Buy eBook. Buy Softcover. FAQ Policy. Show all. Show next xx. Read this book on SpringerLink. A frequent source of confusion about electron counting is the fate of the s-electrons on the metal.
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But the electronic configuration of a free Ti atom, according to the Aufbau principle, is 4s 2 3d 2. The short answer is that the metal s orbitals are higher in energy in a metal complex than they are in the free atom because they have antibonding character. We will justify this statement with a MO diagram in Section 5. Although the electron counting rule we have developed above is useful and works reliably for all kinds of complexes, the assignment of all the shared electrons in the complex to the ligands does not always represent the true bonding picture.
This picture would be most accurate in the case of ligands that are much more electronegative than the metal. But in fact, there all all kinds of ligands, including those such as H, alkyl, cyclopentadienide, and others where the metal and ligand have comparable electronegativity. In those cases, especially with late transition metals that are relatively electropositive, we should regard the metal-ligand bond as covalent.
Green  in order to better describe the different kinds of metal-ligand bonds. The molecular orbital pictures below summarize the difference between L, X, and Z ligands. L-type ligands are Lewis bases that donate two electrons to the metal center regardless of the electron counting method being used. These electrons can come from lone pairs, pi or sigma donors. The bonds formed between these ligands and the metal are dative covalent bonds, which are also known as coordinate bonds.
X-type ligands are those that donate one electron to the metal and accept one electron from the metal when using the neutral ligand method of electron counting, or donate two electrons to the metal when using the donor pair method of electron counting. Z-type ligands are those that accept two electrons from the metal center as opposed to the donation occurring with the other two types of ligands. However, these ligands also form dative covalent bonds like the L-type.
This type of ligand is not usually used, because in certain situations it can be written in terms of L and X. For example, if a Z ligand is accompanied by an L type, it can be written as X 2. Examples of these ligands are Lewis acids, such as BR 3.
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Some multidentate ligands can act as a combination of ligand types. A famous example is the cyclopentadienyl or Cp ligand, C 5 H 5. The addition of one electron makes the Cp - anion, which has six pi electrons and is thus planar and aromatic. Crystal field theory is one of the simplest models for explaining the structures and properties of transition metal complexes. The theory is based on the electrostatics of the metal-ligand interaction, and so its results are only approximate in cases where the metal-ligand bond is substantially covalent. But because the model makes effective use of molecular symmetry, it can be surprisingly accurate in describing the magnetism, colors, structure, and relative stability of metal complexes.
There are two energetic terms we need to consider. The first is the electrostatic attraction between the metal and ligands, which is inversely proportional to the distance between them:. The second term is the repulsion that arises from the Pauli exclusion principle when a third electron is added to a filled orbital. There is no place for this third electron to go except to a higher energy antibonding orbital. This is the situation when a ligand lone pair approaches an occupied metal d-orbital:. Now let us consider the effect of these attractive and repulsive terms as the metal ion and ligands are brought together.
We do this in two steps, first forming a ligand "sphere" around the metal and then moving the six ligands to the vertices of an octahedron. Initially all five d-orbitals are degenerate, i.
In the first step, the antibonding interaction drives up the energy of the orbitals, but they remain degenerate. In the second step, the d-orbitals split into two symmetry classes, a lower energy, triply-degenerate set the t 2g orbitals and a higher energy, doubly degenerate set the e g orbitals. What causes the d-orbitals to split into two sets? Recall that the d-orbitals have a specific orientation with respect to the Cartesian axes. The lobes of the d xy , d xz , and d yz orbitals the t 2g orbitals lie in the xy-, xz-, and yz-planes, respectively.
These three d-orbitals have nodes along the x-, y-, and z-directions. The orbitals that contain the ligand lone pairs are oriented along these axes and therefore have zero overlap with the metal t 2g orbitals.
