Chimica Inorganica 3 Instructors: Unipd
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Chimica Inorganica 3
Instructors:
Maurizio Casarin; Silvia Gross; Marta M. Na7le
Address:
Maurizio Casarin: Via Loredan 4, 35131 - Padova
Phone number: +39 049 - 827 ext. 5164
E-mail address: maurizio.casarin@unipd.it
hRp://wwwdisc.chimica.unipd.it/maurizio.casarin/pubblica/casarin.htm
Chimica Inorganica 3
COURSE OUTLINE – Inorganic Chemistry 3
Instructors: M. Casarin (maurizio.casarin@unipd.it) & S. Gross (silvia.gross@unipd.it)
Examination Board: Maurizio Casarin, Marta M. Natile & Silvia Gross
Overview: Systematic presentation of the applications of group theory to the Inorganic
Chemistry. Emphasis on the formal development of the subject and its
applications to the physical methods of inorganic chemical compounds.
Against the backdrop of electronic structure, the electronic, vibrational, and
magnetic properties of transition metal complexes are presented and their
investigation by the appropriate spectroscopy described. The laboratory
session will be devoted to improve the students’ practical skills in the
synthesis of different molecular and bulk inorganic compounds, as well as
in their spectroscopic characterization.
Chimica Inorganica 3 monday tuesday wednesday thursday friday
Chimica Inorganica 3
Class Schedule
5 10+5
15+3
22+4
Chimica Inorganica 3 The following topics will be considered: 1) Symmetry elements and operations 2) Operator properties and mathematical groups 3) Irreducible representations and character tables 4) Molecular point groups 5) General electronic considerations of metal-ligand complexes 6) Frontier molecular orbitals of σ-donor, π-donor and π-acceptor ligands 7) Octahedral ML6 σ complexes 8) Octahedral ML6 π complexes 9) The weak field 10) The strong field 11) Tanabe-Sugano diagrams 12) Spin orbit coupling, double groups, and ligand fields 13) Lanthanides: electronic structure, properties and reactivity
Chimica Inorganica 3 Textbooks: Ø G. L. Miessler, P. J. Fischer and D. A. Tarr, Inorganic Chemistry, 5th ed. (Upper Saddle River, NJ: Pearson Prentice Hall, 2014) Ø S. F. A. Kettle, Physical Inorganic Chemistry, (Springer-Verlag Berlin Heidelberg GmbH, 1996) Ø R. L. Carter, Molecular Symmetry and Group Theory (New York: John Wiley & Sons, 1998) Ø U. Schubert and N. Hüsing, Synthesis of inorganic materials, 2nd ed., (Weinheim Wiley VCH, 2004) References: • J. Barrett, Atomic Structure and Periodicity (The Royal Society of Chemistry, 2002) • I. B. Bersuker, Electronic Structure and Properties of Transition Metal Compounds (New York: John Wiley & Sons, 2010) • D. M. Bishop, Group Theory and Chemistry (Oxford: Clarendon press, 1973) • J. K. Burdett, Molecular Shapes, Theoretical Models of Inorganic Chemistry, New York: John Wiley & Sons, 1980) • F. A. Cotton, Chemical Applications of Group Theory, 3rd ed. (New York: Wiley, 1990) • B. N. Figgis, Introduction to Ligand Fields (New York: Interscience Publishers,1967) • N. N. Greenwood and A. Earnshaw, Chemistry of the Elements (Oxford, Butterworth and Heinemann, 1998) • J. S. Griffith, The Theory of Transition Metal Ions (Cambridge, University Press, London, 1961) • C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 2nd ed. (Edinburgh Gate, Pearson Education Limited, 2005) • J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (New York: Harper Collins, 1993) • M. Lesk, Introduction to Symmetry and Group Theory for Chemists, (New York: Kluwer Academic Publishers, 2004) • K. F. Purcell and J. C. Kotz, Inorganic Chemistry (Saunders, 1977) • K. F. Riley, M. P. Hobson and S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge, University Press, London, 2006) • J. H. van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford, Clarendon Press, 1932)
Chimica Inorganica 3 Website: A website will be maintained through the “DiSC” website: http://wwwdisc.chimica.unipd.it/maurizio.casarin/pubblica/casarin.htm
Chimica Inorganica 3 Discussion: Discussion sessions are an integral component of the course. The discussion sessions will focus on advanced problems and the chemical literature, but there will also be the opportunity for student questions pertaining to practice problems or any aspect of the course. Most weeks there will be specific work to be prepared for the discussion session, which will be noted on the weekly handout and posted on the course website; discussion preparation and discussion session work is in lieu of graded homework assignments, so this work should be taken as seriously as one would consider graded assignments. Solutions to discussion questions will be posted on the course website. Exams: There will be six three-hours written exams (two at the end of the first semester, two at the end of the second