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Ch 14. Electronic Spectroscopy • Absorption of VIS or UV can lead to transitions between the ground state and excited stated electronic states of atoms and molecules. • The excited state relaxes to the ground state through a combination of fluorescence, internal conversion, intersystem crossing, and phosphorescence. • UV photoemission can be used to obtain information about the orbital energies of molecules. MS310 Quantum Physical Chemistry 14.1 The energy of electronic transitions See the gap of electronic, vibrational, rotational transition. ∆Eelectronic >> ∆Evibrational >> ∆Erotational Range of rotational and vibrational transition : μ-wave & IR range However, range of electronic transition : UV-Vis range → a specific electronic transition will contain vibrational and rotational fine structure Transmitted and reflected light complement the absorbed light. Ex) A leaf is green. (∵Chlorophyll absorbs in the blue and red spectrum.) A human eye is a very sensitive detector of radiation. (One part in 106 - 500 photons/mm2·sec) MS310 Quantum Physical Chemistry Electronic spectroscopy : see electronic state directly → very powerful to see the structure and chemical composition However electronic excitation perturb the state of molecule much more than rotational and vibrational excitation. → Example, (a) bond length in electronically state of O2 is 30% longer than that in ground state. (b) Formaldehyde in its ground state is a planar molecule, but pyramidal in its lowest two excited states. Its chemical reactivity can be quite different from that of ground state molecule. MS310 Quantum Physical Chemistry 14.2 Molecular term symbol How describe the electronic state of molecule? → introduce ‘molecular term symbol’ Component of L and S(ML and MS) : along the molecular axis S : only good quantum number in diatomic molecule define | M L |, L M L L and S M S S 2 S 1 0 1 2 3 Molecular Term Atomic Term S P D F If molecule has a inversion center : use g and u symbol (otherwise, do not use anything) MS310 Quantum Physical Chemistry Consider + and – symbol. 1) all MOs are filled : + 2) partially filled MOs are σ symmetry : + 3) partially filled MOs of π symmetry : if Σ arise, - for triplet and + for singlet Ex) H 2 0, 2 S 1 2, parity g 2 g Ex) O 2 2 x , 2 y 1, 1 (closed shell) g g g 3 g ground state of O 2 : triplet state ( ) sign : 3 g if the two e – s occupy the same , both 1 MS310 Quantum Physical Chemistry 14.3 Transition between electronic states of diatomic molecules Diatomic molecule : most easily interpretable electronic spectra 4 electronic potential energy surface of lowest excited state of oxygen molecule. Using this notation - X : ground state - A, B, C, … : excited state(multiplicity : 2S+1) - a, b, c, … : describe degenerated state See dissociation of oxygen molecule - X, a, b, A state : O(3P) + O(3P) - B state : O(3P) + O(1D) MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry Symbol 3Σg- describes ground-state O2 completely However, for convenient, use ‘molecular configuration’ X 3Σg-, a 1∆g, b 1Σg+ : belong to the ground-state configuration, (1σg)2(1σu*)2(2σg)2(2σu*)2(3σg)2(1πu)2(1πu)2(1πg*)1(1πg*)1 but different ML and MS A 3Σu+, B 3Σu- : belongs to excited-state configuration, (1σg)2(1σu*)2(2σg)2(2σu*)2(3σg)2(1πu)1(1πu)2(1πg*)1(1πg*)2 → several molecular terms are generated from same configuration Selection rule is given by ∆Λ=0, ±1 and ∆S=0 Λ : component of total angular momentum L MS310 Quantum Physical Chemistry ∆Λ=0 : Σ ↔ Σ transition, ∆Λ= ±1 : Σ ↔ Π transition Further selection rule given by +/- and g/u parity Homonuclear diatomic molecule - u ↔ g transition : allowed - u ↔ u and g ↔ g transition : forbidden - Σ- ↔ Σ- and Σ+↔ Σ+ transition : allowed - Σ+ ↔ Σ- transition : forbidden Use this rules in case of O2. - X 3Σg- → a 1∆g and X 3Σg- → b 1Σg+ transition : forbidden (by g↔g transition is forbidden) - X 3Σg- → A 3Σu+ transition : forbidden (by Σ+ ↔ Σ- transition forbidden) Therefore, lowest allowed transition : X 3Σg- → B 3Σu- transition. Energy of this transition : band between 175nm to 200nm → reason of air is transparent. MS310 Quantum Physical Chemistry If molecule