Inorganic Chemistry I
Inorganic Chemistry I CHEM 1311
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This 0 page Class Notes was uploaded by Tierra Ernser on Monday November 2, 2015. The Class Notes belongs to CHEM 1311 at Georgia Institute of Technology - Main Campus taught by Angus Wilkinson in Fall. Since its upload, it has received 11 views. For similar materials see /class/234321/chem-1311-georgia-institute-of-technology-main-campus in Chemistry at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
Molecular Orbital Theory 9 In principle the electronic structure of molecules can be worked out in the same way as for atoms 7 solve the Schrodinger equation 9 This gives molecular orbitals rather than atomic orbitals Q But It is difficult to solve the Schrodinger equation for molecular species only through approximation LCAO approximation Q LCAO Linear Combination of Atomic Orbitals Q The wavefunctions of molecular orbitals can be approximated by taking linear combinations of atomic orbitals 1 13 JEDHJHuthHQ linear combination addition of the wavefunction from two 15 orbitals LCAO approximation 9 A second MO molecular orbital can be obtained via subtraction of two 1 ENJHJ I rle 1 HiH bond axis electron density zero ener ofan electron in this orbital is higher compared to the additive linear combinatio antibom ng orbital nodal plane i 2 linear combination subtraction of the wavefunction from two 15 orbitals Bonding in H2 6 Take two ls orbitals as the basis QGet two MO s l 15A 1sB H H w New mnlmlr One electron inBO V 15A 39 1sB gives 25 eV band A energy but two W i i electrons give only 45 eV Why Na pr Potentials for occupied bonding and antibonding orbitals o Occupying the bonding orbitals of a molecule makes the interaction between atoms attractive they stick together 9 Occupying antibonding o orbitals makes the Energy interaction between atoms 0 v 160 Ego ICPUISiVC Separation pm Frrst Perrod Dratomrc Molecules r y 1 l I E E gt H 1 l 53er l 15 E g Li l Linear combinations of pZ orbitals 9 Addition of two pZ AOs results a bonding 6p MO subtraction will give an antibonding 613 MO with a nodal plane perpendicular to the bond axis In 5 Wm H gt H gt Do OltD Doc 14 Hr Hgt nodal plane OQOQ gt0 Linear combinations of pX and py orbitals containing a nodal plane along the bond ax15 O Subtraction results an antibonding npquot MO With two nodal planes one plane perpendicular and one parallel to the bond HlP 0 Addition of two px or py AOs results a bonding up MO Classifying orbitals by symmetry O Orbitals in diatornics can be classi ed according to their rotational symmetry characteristics as G 7 or These classi cations are strictly only valid for diatomics but we also use them to describe bonds between pairs of atoms in polyatomic molecules G orbitals 7t orbitals 5 Orbltals Foundin quadruply bonded 39 m 127 What types of bond can be formed 9 The type of bond 6 71 or 5 that can be formed depends up on the available atomic orbital types Electron density distribution of different MOS Overlap between orbitals Q The extent to which orbitals overlap can be evaluated using an overlap integral S 7 S 0 indicates that the orbitals do not 47 l 39t t 39th 2231 ap 1n erac W1 one I er 7 S depends on the symmetry of the orbital Overlap 2 Q Do the orbital combinations on the right have S 0 S gt0 or Slt 0 energy O Electrons are filled according to the same guidelines as for multielectron elements Aufbau principle Full energy level diagram for second row diatomics Rules for the use of MOs Q When two AOs mix two MOS will be produced 0 For mixing AOs must have similar energies 9 Each orbital can have a total of two electrons Pauli principle 9 Lowest energy orbitals are filled first Aufbau principle 9 Unpaired electrons have parallel spin Hund s rule Bond order 12 bonding electrons antibonding electrons Molecular oxygen AOs energy mom a an mam morecum Aron a Bond order 2 2 unpaired electrons gt paramagnetic Molecular uo ne AOs V AOs energy uH Mom a shamanquot mmeculs Mom r Bond order 1 0 unpaired electrors