Chimica Inorganica 3...aggirarsi vanamente per un oscuro laberinto. » Galileo Galilei, Il...

Chimica Inorganica 3

COURSE OUTLINE – Inorganic Chemistry 3 Instructors: M. Casarin ([email protected]) & S. Gross ([email protected]) Examination Board: Maurizio Casarin, Marta M. Natile, Silvia Gross & Mauro Sambi 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.


mondaytuesday thursdaywednesday friday


ClassSchedule

15+2 20+4 15+3



Lab.Schedule:firstround,secondround,thirdround


Exams2019-2020;09:00–12:00,roomL1



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


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)


Website: A website will be maintained through the “DiSC” website: http://wwwdisc.chimica.unipd.it/maurizio.casarin/pubblica/casarin.htm


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.


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).



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.)


Top view of a verdant young plant displaying symmetry found in nature.




http://matematica.unibocconi.it/articoli/misura-duomo-leonardo-e-luomo-vitruviano


«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).


Platone ( in greco ant ico Πλάτων , 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.


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.

T Q

T

T

P


solidi platonici






Charge-neutral C2B10H12 or o-carborane Carborane acid anion [CHB11Cl11]- (acidic 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 species



Évariste Galois Bourg-la-Reine, 25/10/1811 – Parigi, 31/05/1832

French mathemaEcian who led a short, dramaEc life and is oFen credited withfoundingmoderngrouptheory,thoughtheItalianPaoloRuffini(1765–1822)cameupwith many of the ideas first. Galois' work wasn't widely acknowledged by hiscontemporaries, partly because he didn't present hismaterial verywell and partlybecauseheheldunpopularpoliEcalviews.Infact,hewasarepublicanrevolu5onarywhowastwice imprisonedbecauseofhisacEviEes.Duringhissecond incarceraEonhefell in lovewiththedaughteroftheprisonphysician,Stephanie-FeliceduMotel,and aFer being released, fought a gun duel over herwith Perscheux d'Herbinville.Mortallywounded intheduel,hewasabandoned inafieldbut foundbyapeasantand taken toahospital.AFera fewdayshediedofan infecEon.Hisdeath startedrepublicanriotsandrallieswhichlastedforseveraldays.Reputedly, the night before his fatal duel, Galois tried to write down as manythoughtsaspossible.Thesenotesandafewotherpaperswerediscovered14yearslaterby JosephLiouville,who recognized themasworksof genius.Galois setoutthe theory of groups and laid down condi5ons for the solvability of variousalgebraicequa5ons.

https://www.terabitcorp.com/galois.htm


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.


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

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.

symmetry operations & symmetry elements


There are five symmetry operations, which will be defined relative to point with coordinate (x1, y1, z1):

1)   identity, Ê

2) reflection,

σ xz x1, y1, z1( ) = x1,−y1, z1( )

E x1, y1, z1( ) = x1, y1, z1( )

σ

Symmetry operations are actions. Symmetry elements are geometrical entities (a point, a line, a plane) about which the actions take place.


3) inversion, î

4) proper rotation, , where convention is a clockwise rotation of the point

i x1, y1, z1( ) = −x1,−y1,−z1( )

θ = 2πn

C2 z( ) x1, y1, z1( ) = −x1,−y1, z1( )


Cn


5) improper rotation, two step operation: followed by through plane ⊥ to Cn

S4 z( ) x1, y1, z1( ) = σ xyC4 z( ) x1, y1, z1( ) = σ xy y1,−x1, z1( ) = y1,−x1,−z1( )

Note: rotation of pt is clockwise; Corollary is that axes rotate counterclockwise relative to fixed point


Sn

Cnσ


symmetry operations & symmetry elements


5) improper rotation, Sn two step operation: Cn followed by σ through plane ⊥ to Cn

S4 z( ) x1, y1, z1( ) = σ xyC4 z( ) x1, y1, z1( ) = σ xy y1,−x1, z1( ) = y1,−x1,−z1( )

Note: rotation of pt is clockwise; Corollary is that axes rotate counterclockwise relative to fixed point


In the example above, we took the direct product of two operators:

σ h ⋅Cn = Sn

for n even: Snn = σ h

n ⋅Cnn = E ⋅ E = E

for n odd: Snn = σ h

n ⋅Cnn = σ h ⋅ E = σ h

for m even: Snm = σ h

m ⋅Cnm = Cn

m

for m odd: Snm = σ h

m ⋅Cnm = σ h ⋅Cn

m = Snm

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪


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

1)   Identity: Ex1y1z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟= ?⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

x1y1z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

x1y1z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

matrix satisfying this condition is: 1 0 00 1 00 0 1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥


is always the unit matrix E =1 0 00 1 00 0 1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

2) plane of reflection,

σ xy

x1y1z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

x1y1−z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

σ xy =1 0 00 1 00 0 −1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

similarlyσ xz =

1 0 00 −1 00 0 1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

σ yz =−1 0 00 1 00 0 1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

σ xy


3) inversion, î

ix1y1z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

−x1−y1−z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

i =−1 0 00 −1 00 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


x1 =v cosα

y1 =v sinα

⎫⎬⎭

Cn θ( )⎯ →⎯⎯x2 =v cos − θ −α( )⎡⎣ ⎤⎦ =

v cos θ −α( )y2 =v sin − θ −α( )⎡⎣ ⎤⎦ = −v sin θ −α( )

⎧⎨⎪

⎩⎪

x2 =v cos θ −α( ) = v cosθ cosα + v sinθ sinα = x1 cosθ + y1 sinθ

y2 = −v sin θ −α( ) = − v sinθ cosα − v cosθ sinα[ ] = −x1 sinθ + y1 cosθ

Cn

x1y1z1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

x1 cosθ + y1 sinθ−x1 sinθ + y1 cosθz1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟; Cn =

cosθ sinθ 0−sinθ cosθ 00 0 1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟; θ = 2π

n


C3 →θ = 2π3

C3 =

cos 2π3

sin 2π3

0

−sin 2π3

cos 2π3

0

0 0 1

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟

=

− 12

32

0

− 32

− 12

0

0 0 1

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟

5) Improper rotation axis

σ h ⋅ Cn θ( ) = Sn θ( )1 0 00 1 00 0 −1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟⋅

cosθ sinθ 0−sinθ cosθ 00 0 1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟=

cosθ sinθ 0−sinθ cosθ 00 0 −1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟


1 0 00 1 00 0 −1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟⋅

−1 0 00 −1 00 0 1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟=

−1 0 00 −1 00 0 −1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

σ h ⋅ C2 θ( ) = i

σ h ⋅ Cn 180( )1 0 00 1 00 0 −1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟⋅

cos180 sin180 0−sin180 cos180 00 0 1

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

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