PChemII Lecture 07 SpectroscopyII P2

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16 16 Term Symbols Term Symbols You may want to You may want to review section 13.9 on review section 13.9 on term symbols for term symbols for atoms. atoms. g 3 17 17 Term Symbols Term Symbols Component of orbital Component of orbital angular about the angular about the internuclear axis, internuclear axis, Λ Λ Multiplicity: 2S+1 Multiplicity: 2S+1 Overall parity, u or g Overall parity, u or g Overall reflection Overall reflection symmetry symmetry g 3 18 18 Term Symbol Term Symbol Component of orbital angular about the Component of orbital angular about the internuclear axis, internuclear axis, Λ Λ Λ Λ is denoted by the symbols: is denoted by the symbols: Σ Σ, , Π Π, , , , … for values of 0, 1, 2, for values of 0, 1, 2, … Example: Example: The single electron in the ground state The single electron in the ground state of H of H 2 + has a value of has a value of Σ Σ since since σ orbitals have zero orbital angular momentum.

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spectroscopy

Transcript of PChemII Lecture 07 SpectroscopyII P2

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Term SymbolsTerm Symbols

•• You may want to You may want to review section 13.9 on review section 13.9 on term symbols for term symbols for atoms.atoms.

−∑ g3

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Term SymbolsTerm Symbols

•• Component of orbital Component of orbital angular about the angular about the internuclear axis, internuclear axis, ΛΛ

•• Multiplicity: 2S+1Multiplicity: 2S+1•• Overall parity, u or gOverall parity, u or g•• Overall reflection Overall reflection

symmetrysymmetry

−∑ g3

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Term SymbolTerm Symbol

•• Component of orbital angular about the Component of orbital angular about the internuclear axis, internuclear axis, ΛΛ

•• ΛΛ is denoted by the symbols: is denoted by the symbols: ΣΣ, , ΠΠ, , ∆∆, , ……for values of 0, 1, 2, for values of 0, 1, 2, ……

•• Example:Example:––The single electron in the ground state The single electron in the ground state

of Hof H22++ has a value of has a value of ΣΣ since since σ orbitals

have zero orbital angular momentum.

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Term SymbolTerm Symbol•• Example:Example:

–– A A ππ electron has one unit of angular momentum electron has one unit of angular momentum about the internuclear axis.about the internuclear axis.

– If there is only one ππ electron outside a closed shell, then ΛΛ = = ΠΠ..

–– If there are two electrons, then If there are two electrons, then ΛΛ can be eithercan be either ΣΣoror ∆∆..•• ΣΣ if they are traveling opposite directions, in if they are traveling opposite directions, in

which case they occupy different which case they occupy different ππ orbitals.orbitals.•• ∆∆ if they are traveling in the same direction, in if they are traveling in the same direction, in

which case they occupy the same which case they occupy the same ππ orbitals.orbitals.

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Term Symbol: MultiplicityTerm Symbol: Multiplicity•• Multiplicity: Multiplicity: 2S+12S+1•• SS = sum of s values from each electron.= sum of s values from each electron.•• ss is always ½. is always ½. •• The total spin angular momentum is The total spin angular momentum is

ΣΣ = 0, = 0, ±±1, 1, ±±2, 2, ±±SS (Note (Note ΣΣ used here is used here is notnot a term symbol)a term symbol)

•• For the ground state of OFor the ground state of O22, , 11σ2σ*21π42 π*2 where there are two unpaired electrons in each the two degenerate π* orbital, the multiplicityultiplicity a triplet since each s value is ½, making S =1, Making the multiplicity = 2(1) +1=0.

• The term symbol is 3ΣΣ..

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Term Symbol: MultiplicityTerm Symbol: Multiplicity

•• The multiplicity for the single electron in The multiplicity for the single electron in HH22

++ is 2, since S= is 2, since S= ½½ and 2(and 2(½½)+1=2.)+1=2.•• This makes the term symbol: This makes the term symbol: 2ΣΣ

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Term Symbol: ParityTerm Symbol: Parity

•• As mentioned earlier:As mentioned earlier:–A bonding σ orbital has even parity, σg .–An antibonding σ orbital has odd parity, σu. –A bonding π orbital has odd parity, πu .–An antibonding π orbital has even parity, πg.

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Term Symbol: Overall ParityTerm Symbol: Overall Parity

• If there are several electrons, the overall parity is calculated by using”

g × g = gu × u = gu × g = u

• These rules are generated by interpreting g as +1 and u as –1.

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Term Symbol: ParityTerm Symbol: Parity

•• The term symbol for the single electron The term symbol for the single electron in in HH22

+ + is therefore: is therefore: 2ΣΣgg..•• The term symbol for the ground state of The term symbol for the ground state of

OO22, with an electron configuration of:, with an electron configuration of:11σ2σ*21π42π*2 or σg

2σu2πu

2 πu2πg

1πg1

• is 3ΣΣgg..

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Term Symbol: Overall Reflection SymmetryTerm Symbol: Overall Reflection Symmetry

• A ± superscript denotes the behavior of the molecular wavefunction under reflection in a plane containing the nuclei.