semester, two before the new academic year starting). Laboratory: Attendance at all laboratory sessions is required, and on-time arrival is essential. Experiments and theoretical background for the laboratory sessions will be introduced in dedicated lectures. The two laboratory sessions will be both held at the 4th floor of the main DiSC building (their schedule will be provided by Silvia Gross). Laboratory lecture notes (dispense) will be provided by the laboratory instructors. Laboratory safety is of utmost importance. Laboratory safety issues will be reviewed during the first laboratory sessions. Each student is required to provide her/his own laboratory notebook, which should contain bound, sequentially numbered pages (loose-leaf binders and spiral-bound notebooks are not acceptable); a standard composition book is sufficient, since duplicate pages are not required. It is acceptable to continue to use a laboratory notebook from a previous chemistry course if sufficient space is available. Notebooks will be collected twice for evaluation. Written reports (a template will be provided) are required for all experiments and should be submitted electronically after the class or laboratory period on the days indicated; there will be a penalty for late submission without prior approval.
Chimica Inorganica 3
Final Grade:
Exams count as 70% of the final grade, and discussion and laboratory work constitute the remaining 30% of the
final grade.
Intellectual Responsibility:
Students enrolled in Inorganic Chemistry 3 are expected to abide by the “Regolamento delle carriere degli
studenti” of the University of Padova. Particular attention should be paid to the items 23 (Deontologia
Studentesca) and 24 (Provvedimenti Disciplinari). The specific implications of the statement for Inorganic
Chemistry 3 are:
• Students are encouraged to study together and to discuss the course material and laboratory experiments, but
all work submitted for evaluation must represent the student’s own work and reflect her/his understanding
of the material.
• In-class exams must be worked individually during the allotted time, with no resources other than those
provided with the exam. No discussion or other communication with other students will be permitted during
exams. The exams will state clearly which reference materials, if any, may be used during the exams.
• Students are strongly invited to produce original written reports, using high level references (scientific
journals or textbooks) and disregarding unreliable sources as Wikipedia. Copying and plagiarism (copying
somebody’s words, written texts, ideas, figures without quoting the sources) are, according to international
legislation, a crime and are punished by the Italian law (Legge 22 aprile 1941 n. 633).
Chimica Inorganica 3
Chimica Inorganica 3 symmetry, n. 1. Mutual relation of the parts of something in respect of magnitude and position; relative measurement and arrangement of parts; proportion. 2. Due or just proportion; harmony of parts with each other and the whole; fitting, regular, or balanced arrangement and relation of parts or elements; the condition or quality of being well-proportioned or well-balanced. In stricter use (approaching or passing into 3b): Exact correspondence in size and position of opposite parts; equable distribution of parts about a dividing line or centre. (As an attribute either of the whole, or of the parts composing it.)
Chimica Inorganica 3
Top view of a verdant young plant displaying
symmetry found in nature.Chimica Inorganica 3
Chimica Inorganica 3
Chimica Inorganica 3 The Vitruvian Man (Le proporzioni del corpo umano secondo Vitruvio), or simply L'Uomo Vitruviano, is a drawing made by Leonardo da Vinci around 1490. It is accompanied by notes based on the work of the Roman architect Vitruvius. The drawing, which is in ink on paper, depicts a man in two superimposed posi7ons with his arms and legs apart and inscribed in a circle and square. The drawing and text are some7mes called the Canon of Propor*ons or, less o^en, Propor*ons of Man. It is kept in the GabineRo dei disegni e stampe of the Gallerie dell’Accademia. Like most works on paper, it is displayed to the public only occasionally, so it is not part of the normal exhibi7on of the museum.
Chimica Inorganica 3 «La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si può intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro laberinto. » Galileo Galilei, Il Saggiatore, Ed. Accademia dei Lincei, Roma (1623).
Chimica Inorganica 3 P l a t o n e ( i n g re c o a n t i c o Π λ ά τ ω ν , traslitterato in Plátōn; Atene, 428 a.C./427 a.C. – Atene, 348 a.C./347 a.C.). Con il suo maestro Socrate e il suo allievo Aristotele ha posto le basi del pensiero filosofico occidentale.