take energy, photodissociation reaction occurs O2 h 2O → Maximum wavelength : 242nm In stratosphere, oxygen atom react with oxygen molecule and form ozone. O O2 M O3 M * Ozone absorb the photon : 220nm to 350nm → filtering UV radiation of the sun. MS310 Quantum Physical Chemistry 14.4 The vibrational fine structure of electronic transition in diatomic molecules Selection rule ∆n= ±1 : only for vibrational transition → not valid for electronic transition Determination of the change of vibrational quanta → see Born-Oppenheimer approximation Apply this approximation, wavefunction is given by (r1 ,..., rn , R1 ,..., R m ) electronic (r1 ,..., rn , R1fixed ,..., R mfixed ) vibrational ( R 1 ,..., R m ) Discuss in 8.5, transition occurs if transition dipole moment is not zero. fi *f (r1 ,..., rn , R1 ,..., R m )ˆ i (r1 ,..., rn , R1 ,..., R m )d 0 MS310 Quantum Physical Chemistry n Dipole moment operator is given by ̂ e ri i 1 Use this equation, transition dipole moment becomes fi S *f (r1 ,..., rn , R 1fixed ,..., R mfixed )ˆ i (r1 ,..., rn , R 1fixed ,..., R mfixed )d l * vibrational ( vibrationa ( R ,..., R )) i ( R 1 ,..., R m )d f 1 m *f (r1 ,..., rn , R 1fixed ,..., R mfixed )ˆ i (r1 ,..., rn , R 1fixed ,..., R mfixed )d See first integral of second equation, it means ‘overlap’ between ground and excited state. Franck-Condon factor S is given by l * vibrational 2 S 2 | ( vibrationa ) d | f i MS310 Quantum Physical Chemistry Franck-Condon principle : transition occurs to vertical line on energy diagram. (when transition occurs, there are no change of atomic position.) See this figure Transition occurs from n=0 to several n when electronic transition and depends on the position of ‘ground state’. MS310 Quantum Physical Chemistry How can Franck-Condon principle determine the n value? When transition occurs, there are no position change. Transition probability depends on the Franck-Condon factor S. → ‘overlap’ between 2 states determine the transition State of ‘maximum’ probability where equilibrium position of ground state, n=0 : excited state, n=4! MS310 Quantum Physical Chemistry If photon energy is so high(ν > E/h, E : corresponding energy of highest bounded state of excited state → continuous energy spectrum Transition to ‘no bounded’ state of molecule, i.e, case of H2+ bonding state to excited(nonbonding) state. MS310 Quantum Physical Chemistry 14.5 UV-vis light absorption in polyatomic molecules Case of polyatomic molecule :large moment of inertia → small gap between 2 rotational levels : more than 1000 rotational levels in ~1cm-1 Therefore, UV-vis spectra of large molecule : broad. Spectra of 1-atom, diatom, and polyatom MS310 Quantum Physical Chemistry The number of allowed state ↓ when temperature↓ Spectra of MeOH at 300K and 9K. - 300K : so many states are allowed and they are overlapped → broad peak - 9K : only a few states are allowed because average energy of molecule is proportional to temperature → very sharp peak MS310 Quantum Physical Chemistry How can discuss it? ‘chromophores’ In large molecule, charasteristic frequency is determined by neighboring 2 atoms. (For example, -C=C- or –O-H, C=C, C=O, C≡N, C=S, etc) Each chromophore : characteristic frequency in UV After, see ground-state and excited-state of formaldehyde (H2CO) MS310 Quantum Physical Chemistry Ground-state configuration in the localized notation : (1sO)2(1sC)2(2sO)2(σCH)2(σ’CH)2(σCO)2(πCO)2(nO)2(πCO*)0 1s and 2s electron of C and O : not used(nonbonding) Also, lone pair of O(nO) is localized into O atom. C-H bond, 1 of C-O bond : σ, another C-O bond : π σ bond of C-O : formed by sp2 hybridization orbital, the lowest energy π bond of C-O : formed by 2p orbital : next lowest energy π* orbital : antibonding, next energy lone pair electrons : between π and π* state MS310 Quantum Physical Chemistry Approximate MO diagram First transition : nO to πCO* : n → π* transition → Result configuration (1sO)2(1sC)2(2sO)2(σCH)2(σ’CH)2(σCO)2(πCO)2(n 1 1 O) (πCO*) Second transition : πCO to πCO* : π → π* transition → Result configuration (1sO)2(1sC)2(2sO)2(σCH)2(σ’CH)2(σCO)2(πCO)1(n 2 1 O) (πCO*) MS310 Quantum Physical Chemistry However, spin of unfilled orbital is not