for the Orca invoices were created; also very nice: Avogadro.

Aqua complexes

Complex compounds are Lewis acid-base adducts - with significant effects on the Lewis base. Water molecules as ligands show this principle, which is the basis of metal catalysis, particularly clearly.

The dative (coordinative) bond

What is the difference between an atomic bond and a dative (coordinative) bond? How far does the similarity go between isosteric molecules like ethane, H3C-CH3, and ammonium borane, the ammonia adduct with borane, H3N → BH3 or H3N+-BH3? Dative bonds and "normal" bonds (atomic bonds and ionic bonds) differ in the different ways in which they disintegrate when the bond dissociation energy is supplied. Dative bonds are created by the bond dissociation energy heterolytic split, normal bonds homolytic (this also applies to ionic bonds; the yellow flame color of sodium chloride is caused by the excitation of the 3s valence electrons of sodiumatomsthat arise during the thermal cleavage of the salt!).

We repeat another detail of the basic lecture: is it in a salt like Na [AlCl4] makes sense, a distinguish coordinative bond from three normal bonds?

Coordination links

Will the Lewis acid bra3 replaced by a metal cation which, depending on its size and charge, is also more or less Lewis acidic, and which usually binds more than one molecule of the Lewis base, a coordination compound is obtained, including a complex compound, metal complex or the like called. The Lewis acid is called Central atom, the bases are the Ligands. The binding of a ligand to a central atom changes the properties of the ligand drastically. This experience forms the basis of the Metal catalysis: in the Organometallic chemistry as the basis for technical catalysis in which Bioinorganic chemistry as a basis for understanding Metalloenzymeswhich make up about half of the known enzymes.

Aqua-, hydroxido and oxido complexes

One of the most important ligands is water, which is a Lewis base because of the two lone pairs of electrons on the oxygen atom. An important property of water, its Brønsted acidity, is a parameter that is greatly changed by the bond to the central atom. So the pKA.- Value of the very weak acid water shifted from 15.7 to the range of strong acids when a water molecule binds as a ligand to a strong Lewis acid. When deprotonating these acidic Aqua complexes metal-bound hydroxide is formed, Hydroxido ligands. Hydroxido ligands are often better ligands over a second metal ion than free water molecules, so hydroxido ligands are often considered Bridging ligands being found.

The processes involved in the precipitation of aluminum hydroxide by gradually alkalizing an acidic aluminum (III) salt solution can be viewed in this sense. Species distribution diagrams, in which the complexes occurring in an interesting pH range are shown, show that due to the multiple formation of hydroxido and also oxido bridges multinuclear complexes are formed. An example of a particularly important species in the neutral range is the thirteen-core aluminum complex [Al13O4(OH)24(H2O)12]7+, which is broken down to tetrahydroxido-aluminate when the pH value is further increased (note the Protonation from oxido ligands to hydroxido ligands Basesadmission!). The structure of the 13-nuclear cation is shown in Figure 3 of. Also note the common construction principle of other hydroxidoaluminium clusters. Figure 2 in shows with NMR spectroscopy a particularly important experimental approach to this chemistry.

The following picture shows such a [Al13O4(OH)24(H2O)12]7+-Ion. Since the positions of the hydrogen atoms were not determined experimentally, the assignment of oxygen atoms to aqua, hydroxido or oxido ligands only results from the charge balance (so that 7+ comes out). The oxido ligands are the four ligands that coordinate the tetrahedral Al atom in the center of the cation. These four oxido ligands are also tetrahedrally surrounded by aluminum central atoms - they are four-fold bridging. This can also be expressed in the formula: [Al134-O)42-OH)24(H2O)12]7+. Instead of μ2 a simple μ is also sufficient: [Al134-O)4(μ-OH)24(H2O)12]7+.

As a transition to the next chapter, we consider a species distribution in an aluminum salt solution with a total concentration of 5 μm. The ordinate is divided into percent, the thirteen-nucleus ion is shown in violet−1 is a missing proton, here a hydroxide ion, H−2 could then be one oxide ion or two hydroxide ions; H−32 encodes the O4(OH)24Part of the 13-nuclear anion, AlH−3(s) is solid aluminum hydroxide]:


W. H. Casey:
Large Aqueous Aluminum Hydroxide Molecules.
Chem. Rev.2006, 106, 1–16.
doi: 10.1021 / cr040095d

Law of mass action and complex formation

Inset: designation of complex compounds

Water as a ligand is called “aqua”, ammonia “ammin”, hydroxide “hydroxido” - it has the ending “o” like all anionic ligands (fluorido, chlorido, sulfato, nitrato, ...). The number of ligands is usually given in Greek (mono, di, tri, tetra, penta, hexa, ...) and the ligand name is appended without brackets; [Al (H2O)6]3+ is therefore the hexaaqua aluminum ion. Especially if the ligand name itself begins or could begin with a numerical word, the count is different (bis, tris, tetrakis, pentakis, ...) and the ligand name is enclosed in brackets so that there is no confusion: This is how the complexes of the detergent additive triphosphate are called triphosphato Complexes, while complexes with three orthophosphato ligands are called tris (phosphato) complexes to distinguish them. If the complex is an anion, the central atom is named in neo-Latin and given the ending "-at": [Al (OH)4] is tetrahydroxidoaluminate.

The current (2005) nomenclature is summarized in detail in IUPAC's Red Book. A short version of this text is also available.

Constants of resistance

Preliminary exercise: We make the species distribution curve for the NH system4+/ NH3 clear and we're talking about dealing with units.

If the law of mass action is applied to the formation of a complex from the central metal in its standard state (usually the aqua complex) and the ligands, constants of resistance are obtained. Usually just has to a Concentration can be measured in order to calculate the constant, since mass balances apply. For example, intended for a simple complex formation reaction

M + L ⇄ ML

the constant of resistance

are determined, then boundary conditions apply, which result from the initial concentration C., the amount of metal and ligand used per volume, namely:

C.(M) / mol L−1 = [ML] + [M]


C.(L) / mol L−1 = [ML] + [L]

(now and in the following all charges are omitted; H stands for H.+). A protonatable ligand - as a rule - introduces further equations into such mass balances. With

and the extension of the equation for C.(L) to

C.(L) / mol L−1 = [ML] + [L] + [HL]

it becomes clear that the only variable to be measured can also be [H], ultimately the pH value. The titration of an acidic solution containing the metal and the protonated form of the ligand with alkali while measuring the pH value after each addition of alkali is therefore the standard method for determining complex formation constants. In principle, the competition between two Lewis acids for the Lewis basic ligand is considered: on the one hand protons, on the other the metal of interest.

Resistance constants are here without exception in the form of Gross resistance constants (β) specified. For the tetraammine copper (II) ion [Cu (NH3)4]2+ (abbreviated CuN4) this is defined as, for example

Many other parameters can be derived from resistance constants: Species distribution curves can be drawn up for different starting concentrations of ligand and metal, so that complex solution equilibria can be displayed in a clear form, such as those in the aqueous system Cu2+/ NH3 are present.

Species Distribution Curves

The figure shows such a species distribution diagram for an aqueous solution that has a total concentration of 0.05 mol L.−1 Copper (II) and 0.5 mol L.−1 NH3/ NH4+ contains. The NH3/ NH4+Excess and the total concentration are chosen so large that no copper (II) hydroxide precipitates around the neutral point. The species distribution in a solution that is obtained by adding ammonia to copper (II) salt in the specified concentration can be read on the right-hand edge of the diagram (pH approx. 11).