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It is easy to see that these three d-orbitals must be degenerate by symmetry. On the other hand, the lobes of the d z 2 and d x 2 -y 2 orbitals the e g orbitals point directly along the bonding axes and have strong overlap with the ligand orbitals. While it is less intuitively obvious, these orbitals are also degenerate by symmetry and have antibonding character. It is informative to compare the results of crystal field theory and molecular orbital theory also called ligand field theory in this context for an octahedral transition metal complex.
In the MO picture at the right, the frontier orbitals are derived from the metal d-orbitals. The lower t 2g set, which contains one electron, is non-bonding by symmetry, and the e g orbitals are antibonding.
The metal 4s orbital, which has a 1g symmetry, makes a low energy bonding combination that is ligand-centered, and an antibonding combination that is metal-centered and above the e g levels. This is the reason that our d-electron counting rules do not need to consider the metal 4s orbital. The important take-home message is that crystal field theory and MO theory give very similar results for the frontier orbitals of transition metal complexes. Strong and weak field ligands. This energy difference is measured in the spectral transition between these levels, which often lies in the visible part of the spectrum and is responsible for the colors of complexes with partially filled d-orbitals.
Ligands that produce a large splitting are called strong field ligands, and those that produce a small splitting are called weak field ligands. An abbreviated spectrochemical series is:. Orbital overlap. Referring to the molecular orbital diagram above, we see that the splitting between d-electron levels reflects the antibonding interaction between the e g metal orbitals and the ligands. Thus, we expect ligand field strength to correlate with metal-ligand orbital overlap. Ligands that bind through very electronegative atoms such as O and halogens are thus expected to be weak field , and ligands that bind through C or P are typically strong field.
Ligands that bind through N are intermediate in strength. Another way to put this is that hard bases tend to be weak field ligands and soft bases are strong field ligands. Thus the energy difference between the t 2g and e g orbitals can range between the energy of a rather weak to a rather strong covalent bond.
The 4d and 5d elements are similar in their size and their chemistry. This trend reflects the spatial extent of the d-orbitals and thus their overlap with ligand orbitals. The 3d orbitals are smaller, and they are less effective in bonding than the 4d or 5d.
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The 4d and 5d orbitals are similar to each other because of the lanthanide contraction. At the beginning of the 5d series between 56 Ba and 72 Hf are the fourteen lanthanide elements 57 La - 71 Lu. Although the valence orbitals of the 5d elements are in a higher principal quantum shell than those of the 4d elements, the addition of 14 protons to the nucleus in crossing the lanthanide series contracts the sizes of the atomic orbitals.
The important result is that the valence orbitals of the 4d and 5d elements have similar sizes and thus the elements resemble each other in their chemistry much more than they resemble their cousins in the 3d series. For example, the chemistry of Ru is very similar to that of Os, as illustrated at the right, but quite different from that of Fe.
Colors of transition metal complexes. The higher the energy of the absorbed photon, the larger the energy gap. However, the color a complex absorbs is complementary to the color it appears i. This is consistent with the idea that CN - is a stronger field ligand than NH 3 , because the energy of a UV photon is higher than that of a red-orange photon. There are three types of pi-bonding in metal complexes:. This results in weakening of the C-O bond, which is experimentally observed as lengthening of the bond relative to free CO in the gas phase and lowering of the C-O infrared stretching frequency.
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This is a common situation for phosphine complexes e. This occurs in early transition metal complexes. This interaction is typically drawn as a metal-ligand multiple bond, e. Using these catalysts, cyclic olefins can be transformed into linear polymers in high yield through ring-opening metathesis polymerization ROMP.
Catalysts of this kind were developed by the groups of Richard Schrock and Robert Grubbs, who shared the Nobel Prize in Chemistry with Yves Chauvin for their discoveries. The Schrock catalysts are based on early transition metals such as Mo; they are more reactive but less tolerant of different organic functional groups and protic solvents than the Grubbs catalysts, which are based on Ru complexes. The splitting of the d-orbitals into different energy levels in transition metal complexes has important consequences for their stability, reactivity, and magnetic properties.