gt diamagnelic Neon energy Alum a an mammw molecule Axon a Bond order 0 gt not a stable molecule Orbital Mixing Q Orbitals with similar energy interact if they have the appropriate symmetries Q The 62p and 625 orbitals are symmetry related and give rise to two new orbitals one with higher and one with lower energy quot Effect of orbital mixing energy mg Mum Ila any Note With mixing the cg orbital is higher in energy than the 12 orbitals Ungerade or gerade O MOS in molecules that are centrosymmetric can be classi ed as g or u 7 Useful for predicting spectroscopic transitions etc 7 g implies that the wavefunction does not change sign on inversion through the center of the molecule 11 means that it does change Sign 71 x iii 21 79 and 7 orbitals 20 GU and 6H orbitals Photoelectron Spectroscopy PES 9 UVphotoelectron spectroscopy can be used to verify the MO energy level diagram 7 Molecules are ionized With monochromatic light N2g hv gt NM e The kinetic energy of the resulting photoelectrons are measured and a plot of number of photoelectrons versus photoelectron energy drawn this is a photoelectron spectrum The PES experiment Fhomnlamon mummy m gunmanhumugvmmm x inelu nqv l m krunn mm 1 mm mugv m m peclmmuev Imus mi mmm m pnmmmm w miklml kmrlm um The PES spectrum of N2 Vibrntiunal iovais N2 izis ev 167 ev mi m The uv Mmudutmn sputum of N1 nu m mam in thrspe t a nu almnativr omenng oi nvbilal c mm l arms min Ht mum of vmlznuns m E zlgirs m cahnn 1mm iw nhotmjcdtun mud in humanuclear mammn mulwtks nom ti1 Io N1 Note nitrogen atoms have a first ionization energy of 145 oV Molecular Nitrogen 0 According to calculations the GS orbital is higher in energy than the two 712 orbitals energy N alum n Beryllium Bez Molecule all energy Be alum b Es alum a Be2 molecule Bond order 0 9 not a stable molecule Wes detected 81 ver lowlemperalure bond energy 4kJm0l l Lithium Liz Molecule energy Li atom 17 Li amm 3 Liz molecule Bond order 1 known in the 925 phese N0 unpaired electrors 9 diamagnelic Bond Order vs Bond Length amp Energy Specles Bond order Bond uengmpm Bond energyrkd molquot H2 V2 H2 1 A 1 422 Hg 12 7 10mm He2 o 297 0139 L12 1 2673 101 Be a 7 4 B2 1 1 285 oz 2 12425 599 N2 3 105 a 942 oz 2 120 7 493 02 2 12 1n 6 613 0239 1 12 135 395 022 1 149 7 F2 1 1M 2 155 310 u 239 Ne 2 a Van der Waa lorcas Hetronuclear diatomics Q The contributions to the MO from each of the atoms is unequal 7 w cA A cB B O The more electronegative atom contributes strongly to the bonding orbital Q The less electronegative atom contributes strongly to the antibonding orbital 7 gives rise to polarity Orbital mixing O The difference in energy wzcwrwm39caguz between orbitals on W different atoms leads to reduced mixing in 7 The reduced mixing does not imply weaker bonding VCWAEB 5 2 2 320 When two atomic orbltals with 39 mnumgiesumlapn l war 2 same energy in the atoms Heteronuclear Molecules O The relative energy of the bonding orbitals determines the magnitude of the covalent bond energy ABM Mia73 Muckless ms More mummnegmwc em mnegalwg elecsranegshve mm zwm mm Hydrogen Fluoride Q In HF the ls orbital of H is energetically well above the ls and 2s orbitals of F 7 it interacts only with the 2pz orbital all remaining electrons are in non bonding orbitals nonbondingMO s Mumn I u mm s molech Emmy level mnnum lnr HF in n no Lithium Fluoride Q As the polarity difference between two atoms increases the orbital energy difference also increases 7 electrons shift towards the more electronegative atom 9 Limiting case Ionic compounds o W Ions are held together in a N 3dimensional lattice b covalent Intermtlo s 9 T ere are no directional bo urv Carbon monoxide 1 22 Tn malrcnlar orkmal cmgy ml v gvam Df cu Note that the HOMO and LUMO are largely on c Important for metal Molecular Orbitals of Polyatomic Molecules 9 Concept of linear combination can be also applied to polyatomic molecules 7 the resulting MOS are delocalized over the entire mo CCU C 9 Symmetry analysis by group theory predicts those linear combinations which lead to bonding