To draw the graph, the following gross persistence constants were used for the species CuiNj and the ionic product of water with 10−14 and the pKA.-Value of the ammonium ion with 9.53 inserted:

ijlog β
11 4.0
12 7.4
13 10.2
14 12.0
15 11.1

Chelate effect and macrocyclic effect

Strikingly large constants of resistance are found in Chelate complexes certainly; these are usually a few powers of ten larger than those of related complexes with monodentate ligands (these are ligands for which a Atom creates a bond to the metal). This Chelate effect is essentially an entropic effect, since a chelating ligand releases two or more monodentate ligands in solution equilibrium, so that the greater disorder in the system prevails on the side of the chelate complex. The is explained in the same way macrocyclic effect, which we talk about when all the atoms of a multidentate ligand are part of a ring. Two of these macrocycles, which are important as ligands, are [14] aneN4 (also: cyclam) and [12] aneN4 (also: cyclen), a 14- and a 12-membered ring made of CH2-Groups in which four CH2-Groups are replaced by nitrogen atoms:

When comparing the constants of resistance of the [CuII(cyclen)]2+Complex (lg β = 23.3) with the complex [CuII(trien)]2+ (lg β = 20.1) of the open-chain N4-Liganden triene (formula below), which is formally guaranteed by the removal of an ethylene group from cyclene, it becomes clear that entropy can not only be found in the sheer number of particles, but also in the mobility of a molecule.

Incidentally, it is not that easy to build such large rings using standard organic chemistry. One possibility to use the high tendency to form chelate complexes for the production of such macrocycles is that Template synthesis, with which cyclam can also be built up (can you suggest a method to build cyclam from a complex of the open-chain precursor 3,2,3-tet? 3,2,3-tet is N,N'-Bis (3-aminopropyl) ethane-1,2-diamine).

The chapter closes with a reference to the Irving Williams series and an introduction to the HSAB conceptthat was originally derived from complex formation constants.

Chelating ligands

Finally, a brief overview of multidentate ligands is given. Under the bidentate ligands - these would occupy two cis coordination positions with octahedral coordination - are common: ethylenediamine (en), 2,2'-bipyridine (bpy), 1,10-phenanthroline (phen), oxalate (ox), the anion of diacetyldioxime = Dimethylglyoxime (dmg), the anion of oxine = 8-hydroxyquinoline (hych) and the anion of acetylacetone (acac).

Tartrates (as ligand: tart), the dianions of the various tartaric acid isomers (meso-, d-, and l-tart) are an example of how diverse the binding possibilities of a ligand can be. (For exercise, draw d-, l-, and meso-Tartrate.) The form shown is found in weakly acidic solution with excess tartrate, if the Lewis acidity of the central metal is not too high. If it is high or if the solution is neutral to slightly alkaline, the coordinating OH group is deprotonated. If the solution is strongly alkaline, the two middle O atoms bind the central metal in a deprotonated form - so copper (II) is present in Fehling's solution, namely as [Cu (l-tartH−2)2]6−. If tartrate is not added in excess, four O atoms of the tartrate ligand, which is then tetradentate, can bind to two metal atoms (indicated by dashed lines in the figure).

Tridentate ligandsthat can cover an area of ​​an octahedron (faciale arrangement, in formulas fac) are diethylenetriamine (diene), more reliable hydrido-trispyrazolyl-borate (tpb); those that have the second possible arrangement on the octahedron - the meridionale (in formulas: mer - can realize are dien or the dianion of O,O'-Dipicolinic acid (dipic). Note that the bidentate en is supplemented by an aminoethyl residue for dien.

This is a ligand that is important in nature and technology Triphosphate anion. In technical cleaning agents it is still used today as an effective ligand for calcium ions, i.e. to mask the hardness components in water. The complex is similar to a structurally elucidated calcium complex in which the central ion is coordinated by two adenosine triphosphate ligands. In the picture, the two adenosyl residues on the triphosphate of the ATP are omitted (the C5 'atoms on the two ribose residues bind to the leftmost O atom shown):

Known tetradentate ligands are triethylenetetramine (triene), tris (2-aminoethyl) amine (tren) and nitrilotriacetate (nta). Note the isomerism between trien and tren. Triene is formed from diene by aminoethylation of one of the two outer N atoms, tren by addition of an aminoethyl function to the middle nitrogen atom of diene.

Ethylenediaminetetraacetate (edta) can form up to six coordinative bonds.

The octahedral coordination that is possible with the hexadentate edta ligand looks similar to what was found in a structural analysis of crystals of a chromium (III) complex with the homologous ligand ethylenediamine triacetate propionate (only the chromate ion is shown; note the carboxyethyl instead of a fourth carboxymethyl substituent):

Animate nature applies the same principles to build particularly stable complexes. Bacteria aggressively acquire iron, which is essential for their growth, by using the hexadentate ligand Enterobactin release. The iron (III) complex contains three bidentate Catecholato ligandsthat are spatially fixed by a triserin cycle (to date, the structure of the iron (III) complex has not been determined by crystal structure analysis; however, the depicted vanadium (III) complex should have the same structure):

Do you recognize special interactions in the picture that contribute to the rigidity of the ligand?

Rate and mechanism of ligand substitution

Inert and labile complexes

The sufficiently high resistance constants of the ammine-copper (II) complexes mean that when an excess of ammonia is added, these blue, soluble complexes are formed and instead of the increase in pH copper (II) hydroxide precipitates - which with a small amount of ammonia, yes can also be observed. An aqueous acidic solution in which hexaaqua-chromium (III) ions, [Cr (H2O)6]3+, present, behaves differently. A small amount of ammonia solution also precipitates the hydroxide here, namely Cr (OH)3 - due to the same processes as with aluminum (see above). The hydroxide is very sparingly soluble, its solubility product is:

L. = [Cr3+][OH]3 = 6.7 × 10−31

But the hexaammine-chromium (III) complex is also extremely stable, so that the formation of this purple complex can be expected. In the experiment - which is also part of the separation process - the hydroxide is produced (the formation of the ammine complex to be expected is treated as a disruption in Jander-Blasius!). This case, that something should happen, but does not happen based on the thermodynamic data, is known from simple experiments in the basic lecture: For example, ammonia should burn in air to form nitrogen and water - but what does not happen at room temperature: the ammonia-air mixture is metastable, i.e. the process under consideration requires a certain activation energy, which is not available under the conditions under consideration. This is exactly what happens in the chromium example: the equilibrium setting in the ligand substitution equilibrium

[Cr (H2O)6]3+ + 6 NH3 ⇄ [Cr (NH3)6]3+ + 6 H.2O

is by an unusually high Activation barrier with special needs. In contrast to the aqueous Cu2+/ NH3-System in which no activation barrier is recognizable for ligand exchange - the copper complexes are unstable -, are the chromium complexes inert. In practice, one speaks of inert behavior when the expected reaction takes minutes or longer. The thermodynamic statement (stable or unstable) must be strictly separated from the kinetic statement (labile or inert) (the term "metastable" is unfortunately not very helpful): The ammine copper complexes are stable and unstable, the chromium complexes are stable and inert - the thermodynamic quantity is completely independent of the kinetic one! However, there seems to be a contradiction: if the exchange of aqua for amine ligands is greatly slowed in chromium (III), why is the transition from aqua to hydroxido ligands as fast as in aluminum and iron (III), the two other ions that fall as hydroxides with ammonia or urotropine - in a fraction of a second? Answer this question yourself by considering the formation of hydroxido ligands from aqua ligands by deprotonation of the latter: In order to precipitate chromium (III) hydroxide, no (inert) Cr-O bonds have to be broken!

