Molecular Spectra and Molecular Structure - Lec 14

Page 1 of 5 pages Lecture #14: Laser Schemes for Rotational Assignment First Lines for Ω′, Ω″ Assignments Last Time: Lagerqvist Strips – use of known ∆2F(J) for either upper or lower state. Simultaneous analysis of two vibrationally linked bands: search for a C.D. that appears once in each band correct numbering of R relative to P branch and correct absolute numbering Computer automated term value method — valuable when there is no pattern. Based on frequency redundancies from two linked bands and supplemented by intensity regularity. Today: Patterns revealed by laser spectroscopy Fluorescence Excitation Spectroscopy = Laser Induced Fluorescence (LIF) Dispersed Fluorescence (DF) Wavelength Selective Fluorescence Excitation Introduction to spectra for Λ ≠ 0 and/or S ≠ 0 states Diagrams of allowed transitions First lines as diagnostics Unlinked sub-manifolds — need a model Next time: Read * JTH, pp. 1-9 (at least) * Symbols for Spectroscopy * Report of sub-committee f * nomenclature * Rotation and Angular Momenta II * Energy level Structure of 2∏ and 2∑+ states and JTH pages 9-13 What advantages might a laser bring to the assignment of an electronic band system? 1. Fluorescence Excitation Spectrum (known as LIF) Scan laser, recording total fluorescence resulting as laser frequency is tuned. Obtain spectrum essentially identical to an absorption spectrum. * A few exceptions when “quantum yield” for detected fluorescence is not identical for each line in spectrum. Reasons? 2. Predissociation (no fluorescence) fluorescence branching ratios perturbations lifetime differences, collisional quenching, self-absorption, and transport out of field of view. Dispersed Fluorescence Spectrum (DF) Tune laser into single e′v′J′ ← e″v″J″ line and record spectrum of resultant fluorescence. Page 2 of 5 pages See nothing but combination differences! e′v′J′ laser P(J + 1) v″ + n R(J – 1) J″ = J′ + 1 ² 2 Fv′′′′+n ( J′) ⇒ B′′v′′+n if J′ is known J″ = J′ – 1 ∆G″ (v″ + n – 1/2) - α′′e ( J ′ − 1)( J ′ )   small v″ + n – 1 B″(4J + 2) etc. ∆G″(v″ + 1/2) Now, if we do not know either J′ or B″, we do know that ∆2F″(J)’s change in steps of 4B″, so if we view fluorescence excited via two consecutive lines in a suspected branch, we see ∆2F″(J′) – ∆2F″(J′ – 1) = 4B″ Once B″ is known, we know J′ and all is settled. This works provided that: * precision for ∆2F″(J) is better than ≈ 2B″ * J is not so large that centrifugal distortion effects are important. * There are not many isotopic species present. There are not many superimposed vibrational sequences. There are not more complicated band systems with S ≠ 0 present. Page 3 of 5 pages If there are many unrelated lines clustered together, the resultant dispersed fluorescence spectra will bear no systematic relationships to each other. 3. Wavelength selective fluorescence excitation spectra requires tunable laser and monochromator. Fortrat Parabola R J–3 J J–2 J–1 low J region of R or P branch P J–1 J+2 ν Expt. 2 monochromator Expt. 1 monochromator acceptance window acceptance window What happens in Expt. 1? See two groups of lines — the high-J lines {R(J – 3), … R(J)} linked to {P(J – 1), … P(J + 2)} and some low-J lines linked to the other branch of the Fortrat parabola. Expt. 2? See only the single group of high-J P-lines. monochromator accuracy (~0.3 cm–1) vs. laser accuracy (0.003 cm–1) monochromator identifies R,P linked lines, laser measures their accurate frequencies! Now we are ready for more complexity. We have been ignoring the possibility that molecules might have electronic angular momenta in addition to nuclear rotation. Page 4 of 5 pages Λ: projection of resonant of atomic L onto body fixed z-axis S: total spin ∑ projection of S on z-axis Ω ≡ Λ + ∑ OR projection of J on z-axis. Convenient diagrams for summarizing levels and transitions. S=0 1 Λ states = Λ (because S = ∑ = 0) J ≥ Ω (because J can never be smaller than its projection on any axis) When Ω ≠ 0, have double parity (Ω > 0 and Ω < 0) called Ω-doubling or Λ-doubling (parity is σv symmetry of 2–1/2[|Ω〉 ± |–Ω〉]). Can have ⊥ (∆Ω = ∆Λ = ±1) and || (∆Ω = ∆Λ = 0) type transitions. Always + ↔ – parity selection rule. 1 ∏ – 1∑+ 1 +– J′ parity J″ parity 2 –+ 3 +– |Q /R \P 0 + 1 – 2 + 3 – Note that first lines in each branch are determined by Ω′ and/or Ω″: * R(0) implies Ω″ = 0 and Ω′ ≤ 1 * Q(1) implies Ω″ or Ω′ is double parity because there are no Q branches for ∑–∑ transitions absence of Q(0) implies nothing because J′ = 0 – J″ = 0 is always forbidden * P(2) implies Ω′ = 1. Absence of P(1) implies Ω′ ≠ 0. Note that upper levels of Q branch lines are only sampled via Q lines! No linkage between (1∏+, odd-J 1∑+) and (1∏–, even-J 1∑+). Must have a model for either 1∑+ or 1∏ that links the two groups of levels! Alternatively, could have microwave spectrum for 1∑+ state which links the two groups. Page 5 of 5 pages 1 1 ∆– ∏ 1 2 +– ² 4 +– 3 –2+ |Q \P /R 1 +– 1 First lines –+ 2 +– 3 2 –+ 4 R+–(1), R–+(1) ⇒ Ω″ = 1, Ω′ ≤ 2 Q+–(2), Q–+(2) ⇒ Ω′ > 1 (absence of Q) P+–(3), P–+(3) ⇒ Ω′ = 2 Usually can't resolve +– and –+ line pairs at low J. No linkage between (1∆+, 1∏–) and (1∆–, 1∏+). Model required again! Work out situation for 1∏ – 1∏ yourselves. 1st lines R(1) Q(1) P(2) again absence of linkage between (1∏+, 1∏–) and (1∏–, 1∏+). One example of an S = 1 band system. (case b) N is pattern forming 0 N 3 J parity + ∑ 3 1 2 3 + + + O R Ω=2 ∏ 2 0 1 2 – – – P Q (case a) J is pattern forming 1 1 + + – 1 – 0 J + 0 – – 1 + + – + + – 2 N′ – J″ is difference between pattern-forming quantum numbers. Use this to name branches. Always looking for pattern-forming rotational quantum number that gives 1∑+-like level pattern! For S ≠ 0 the pattern of branches, fine structure, and first lines is much more complicated than for S = 0. Need to compute level positions and relative intensities. Next time: HROT and HSO.