antibonding or nonbonding M05 0 The energy of the resulting M05 is measured Via photoelectron spectroscopy or estimated with quantum chemical calculations Beryllium Dihyd de BeHZ o VSEPR analysis linear geometry 9 Set of AOs I y Be one 23 three 2p was H H two 1s orbitals Note the 2px and 2py orbitals result nonbonding intermtions 9 Form group orbitals with 1s orbitals of H and Overlapwith2pZBe G a M m I g PuHgt 1 nH39 Gmquot r quot if nia B Q WA wHgt PltHgt Overlap with 25 Be Group Orbitals Interact with Be A05 5 interacts with the 25 orbital ofBe to form a bonding 039s and antibonding 05 orbital wanm Sig interacts with the 2pz orbital ofBe to form a bonding 0 and antibonding 019 orbital mama mm r v pun We MO s in linear triatomic molecules BeH2 I The electronegativity of hydrogen is greater than that of beryllium so the hydrogen orbital are lower in energy I Take linear combinations ofterminal quot39 39 39 they can overlap with orbitals on the E central atom I Construct energy level diagram I Distribute electrons starting with the lowest energy orbital I What is bond order ofthe individual BeH bonds I BeH2 is strongly Lewis acidic as a result of its electron de ciency vacant p orbitals Z MOS of Water H20 O VSEPR analysis bent geometry y 9 Set of AOs 7 0 one 25 three 2p H z o mthexrz planeWiLhZ Hi W0 15 orbitals bisectmg the HVOVH angle Note the 2py orbital is nonbonding 9 Form goup orbitals With ls orbitals ofH and H Overlap with2pxO u FET1Hgt P1HI e CW 9 WA wHgt ml Overlap with 25 2pz The Two TA Group Orbital Interactions EVA interacts with two AOs of Oxygen The 25 and 2pZ orbital QD 9 this results in one bonding one antibonding and one nonbonding approximately orbital Oxygen A03 03952quot Group Orbital The TB Group Orbital Interaction EVE interacts with the 2pX orbital of oxygen to form a bonding 0 and antibonding of orbital 0 Own phase a 0 a a 711 HUB mime 21 To Give the Final Energy Level Diagram aw energy on who MO s in bent triatomic molecules OH2 22 23 the presence of non equivalent one pairs PES spectrum confirms Four ionizations in the 5 rev Photoelectron spectroscopy PES hv IE KE ejected electron Evidence for nonequivalent one pairs 3D contours of MO s for water Composition of NH3 MOS J3 3 2 Me WWWquot 239 m mumAm mum Nu m Mn airman r in mm mm m m mm mm mm mam w m wvw ammw mmm M w M m Km m m Wm m m w i Am in m m m Vhtugni m m mmuk m gimme a MO diagram PBS for NH3 15 ionizaxiun energy2V 3m Ihe uv phomtlcctmn spmmm M NH using helium 2 eV radiation 133 m mm mm mum 4m mm a w m M mme m n mm m m mm M mm mm 24 H3 O This species is postulated as an intermediate in some reactions ilt is the simplest triatomic molecule Linear H3 16 1214A 2 2C121503 C12150 20 1SA 1SC quot 39 2 30 1SA 211503 12150 mum whm39 qu mm m guw lmuh umwsn us M 1m x39mvuv mvcwm 25 Three center two electron bonds O The orbitals in H3 are delocalized over the entire molecule Oln H3 2 electrons hold the molecule together 7 this is an example of a three center two electron bond Diborane and electron de cient compounds Q BZH6 is a compound that you can not draw a reasonable Lewis structure for I J H H H B B H H H J J J J Electron de cient as the three atoms the BHB bridge are held together using only two electrons 26 SF6 and hypervalence 334 A schematic molecular nrbltal energy level diagram for SF XeF2 and electron excess compounds O The electronic structure of Xer and it s stability can be rationalized by invoking a 3 center 4 electron bond 27 MO s for Polyatomic chains Constructing MOS for polyatomic chains W27 28 MO s in onedimensional arrays of like orbitals OThere Will be as many MO s as orbitals in the array Every molecular orbital is characterized by a speci c pattern of nodes OThe lowest energy orbital will have zero nodes the next highest Will have one node the next two etc The highest energy molecular orbital Will have nl nodes Where n is the number of atomic orbitals involved OW39hen symmetrical placement of a node causes it to fall on an atom then that atom does not contribute to the molecular orbital 