Mechanism of ligand substitution

How does a ligand substitution reaction proceed in detail? The rate of exchange of aqua ligands has been studied for a large number of central metals. In the individual steps of ligand substitution, the dissociative of the associative progressive substitution can be distinguished if the activation volumes are known from the reaction rates measured as a function of pressure. It turns out that the ligand exchange in octahedral complexes is more dissociative, i.e. one of the six ligands leaves the complex before the new ligand enters. One of the control parameters of this process can be expected due to the electrostatic attraction between the central metal and the ligand, namely the charge density on the central metal. The larger this is, the more the cleavage of a ligand should be hindered. A comparison with other trivalent central metal atoms such as aluminum shows that for chromium (III) the very slow ligand exchange observed there is not adequately explained by the charge alone. The chemical bond in coordination compounds is therefore examined in more detail below.

The electronic structure of coordination compounds

The chemistry of the coordination compounds of the first transition series, in which the 3d level is filled, is determined by the interplay between Hund's rule (high-spin complexes) and the structural principle (low-spin complexes). In the second and third transition series, on the other hand, high-spin complexes hardly play a role, since here the metal-ligand bonds dominate over the spin pairing energy.

In the following we recognize some of the factors that contribute to the structure and the electron distribution of a coordination compound in quantum chemical calculations on the hexaammine iron (II) cation. An ammine complex is selected for this first introduction, since metal-ligand π interactions are irrelevant here, then we come back to the hexaquachrome (III) ion.

The hexaammine iron (II) cation - a quantum chemical analysis

The stability of ammine complexes varies greatly. While the divalent ions of cobalt, nickel, copper and zinc form ammine complexes in aqueous solution, very high ammonia concentrations are required in the case of iron, and the manganese complex has so far only been crystallized from liquid ammonia. We won't ask why this is so until later. Here first the result of a quantum chemical calculation on the hexaammine iron (II) cation with a pure density functional. Crystal structure analyzes show an octahedral complex cation with Fe-N distances of 2.206 (8) in the chloride and 2.215 (3) Å in the bromide.

The result of the calculation shows a very weakly elongated octahedron in which the four Fe-N bonds in a plane (xy) are 2.210 Å, while the two remaining bonds (along z) are 2.225 Å long.

The following scheme results for the frontier orbitals of the hexaammine iron (II) complex (for numbering: the complex contains 24 + 6 × 10 = 84 electrons; when the electrons are assigned to iron 3d orbitals according to Hund's rule, 4 unpaired electrons remain, So there are 44 α and 40 β spins).

Occupied frontier orbitals of a [Fe (NH3)6]2+-Complexcations in a DFT calculation. α and β spin orbitals are listed separately. The complex is slightly stretched along z (technical note: bp / def2-tzvp, orbitals drawn with 0.04 isovalue).

The α spin orbitals look like this (z is the vertical axis):






The only occupied 3d β spin orbital has the following shape; it becomes clear that the 42a-α-electron and the 40b-β-electron occupy the same orbital:


Now to the deeper meaning of it all: we put together a series of observations that we then want to analyze. The following peculiarities can be recognized:

• d-orbitals of type xy, xz and yz are non-binding, while x2-Y2 and Z2 Fe-N antibonding.

• The calculation uses extensive linear combinations, 40b is clearly made up of approximately equal parts from xz and yz.

• Spin pairing and ligand influences lead to comparable orbital energy changes in the iron (II) complex: among the α-spin orbitals, the orbital 42a loaded by the β-spin is similarly destabilized as the two Fe-N antibonding orbitals 43a and 44a.

• The β-spin electron is the most unstable (Hund's rule). This would be removed during the oxidation to iron (III).

• The z-axis, along which a slight stretching of the octahedron was calculated, comes closest to the doubly occupied orbital. We will learn more about this phenomenon when we discuss the Jahn-Teller distortion.

In sum, it can be said that the orbital scheme reflects two dominant influences: the spin pairing energy and the metal-ligand interaction. In the following, these two parameters are first examined in detail in order to then add two more important influencing variables: the Jahn-Teller distortion, which is significantly more dominant in many complexes than in the hexaammineiron (II) example, and metal-ligand π interactions, which play no role in ammine complexes.

The spin pairing energy

Typical energy values ​​for the electron repulsion (including the spin pairing energy) in transition metal centers can be obtained if the calculation on the amine iron dication for the free Fe2+-Ion is repeated. In the following scheme, only the frontier orbitals are taken into account. An iron dication has a total of 24 electrons. The frontier orbitals are the 3d orbitals (the 4s orbital is only occupied by the free atom). When they are filled, according to Hund's rule, 14 α and 10 β spin electrons result.

Occupied frontier orbitals of a Fe2+-Ions in a DFT invoice. α and β spin orbitals are listed separately. The axes are chosen arbitrarily and do not correspond to the axis selection in the illustration of the complex! (Technical note: bp / def2-tzvp)

In order to be able to compare with the scheme of the ammine complex, we note that the ordinate extension is the same for both schemes. At first, no importance is attached to the energy values ​​themselves (we will see that the destabilization of the iron orbitals in the complex has to do with a simple charge shift ["electronegativity compensation"]). We discuss the energetic sequence in terms of a different repulsion between the 3d electrons.

d orbitals

You will get used to the very informal handling of quantum chemical software with the linear combination of orbitals if the common representation of d-orbitals is examined more closely.

The spatial orientation of the five orbitals of a shell depends on the indices xy, xz, yz, x2 - y2 and Z2 from; the form that falls out of line at first glance in z2-The case comes about through the arithmetical superposition of orbitals that correspond to the orbital with the index x2 - y2 correspond, namely z2 - x2 and Z2 - y2; instead of the short form z2 therefore sometimes the extensively written sum 2z2 - x2 - y2 or 3z2 - r2 with r2 = x2 + y2 + z2 used.

The crystal field theory - a first approach to the metal-ligand interaction

Now back to the hexaquametal (III) complexes. The basic state of the d3-Ions Cr3+ is [Ar] 3d3. In order to examine the valence shell in more detail, we begin our consideration with a similar trivalent ion, but which has only one d electron, namely Ti3+ with the electron configuration [Ar] d1. The d electron can choose between 5 d orbitals of the same energy.

The crystal field splitting of an octahedral complex

Becomes the Ti3+Ion and 6 water molecules of the complex [Ti (H2O)6]3+ formed, this has an impact on the energy of the individual d orbitals of titanium. The simplest model that can be used to describe the changed energy scheme for the d orbitals is the crystal field model - an electrostatic model in which the ligands are viewed as negative point charges (6 × •), whose repulsion with the d electrons is observed . In this repulsion model, the five d orbitals fall into two groups. The higher repulsion and thus the higher energy show electrons in the x2-Y2- and in z2-Orbital, the orbital lobes of which are precisely aligned with the approaching point charges. Electrons are repelled less in the three xy, xz and yz orbitals with the same energy, whose orbital lobes are more favorably located between the negative point charges.