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Term Symbol: Overall Reflection SymmetryTerm Symbol: Overall Reflection Symmetry

• If, for convenience, we think of O2 as having one electron in 2πx, which changes sign under reflection in the yz-plane, and the other electron in 2πy, which does not change sign under reflection in the same plane, the overall reflection symmetry is

(closed shell) × (+) × (–) = (–)• and the full term symbol of the ground

electronic state of O2 is 3Σg–

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Term Symbol: Overall Reflection SymmetryTerm Symbol: Overall Reflection Symmetry

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Term Symbols and Term Symbols and the Excited Statethe Excited State

• The term symbols of excited electronic states are constructed in a similar way.

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OO22 in Ground and Excited Statesin Ground and Excited States

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Selection RulesSelection Rules• A number of selection rules govern which

transitions between allowed states of a molecule will be observed in its electronic spectrum.

• The selection rules concerned with changes in angular momentum are:∆Λ= 0, ±1 ∆S = 0 ∆Σ= 0 ∆Ω= 0, ±1

• where Ω= Λ + Σ is the quantum number for the total angular momentum (orbital and spin) along the internuclear axis

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Ω= Λ + Σ

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Selection RulesSelection Rules

•• These selection rules arise from the These selection rules arise from the conservation of angular momentum and conservation of angular momentum and the fact that a photon has a spin of 1.the fact that a photon has a spin of 1.

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Selection RulesSelection Rules

Two of the selection rules are concerned Two of the selection rules are concerned with changes in symmetry.with changes in symmetry.

•• For For Σ terms, only Σ– ↔ Σ– and Σ+ ↔ Σ+

are allowed.• The Laporte Selection Rule states

that the only allowed transitions are transitions that are accompanied by a change in parity.

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Forbidden TransitionsForbidden Transitions•• Since only, g Since only, g →→ g and g and

u u →→ u transitions are allowed, u transitions are allowed, g g →→ g transitions are g transitions are forbiddenforbidden. .

•• However, if the molecule However, if the molecule eliminates its center of eliminates its center of symmetry through a vibration, symmetry through a vibration, a a vibronicallyvibronically allowed allowed transitiontransition may occur may occur (although it may be weak).(although it may be weak).

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PracticePractice

•• Be sure to practice SelfBe sure to practice Self--test 17.1 test 17.1 without looking at the answer.without looking at the answer.

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Vibrational StructureVibrational Structure

The Franck–Condon principle states:• Because the nuclei are so much more

massive than the electrons, an electronic transition takes place very much faster than the nuclei can respond.

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Vibrational StructureVibrational Structure• As a result of the transition, electron density

is rapidly built up in new regions of the molecule and removed from others, and the initially stationary nuclei suddenly experience a new force field.

• They respond to the new force by beginning to vibrate, and (in classical terms) swing backwards and forwards from their original separation, which was maintained during the rapid electronic excitation.

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Vibrational StructureVibrational Structure• The stationary equilibrium

separation of the nuclei in the initial electronic state therefore becomes a stationary turning point in the final electronic state.

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Franck–Condon Principle and Quantum Mechanics

• The quantum mechanical version of the Franck–Condon principle refines this picture.

• Before the absorption, the molecule is in the lowest vibrational state of its lowest electronic state; the most probable location of the nuclei is at their equilibrium separation, Re.

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Franck–Condon Principle and Quantum Mechanics

• The electronic transition is most likely to take place when the nuclei have this separation. When the transition occurs, the molecule is excited to the state represented by the upper curve.

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Franck–Condon Principle and Quantum Mechanics

• According to the Franck–Condon principle, the nuclear framework remains constant during this excitation, so we may imagine the transition as being up the vertical line

• The vertical line is the origin of the expression vertical transition, which is used to denote an electronic transition that occurs without change of nuclear geometry.

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Vibrational StructureVibrational Structure• The vertical transition cuts through several

vibrational levels of the upper electronic state. The level marked * is the one in which the nuclei are most probably at the same initial separation Re (because the vibrational wavefunction has maximum amplitude there), so this vibrational state is the most probable state for the termination of the transition.

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Vibrational StructureVibrational Structure• However, it is not the only accessible

vibrational state because several nearby states have an appreciable probability of the nuclei being at the separation Re. Therefore, transitions occur to all the vibrational states in this region, but most intensely to the state with a vibrational wavefunction that peaks most strongly near Re.

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Transitions Between Energy Transitions Between Energy Levels and Nuclear SeparationLevels and Nuclear Separation

•• The upper curve is usually The upper curve is usually displaced to greater bond displaced to greater bond lengths because lengths because electronically excited electronically excited orbitals usually have more orbitals usually have more antibonding character.antibonding character.

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Electronic Spectra of Polyatomic MoleculesElectronic Spectra of Polyatomic Molecules

• The absorption of a photon can often be traced to the excitation of specifc types of electrons or to electrons that belong to a small group of atoms in a polyatomic molecule, a R-C=O.

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ChromophoresChromophores

•• Groups with characteristic optical absorption Groups with characteristic optical absorption are called are called chromophoreschromophores..

