Resources Molecular rbitals in Inorganic Chemistr Dr. P. unt p.hunt@imperial.ac.uk Rm 67 (Chemistr) http://www.ch.ic.ac.uk/hunt/ Web notes AND slides link to panopto when it becomes available model answers to in class activit questions model answers to self-stud problems / eam prep optional background support for beginners questions answered section (from student queries) files for visualising Ms optional material to for eperts links to interesting people and web-sites links to relevant research papers on Ms Recommended Tet Kieran Mollo, Group Theor for Chemists, arwood Publishing, Chichester. onl specific sections!! Reading PTINAL background material, supports lectures adds more details and eplanation some elective reading is advisable if ou are interested in a wider perspective and more comple problems see me! Resources Resources Find m web page tpe unt theoretical chemistr into search engine top hit should be m website Use Socrative www.socrative.com student login!! join http://www.huntresearchgroup.org.uk/ click on teaching under Year Two find Molecular rbitals in Inorganic Chemistr goto Lecture click on slides as presented in the lecture WZ9KBWC wait for me to start the test qui complete the qui!! we share the results qui will appear on our device our website is a god send when ou miss out one little part or need something clarified I reall like that model answers to the tutorial problems are online. This was ver helpful because I could look through them mself 4 L_Slides_07.ke - November 07
Lecture utline introduction wh stud M theor what this course is about revision: smmetr smmetr operations, elements and operators point groups and flow chart character tables what is a character table? using a character table multiple smmetr operations degenerate smmetr labels improper rotations equivalent smmetr operations Wh Stud M Theor? Supersedes VSEPR theor valence shell electron pair repulsion theor VSEPR predicts diamagnetic (paired electrons) the eperimental evidence is that is paramagnetic (unpaired electrons) Fig. Δoct larger [ Ti()6]+ smaller [TiF6]- das Supersedes Crstal Field Theor das are split b the field of the ligands negative ligands should produce a larger Δoct Fig. but eperimentall it is found that F- ligands have a smaller Δoct than Required for odd bonding situations Wh Stud M Theor? Learning how M theor can be used to understand and predict the bonding, structure and reactivit of molecules All relating back to other chemistr courses Main group chemistr, rganometallic and Coordination chemistr, Crstal and Molecular Architecture, Theoretical Methods, Quantum Mechanics, Electronic Properties of Solids Labs and workshops Nobel prie in 998 C6 Fig. see F ig our. 4 in notes development of multiscale models for comple chemical sstems see Fig. 6 in our notes ACS rganometallic Chemistr Award dile Eisenstein computational chemistr labs our final ear research project for the development of modern computational methods Walter Kohn John Pople Martin Karplus Michael Levitt Arieh Warshel C orbital smmetr interpretation of chemical reactions Kenichi Fukui Roald offmann Nobel prie in 0 C The Course Learning how to interpret M diagrams B structure of ethane is well known, diborane B6 was assumed to be similar! while a nd ear undergraduate,. Christopher Longuet-iggins proposed the structure of diborane together with his tutor R. Bell Nobel prie in 98 B 6 Learning how to construct M diagrams B6 5 Learning how to describe and use smmetr specialises in the use of quantum theoretical methods for the stud of cataltic mechanisms Fig. 5 dile Eisenstein, reproduced with permission 7 8 L_Slides_07.ke - November 07
Smmetr Were have ou met smmetr alread? equivalent or C atoms in NMR chiralit labelling of atomic orbitals s and p orbitals octahedral transition metal complees isomerisation: cis/trans fac/mer staggered/eclipsed chair/boat Where understanding smmetr is crucial M diagrams => photoelectron spectrum determines form of M and LUM => reactivit stereo-electronic effects => organic mechanisms smmetr breaking => Jahn-Teller distortions determines allowed vibrations => IR and Raman spectrum determines electronic interactions => dipole moment, UV-vis spectrum Eamples Cv D h Td Point Group Use the flow chart from last ear available in our eam Determined b the number and tpe of smmetr operations 9 Smmetr perations Phsical act of performing a motion eample phsical rotation of water around C ais if nuclei are labeled specific atoms move a and b echange places ( rotates in place) Initial and final states are identical with respect to nuclei smmetr element ou should be able to draw neat diagrams showing smmetr operations (a) smmetr smmetr operation operator => action a b b (b) operation a Fig. 7 Smmetr elements 0 Smmetr Elements objects about which smmetr operations occur rotation ais reflection plane inversion point Include aial information alwas put an ais definition on our diagram correctl orientate the aial sstem -ais is aligned along the highest n-ais watch out for diatomics! -ais is along the bond (wh?) Important! L L see Figure 8 in our notes for revision of different smmetr elements smmetr element => ais M C 4 () L C 4 L L L M L L rotation smmetr operation => action Fig. 8 L_Slides_07.ke - November 07