With octahedral symmetry (point group OH) the two less stable orbitals have the symmetry symbol eG, the three orbitals that are lower than the center of gravity have the symmetry symbol t2g. The energy difference between the two orbital groups in the octahedral complex becomes 10 Dq or ΔO called. Since in the d1-If there is no need to consider electron repulsion within the 3d sub-shell, the following diagram comes close to an orbital scheme. It should be noted above all that the increased repulsion occurs along the axes where an antibonding interaction has been formulated in the molecular orbital scheme.

The color of a d1-Complex

The possibility of a d electron to absorb light energy, thereby overcoming 10 Dq and so of its t2g-Ground state for a short time in the excited eG-State change (to then return to the ground state with the release of energy) is one of the reasons for the color of transition metal complexes. In order for the example of [Ti (H2O)6]3+-Ions to describe the color quantitatively, a solution is required that certainly only contains this one colored species, for example a clearly acidic solution of titanium (III) perchlorate in perchloric acid (why not hydrochloric acid, why acid at all? Compare the reactions of the hydrated aluminum ion).The absorption spectrum of this solution shows a broad band extending over the entire visible range, the absorption maximum of which is around 500 nm (maximum absorption with yellow, the eye then sees the complementary color violet).

The intensity of the absorption is approx. 5 L mol−1 cm−1 quite low. In the ultraviolet range, the absorption then increases again sharply. While the cause of the UV absorption will only be discussed in a further teaching unit together with the observation of why the color of the solution is only pale, the crystal field model will continue to be used here. The wave number of approx. 20,000 cm−1, at which the highest absorption is measured, is equated with 10 Dq for the hexaaquatitane (III) ion. It is common to use the abscissa in wave numbers - the reciprocal of the wavelength - in cm−1 because these are a unit of energy. In doing so, it is mostly carried away from the higher to the lower energy - i.e. with increasing wavelength. In order to convert a wavelength λ in nm (nanometers) into a wave number, 1 cm = 107 nm, 107 nm cm−1 divided by λ. The visible spectrum therefore extends from 25,000 cm−1 (= 107 nm cm−1 divided by 400 nm) up to 12500 cm−1 (800 nm). The width of the band is indicated by the oscillations of the ligands relative to the central metal. In the case of the most symmetrical oscillation, in which all six ligands swing towards and away from the central metal at the same rate, 10 Dq becomes larger and smaller at the rate of the oscillation - the observed broad band arises. Another clearly visible property of the absorption band - its asymmetrical shape - is taken up in the chapter "Jahn-Teller distorted complexes".

The crystal field stabilization energy in the crystal field model

The next observation, which should be interpreted with the help of the crystal field model, is the kinetic inhibition of ligand exchange in chromium (III) complexes, which is at the beginning of the observation. In the series of hexaqua complexes [MIII(H2O)6]3+ with MIII = Sc, Ti, V, Cr the Aqualigand exchange rate slows down very clearly with the number of d electrons in the series Sc3+, Ti3+, V3+, Cr3+, 0, 1, 2 and 3. The number of d electrons also changes an important energy variable that can be derived from the crystal field model, namely the crystal or ligand field stabilization energy ("CFSE", "LFSE“From engl. C.rystal or L.igand F.ield S.stabilization E.nergy). For this purpose, as in the picture above, the energetic position of the three t2g- and the two eG-Orbitals considered relative to an imaginary center of gravity. The energy 10 Dq is then split into a decrease in the three stabilized orbitals by −4 Dq and an increase in the two destabilized orbitals by 6 Dq (see above). For example, if every d orbital is occupied by 1 electron, there is no stabilization energy, because: 3 × (−4 Dq) + 2 × 6 Dq = 0. The balance looks different if eG-Orbitals remain unoccupied. With 0, 1, 2 and 3 electrons the LFSE values ​​are 0, −4, −8 and −12 Dq. If an aqua ligand is to be removed from the hexaqua complex of chromium (III) - the first step in the dissociative ligand exchange - the number of negative point charges repelling the d electrons and thus the crystal field splitting is reduced according to the crystal field model. If the field splitting becomes smaller, the LFSE also decreases. The greater the LFSE of the starting complex, the greater the loss - which appears as the required activation energy in the course of a ligand substitution reaction, the amount of which determines the exchange rate.

Crystal fieldStabilization (?)-Energy

Why should there be stabilization in reality only if some orbitals are below an imaginary line? A quantitative treatment shows that the conclusions from the crystal field model are entirely useful, and above all it conveys an idea about the nature of the LFSE. For this purpose, we consider a series of computer-chemical structure optimizations on the hexaaquametal (III) cations of the elements scandium to iron. In the textbooks you will find plots of numerous energy values ​​over the number of d electrons, for example lattice energies of metal (II) chlorides, hydration enthalpies of bivalent or trivalent 3d ions and the like. The numerical values ​​of these energies are always large when small metal-ligand / counterion distances occur. We interpret the following figure in this sense, which shows the metal (III) -O (Aqualigand) equilibrium distances instead of energy values.

Calculated M-O distance in hexaquametal (III) complex cations as a function of the number of d electrons (Sc: 0,…, Fe: 5). The blue line connects three cations with spherically symmetrical electron distribution: the d0-Sc-, the high-spin d5-Fe-, and, not shown, the d10-Ga-Hexaaqua-Trication (technical note: bp / tzvp).

The blue line serves as the expected value when walking through a period of the PSE. Along this, the M-O distances should decrease (bond, lattice and solvation energies increase) if no special electronic effects modify the influence of the increasing atomic number. But these are obviously there. We realize that the first three d electrons are filled into such orbitals (t2g in OH), which “avoid” the ligands and thus hinder their approach less than an isotropic electron distribution would.

The importance of the repulsion between metal d and ligand electrons is particularly emphasized in d4Case clear: If, as in this case, the crystal field splitting is not sufficient to compensate for the spin pairing energy, the incorporation of the fourth electron follows Hund's rule. There remains only one of the eG-Orbitals. This, however, severely hinders the approach of the ligands - in the crystal field model by electrostatic repulsion, in the MO scheme by antibonding. The result can be seen from the Mn point in the graph: the octahedral arrangement of the six ligands is severely disturbed; a “Jahn-Teller distortion” has arisen, which will be discussed in more detail later. The following picture shows this M-O antibonding interaction of the highest occupied orbital of [Mn (H2O)6]3+-Ions.

The α-HOMO (43a) of the elongated octahedral ion [Mn (H.2O)6]3+. The straight axis runs vertically (technical note: bp / tzvp, isovalue 0.06).

Before deepening the Jahn-Teller distortion, the interpretation of the spectra should be further developed by treating tetrahedral complexes and the spectroscopic selection rules.