Chimica Inorganica 3
Q
T
P
T
T L'aspetto più appariscente dei solidi platonici, oltre a quella di poter
essere inscritti in una sfera, è di utilizzare solo una delle prime tre figure
piane della geometria (triangolo g tetraedro, ottaedro, icosaedro;
quadrato g cubo; pentagono g dodecaedro). Se si vuole proseguire con
successive forme si è costretti ad utilizzare contemporaneamente due
figure geometriche come fece Archimede disegnando i successivi tredici
solidi semi-regolari.Chimica Inorganica 3
solidi platoniciChimica Inorganica 3
Chimica Inorganica 3
Chimica Inorganica 3
Chimica Inorganica 3
Chimica Inorganica 3
Carborane acid anion [CHB11Cl11]- (acidic
Charge-neutral C2B10H12 or o-carborane
proton not displayed)
These boron-rich clusters exhibit unique organomimetic properties with chemical
reactivity matching classical organic molecules, yet structurally similar to metal-
based inorganic and organometallic speciesChimica Inorganica 3
Chimica Inorganica 3
Évariste Galois
Bourg-la-Reine, 25/10/1811 – Parigi, 31/05/1832
French mathema7cian who led a short, drama7c life and is o^en credited with
founding modern group theory, though the Italian Paolo Ruffini (1765–1822) came up
with many of the ideas first. Galois' work wasn't widely acknowledged by his
contemporaries, partly because he didn't present his material very well and partly
because he held unpopular poli7cal views. In fact, he was a republican revolu5onary
who was twice imprisoned because of his ac7vi7es. During his second incarcera7on
he fell in love with the daughter of the prison physician, Stephanie-Felice du Motel,
and a^er being released, fought a gun duel over her with Perscheux d'Herbinville.
Mortally wounded in the duel, he was abandoned in a field but found by a peasant
and taken to a hospital. A^er a few days he died of an infec7on. His death started
republican riots and rallies which lasted for several days.
Reputedly, the night before his fatal duel, Galois tried to write down as many
thoughts as possible. These notes and a few other papers were discovered 14 years
later by Joseph Liouville, who recognized them as works of genius. Galois set out
the theory of groups and laid down condi5ons for the solvability of various
algebraic equa5ons.
https://www.terabitcorp.com/galois.htmChimica Inorganica 3
Niels Henrik Abel
Finnøy, 05/08/1802 – Froland 06/04/1829
Norwegian mathematician born at Findö, Christiansand, who,
independently of his contemporary Évariste Galois, pioneered group
theory and proved that there are no algebraic solutions of the general
quintic equation. Both Abel and Galois died tragically young – Abel of
tuberculosis, Galois in a duel. While a student in Christiania (now Oslo),
Abel thought he had discovered how to solve the general quintic
algebraically, but soon corrected himself in a famous pamphlet published
in 1824. In this early paper, Abel showed the impossibility of solving the
general quintic by means of radicals, thus laying to rest a problem that
had perplexed mathematicians since the mid-16th century.
Abel, chronically poor throughout his life, was granted a small stipend by the Norwegian
government that allowed him to go on a mathematical tour of Germany and France. In Berlin he
met Leopold Crelle (1780–1856) and helped him found, in 1826, a famous journal, the first in the
world devoted to mathematical research. Its first three volumes contained 22 of Abel's papers,
ensuring lasting fame for both Abel and Crelle
.
Abel revolutionized the important area of elliptic integrals with his theory of elliptic functions,
contributed to the theory of infinite series, and founded the theory of commutative groups, known
today as Abelian groups. Yet his work was never properly appreciated during his life and,
impoverished and ill, he returned to Norway unable to obtain a teaching position. Two days after
his death, a delayed letter was delivered in which Abel was belatedly offered a post at the
University of Berlin.Chimica Inorganica 3
Consider the symmetry properties of an object (e.g. atoms of a molecule, set of
orbitals, vibrations). The collection of objects is commonly referred to as a basis set.
[ classify objects of the basis set into symmetry operations
[ symmetry operations form a group
[ group mathematically defined and manipulated by group theory
symmetry operations & symmetry elements
A symmetry operation moves an object into an indistinguishable orientation. Symmetry
operations are actions.