specified : cannot describe completely Energy gap between singlet and triplet : typically lies 2 to 10eV. MS310 Quantum Physical Chemistry Order of transition energy : n → π*, π → π*, σ → σ* transition n → π* : require both nonbonding pairs and multiple bonds. occurs in molecule containing carbonyls, thiocarbonyls, nitro, azo, and imine groups and in unsaturated halocarbons π → π* : require multiple bonds. occurs in alkenes, alkynes, and aromatic compounds σ → σ* : if none of the other transitions is possible, it occurs. MS310 Quantum Physical Chemistry 14.6 Transition among the ground and excited states Generalization of the transition to arbitrary molecules → ground state : singlet / excited states : either a singlet or triplet In transition, singlet →singlet. → Triplet state is generated by ‘internal conversion’, not direct. Radioactive transition : photon emission and absorption (solid vertical lines) Nonradiactive transition : energy transfer between different degree of freedoms and forbidden by dipole selection rule (singlet → triplet, dashed line) Pathway of excited states to ground state : depends on rate of number of competing processes. MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry 14.7 Singlet-triplet transitions : absorption and fluorescence Atomic spectroscopy : selection rule ∆S=0 strictly obeyed. Molecular spectroscopy : forbidden transition occurs but transitions corresponding to ∆S=0 are much stronger than forbidden transition by selection rule Beer’s law(also called Beer-Lambert’s law) : If I0 is incident light intensity and It is transmitted light intensity, dependence of It/I0 on the concentration c and the path length l log( It ) lc I0 Molar extinction coefficient ε : measure of the strength of the transition, measured at maximum spectral line Integral absorption coefficient A=∫ε(ν)dν : integration over the spectral line includes associated vibrational and rotational transitions : probability of absorption MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry εmax of spin-allowed and singlet-triplet transition. - spin-allowed transition(∆S=0) : 10~5x104 dm3 mol-1 cm-1 - spin-forbidden transition(∆S=1) : 1x10-4~1 dm3 mol-1 cm-1 Spin-orbit coupling is not negligible, ∆S=1 transition is not forbidden but intensity of this transition is weak. (ten thousand to ten million times weak) → However, this transition is very important when discuss the phosphorescence. Nonradioactive transition by collision : internal conversion Nonradioactive transition to excited vibrational state : intersystem crossing In experiment, wavelength of absorption and fluorescence is small different. Why? : ‘difference’ of vibrational and rotational state MS310 Quantum Physical Chemistry Pattern of absorption and fluorescence MS310 Quantum Physical Chemistry 14.8 Intersystem crossing and phosphorescence Intersystem between singlet and triplet : forbidden in the Born-Oppenheimer approximation. However, it occurs in many molecules. This probability depends on 2 factors : very similar molecular geometry, strong spin-orbit coupling MS310 Quantum Physical Chemistry S0 → S1 transition : dipole-allowed transition → high probability. → By Franck-Condon principle, electron : same position of excited state (n=4 state) Energy of ground state of S1 : approximately same as vibrational excited state of T1 - If spin-orbit coupling is strong enough to initiate a spin flip : S1 → T1 transition occurs - S1 → T1 transition : molecule cross over from S1 to T1 state and it rapidly relax to the lowest vibrational excited state of T1 However, T1 state decays radiatively to the ground state, S0 in the dipole transition forbidden process, called as ‘phosphorescence’. - Time of fluorescence : less than 10-7 s - Time of phosphorescence : more than 10-3 s MS310 Quantum Physical Chemistry State energy diagrams : electronic and spin isomers Singlet orbital orbital configuration ⑨ Ψ* Ψ Triplet orbital orbital configuration ⑦ S1 kF ε( S0 S1 ) Ψ* Ψ S0 ⑧ Ground state orbital configuration ①. ②. ③. ④. ⑤. ⑥. ⑦. ① ② ③ 25% ⑩ kST T1 kIC kP Ψ* Ψ kTS ε( S0 T1 ) ④ ⑤ ⑥ 100% Allowed : Singlet-singlet absorption (S0 +hv S1) Allowed : Singlet-singlet emisstion, fluorescence (S1 S0 + hv) Allowed : Transition btw state of the same spin, internal conversion (S1 S0 + heat) Forbidden : Triplet-singlet absorption (S0 + hv T1) Forbidden : Triplet-singlet emission, phosphorescence (T1 S0 +hv) Forbidden : Transition btw triplet state & ground state, ISC (T1 S0 + hv) Forbidden : Transition btw excited state of different spin, ISC (S1T1 +heat) Heavy metals core based triplet emitters Need to Mix singlet and triplet states ; make both singlet and triplet decay allowed Use metal-Organic complex with heavy transition metals. S1 Heavy metals (Pt, Ir, etc…) T1 Spin orbital coupling (T1S0) Ligand molecular orbitals S0 Transitions between singlet and triplet states are called intersystem crossing (ICS) (S1T1) ; ISC is spin-forbidden spin orbital coupling ISC generate (S1T1) Phosphorescence (T1S0) MS310 Quantum Physical Chemistry Toward 100% internal quantum efficiency Spin-orbital coupling -Intersystem crossing(S1T1) - phosphorescence (T1S0) Solution process Introduce of Nano structure MS310 Quantum Physical Chemistry 14.9 Fluorescence spectroscopy and analytical chemistry Laser-induced fluorescence spectroscopy 1. section of DNA is cut into small lengths of 1000~2000 bp using mechanical shearing. 2. it replicates in the solution with A,T,G,C. - We also add small fraction of ‘modified’ base and this modified base terminate the replication. - In real case, this modified base is derivative of 2,3dideoxyribonucleotide. - DNA polymerase III put the new basis on the 3’-OH of DNA and cannot catalyze the polymerization when this position changes to H. → many ‘pieces’ of original DNA. - Dye(fluorescence at known wavelength) into the modified base MS310 Quantum Physical Chemistry - In real technique, we prepare 4 solutions and each solution has one type of modified base. → one solution has modified A, another solution has modified T, etc. Trivially, these solutions have normal A,T,G,C) 3. This DNA pieces are sorting with molecular weight by electrophoresis. Add LASER, fluorescence occurs and see the ‘order’ of DNA sequence. Sensitivity of this method : 130±30 molecules in the volume illuminated by LASER!(It is also 2x10-13 mol/L) MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry 14.10 UV photoelectron spectroscopy UV spectroscopy : closest to see orbital energy directly Photoionization : molecule ionize with light(photon) Kinetic energy of emitted electron is given by 1 Ekinetic h [ E f ( n f )h vibration] 2 - In UV spectroscopy, must used delocalized model because of initial of final state is ‘radical’. - If these assumptions are satisfied, we can calculate Ef by orbital energy. 1) Nuclear positions are unchanged in the transition(B-O app) 2) Orbitals for atom and ion are same (frozen orbital approximation) 3) Total electron correlation energy in the molecule and ion are same. MS310 Quantum Physical Chemistry Case of O2 UV spectroscopy MS310 Quantum Physical Chemistry In neutral molecule, this assumption is valid and known as ‘Koopmans’ theorem’ In real case, difference of numerical calculation and real value is 1 to 3 eV and reason is second and third assumption is not valid any more. Water molecule. - Experiment with 21.4eV, there are 3 groups of peaks. - By HF calculation, we obtain 4 MOs. With localized MO model, there are 2 O-H bond and 2 lone pairs → 2 groups Discrepancy of experiment and model : understood by coupling with bonding MOs and lone pairs. It leads to symmetric combinations and antisymmetric combinations. S : symmetric, A : antisymmetric, σ : bonding, n : nonbonding MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry 13eV peak : attributed to εnA Corresponding MO : 1b1 Associated with antisymmetric combination 14~16eV peak : attributed to εnS Corresponding MO : 2a1 Associated with symmetric combination MS310 Quantum Physical Chemistry 17~20eV peak : attributed to εσA Corresponding MO : 1b2 Associated with antisymmetric combination Peak attributed to εσS : not observed (higher than experimental energy) Corresponding MO : 1a1 Associated with antisymmetric combination MS310 Quantum Physical Chemistry This analysis solve this question. ‘Why do equivalent bonds or lone pairs give rise to several different orbital energies?’ Equivalent O-H bond and lone pairs are ‘interacting’ each others. MO of each bond or lone pairs are mutually orthogonal, but electron distribution in one bond(or lone pair) is not independent to another bond or lone pair by ‘Coulombic interaction’ Case of water, 2 equivalent O-H bonds give 2 distinct MO energy. However, only 2 levels in case of ammonia(3 equivalent bond) and 2 levels in case of methane(4 equivalent bond). MS310 Quantum Physical Chemistry 14.11 Single molecule spectroscopy The conformation of a biomolecule refers to the arrangement of its constituent atoms in space and can be discussed in terms of primary, secondary, and tertiary structure. The primary structure is determined by the backbone of the molecule. The term secondary structure refers to the local conformation of a part of the polypeptide. Tertiary structure refers to the overall shape of the molecule. MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry 14.12 Fluorescent resonance energy transfer We refer to the molecule that loses energy as the donor, and the molecule that accepts the energy as the acceptor. Resonance energy transfer - the photon energy for fluorescence in the donor is equal to the photon energy for absorption in the acceptor MS310 Quantum Physical Chemistry FRET rate Rab is the distance between donor a and acceptor b τa is the fluorescence lifetime of donor a R0 is the Föster radius at which kT equaals 1/τa FRET Efficiency 1 E 1 ( R / R0 ) 6 1.0 0.8 E 0.6 0.4 Ro 50 Å 0.2 0.0 0 25 50 R (Å) MS310 Quantum Physical Chemistry 75 100 1 E 1 ( R / R0 ) 6 Ro = 0.21( JqD n k -4 2 ) 1 6 Fluorescnece Intensity Then, how to increase R0 J(λ) Donor fluorescnece Acceptor absorption Wavelength • J is the normalized spectral overlap of the donor emission and acceptor absorption • qD is the quantum efficiency for donor emission in the absence of acceptor (qD = number of photons emitted divided by number of photons absorbed). • n is the index of refraction • k2 is a geometric factor related to the relative orientation of the transition dipoles of the donor and acceptor and their relative orientation in space. D A R0 D D A A Donor Acceptor (R0, nm) Naphthalene LY Dansyl LY FITC BPE Dansyl TNP-ATP ODR EM EM CY5 2.2 3.5 4.3 5.3 6.0 7.2 Conclusion FRET provides an efficient way to measure the distance between a donor and an acceptor chromophore by measuring the FRET efficiency, one can easily get the precise distance between the donor and the acceptor If choosing the donor and acceptor properly, this experiment can also be carried out in vivo 14.13 Linear and circular dichroism MS310 Quantum Physical Chemistry MS310 Quantum Physical Chemistry 14.14 Assigning + and – to Σ terms of diatomic molecules + and - : change in sign of the molecular wavefunction on reflection in a plane contains the molecular axis. Sign preserve : +, opposite sign : Case of σ MO : sign preserve → + O2 : (1σg)2(1σu*)2(2σg)2(2σu*)2(3σg)2(1πu)2(1πu)2(1πg*)1(1πg*)1 MS310 Quantum Physical Chemistry Next, see 1πg* and 1πg’* wavefunction. There are 6 combinations of ml = ±1 and s = ±1/2. However, these π(2px) and π(2py) wavefunctions are not eigenfunctions of Lz operator. Eigenfunction of Lz operator Lˆ z i , ( ) Ae i MS310 Quantum Physical Chemistry In π2 configuration, 6 combinations are possible. 1 1 1 ( (1) ( 2) (1) ( 2)) 2 1 1 ( (1) ( 2) (1) ( 2)) 3 ( 1 1 1 1 )( (1) ( 2) (1) ( 2)) 4 ( 1 1 1 1 ) (1) ( 2) 5 ( 1 1 1 1 )( (1) ( 2) (1) ( 2)) 6 ( 1 1 1 1 ) (1) ( 2) Can check easily ψ1~ψ3 are triplet and ψ4~ψ6 are singlet. Also, ψ1, ψ2 are ∆ term and ψ3~ ψ6 are Σ term. MS310 Quantum Physical Chemistry Eigenfunction of Lz : reflection is same as change of sign of Λ : π+1 → π-1 and π-1 → π-1 Therefore, ψ1~ψ3 : does not change the sign because of (-1)x(-1)=1 → these 3 wavefunctions are 1Σg+ However, ψ4~ψ6 : change the sign because (-1)x(+1)=-1 → these 3 wavefunctions are 3Σg- MS310 Quantum Physical Chemistry Summary - Electronic spectroscopy : see the ‘level’ of molecule - Study term symbol and application - Beer-Lambert’s Law : connection between theoretical allowed and forbidden transition to experimental spectroscopy - Real application : genome project MS310 Quantum Physical Chemistry