Tetrahedral complexes

The crystal field model can also be set up for other ligand arrangements. In addition to the octahedral arrangement, an important arrangement is the tetrahedral arrangement, which occurred among the complexes discussed so far in the case of tetrahydroxido-aluminate. A consideration analogous to the octahedron shows that the orbitals x2 - y2 and Z2 are stabilized, while the xy, xz, and yz orbitals experience higher repulsion. The splitting scheme seems to be the opposite of that in the case of the octahedron, but note the different choices of the Cartesian coordinates. Because of the missing centrosymmetry of the tetrahedron, the symbol for symmetry is now e and t2, but above all the splitting for the same central metal-ligand combination is only about half the octahedron splitting:

Δt = 4/9 ΔO ≈ 1/2 ΔO

The color of cobalt (II) complexes

The rule helps in interpreting the colors of complexes. A tetrahedral complex is formed, for example, when a cobalt (II) nitrate solution, which, as a colored component (“chromophore”), contains the [CoII(H2O)6]2+-Ion, is mixed with plenty of concentrated hydrochloric acid. Under these conditions, the exchange of the six aqua-neutral ligands by four anionic chlorido ligands forms the tetrachloridocobaltate (II), [CoCl4]2− (We discuss what speaks against a hexachloridocobaltate (II); we also compare the LFSE for a tetrahedral and an octahedral complex of the d7-Ions cobalt (II); What is noticeable?) The color change associated with the ligand exchange is clear: the pale pink cobalt (II) nitrate solution turns ink blue. The change in color can be expected according to the rules recognized so far. Assuming that a chlorido and an aqua ligand do not cause too strongly different crystal field splittings (this is dealt with under the heading “spectrochemical series” below), the main reason is that the splitting is halved by changing from the octahedral to the tetrahedral structure to be observed. The excitation of an electron should therefore require less energy in the chloride complex, the absorbed radiation should be shifted to the low-energy side of the spectrum, i.e. into the red. The non-absorbed radiation - which our eye perceives as color - should be shifted in the direction of blue, which corresponds to the observation.

Spin and Laporte ban

But how does the strong increase in the intensity of the color come about? This is expression spectroscopic selection ruleswhich state the conditions as to whether an excitation by the available radiation is physically possible. There are two rules to be queried here: the Laporte ban and the spin ban.

The Laporte ban can usefully be divided into two queries: (1) Is the complex centrosymmetric (inversion symmetric; symmetric with respect to the point reflection)? If no (for example a tetrahedron), then excitation is allowed; if so (for example an octahedron), then (2) has to be asked: Does the excitation change the parity of the orbital? The parity describes the behavior of the orbital during point reflection; If it remains unchanged, the parity is “even”, “g” for short (s and d orbitals), the orbital lobes change sign, the parity is “odd”, “u” for short (p and f orbitals). Excitation by light is only permitted if the parity changes, for example if an electron is excited from a p to a d orbital. Crystal field transitions in which electrons are excited from ad to d orbital are therefore prohibited in octahedral and other centrosymmetric complexes, but allowed in tetrahedral and other non-centrosymmetric complexes. That the [CoII(H2O)6]2+-Ion shows a color at all is based on processes that affect the Laporte prohibition. Among the vibrations that the ligands perform relative to the central metal are those that briefly cancel the centrosymmetry so that electron excitation becomes possible.

The second major selection rule is that Spin ban. Excitation is only allowed if the total spin does not change, i.e. if the same number of unpaired spins is present before and after the electron shift. d5Ions such as [MnII(H2O)6]2+ or [FeF6]3−, in which all five d orbitals are single and have the same spin (Hund's rule), are colorless due to the spin prohibition - no suggestion can be formulated here in which a spin pairing in the eGLevel is avoided.


R. Eßmann, G. Kreiner, A. Niemann, D. Rechenbach, A. Schmieding, T. Sichla, U. Zachwieja and H. Jacobs:
Isotype structures of some hexaammine metal (II) halides of 3d metals: [V (NH3)6] I2, [Cr (NH3)6] I2, [Mn (NH3)6] Cl2, [Fe (NH3)6] Cl2, [Fe (NH3)6] Br2, [Co (NH3)6] Br2 and [Ni (NH3)6] Cl2.
Z. Anorg. General Chem.1996, 622, 1161–1166.
doi: 10.1002 / zaac.19966220709

Jahn-Teller distorted complexes

The unequal occupation of x2-Y2- and Z2Strong distortion of the hexaaquamangane (III) octahedron caused by orbitals occurs in the same way in other complexes with this peculiarity. A more complete diagram for nine existing and two hypothetical (Sc and Ti) hexaaquametal (II) complex cations is shown in the following graph:

Calculated M-O distance in hexaquametal (II) complex cations as a function of the number of d electrons (Ca: 0,…). The blue line connects three cations with spherically symmetrical electron distribution: the d0-Ca-, the high-spin d5-Mn-, and the d10-Zn-Hexaaqua-Dication (technical note: bp / tzvp). Sc and Ti are in brackets because no hexaquametal (II) ion has been synthesized here.

The strong calculated stretching of the octahedron in the chromium (II) and copper (II) hexaaqua ion is confirmed by the experiment. For the [CrII(H2O)6]2+Ion is an X-ray structure analysis on the double salt (NH4)2[CrII(H2O)6](SO4)2 before, in which four of the six aqua ligands are found in a square arrangement with Cr-O distances of 2.08 Å; the remaining two ligands perpendicular to it are, in very good agreement with the calculation result on the cation, 2.39 Å from the central atom. The [CuII(H2O)6]2+-Ion was crystallized with numerous counterions. An example with a larger deviation from the calculation reminds us that the approximations of the calculation (method, basic set) and the influence of cation-anion contacts in real crystal structures can add up to larger deviations between calculation and measurement. In the perchlorate [Cu (H2O)6] (ClO4)2; the distances between the central metal and the oxygen atoms of the four aqua ligands in the equatorial plane 1.95 Å, perpendicular to it 2.38 Å:

The Jahn-Teller distortion in the crystal field model

An evasion of the ligands from the octahedral position, albeit less, can also be assumed for those complexes in which the orbitals of the types xy, xz and yz are unequally occupied. The following shows (1) that the crystal field model can be used to decide whether a distortion is to be expected at all, (2) that the d-orbital order in the event of a distortion can be approximately determined with the crystal field model, and (3) whether also has a weak distortion confirmed experimentally.

The first point concerns the question of how an expected deviation from a high level of symmetry can be recognized quickly. Proceed as follows: In the case of a six-coordinate complex, draw the splitting scheme according to the crystal field model. Now fill in the existing electrons. If there is only one way to do this, no bias is to be expected. If the orbitals are occupied according to Hund's rule, this is the case with d3-, d5- and d8-Configuration. In the remaining cases, more than one possibility can be formulated for a particular electron arrangement. For the d9-Ion Cu2+ for example, two possibilities can be drawn:

Both arrangements have the same energy, they are energetically degenerate, here: doubly or doubly degenerate. Energetically degenerate states are unstable; they can be canceled out by distorting the highly symmetrical structure with energy gain. If in the example the distortion occurs in such a way that the doubly occupied eG-Orbital is energetically lowered and the one that is simply occupied is raised, because of the unequal occupation there is a gain in energy, since two electrons are stabilized during the lowering, but the raising only destabilizes one electron. The distortion of degenerate states with loss of symmetry and gain in stability is called Jahn-Teller distortion. The procedure derived here for potentially octahedral complexes is also valid for other coordination figures. Derive for the exercise that paramagnetic tetrahedral complexes occur undistorted if the electron configuration d2, d5 or d7 is.