A symmetry element is a point, line or plane about which a symmetry operation is
performed. Symmetry elements are geometrical entities (a point, a line, a plane) about
which the actions take place.Chimica Inorganica 3
There are five symmetry operations, which will be defined relative to point with
coordinate (x1, y1, z1):
1) identity, Ê
Ê ( x1, y1, z1 ) = ( x1, y1, z1 )
Symmetry operations are actions.
Symmetry elements are geometrical
entities (a point, a line, a plane)
2) reflection, σ̂ about which the actions take place.
σˆ xz ( x1, y1, z1 ) = ( x1, −y1, z1 )Chimica Inorganica 3
3) inversion, î
iˆ ( x1, y1, z1 ) = ( −x1, −y1, −z1 )
2π
4) proper rotation, Ĉn , where θ= Symmetry operations are actions.
n
Symmetry elements are geometrical
convention is a clockwise rotation of the point
entities (a point, a line, a plane)
about which the actions take place.
Ĉ2 ( z ) ( x1, y1, z1 ) = ( −x1, −y1, z1 )Chimica Inorganica 3
Symmetry operations are actions.
Symmetry elements are geometrical
5) improper rotation, Ŝn entities (a point, a line, a plane)
about which the actions take place.
two step operation: Ĉn followed by σ̂ through plane ⊥ to Cn
Ŝ4 ( z ) ( x1, y1, z1 ) = σˆ xyĈ4 ( z ) ( x1, y1, z1 ) = σˆ xy ( y1, −x1, z1 ) = ( y1, −x1, −z1 )
Note: rotation of pt is clockwise; Corollary is that axes rotate counterclockwise relative
to fixed pointChimica Inorganica 3 symmetry operations & symmetry elements
Chimica Inorganica 3
5) improper rotation, Sn
two step operation: Cn followed by σ through plane ⊥ to Cn
Ŝ4 ( z ) ( x1, y1, z1 ) = σˆ xyĈ4 ( z ) ( x1, y1, z1 ) = σˆ xy ( y1, −x1, z1 ) = ( y1, −x1, −z1 )
Note: rotation of pt is clockwise; Corollary is that axes rotate counterclockwise relative
to fixed pointChimica Inorganica 3
In the example above, we took the direct product of two operators:
⎧for n even: Ŝnn = σˆ hn ⋅ Ĉnn = Ê ⋅ Ê = Ê
⎪
⎪for n odd: Ŝnn = σˆ hn ⋅ Ĉnn = σˆ h ⋅ Ê = σˆ h
⎪
σˆ h ⋅ Ĉn = Ŝn ⎨
⎪
⎪for m even: Ŝnm = σˆ hm ⋅ Ĉnm = Ĉnm
⎪for m odd: Ŝnm = σˆ hm ⋅ Ĉnm = σˆ h ⋅ Ĉnm = Ŝnm
⎩Chimica Inorganica 3
Symmetry operations may be represented as matrices. Consider the vector v
Convention is that the principal axis of
rotation (rotation axis with highest n)
