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Photoelectron Spectroscopy • Lecture 2: Ionization Transitions – Transition moment integral – Ionization selection rules and probability – Atomic and molecular term symbols – A bit of molecular orbital theory Ionization is still a transition between states • Initial State: Neutral (or anion) • Final State: Atom/Molecule/Anion after an electron is removed, plus the ejected electron • M → M+ + einit = M final = M+ + e• Transition Probability = ∫ init m final d • For direct photoionization, transition probability is always > 0 • Photoionization probability is typically described in terms of a cross-section (much more on this later) e- + Molecule+ hn + Molecule Ehn - Ee- = EM+ - EM = Ionization Energy IE = Difference in energy between states of M, M+ How do we label states? Each electronic state has its own term symbol Use Russell Saunders Coupling to describe electron-electron repulsion orbital angular momentum spin multiplicity 2S+1 LJ L=0 L=1 L=2 L=3 S term P term D term F term When considering symmetry use the Mulliken symbol spin orbit coupling J = |L+S| ...|L-S| L = 0, 1, 2…total orbital angular momentum (term) ML = -L…+L component of L (ML = S ml) S = total spin quantum number (S = S s) Ms = -S….+S component of S (MS = S ms) Within each term, there can be several degenerate microstates with different ML and MS Photoelectron Spectra of Atoms (Noble Gases) Ar We are observing transitions between the neutral ground state and cation states formed by removing an electron from the highest occupied orbital. What’s the term symbol for the ground state of Ar? Ground State: 1s22s22p63s23p6 Kr No unpaired electrons: 1S Remove one 3p electron: First Ion State: 1s22s22p63s23p5 Xe S = |1/2| (2S+1) = 2 L = 1 (P) J = L+S ...L-S 17 16 15 14 J = 1/2 and 3/2 13 12 11 Ionization Energy (eV) 2P 1/2 and 2P3/2 Ar 2P 1/2 Energy Kr 2P 3/2 Xe 1S 17 16 15 14 13 12 11 Ionization Energy (eV) What about molecules? σ* H 1s ↿ ⇂ H 1s ↿⇂ σ 18 17 16 Ionization Energy (eV) 15 Transitions between molecular potential energy surfaces During an electronic transition the complex absorbs energy electrons change orbital Excited State molecular rotations lower energy microwave radiation the complex changes energy state electron transitions higher energy visible and UV radiation Timescale : ≈10-15 sec Timescale of geometry changes (vibrations): ≈10-12 sec Ground State molecular vibrations medium energy IR radiation As a result, observe vertical (Franck-Condon) transitions In other words, we assume that we only have to consider the electronic portion of the ground- and excited-state wavefunctions to understand these transitions: Born-Oppenheimer approximation Potential Energy Surface Description of the Ionization of Dihydrogen Ionization Energy (eV) 18 H2+ 17 16 15 H2 0 0 1 r (Å) 2 Much more on this next time!! Molecular Term Symbols Use Russell Saunders Coupling to describe electron-electron repulsion molecular orbital angular momentum spin multiplicity 2S+1 LJ When considering symmetry use the Mulliken symbol spin orbit coupling (we will ignore this for now) L = total orbital angular momentum expressed by orbital symmetry (term) S = total spin quantum number (S = S s) Ms = -S….+S component of S (MS = S ms) Consider Dinitrogen First ion state (X) = 2Sg+ 2u Second ion state (A) = 2u 1g 2p Third ion state (B) = 2Su+ 2p 2g+ 1u 2s 1u+ 2s 1g+ :N≡N: Ground state (X) = 1Sg+ 20 19 18 17 16 Ionization Energy (eV) 15 Potential Well Description 2u Eu+ 2 1g 2p 2p 2g+ A u+ 2 Eg+ 2 1u 2s 1u+ 1g+ :N≡N: Ground state (X) = 1Sg+ 2s N2 1Eg Models to describe molecular electronic structure MO Theory compared to Valence Bond Theory Consider methane. VSEPR gives 4 sp3 hybrid orbitals. Photoelectron Spectroscopy CH 4 2p sp3 2s 24 22 20 18 16 14 Ionization Energy (eV) So why are there two valence ionizations separated by almost 10 eV? 12 Use of reducible representations in M.O. theory Consider transformation properties of vectors aligned with the 4 C-H bonds. Td E 8C3 3C2 6S4 6σd σ 4 1 0 0 2 Apply Reduction Formula: 1 a A1 [4 8 0 0 12] 1 24 1 a A2 [4 8 0 0 12] 0 24 1 aE [8 8 0 0 0] 0 24 1 aT1 [12 0 0 0 12] 0 24 1 aT1 [12 0 0 0 12] 1 24 C-H = A1 + T2 http://www.mpip-mainz.mpg.de/~gelessus/group.html LCAO Description of Methane 2p (t2) CH4 t2 (1, 2, 3) a1 (1) 2s (a1) 24 C CH4 H4 22 20 18 16 14 Ionization Energy (eV) 12 M(CO)6 M = Cr, Mo, W, d6 metals t1u* L a1g* L L L L L t2g* t1u a1g 4s eg* t1g + t2g + t1u + t2u Ligand * orbitals Doct eg t2g 3d t2g eg t1u a1g 6 x LGO a1g eg t1u Ligand orbitals t1g + t2g + t1u + t2u Photoelectron spectra of d6 metal hexacarbonyls M(CO)6 vertical 2T • Neutral molecules are closed shell; term symbol for ground state in Oh symmetry is 1A1g • First ionization is from metal t2g orbital; term symbol for resultant state is 2T2g 2g Cr Mo • Followed by series of overlapping ionizations due to ionization from CO orbitals; M-C σ orbitals, etc. • States due to ionization from CO orbitals: – t1g → 2T1g – t2g → 2T2g W 18 16 12 10 8 14 Ionization Energy (eV) – t1u → 2T1u – t2u → 2T2u Open shell ground states To this point we have only considered molecules with closed shell ground states: What if there are unpaired electrons in the ground state? V(CO) 6 V(CO)6 a 17 e- complex. Ground State: t2g5 : 2T2g 20 18 16 14 12 10 Ionization Energy (eV) First ion state: t2g4 : T2g x T2g = 3T1g, 1T2g, 1E1g, 1A1g 8 6 Second ion state: t1u5t2g5 : T1u x T2g = 3,1T2u, 3,1T1u, 3,1Eu, 3,1A2u And so on and so on… But, open-shell molecules aren’t always this complicated… H2(oep) 2 2 Au B1u Mg(oep) 2 2 A1u A2u VO(oep) 10 9 8 7 Ionization Energy (eV) 6 • Energy splitting of ionizations is dependent upon the amount of electronic communication between the unpaired electrons as defined by the exchange integral. • This is referred to as the exchange splitting. • If exchange splitting is relatively small, spectra of molecules with open shell ground states can be treated as though they are closed shell systems. For low symmetries, term symbols often aren’t that useful Summary • Photoionization is a transition between states • States are described using term symbols • Simple valence bond theory does not explain all features observed in spectroscopy, requiring use of molecular orbital theory. • “Koopmans’ Theorem” begins to break down for systems with unpaired electrons in the initial state