Lecture 11: Transition metals (1) Basics and magnetism Oxidation states in transition metal compounds Ligand field theory Magnetism Susceptibility Temperature dependence Magnetic moments Figure: Wikipedia Figure: Müller Solid State Chemistry CHEM-E4155, Antti Karttunen, Aalto University, 2017 1
Literature 2
Transition metals (d-block) Many oxidation states, very rich chemistry Many magnetic compounds (unpaired d-electrons) Many colorful compounds due to d-d transitions Figure: Wikipedia 3
Elemental transition metals Legend:.. /.. = mixed structure [...] = predicted structure Figure: Wikipedia Cu (fcc) cf (fcc) Fe (bcc) ci (bcc) Zn(hcp) hp Figures: AJK 4
Electron configurations (3d metals) Ref: chem.libretexts.org 5
Oxidation state The oxidation state of a transition metal is a key concept for understanding the chemistry of transition metal compounds Indicates the degree of oxidation (loss of electrons) of an atom in a compound For example Fe: FeCl 2 -> Cl and Fe 2+ / Fe(II) -> iron(ii) chloride FeCl 3 -> Cl and Fe 3+ / Fe(III) -> iron(iii) chloride The exact definition of an oxidation state is actually still debated IUPAC Technical Report Toward a comprehensive definition of oxidation state: P. Karen et al. Pure Appl. Chem. 2014, 86, 1017 1081 The oxidation state of a bonded atom equals its charge after ionic approximation In the ionic approximation, the atom that contributes more to the bonding molecular orbital (MO) becomes negative The sum of oxidation states in a compound must be zero! The oxidation state of an atom in a compound is a useful concept, but it is really just a concept. In particular, the charges are not real! 6
Known oxidation states for d-block Year 2016 Transition metals show a larger number of oxidation states in comparison to main group elements The most common oxidation states are shown in bold Ref: https://en.wikipedia.org/wiki/ List_of_oxidation_states_of_the_elements (based on Greenwood and Earnshaw + recent literature) Year 2014 7
Nature 2014, 514, 475. 8
Ligand field theory (1) The mutual interaction between bonding electron pairs is the same for transition metal compounds as for compounds of main group elements However, nonbonding valence electrons behave differently For transition metal atoms these generally are d electrons that can be accommodated in five d orbitals. In what manner the electrons are distributed among these orbitals can be judged with the aid of ligand field theory (LFT) LFT considers how the d electrons have to be distributed so that they attain a minimum repulsion with each other and with the bonding electron pairs In its original version by Hans Bethe, it was formulated as crystal field theory (CFT) Consider only electrostatic repulsion between the d electrons and the ligands, which are treated as point-like ions The ligand field theory is in principle superseded by the molecular orbital theory, but it still is a convenient and simple tool to understand the bonding and magnetism of transition metal compounds Ref: Müller p. 73 9
Crystal Field Theory Degeneracy breaks Electrostatic repulsion between the surrounding anions and metal d-electrons d-electrons still degenerate Figures: libretexts.org 10
Ligand field theory (2) In ligand field theory, the ligands are not just considered as negative point charges, but the covalent nature of the sigma-bonding is also taken into account The basic concept of the d-orbital splitting remains Ligand-Field scheme summarizing σ-bonding in octahedral [Ti(H 2 O) 6 ] 3+ [Ti(H 2 O) 6 ] 3+ solution is violet Figure: Wikipedia 11
Ligand field theory (3) Ref: Müller p. 74 In an octahedral geometry, The energy difference between the occupation of a t 2g and an e g orbital is termed Δ O The value of Δ O depends on the repulsion exercised by the bonding electron pairs on the d electrons Compared to a transition metal atom, the bonded ligand atoms are usually much more electronegative The centers of charge of the bonding electron pairs are much closer to the ligand atoms, especially when they are strongly electronegative. Therefore, one can expect a decreasing influence on the d electrons and thus a decrease of Δ O with increasing ligand electronegativity Decreasing Δ O values also result with increasing sizes of the ligand atoms (the electron pairs are distributed over a larger space -> less repulsion with d-elec.) In the presence of multiple bonds between the metal atom and the ligands, as for example in metal carbonyls, the electron density of the bonds is especially high and their action is correspondingly large Δ O can be measured with spectroscopic methods and the spectrochemical series is obtained by ordering different ligands according to decreasing Δ O : 12
Ligand field theory (4) Ref: Müller p. 75 LFT can be used to explain the magnetism of transition metal compounds Because of the splitting of the d-orbitals, there is an energetical competition between high-spin and low-spin configuration of the d-orbitals The first three d-electrons occupy the t 2g orbitals in accordance to Hund s rule When four nonbonding electrons are present, there are two alternatives for the placement of the fourth electron The energy necessary to include a second electron in an already occupied orbital is called the electron pairing energy P If P > Δ O, the fourth electron will occupy an e g orbital (high-spin) If P < Δ O, the fourth electron will occupy a t 2g orbital (low-spin) 13