positioned to be coincident with the z axis
⎛ x1 ⎞ ⎡ ⎤ ⎛ x1 ⎞ ⎛ x1 ⎞
⎢ ⎥⎜ ⎟ ⎜ ⎟
1) Identity: Ê ⎜ y1 ⎟ = ⎢ ? ⎥ ⎜ y1 ⎟ = ⎜ y1 ⎟
⎜ ⎟
⎝ z1 ⎠ ⎢⎣ ⎥⎦ ⎝ z1 ⎠ ⎝ z1 ⎠
⎡ 1 0 0 ⎤
⎢ ⎥
matrix satisfying this condition is: ⎢ 0 1 0 ⎥
⎢⎣ 0 0 1 ⎥⎦Chimica Inorganica 3
⎡ 1 0 0 ⎤
⎢ ⎥
Ê = ⎢ 0 1 0 ⎥ is always the unit matrix
⎢⎣ 0 0 1 ⎥⎦
2) plane of reflection, σˆ xy
⎛ x1 ⎞ ⎛ x1 ⎞ ⎛ 1 0 0 ⎞
σˆ xy ⎜ y1 ⎟ = ⎜ y1 ⎟ σˆ xy = ⎜ 0 1 0 ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ z1 ⎠ ⎝ −z1 ⎠ ⎜⎝ 0 0 −1 ⎟⎠
similarly ⎛ 1 0 0 ⎞
σˆ xz = ⎜ 0 −1 0 ⎟
⎜ ⎟
⎜⎝ 0 0 1 ⎟⎠
⎛ −1 0 0 ⎞
σˆ yz = ⎜ 0 1 0 ⎟
⎜ ⎟
⎜⎝ 0 0 1 ⎟⎠Chimica Inorganica 3 3) inversion, î ⎛ x1 ⎞ ⎛ −x1 ⎞ ⎛ −1 0 0 ⎞ iˆ ⎜ y1 ⎟ = ⎜ −y1 ⎟ iˆ = ⎜ 0 −1 0 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ z1 ⎠ ⎝ −z1 ⎠ ⎜⎝ 0 0 −1 ⎟⎠ 4) Proper rotation axis: because of convention, φ, and hence zi, is not transformed under Cn(θ) projection into the xy plane need only to be considered; i.e., rotation of vector v(xi,yi) through θ
Chimica Inorganica 3
x1 = v cos α ⎫ Ĉn (θ ) ⎧⎪ x2 = v cos ⎡⎣ − (θ − α )⎤⎦ = v cos (θ − α )
⎬ ⎯ ⎯⎯ →⎨
y1 = v sin α ⎭
⎩⎪ 2
y = v sin ⎡
⎣ − (θ − α ) ⎤
⎦ = − v sin (θ − α )
x2 = v cos (θ − α ) = v cosθ cos α + v sin θ sin α = x1 cosθ + y1 sin θ
y2 = − v sin (θ − α ) = − [ v sin θ cos α − v cosθ sin α ] = −x1 sin θ + y1 cosθ
⎛ x1 ⎞ ⎛ x1 cosθ + y1 sin θ ⎞ ⎛ cosθ sin θ 0 ⎞
Ĉn ⎜ y1 ⎟ = ⎜ −x1 sin θ + y1 cosθ ⎟ ; Ĉn = ⎜ −sin θ cosθ 0 ⎟ ; θ = 2π
⎜ ⎟ ⎜ ⎟ ⎜ ⎟ n
⎝ z1 ⎠ ⎝ z1 ⎠ ⎜⎝ 0 0 1 ⎟⎠Chimica Inorganica 3
2π
Ĉ3 → θ =
3
⎛ 2π 2π ⎞ ⎛ 1 3 ⎞
cos sin 0 ⎟ ⎜ − 0 ⎟
⎜ 2 2
⎜
3 3
⎟ ⎜ ⎟
2π 2π ⎜ ⎟
Ĉ3 = ⎜ −sin ⎟ 3 1
cos 0 =⎜ − − 0 ⎟
⎜ 3 3 ⎟ 2 2
⎜ ⎟ ⎜ ⎟
⎜ 0 0 1 ⎟ ⎜ 0 0 1 ⎟
⎜⎝ ⎟⎠ ⎜⎜ ⎟
⎟⎠
⎝
5) Improper rotation axis
σˆ h ⋅ Ĉn (θ ) = Ŝn (θ )
⎛ 1 0 0 ⎞ ⎛ cosθ sin θ 0 ⎞ ⎛ cosθ sin θ 0 ⎞
⎜ 0 1 0 ⎟ ⋅ ⎜ −sin θ cosθ 0 ⎟ = ⎜ −sin θ cosθ 0 ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜⎝ 0 0 −1 ⎟⎠ ⎜⎝ 0 0 1 ⎟⎠ ⎜⎝ 0 0 −1 ⎟⎠Chimica Inorganica 3
σ̂ h ⋅ Ĉn (180 )
⎛ 1 0 0 ⎞ ⎛ cos180 sin180 0 ⎞
⎜ 0 1 0 ⎟ ⋅ ⎜ − sin180 cos180 0 ⎟
⎜ ⎟ ⎜ ⎟
⎝ 0 0 −1 ⎠ ⎝ 0 0 1 ⎠
⎛ 1 0 0 ⎞ ⎛ −1 0 0 ⎞ ⎛ −1 0 0 ⎞
⎜ 0 1 0 ⎟ ⋅ ⎜ 0 −1 0 ⎟ = ⎜ 0 −1 0 ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜⎝ 0 0 −1 ⎟⎠ ⎜⎝ 0 0 1 ⎟⎠ ⎜⎝ 0 0 −1 ⎟⎠
σˆ
h ⋅ Ĉ (θ )
2 = iˆYou can also read