The process can be clearly illustrated in the context of the crystal field model. If - as found in the calculation and the crystal structure analysis - two trans ligands are moved away from the central atom, the orbitals that have the greatest interaction with these ligands stabilize because of the now reduced repulsion between the negative charge on the ligand and the d electrons . If the z-axis is selected as the direction for the octahedron, the z2-Orbital lowered the most, while the xz and yz orbital experience less stabilization. This situation is sketched in the following diagram under the assumption that the sum of the orbital energies remains unchanged.

The simple derivation of orbital energy sequences shown is one of the strengths of the crystal field model. We will later use the same considerations to conveniently analyze square-planar complexes and only learn the limits of the model when we consider metal-ligand π interactions.

The scheme obtained is intended to explain the spectrum of the [CuII(H2O)6]2+-Ions are used. Since the other orbitals are filled, an excitation can only be in the x2-Y2-Orbital take place. Because of the spin prohibition, only one electron with β-spin (↓) can be excited. A transition x2-Y2 ← z2 requires so little energy that it will not be observable in the visible range; So only two stimuli are expected: one with lower energy from the xy orbital and one with higher energy from the xz or yz orbital. In accordance with this consideration, the shape of the absorption band allows the conclusion that it consists of two components.

Compare with the measured spectrum (as well as with the spectrum of the hexaaquatitanium (III) ion shown above):

Weak JT distortion

The Jahn-Teller distortion is found in hexacoordinate complexes with d4- and d9-Configuration in experiment and calculation very clearly. In principle, however, they should also be used in the d-electron arrangements d1, d2, d6, and d7 occur. Such distortions are shown in the calculation, but about 1 order of magnitude weaker than for the d4/ d9-Complexes.

An example is the [TiIII(H2O)6]3+-Ion.

The α-HOMO (40a) of the weakly trigonal distorted ion [Ti (H2O)6]3+. The Ti-O bonds enclosing the 40a orbital are at 90.8 ° angles to one another, the individual Ti-O distances are the same (technical note: bp / tzvp, isovalue 0.06).

The figure underlines some rules. It is often impossible to predict the direction in which the distortion can be expected. In the d1-Case the occupation of an xy-orbital together with a compression along z appears to be a plausible possibility (which should certainly emerge from a calculation as only slightly less stable). At the selected theoretical level, however, it is a weak trigonal distortion that corresponds to the energetic minimum. In keeping with the trigonal distortion, the 40a electron is also not in one found the orbitals of the type xy, xz and yz, but you can see a linear combination of all three orbitals in the picture.

The most important point, however, is that the distortion is small here and in the other cases in this chapter, and indeed smaller than the influences mentioned above to which an aquacation as a component of a salt structure is exposed. This and the possibility that a small JT effect can occur dynamically usually prevents its structural analysis in d1-, d2-, ls-d4-, ls-d5-, hs-d6- and hs-d7-Complexes.

We close the chapter with another quality of [TiIII(H2O)6]3+-Ions: why does the electron spectrum of this ion show a band splitting, which is not inferior to that in the aquacopper complex, despite the barely noticeable JT distortion? One catchphrase here will be the Franck-Condon principle, the other the Laporte ban.

Some nomenclature

So far we have become acquainted with distorted and undistorted octadric and tetrahedral complexes. The IUPAC has in its Red Book from 2005 a number of Polyhedron symbols introduced, which should lead to a simple description of the ligand arrangement. The idea is that a complex like the weakly JT-distorted [Ti (H2O)6]3+-Ion looks octahedral, but not one of the cubic point groups T or O belongs (for example, the symmetry group of the aquatitan ion in the depicted conformation is S.6). None of the aqua and ammine complexes treated so far have either OH-Symmetry, as one might believe after reading a textbook, because the H atoms create the fourfold symmetry of the group OH is broken. The IUPAC takes exactly this into account through the polyhedron symbol. For octahedral complexes this is OC-6 and means any complex in which any six ligands form what looks like an octahedron. Other symbols include, for example (see Table IR-9.2 of the Nomenclature of Inorganic Chemistry): T-4 for tetrahedral, SP-4 for square planar, SS-4 (from see-saw) for rocker-shaped (an octahedron where a cis-Ligand pair missing), TBPY-5 for trigonal-bipyramidal and SPY-5 for square-pyramidal complexes. The analysis of structures that lie between the ideal polyhedra is not always trivial and has led to attempts to quantitatively define polyhedra using suitable parameters (shape measures, more on this in coordination chemistry II).

The can be attached to the polyhedron symbol Configuration index, with the help of which structures can be clearly described.

Spectra of dn-Complexes

d3-Chrome (III)

The spectrum of [CrIII(H2O)6]3+ shows two bands in the visible area. The nature of these transitions can be made plausible from the electron configuration. As with the [TiIII(H2O)6]3+-Ion, the absorbed light energy is used to raise an electron from the t2g- in the eG-Level. In contrast to the d1-Case, however, different amounts of energy are required, for example to move from the xy orbital to the x2-Y2-Orbital or the z2-To stimulate orbital. The cause is the repulsion of the electrons among themselves. With the excitation of xy to z2 The excited electron compresses the charge density in the area around the z-axis, in which there are already half-filled orbitals with z-components, namely xz and yz. In addition to 10 Dq, an additional repulsion must therefore be overcome. This does not apply to the excitation of xy to x2-Y2, because here the electron's living space is only rotated by 45 ° in the xy plane. With the same consideration, the remaining possible transitions can be divided into two groups. The stimuli at low energy, at which only 10 Dq is overcome, can be summarized in a set of three energetically degenerate stimuli:

The transitions at higher energy, which also contain the increased repulsion between the electrons, also form a set of threefold degenerate excitations:

Since the low-energy absorption is free of amounts from additional electron repulsion, its energy can be equated with 10 Dq.

d8-Nickel (II)

A similar picture can be found for the d8-Ion [NiII(H2O)6]2+ to be expected. Note in the following schemes that the three electrons with β-spin (↓) result in the same splitting pattern in a constant neighborhood of five α-spins (↑) as the three electrons in the chromium (III) complex. Because of the lower oxidation state, two lower energy absorptions are expected. The measured spectrum is therefore somewhat unexpected. Two bands that are shifted too low in energy (“red-shifted”) appear - the cause of the splitting of the band at 700 nm will be discussed briefly later - but the third absorption at the edge of the visible range towards the ultraviolet is new. In the following picture the green spectrum is that of the aquanickel complex; the purple spectrum, which will be discussed later, is that of the hexaammine nickel (II) ion:

Since the energy of this third absorption is about twice that of the stimulation one Electrons, the assumption is that two electrons are lifted over the 10-Dq barrier, whereby the eG-Level is fully occupied. This excitation, too, is energetically degenerate threefold, so that the [NiII(H2O)6]2+Ion result in a total of three sets of triply degenerate excitations, the two of which with lower energy correspond to the transitions observed in the chromium (III) complex, namely:


The excitation of two electrons from the t2g- in the eGLevel correspond to these three transitions of equal energy:

The last considerations show that it is quite an effort to reconsider how the observed spectrum is to be interpreted for each complex. It would be very helpful to be able to use a schematic procedure such as adn-Spectrum should look like. Various types of correlation diagrams can help, of which the Tanabe-Sugano diagrams are the best known. Such diagrams or the formulas on which they are based are not only required for the interpretation of spectra, but also to determine fundamental quantities such as the field splitting 10 Dq from the energy values ​​of the individual bands. It is not always the case that 10 Dq results as the energy of the long-wave band, as with the Aquachrome (III) and Aquanickel (II) ions. The d2-Ion [VIII(H2O)6]3+-Ion is an example of a complex in which the excitation eG ← t2g obviously leads to a reduction in the repulsion between the electrons: 10 Dq in this example is somewhat greater than the energy of the long-wave band. A Tanabe-Sugano diagram helps d2-Spectrum to decipher.