Jahn-Teller effect (1) Ref: Müller p. 76 In a high-spin d 4 complex only one of the two e g orbitals is occupied If it is the d z2 orbital, then it exerts a strong repulsion on the bonding electrons of the two ligands on the z axis These ligands are forced outwards and the coordination octahedron suffers an elongation along the z axis. This effect is known as the Jahn Teller effect Instead of the d z2 orbital the d 2 x -y2 orbital could have been occupied which would have produced elongations along the x and y axes However, more energy would be needed to stretch four bonds The Jahn-Teller effect is always to be expected when degenerate orbitals are unevenly occupied with electrons. Strong J-T effect is observed for the following electronic configurations (e g orbitals unevenly occupied): 14
Jahn-Teller effect (2) Illustration of tetragonal distortion (elongation) for an octahedral complex Point group changes from O h to D 4h Figure: libretexts.org O h D 4h 15
Other coordination geometries The energetics and the splitting of the d-orbitals are different for other coordination geometries. The figure below shows the most typical geometries for transition metals T d O h D 4h D 4h A group theoretical resource: http://symmetry.jacobs-university.de/ 16
Most common coordination polyhedra for CN 2-6 Ref: Müller p. 81 17
Magnetism (1) Ref: West p. 445-446 Diamagnetism is a property of all substances Induced magnetic field is created in a direction opposite to an external field Inorganic solids that have unpaired electrons in their outer valence shells can exhibit magnetic effects other than diamagnetism Electrons in inner core levels are always paired in fully occupied orbitals Unpaired electrons are usually located on metal cations (d- or f-metal) The unpaired electrons can have both spin and orbital motion, which together generate a magnetic moment associated with the electrons 18
Magnetism (2) Another summary of magnetic phenomena in a 1D crystal: Figure: Rob McQueeney / Iowa State U. 19
Family tree of magnetism Ref: HP Meyers, Introductory solid state physics (1997) / Wikipedia 20
Magnetic susceptibility Ref: West p. 446 High M = high χ 21
Classification based on χ The different kinds of magnetic behaviour may be distinguished by the values of χ For diamagnetic substances, χ is very small and slightly negative Diamagnetism is associated with orbital motion of electrons in atoms. This orbital motion generates a small electric field In the presence of an external field, the orbital motion is modified slightly to give a magnetic moment that opposes the applied field leading to a slight repulsion effect which is explained by Lenz s law of electromagnetism. Superconductors represent a special, extreme type of diamagnetism since they repel magnetic fields completely Ref: West p. 447 22
Para-, ferro-, and antiferromagnetism For paramagnetic substances, χ is small and positive Thus, when placed in a magnetic field, the number of lines of force passing through a substance is greater if it is paramagnetic and slightly less if it is diamagnetic than would pass through a vacuum Consequently, paramagnetic substances are attracted by a magnetic field whereas diamagnetic substances experience a slight repulsion Since superconductors show perfect Diamagnetic diamagnetism, they expel magnetic fields completely, leading to levitation In ferromagnetic substances, χ > 1 and such materials are strongly attracted to a magnetic field. Paramagnetic In antiferromagnetic substances, χ is positive and comparable to or somewhat less than that for paramagnetic substances. 23
Antiferromagnetic ordering: superexchange One process, by which spins couple to give antiferromagnetism in, e.g. NiO, is superexchange Ni 2+ in NiO has 8 d electrons (two in e g orbitals d z2 and d 2 2 x -y pointing directly at adjacent oxide O ions Ni The unpaired electrons in these e g orbitals couple with electrons in the p orbitals of the O 2 ions Figure: AJK 24
Pauli paramagnetism In addition to the strong ferro- and antiferromagnetic coupling shown by some transition metals, most metals display a weak paramagnetism in the presence of a magnetic field, known as Pauli paramagnetism Only small number of electrons near E F contribute to the Pauli paramagnetism Ref: West p. 458 25
The effect of temperature: Curie and Curie Weiss laws The susceptibilities of different kinds of magnetic material are distinguished by both their temperature dependences and their absolute magnitudes Ordered magnetic structures, whether ferro-, ferri-, antiferro-, heli-magnetic or spin glass, lose their ordered structures above a certain temperature Curie temperature, T c for ferro- and ferrimagnets Néel temperature, T N for antiferro- and heli-magnets The spins become disordered and the materials are therefore paramagnetic 26
Examples of behavior close to T c Figure: Robert John Lancashire 27
Magnetic moments (1) Magnetic properties are often expressed in terms of the magnetic moment μ = M/V (M = magnetization, V = unit volume) The magnetic properties of unpaired electrons arise from two causes, electron spin and electron orbital motion The spin component is the most important one. An electron may be considered as a bundle of negative charge spinning on its axis. The magnitude of the resulting spin moment, μ S, is 1.73 BM, Bohr Magneton: where s is the spin quantum number, ½, and g is the gyromagnetic ratio ~2.00. Substituting for s and g gives μ S = 1.73 BM for one electron Ref: West p. 451 28
Magnetic moments (2) For atoms or ions that contain more than one unpaired electron, the overall spin moment is given by 29
Magnetic moments (3) 30
Experimental characterization of magnetic ground state χ SQUID (Superconducting Quantum Interference Device) Very sensitive magnetometer (measure susceptibility as a function of T) Neutron diffraction Neutrons carry a spin and interact with magnetic moments T N = 26 K T N = 116 K T (K) SQUID data for antiferromagnetic SrU2F12 (Otto Mustonen) 31