Because the complexes are octahedral, they all have the same energy level diagram:. The spins align parallel according to Hund's rule, which states that the lowest energy state has the highest spin angular momentum. For each of these complexes we can calculate a crystal field stabilization energy, CFSE , which is the energy difference between the complex in its ground state and in a hypothetical state in which all five d-orbitals are at the energy barycenter.
Now we can have a high spin configuration t 2g 3 e g 1 , or a low spin configuration t 2g 4 e g 0 in which two of the electrons are paired. What are the energies of these two states? The pairing energy P is the energy penalty for putting two electrons in the same orbital, resulting from the electrostatic repulsion between electrons. For 3d elements, a typical value of P is about 15, cm Note that high and low spin states occur only for 3d metal complexes with between 4 and 7 d-electrons.
Complexes with 1 to 3 d-electrons can accommodate all electrons in individual orbitals in the t 2g set. Complexes with 8, 9, or 10 d-electrons will always have completely filled t 2g orbitals and electrons in the e g set.
Magnetism of transition metal complexes Compounds with unpaired electrons have an inherent magnetic moment that arises from the electron spin. Such compounds interact strongly with applied magnetic fields. Their magnetic susceptibility provides a simple way to measure the number of unpaired electrons in a transition metal complex. If a transition metal complex has no unpaired electrons, it is diamagnetic and is weakly repelled from the high field region of an inhomogeneous magnetic field. Complexes with unpaired electrons are typically paramagnetic. The spins in paramagnets align independently in an applied magnetic field but do not align spontaneously in the absence of a field.
Such compounds are attracted to a magnet, i. In octahedral 3d metal complexes, the orbital angular momentum is largely "quenched" by symmetry, so we can approximate:. This spin-only formula is a good approximation for first-row transition metal complexes, especially high spin complexes. The small deviations from the spin-only formula for these octahedral complexes can result from the neglect of orbital angular momentum or of spin-orbit coupling.
Tetrahedral d 3 , d 4 , d 8 and d 9 complexes tend to show larger deviations from the spin-only formula than octahedral complexes of the same ion because quenching of the orbital contribution is less effective in the tetrahedral case. Colors and spectra of transition metal complexes Transition metal complexes often have beautiful colors because, as noted above, their d-d transition energies can be in the visible part of the spectrum. With octahedral complexes these colors are faint the transitions are weak because they violate the Laporte selection rule.
However octahedral complexes can absorb light when they momentarily distort away from centrosymmetry as the molecule vibrates. Spin flips are also forbidden in optical transitions by the spin selection rule, so the excited state will always have the same spin multiplicity as the ground state. The spectra of even the simplest transition metal complexes are rather complicated because of the many possible ways in which the d-electrons can fill the t 2g and e g orbitals.
There are actually 45 different such arrangements called microstates that do not violate the Pauli exclusion principle for a d 2 complex. Usually we are concerned only with the six of lowest energy, in which both electrons occupy individual orbitals in the t 2g set and all their spins are aligned either up or down. This ion is d 3 , so each of the three t 2g orbitals contains one unpaired electron.
We expect to see a transition when one of the three electrons in the t 2g orbitals is excited to an empty e g orbital.see
Interestingly, we find not one but two transitions in the visible. The reason that we see two transitions is that the electron can come from any one of the t 2g orbitals and end up in either of the e g orbitals. Let us assume for the sake of argument that the electron is initially in the d xy orbital. It can be excited to either the d z 2 or the d x 2 -y 2 orbital:.
The first transition is at higher energy shorter wavelength because in the excited state the configuration is d yz 1 d xz 1 d z 2 1. All three of the excited state orbitals have some z-component, so the d-electron density is "piled up" along the z-axis. You can leave a response , or trackback from your own site. Name required. Mail will not be published required. Henry Rzepa's Blog Chemistry with a twist.
All might become clear shortly! But also notice that the Pt orbital is rather more anti-bonding in the C-C region than Ag analogue. The C-C computed length 1. It is symmetric with respect to all three elements of symmetry axis and two planes and hence is labelled A 1. Where Dewar writes that the two molecular bonds are distinct, he means that they have different symmetries and hence cannot interact with each other they are orthogonal.