Smmetr perators Same Notation! Smmetr operator mathematical representation of the action operator acts on the wavefunction or molecule (hence brackets) Advanced (not required) operator is a matri ie C rotation matri ψ operator acts on wavefunction = ψ Smmetr operation the act of performing a motion Smmetr elements objects about with smmetr operations occur Smmetr operator mathematical representation of the action operation rotate b 80º Fig. 7 element Chemical Bonding course Math courses Spectroscop and Characterisation course Quantum mechanics operator acts on molecule Fig. 9 operator ψ = ψ Fig. 8 Fig. 9 Eample: 4 In-Class Activit Smmetr elements for : identit E C rotation ais reflection plane σv() reflection plane σv() Flow chart for identifing the point group is the molecule linear? N are there two or more Cn N>? N is there a Cn? YES are there nc perpendicular to Cn? N is there a σh? N is there a σv? YES point group: v () () () Fig. 0 socrative qui! The question was part of an eam and related to a M diagram for What is the point group of this molecule? The -ais should align The principle ais is WZ9KBWC what is wrong with this answer! Fig. 5 6 L_Slides_07.ke - November 07
In-Class Activit In-Class Activit What is wrong with this answer to part of the 006 eam? wrong point group wrong principle ais What is the point group of this molecule? point group: D h The -ais should align along the bond with the principle ais of the molecule The principle ais is principle ais is highest C ais, C ais Problems? see Revision notes Additional material on m web-site The question Given this molecule of cis-4 clearl indicate all of the smmetr elements on a diagram. (4 marks) what is wrong with this answer! Fig. 7 8 In-Class Activit What is wrong with this answer? Character Tables ke part of this course is learning how to use character tables determine smmetr of Ms other uses not covered in this course... but covered net ear in Find our Character Tables bring to EVERY lecture v character table /4 what is wrong? does not include an ais definition does not include aial information in element names what is correct? all of the smmetr elements identified and drawn on the molecule molecule is correctl orientated diagram is tid and clear Spectroscop & Characterisation character table handout includes character tables of all main smmetr groups a cop of these character tables will be available to ou in the eam v A A B B E () '() h=4 - - - - - - Fig. 9 0 L_Slides_07.ke - November 07
Character Table Components Using Character Tables smmetr labels v A A B B smmetr operations E () '() - - - - - - h=4 number of smmetr operations smmetr of cartesian aes best wa to understand character table is to use it eample: lowest energ M of water s atomic orbital on each of the and atoms has Cv smmetr so use Cv character table start b constructing a representation table: smmetr operations as in character table Fig. 4 irreducible representation s and - s are characters unknown representation v E () '() Fig. 5 Using Character Tables Using Character Tables Determine how the orbital transforms under each smmetr operation of the group orbital is unchanged => character= a sign change => character= - smbol representing a character Determine how the orbital transforms under each smmetr operation of the group orbital is unchanged => character= a sign change => character= - () () () E No change under E χ = No change under χ = v E () '() Fig. 6 v E () '() Fig. 6 4 L_Slides_07.ke - November 07
Using Character Tables Using Character Tables Determine how the orbital transforms under each smmetr operation of the group orbital is unchanged => character= a sign change => character= - () () () Determine how the orbital transforms under each smmetr operation of the group orbital is unchanged => character= a sign change => character= - () () () () No change under χ = () No change under χ = v E () '() Fig. 6 v E () '() Fig. 6 5 6 Using Character Tables In-Class Activit same set of characters as the irreducible representation a v E () '() the second highest energ M for water out of phase s atomic orbitals on the hdrogen atoms and a p atomic orbital on the ogen atom our turn: Fig. 8 Important! Use small letters when referring to the smmetr labels of Ms A -> a v A A B B E () '() - - - - - - h=4 Fig. 7 v E () '() () () () 7 8 L_Slides_07.ke - November 07
In-Class Activit D h Character Table () () χ = χ = v E () '() - - σ C v D h E S A ' A ' E' - - 0 - - 0 (T, T ) () () χ = this orbital has b smmetr () () Find the D h character table in our set of Character Tables A " A " E" - - - - - - - 0-0 T Fig. 9 () 9 0 D h Character Table Multiple perations Show b eample Use simple molecule or + Planar equilateral triangle common orbital fragment B, N, ER, ML etc Model for heavier elements such as Au highest active orbital is 6s orbital + is interesting! Most abundant ion in universe Important for interstellar chemistr Use spectroscop to detect new interstellar species, also provide information on interstellar chemical and phsical conditions Links on the web-site Smmetr operations of Dh E identit C rotations C rotations σh reflection S improper rotations σv reflections number of operations h=total number of operations =+++++= D h E S A ' A ' - - E' - 0-0 A " - - - A " - - - E" - 0-0 (T, T ) T Fig. 9 Fig. 0 L_Slides_07.ke - November 07