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Absorption Characteristics Some Absorption Characteristics Some Groups and MoleculesGroups and Molecules

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dd--dd TransitionsTransitions• All five d orbitals of a given shell are

degenerate in a free atom. • In a d-metal complex, where the immediate

environment of the atom is no longer spherical, the d orbitals are not all degenerate, and electrons can absorb energy by making transitions between them.

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LigandLigand--Field SplittingField Splitting

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dd--dd TransitionsTransitions• In an octahedral

complex, such as [Ti(OH2)6]3+, the five d orbitals of the central atom are split into two sets, a triply degenerate set labeled t2g and a doubly degenerate set labeled eg.

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dd--dd TransitionsTransitions

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dd--dd TransitionsTransitions• The three t2g orbitals lie below the two

eg orbitals; the difference in energy is denoted ∆O and called the ligand-field splitting parameter (the “O” denoting octahedral symmetry).

• The d orbitals also divide into two sets in a tetrahedral complex, but in this case the e orbitals lie below the t2 orbitals and their separation is written ∆T.

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dd--dd TransitionsTransitions

• Neither separation is large, so transitions between the two sets of orbitals typically occur in the visible region of the spectrum.

• The transitions are responsible for many of the colors that are so characteristic of d-metal complexes.

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dd--dd TransitionsTransitions• As an example, the

spectrum of [Ti(OH2)6]3+

near 20 000 cm-1 (500 nm) is shown here, and can be ascribed to the promotion of its single d electron from a t2g orbital to an eg orbital. The wavenumber of the absorption maximum suggests that ∆O = 20 000 cm-1.

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dd--dd TransitionsTransitions

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dd--dd Transitions and the Transitions and the LaporteLaporte RuleRule

•• Since g Since g ←← g transitions g transitions are forbidden by are forbidden by the the LaporteLaporte rulerule,, we can we can deduce that these deduce that these transitions from transitions from a t2gorbital to an eg orbital are vibronically allowed transition because of asymmetric vibrations.

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ChargeCharge--Transfer TransitionsTransfer Transitions• A complex may absorb radiation as a result of

the transfer of an electron from the ligands into the d orbitals of the central atom, or vice versa.

• In such charge-transfer transitions the electron moves through a considerable distance, which means that the transition dipole moment may be large and the absorption is correspondingly intense.

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ChargeCharge--Transfer TransitionsTransfer Transitions• This mode of chromophore activity is

shown by the permanganate ion, MnO4–,

and accounts for its intense violet color (which arises from strong absorption within the range 420–700 nm).

• In this oxoanion, the electron migrates from an orbital that is largely confined to the O atom ligands to an orbital that is largely confined to the Mn atom.

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SatinSatin--Ribbon Dyed Using a Ribbon Dyed Using a Permanganate CompoundPermanganate Compound

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ChargeCharge--Transfer TransitionsTransfer Transitions

• It is therefore an example of a ligand-to-metal charge-transfer transition (LMCT).

• The reverse migration, a metal-to-ligand charge-transfer transition (MLCT), can also occur.

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ChargeCharge--Transfer TransitionsTransfer Transitions• An example is the transfer of a d

electron into the antibonding π orbitals of an aromatic ligand.

• The resulting excited state may have a very long lifetime if the electron is extensively delocalized over several aromatic rings, and such species can participate in photochemically induced redox reactions.

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ππ* * ←← ππ TransitionsTransitions

• Absorption by a C=C double bond excites a π electron into an antibonding π* orbital.

•• The chromophore is hence a The chromophore is hence a ππ* * ←← ππ transition.transition.

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ππ* * ←← ππ TransitionsTransitions• Its energy is about 7 eV for an

unconjugated double bond, which corresponds to an absorption at 180 nm (in the ultraviolet).

• When the double bond is part of a conjugated chain, the energies of the molecular orbitals lie closer together and the π* ← π transition moves to longer wavelength.

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ππ* * ←← ππ TransitionsTransitions• The transition may even lie in the visible

region if the conjugated system is long like in the molecules in retina.

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ππ* * ←← nn TransitionsTransitions

•• Lone pairs of electrons on the oxygen atom in Lone pairs of electrons on the oxygen atom in carbonyl compounds (Rcarbonyl compounds (R--C=O) can also C=O) can also undergo electronic transitions.undergo electronic transitions.

•• Although molecular orbital theory assumes Although molecular orbital theory assumes that electrons are spread throughout the that electrons are spread throughout the entire atom, lone pairs (from a Lewis entire atom, lone pairs (from a Lewis structure perspective) are electrons that are structure perspective) are electrons that are essentially confined around an given atom essentially confined around an given atom and do not and do not involvrinvolvr themselves in bonding.themselves in bonding.

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ππ* * ←← nn TransitionsTransitions•• One of the “lone pairs” One of the “lone pairs”

electrons can be excited to electrons can be excited to a a ππ* * orbital of the carbonyl orbital of the carbonyl group.group.

• Typical absorption energies are about 4 eV (290 nm).

• Because ππ * ←n transitions in carbonyls are symmetry-forbidden, the absorptions are weak.