Tanabe-Sugano diagrams for spin-allowed suggestions

Complete Tanabe-Sugano diagrams contain all conceivable stimuli, including those that are forbidden to spin (see, for example, the diagrams in I.-P-Lorenz: Molecular symmetry and spectroscopy). In order to be able to interpret the stronger absorptions, however, it is usually sufficient to only consider the spin-permitted transitions, i.e. those in which the total spin does not change compared to the basic state (“mostly” means, of course, that there are exceptions; meets the spectrum that is usual in textbooks this relates to the spectrum of the Aquanickel ion shown above; here the band at 700 nm is clearly split, since a spin-forbidden excitation with almost the same energy is added to the permitted excitation and this “steals intensity”). In correlation diagrams, the spin state is usually called “multiplicity” 2 S. + 1 indicated, at the d3-Ion Cr3+ with a S.= 3/2 ground state i.e. 4, for the d8-Ion Ni2+ with a S.= 1-ground state, i.e. 3. The multiplicity is given at the top left of the symbol that characterizes the electronic state (the “term symbol”). In the case of chromium (III), terms denote such as 4A.2g or 4T2g the sought electronic states with a total spin of 3/2, for nickel (II) complexes the corresponding terms are of the type 3T2g. The d2Vanadium (III) center is also in the triplet ground state. The following scheme shows a Tanabe-Sugano diagram for d2-Complexes in which only terms with the multiplicity of the basic term are entered - i.e. triplet terms - so that only the spin-allowed transitions that are of interest here appear. The crystal field splitting is plotted on the abscissa, the energy of the excited states relative to the ground state (which is therefore on the abscissa) on the ordinate. Both axes are divided into units of the Racah B parameter. This describes the repulsion between electrons with the same spin; for many transition metal ions, B is very approximately 1000 cm−1so that most of the complexes are found roughly in the range between 10 and 30 B on the abscissa. More precise values ​​for some bivalent and trivalent ions are summarized in the following table (according to Lever, p. 115):

M. B.(M2+)/cm−1B.(M3+)/cm−1
Ti 718
V 766 861
Cr 830 918
Mn 960 1140
Fe 1058
Co 971 1100
Ni 1041
Cu 1240

Some details can be taken directly from the diagram, some of which have already been mentioned:

  • The energetic degeneration of the individual terms. Also in the d2- In the case of microstates of the same energy, the terms can be summarized, the degree of degeneration of which corresponds to the number of microstates. Terms of type “T” are energetically degenerate three times, “A” denotes a non-degenerate term (“E” denotes a doubly degenerate term; such a term does not appear in the diagrams shown). The threefold degeneracy of the 3T1g-Ground state (xy1 xz1 Y Z0, xy1 xz0 Y Z1, xy0 xz1 Y Z1) has already been found in the treatment of the Jahn-Teller effect.
  • The number of absorption bands to be expected. Starting from the basic term, three states can be excited: 3T2g3T1g, 3T1g(P) ← 3T1g, 3A.2g3T1g. Note the two usual types of notation: excited state ← ground state or: ground state → excited state; the first notation was chosen here.
  • The number of excited electrons. The 3T2g-Ast runs approximately with the slope 1, so the energy of the excitation is essentially used for 10 Dq once to overcome. The rise of the 3A.2g-Astes is about 2, it represents the energy for a 2-electron transition. The given configuration (t2g2 eG0, ...) is therefore left out in many books because it is easy to recognize.
  • The excitation in terms with higher repulsion between the electrons. The 3T1g-Term of t2g1 eG1-Configuration is approx. 15 B above the long-wave transition and provides the excitation (with a slope of approx. 1) one Electrons in a state in which both 10 Dq and an increased repulsion between the electrons must be overcome. The contribution from electron repulsion should hardly be influenced by 10 Dq. In fact, the term runs roughly parallel to the first excited state and ends on the ordinate at 15 B above the ground state of the central metal ion, which is no longer influenced by any ligands (10 Dq = 0).
  • The terms of the central metal ion without field splitting. In analogy to the number of orbitals with the same name, the term symbols give 3F and 3P indicates the number of degenerate states (seven for F, three for P, so a total of ten states). Using the same considerations as with the aqua complexes of chromium (III) and nickel (II), the ten microstates without (left) and with crystal field splitting (right) can be classified in a plausible scheme. The in 3P-term summarized three states of higher energy can be recognized as electron arrangements in which higher repulsion prevails. Only combinations of type xy occur1 (x2-Y2)1 in which the two electrons are in greater spatial proximity than in the case of the below 3F compiled micro-states of the ground state. (Note: with ml, the orbital moment of the respective orbital for which at d electrons with l = 2 appear as possible values ​​2, 1, 0, −1 and −2 can be M.l, specify the total orbital moment as the sum of the orbital moments of the two electrons; note that the M.lValues ​​of the P term run from 1 to −1, those of the F term from 3 to −3); note further that a threefold degenerate P-term splits in the octahedral field like three p-orbitals, a sevenfold degenerate F-term like seven f-orbitals):

The Tanabe-Sugano diagram ad8-Complex looks very similar. The ground state of the non-Jahn-Teller ion [Ni (H2O)6]2+ bears, as expected, the symbol of symmetry “A”, furthermore all excited states are threefold degenerate - as it was shown above. The total number of three bands can be seen immediately, the two-electron excitation at the transition with the highest energy is immediately noticeable due to the slope of about 2 of the top branch. But if the individual micro-states are assigned to the terms, it is noticeable that the band with the second highest energy, which is caused by the excitation one Electron comes into a state of increased repulsion, not as expected from the 3P-term, but comes from the basic state of the atom - which is what the considerations for d2-Case is somewhat upside down. A special feature becomes visible here, namely the “crossover prohibition”. If the two upper lines of the diagram were replaced by the two dashed lines, the diagram would correspond to the expectation. Unlike in the d2- In the case, the two intersecting lines now have the same symbol of symmetry 3T1g. In this case, the prohibition, which is not justified here, that the terms of the crossover avoid the way in which the states are exchanged, applies. This case often occurs in Tanabe-Sugano diagrams: whenever a curved line occurs, there is a second line with the same symbol of symmetry and opposite curvature (vulgo: “The terms repel each other”).

The formal equal treatment of d8- and d3-Spectra had already been pointed out. This can of course also be seen in the Tanabe-Sugano diagrams. Both diagrams are the same, only the labeling has changed due to the different configurations and spin multiplicities.

So it should also be with the [CrIII(H2O)6]3+-Ion a third absorption can be observed, which, however, because of the larger value for 10 Dq, is far outside of the visible in the ultraviolet range of the electromagnetic spectrum. If this area is included in the measurement, this band actually becomes at an energy of 37,800 cm−1 (265 nm) found - almost hidden by a rapidly increasing, intensive absorption in this energy range, the cause of which will be discussed later.

