Orbitals and energitics

RDCH 702 Lecture 4: Orbitals and energeticsMolecular symmetryBonding and structureMolecular orbital theoryCrystal field theoryLigand field theory

Provide fundamental understanding of chemistry dictating radionuclide complexes

Structure based on bondingCoordination important in defining structureStructure related to spectroscopic behaviorElectron configuration important in structured8 are square planard0 and d10 tetrahedral

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Molecular symmetryEvaluation of point groupsDescription of symmetry present in moleculesAxisPlanesInversionRotationUse with group theory to determine spectroscopic properties

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Method for determining molecular symmetry and point group

Use molecular geometry to follow chain

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Non-linear, less than 2 unique C3 axis

4-#Identifying Point Group

Cs,C2,C3,D3,C2v,C3v,C3hC3D3h

4-#Point GroupsH2O point groupC2v symmetrySymmetry elementsE, C2 (180 rotation), 2 vertical mirror planes (sv)E, C2, sv, svNH3 point groupC3v point groupElementsE, C3 (each N-H), three vertical mirror plane through each N-H (3sv)E, C3, 3svApply to identification tree

4-#Symmetry and spectroscopya1 vibration generates a changing dipole moment in the z-directionb1 vibration generates a changing dipole moment in the x-direction b2 vibration generates a changing dipole moment in the y-directiona2 vibration does not generate a changing dipole moment in any direction (no x, y or z in the a2 row). a1, b1 and b2 vibrations provide changes dipole moments and are IR activea2 vibrations have no dipole moments IR inactiveC2vEC2v (xz)v (yz) A11111zx2, y2, z2A211-1-1RzxyB11-11-1x, RyxzB21-1-11y, Rxyz.

4-#Coordination numberGeometry strongly influence by coordination numberCan assess information on potential structure and geometry from coordination number (CN) CN=5Interconvertibility between geometriesCompounds can vary between shapesTrigonal bipyramid seems to be more commonCommon with metal pentachloride species

PuOONHHHCNGeometries2Linear (Dh)Bent (C2v)3Planar (D3h)Pyramidal (C3v)Some T-shaped forms (C2v)4Tetrahedral (Td)Square geometry (C4h)One lone pair (C2v)5Trigonal bipyramid (D3h)Square pyramid (C4v)BHHH CHHHHXeFFFF CuClClClClCl InClClClClCl

4-#Coordination NumberCoordination number 6Very common coordination numberLigands at vertices of octahedron or distorted octahedronOctahedron (Oh)Tetragonal octahedron (D4h)Elongated or contracted long z axisRhombic (D2h)Changes along 2 axisTrigonal distortion (D3d)

Oh ->D4hOh ->D2hOh ->D3dor

4-#Higher coordination: Relevant for actinides

7 coordinationPentagonal Bipyramidal, Capped Trigonal Prismatic and Capped Octahedral.

8 coordination: Cubic structure, the Square Antiprism, Dodecahedron

9 coordination: Tricapped trigonal prismatichttp://www.d.umn.edu/~pkiprof/ChemWebV2/Coordination/CN8.html

4-#Hard and soft metals and ligandsBased on Lewis acid definitionLigand acts as basedonates electron pair to metal ionHard metal ion interact with hard basesHard ligands N, O, FSoft ligands P, S, ClLigand hardness decreases down a groupHard metalsHigh positive chargesSmall radiiClosed shells or half filled configurationsSoft metalsLow positive chargesLarge ionic radiusNon-closed shell configurationsTend to be on right side of transition seriesLanthanides and actinides are hardActinides are softer than lanthanidesLigands with soft groups can be used for actinide/lanthanide separations

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Hard

Intermediate

Soft

4-#Chelation and stabilityLigands with more than 1 complexing functional groupCarbonate, ethylenediamineEnhanced stability through chelation effectethylenediamine binding stronger than 2 ammonia groupsBidentateTridentateLigands can wrap around metal ion forming stronger complex

4-#Effective atomic numberMetal bonding can be described with effective atomic numberNumber of electrons surrounding metal is effective atomic numberTransitions metal have 9 possible bonds5 d, 3p, 1 s18 electronsPossible to have effective atomic number different than 18Few d electronsElectronegative ligands

4-#Effective atomic number16 electron Square planard8 configuration (Au, Pt)Greater than 18 electron8-10 d electrons

Expand metal-ligand interactions to exploit bonding and geometryMolecular orbital theoryCrystal field theoryLigand field theory

4-#Molecular orbital theoryMolecular orbitals are comprised from the overlap of atomic orbitalsNumber of molecular orbitals equals the number of combined atomic orbitalsDifferent type of molecular orbitals bonding orbital (lower energy) Non-bonding (same energy as atomic orbitals)Anti-bonding orbital (higher energy)Electrons enter the lowest orbital available maximum number of electrons in an orbital is 2 (Pauli Exclusion Principle) Electrons spread out before pairing up (Hund's Rule)

4-#Molecular orbital

4-#Molecular orbitalsSigma, Pi, deltaGerade and ungeradeN molecular orbitals from N atomic orbitalsN=8 in period 24 sigma, 4 PiPi degenerate bonding and antibonding

O and F

Li to N

4-#Molecular orbitalsMixture of different atomsSome bonding characteristics dominateNonbonding orbitalsNo Pi from HHigh occupied electron orbitalLowest unoccupied electron orbitalBond orderOverall shared electronB=0.5(n-n*)

4-#Symmetry adapted orbitalsCombination of orbitals with symmetry considerationsIf molecule has symmetry degenerate atomic orbitals with similar atomic energy can be grouped in linear combinationsgroups are known assymmetry-adapted linear combinations

4-#20Crystal Field TheoryBehavior of electrons with ligandschanges degenerate statesd and f electronsLone pair modeled as pointRepels electrons in d or f orbitald orbitals have energy differences due to pointResults in ligand field splittingAbout 10 % of metal-ligand interactione and t orbitalsIgnores covalent contributionEnergy difference is ligand field splitting parameter (o)Can be determined from absorption spectrumeg t2g transition

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Crystal Field TheoryTi(OH2)63+Absorbance at 500 nm, 20000 cm-11000 cm-1 = 11.96 kJ/molD0=239.2 kJ/mol D0 found to vary with ligandFor metal ion increases with oxidation state and increases down a groupI- < Br- < SCN- ~Cl- < F- < OH- ~ ONO-