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+ + e- init = 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 = EM+ - EM Ehn - Ee- = Ionization Energy IE = Difference in energy between states of M, M+
2S+1 L J 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 L = 0 S term L = 1 P term L = 2 D term L = 3 F term When considering symmetry use the Mulliken symbol spin multiplicity spin orbit coupling J = |L+S| ...|L-S| L = 0, 1, 2…total orbital angular momentum (term) ML = -L…+L component of L (ML = Sml) S = total spin quantum number (S = S s) Ms = -S….+S component of S (MS = Sms) Within each term, there can be several degenerate microstates with different ML and MS
Ar Ar Kr Kr Xe Xe 17 17 16 16 15 15 14 14 13 13 12 12 11 11 Ionization Energy (eV) Ionization Energy (eV) Photoelectron Spectra of Atoms (Noble Gases) 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 No unpaired electrons: 1S Remove one 3p electron: First Ion State: 1s22s22p63s23p5 S = |1/2| (2S+1) = 2 L = 1 (P) J = L+S ...L-S J = 1/2 and 3/2 2P1/2 and 2P3/2
Ar Ar Kr Kr Xe Xe 17 17 16 16 15 15 14 14 13 13 12 12 11 11 Ionization Energy (eV) Ionization Energy (eV) 2P1/2 2P3/2 Energy 1S
18 17 16 15 Ionization Energy (eV) What about molecules? σ* ↿ ⇂ H 1s H 1s ↿⇂ σ
Transitions between molecular potential energy surfaces Excited State During an electronic transition the complex absorbs energy electrons change orbital the complex changes energy state molecular rotations lower energy microwave radiation electron transitions higher energy visible and UV radiation Ground State Timescale : ≈10-15 sec Timescale of geometry changes (vibrations): ≈10-12 sec 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-statewavefunctions to understand these transitions: Born-Oppenheimer approximation molecular vibrations medium energy IR radiation
H2+ 18 17 16 15 Ionization Energy (eV) H2 0 1 0 2 r (Å) Potential Energy Surface Description of the Ionization of Dihydrogen Much more on this next time!!
2S+1 L J Molecular Term Symbols Use Russell Saunders Coupling to describe electron-electron repulsion molecular orbital angular momentum When considering symmetry use the Mulliken symbol spin multiplicity 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 = Sms)
20 19 18 17 16 15 Ionization Energy (eV) Consider Dinitrogen First ion state (X) = 2g+ 2u Second ion state (A) = 2u 1g Third ion state (B) = 2u+ 2p 2p 2g+ 1u 2s 2s 1u+ 1g+ :N≡N: Ground state (X) = 1g+
2 + E u 2 + A u 2 + E g Potential Well Description 2u 1g 2p 2p 2g+ 1u 2s 2s 1u+ 1g+ 1 E N 2 :N≡N: g Ground state (X) = 1g+
Models to describe molecular electronic structure MO Theory compared to Valence Bond Theory
CH CH 2p 4 4 sp3 2s 24 24 22 22 20 20 18 18 16 16 14 14 12 12 Ionization Energy (eV) Ionization Energy (eV) Consider methane. VSEPR gives 4 sp3 hybrid orbitals. Photoelectron Spectroscopy So why are there two valence ionizations separated by almost 10 eV?
Use of reducible representations in M.O. theory Consider transformation properties of vectors aligned with the 4 C-H bonds.
Apply Reduction Formula: C-H = A1 + T2 http://www.mpip-mainz.mpg.de/~gelessus/group.html
CH CH 4 4 24 24 22 22 20 20 18 18 16 16 14 14 12 12 Ionization Energy (eV) Ionization Energy (eV) LCAO Description of Methane 2p (t2) t2 (1, 2, 3) a1 (1) 2s (a1) C CH4 H4
M(CO)6 M = Cr, Mo, W, d6 metals L L L L L L Doct t1u* a1g* t2g* t1u t1g + t2g + t1u + t2u Ligand * orbitals a1g eg* 4s eg t2g 6 x LGO 3d t2g a1g eg t1u Ligand orbitals eg t1g +t2g + t1u + t2u t1u a1g
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 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 t1u → 2T1u t2u → 2T2u Photoelectron spectra of d6 metal hexacarbonyls M(CO)6 vertical 2T2g Cr Mo W 18 12 10 8 14 16 Ionization Energy (eV)
V(CO) V(CO) 6 6 20 20 18 18 16 16 14 14 12 12 10 10 8 8 6 6 Ionization Energy (eV) Ionization Energy (eV) 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 a 17 e- complex. Ground State: t2g5 : 2T2g Second ion state: t1u5t2g5 : T1u xT2g = 3,1T2u, 3,1T1u, 3,1Eu, 3,1A2u First ion state: t2g4 : T2g xT2g = 3T1g, 1T2g, 1E1g, 1A1g And so on and so on…
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. But, open-shell molecules aren’t always this complicated…
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