MO scheme of an octahedral complex, LMCT junctions

The failure of the crystal field model: metal-ligand π interactions

When implementing the purple [CrIII(H2O)6]3+-Complexion with an excess of alkali hydroxide in aqueous solution forms the green hexahydroxidochromate (III) [CrIII(OH)6]3−. The color indicates that the crystal field splitting is smaller than with the aqua complex.Correspondingly, the crystal field transitions are red-shifted, they appear at longer wavelengths (the fact that the two-electron excitation is covered by a strong absorption that now protrudes further out of the UV range will be discussed at the end of this teaching unit):

In terms of a point charge model as represented by the crystal field theory, the opposite would of course be expected, namely that the more highly charged hydroxido-O-atom generates a stronger field splitting than a water-O-atom. However, the two chromium complexes are not isolated cases. The crystal field model is generally unsuitable for making the amount of 10 Dq plausible. This becomes clear when the contributions from the central metal and ligands are separated to 10 Dq. The field splitting can be according to this

10 Dq = GM. · fL.

represent as a product of a metal and a ligand contribution. Some values ​​are compiled in the following two tables.

M. GM./ 1000 cm−1

The order of the ligands with increasing fL.-Values ​​is the spectrochemical series:

L. fL.
H2O 1.00
py 1.23
en 1.28
bpy 1.33

It becomes clear that, on the one hand, the wide range of the GM.Values ​​is not comprehensible, on the other hand the negative loading of the ligand seems to be irrelevant for its contribution to 10 Dq - the impression is rather that the typical anionic ligands tend to cause small field splittings. The reason for these irritating statements is the weakness of the crystal field model, only to consider orbitals at the central metal, but not at the ligand. This is to be done in two steps below.

The MO model of a complex with M-L-σ bonds

In the first step, metal-ligand interactions with local σ-symmetry are considered. This includes, for example, coordinative bonds between a Lewis acidic central metal and Lewis basic ligands. In this case, the electron pairs of the ligands bind in the empty or partially occupied valence orbitals of the metal atom. In the case of central metals in the first transition row (“3d metals”), these are the (partially occupied) 3d and the (empty) 4s and 4p orbitals, which offer a total of 18 electrons. The following molecular orbital scheme shows that binding and antibonding interactions between matching Ligand group orbitals and construct six of the nine metal orbitals, only the interaction of the three t2g -Orbitals from the 3d subshell with the ligand orbitals remain non-binding; 10 Dq is now the energy difference between t2g and eG*, as will be explained in more detail later:

Since the case of occupied antibonding t1u- and a1g-Orbitals does not occur, we will use a shortened version of this scheme for further discussion. It should also be noted that in this qualitative treatment the energetic sequence of the orbitals eG, a1g and t1u typical, but first and foremost arbitrary:

The relation to the crystal field model becomes clear when electrons are poured into this scheme. the hexaquachrome (III) cation should be considered as an example. The six aqua ligands contribute a total of six electron pairs, the central metal three α-spin electrons:

Metal-ligand π interactions

So far, the bond between the central atom and the ligand has been understood as a coordinative or polar covalent bond with local σ symmetry. π interactions are possible when metal d and ligand p orbitals are arranged in the following way (an antibonding interaction is shown):

In an octahedral ML6In this way, binding and antibonding molecular orbitals are added to the complex, to which the central metal contributes xy, xz and yz orbitals (the xy plane is shown with one of three degenerate binding MOs and the corresponding antibonding MO with t2g-Symmetry):

π-interactions between filled ligand orbitals and empty, partially or completely filled metal orbitals seem possible for the ligands, which in the spectrochemical series is possible for small ones fL. can be found. For example, a fluorido ligand has three occupied p orbitals. One of these binds to the central metal with local σ-symmetry (the bond will have an s-orbital involvement, which in the context of the VB model would be called hybridization). The other two p orbitals are perpendicular to the M-L bond and can participate in the interaction shown.

In the point group OH the 6 × 2 = 12 orbitals of this type decay according to t1g + t1u + t2g + t2u. The interaction between the metal t2g- and the ligand group t2g-Orbital theorem has already been sketched in the figure above. The races t1g and t2u do not occur in the metal orbitals, they are metal-ligand non-binding. The additional ligand metal t1u-Interaction stabilizes the corresponding σ-bonds. After the formal treatment, we will look at what this looks like in a quantitative example; in the following scheme, this complementary interaction is neglected for the time being. Due to π interactions, the scheme of the six σ-M-L interactions (left) changes as shown on the right:

The effect of π interactions on 10Dq becomes clear when electrons are filled in again. In the case of an octahedral chromium complex, these would be the 15 electrons previously considered, plus 3 electron pairs in the t2g-Ligand group orbitals. It becomes clear that the three previously non-binding t2g-Electrons now in an antibonding t2g* Orbital are destabilized. The figure shows very schematically that an M-L-π interaction reduces the value for 10Dq, that is, that π-basic ligands in the spectrochemical series are small fL.Values ​​may be expected. ("Very schematic" because in a real example a change in ligands, for example the deprotonation of less π-basic aqua ligands to strongly π-basic, anionic hydroxido ligands, messes up the whole scheme, including the σ range.)

LMCT transitions

In the spectrum of the [CrIII(H2O)6]3+-Ions, in addition to the three crystal field bands, there is an intense absorption that begins at approx. 250 nm and quickly gains in intensity with increasing energy (decreasing wavelength). In the spectrum of [CrIII(OH)6]3− This strong absorption appears at so much lower excitation energy that it obscures the two-electron crystal field transition. The MO schemes allow these absorptions to be interpreted.

In addition to the crystal field transitions (d-d) between orbitals with a predominantly metal d component (in the scheme the essential contribution is highlighted by double underlining), electrons from the area of ​​the ligand-related orbitals can be excited in MOs with a high metal content. Such an excitation shifts an electron from the ligand sphere to the metal, which corresponds to a reduction of the metal and an oxidation of the ligand for the duration of the excitation. Because of the charge transfer, such stimuli are called “charge-transfer transitions” (CT ​​transitions). The type of charge transfers - from ligand to metal - is an "LMCT transition" ( al C.harge Transfer). It is possible with both aqua and hydroxido ligands. In the latter case it appears with a lower excitation energy, since the orbital energies of the anion OH higher - closer to the metal - than to the neutral ligand water; an electron is easier to remove from the anion than from the neutral molecule.

In a CT transition, an electron is excited from an (odd) p orbital to an (even) d orbital, so the transition is also Laporte-allowed in a centrosymmetric complex. Since CT transitions can always be formulated with spin permission, CT absorptions are intense. They are particularly noticeable when d-d transitions are spin and Laporte forbidden, i.e. the connection does not have a crystal field color. Examples are iron (III) compounds such as FeCl3 (orange-yellow), FeBr3 (dark brown) or the deep red thiocyanato complex used for iron (III) detection. Furthermore, the intensive CT transitions are noticeable where, due to the lack of d electrons, no crystal field transitions are possible. One example is the deep purple color of the d0-Ions manganate (VII), MnO4.

Note also the numerous trends in the periodic table: The ionization energies decrease in the series fluoride> chloride> bromide> iodide, so it is always easier to oxidize the halide. The colors of the copper (II) halide hydrates, which have the same square-planar [Cu (H2O)2X2