Rotations Rotations in General = E Fig. Each rotation of order n has n rotations for eample C 4 C 4 C 4 final rotation returns to starting geometr =E onl keep unique operations if alread counted in a smmetr element to the left on the character table, or under a rotation of lower n it is not counted again C 4 4 each set of rotations forms a group rotation groups mathematical entities whole area of mathematics devoted to groups 4 Rotations Multiple perations three separate C aes each contributes one C rotation find one C ais and use C to find the rest each element is distinct: = E Fig. C and C appear in the character table of Dh it doesn t matter if these are the SAME or DIFFERENT smmetr elements the table onl cares about operations E S one element operations three elements operations Fig. 5 6 L_Slides_07.ke - November 07
Smmetr Labels Smmetr Labels A and B singe representations atoms/orbitals map onto each other D h E S A ' A ' - - E' - 0-0 A " - - - A " - - - E" - 0-0 (T, T ) T Fig. 9 A and B singe representations atoms/orbitals map onto each other E doubl degenerate don t confuse with E operation! orbitals as a group map onto each other character = under E operation T tripl degenerate tetrahedral point groups (Td) character = under E operation D h E S A ' A ' - - E' - 0-0 A " - - - A " - - - E" - 0-0 (T, T ) T Fig. 9 7 8 Smmetr Labels A and B singe representations atoms/orbitals map onto each other E doubl degenerate don t confuse with E operation! orbitals as a group map onto each other character = under E operation T tripl degenerate tetrahedral point groups (Td) character = under E operation das e g doubl degenerate t g tripl degenerate You have alread seen e and t smmetr labels! D h E S A ' A ' E' A " A " E" - - - 0-0 - - - - - - - 0-0 (T, T ) T Fig. 9 Degenerate Representations degenerate representations touched on in our maths course eample: (p,p) have e smmetr in Dh B Fig. 9 40 L_Slides_07.ke - November 07
Degenerate Representations Degenerate Representations degenerate representations eample: (p,p) have e smmetr in Dh character refers to BT components how to work out the character? take point on tip of each orbital write the position in coordinates as form matri b combing the coordinates point on tip p p Fig. p p 0 0 = 0 0 degenerate representations eample: (p,p) have e smmetr in Dh character refers to BT components how to work out the character? take point on tip of each orbital write the position in coordinates as form matri b combing the coordinates perform the operation p p p after operation p E E 0 0 = 0 0 0 Fig. 4 4 Degenerate Representations Degenerate Representations degenerate representations eample: (p,p) have e smmetr in Dh character refers to BT components how to work out the character? take point on tip of each orbital write the position in coordinates as form matri b combing the coordinates perform the operation the character is the TRACE of this matri trace=sum of diagonal terms for this eample (E) trace=+= character is p E 0 p Fig. p p E 0 0 = 0 0 the character for the σv operation under Dh 0 PTINAL: More details about degenerate representations on m web-site 0 0 0 0 0 D h E S A ' A ' E' A " A " E" - - - 0-0 - - - - - - - 0-0 Fig. 4 (T, T ) T 4 44 L_Slides_07.ke - November 07
In-Class Activit In-Class Activit find character for the C operation under Dh find character for the C operation under Dh 0 Fig. 5 C 0 C 0 0 0 0 0 D h E S A ' trace=sum of diagonal terms trace=+-=0 character is 0 A ' E' A " - - - 0-0 - - - (T, T ) Model answer on the web-site A " E" - - - - 0-0 T 45 Improper Rotations 46 Equivalent perations rotation rotation followed b reflection in mirror plane perpendicular to the ais of rotation phase changes are important use pas to visualise Important! R take a point off the mirror plane and ais (black circle above) sometimes it requires two full rotations to return to starting state S reflection Fig. 6 S E S 6 = E onl keep unique operations count smmetr element to the left on the character table does not appl to rotations count lowest n for Cn operations first for eample count C over C 4 final rotation in a group =E man improper rotations will have alread been counted watch out for odd Sn n=odd S n n E 47 48 L_Slides_07.ke - November 07
Improper Rotations Ke Points diagram showing S E = Be able to define smmetr element, operation and operator S S Be able to draw clear diagrams showing the smmetr elements of a molecule and the action of a smmetr operation Be able to define all the components of a character table Be able to use character tables to find the smmetr label of Ms S Be able to identif when operations in the header row are due to multiple smmetr elements or multiple smmetr operations S = S E Fig. 7 Be able to identif degenerate irreducible representations Be able to determine the characters of degenerate IRs Be able to perform and illustrate Sn operations PTINAL: Supporting information about improper rotations on m web-site Be able to identif and show when operations are not unique 49 50 Finall http://www.huntresearchgroup.org.uk/ See m web-site notes AND slides link to panopto when it becomes available optional background support for beginners optional material to take ou a little further links to interesting people and web-sites links to relevant research papers on Ms model answers!! 5 L_Slides_07.ke - November 07