8888 888888 3 8888 88 888888 88 8888 88 88 888888 8888 88888 888888 888888 E88 8 8 8 8 8 MO patterns in some common systems Allyl 1 system Benzene 1 system T T H c H H c H ltgt f c f f H x quotH H H 88 29 MO s and reactions of allyls l H l e HCCdH HC C6 H x l l 39 l l H X H H l 9 H H 3C 3 H Three parallel p l H atomic orbitals t KCRS H l l H H H H l H H q l I TR NikiH H H D D H Three parallel p atomic orbitals generates three 7 k 6H Formed In equal amounts because the terminal type molecular orbitals l atoms contribute equally to the occupied H H HOMO in the anion The red and blue carbons represent different carbon isotopes MO s and reactions of allyls l HC C 7 7 7 l H H He Three parallel p H atomic orbitals H H HC 7H 7 7 7 l l C Tut u H H H H 9 359 C l H H q l a EE g I D39 a pro relH V H D D H Three parallel p atomic T orbitals generates three 7i kEKC7H Formed in equal amounts because the terminal type molecular orbitals l atoms contribute equally to the occupied HOMO in the anion The red and blue carbons represent different carbon isotopes 30 Bonding and electronic structure of metals and other solids OAny successful model for the bonding in solids must be able to explain good thermal and electrical conductivity of metals Origin of semiconducting and insulating behavior QMolecular Orbital theory can be extended to solid materials including metals Metals insulators and semiconductors insulators semiconductors metals E 2 c to E 3 a o fused silica diamond glass iron copper q Silicon b I I l 103920 103916 103912 10398 100 1o Conductivity 2 391cm 1 31 Molecules of metal atoms Crystals can be thought of as very large molecules made up of metal atoms Na Atomic Molecular 39 orbitals orbitals 11 Li Lin Ha fmed band Continuum of orbitals on diagram is a band Electrical conductivity and band theory QSolids only conduct electrons When they have unpaired electrons in orbitals This is the same as saying they must have partly lled bands to conduct electrons Q Metals have partly lled bands even at OK 9Semiconductorsinsulators have lled and empty bands at OK 32 Band structure for Be Mg etc Atomic Molecular orbitals orbitals 71 Be Ben p band s band s and p bands overlap in energy range so both bands are partly filled Band structure for semiconductors conduc on band Band gap 159 semiconductor metal 2 Conduction in an intrinsic very pure semiconductor can be achieved by the thermal promotion of electrons across the band gap giving two partly filled bands 33 Doping semiconductors O The addition of very small amounts of dopant can dramatically in uence semiconductor properties 7 P As added to silicon gives n type material gtgt they are providing more electrons than the silicon that they replace 0 They effectively put electrons in the conduction band 7 B Al Ga gives p type material gtgt they are providing fewer electrons than the silicon that they rep ace 0 They effectively generate holes absence of electron in the valence band 9 The conductivity of doped semiconductors varies less than that for an intrinsic semiconductor with temperature Extrinsic semiconductors O Doping can be used to increase the conductivity of a semiconductor conduction band lt valence band p doping n doping 34 Temperature dependence of conductivity O The conductivity of a metal decreases with increasing temperature mobile electrons are scattered by lattice vibrations Q The conductivity of a semiconductor increases with increasing temperature as more charge carriers become available semiconductor or insulator resistivity reSIstIVIty metal temperature temperature Figure 78 The resistivities of metals and semiconductors or insulators show different behavior when the temperature is changed As the temperature is increased the resistivity of a metal increases slightly but the resistivity of a semiconductor or insulator decreases dramatically The relative size of the effect is not shown to scale in this gure Lightemitting diodes Electmns A 139 Sirs life current flaws accrues junctian 35
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