Slide #1 THE STIMULATED EMISSION PUMPING AND DISPERSED FLUORESCENCE SPECTRA OF ACETYLENE ARE NOT INTRINSICALLY UNASSIGNABLE IT’S WHAT YOU PLUCK! A TUTORIAL ON INTRAMOLECULAR DYNAMICS FROM A QUANTUM MECHANICAL H eff TO A CLASSICAL MECHANICAL H eff : VIEWS OF INTRAMOLECULAR DYNAMICS

Slide #2 LOST IN A SEA OF FIT PARAMETERS 4 ATOMS, 3N–6=6 MODES, IGNORE SYMMETRY CUBIC:6[iii] + 30[ijj] + 20[ijk] = 56 [total] QUARTIC:6[iiii] +30[ijjj] + 15[iijj] + 60[iijk] + 15[ijkl] = 126 [total] V(Q)  E(V) BY PERTURBATION THEORY total [83]

Slide #3  PERTURBATION THEORY AND “RESONANCE”  H (0)  n (0)  E n (0)  n (0)  n  n (0)  k  n H kn (1) E n (0)  E k (0)  k (0) E n  E n (0)  H nn (1)  H kn (1) 2 E n (0)  E k (0) VALID IF 1  H kn (1) E n  E k (0) DEFINE “ZERO-ORDER” BASIS SET OTHERWISE “RESONANCE” MUST DIVIDE BASIS STATES INTO QUASI- DEGENERATE GROUPS VAN VLECK TRANSFORM AND DIAGONALIZE EACH (0) kn  

Slide #4 IS RESONANCE BAD NEWS? CAN’T USE NONDEGENERATE PERTURBATION THEORY CAN’T DERIVE SIMPLE ENERGY LEVEL FORMULAS “x-k RELATIONSHIPS” A FEW k ijk AND k ijk l ARE SINGLED OUT FOR SPECIAL TREATMENT * NOT BECAUSE OF THEIR MAGNITUDE * BECAUSE THEY ARE LARGE WRT AN ENERGY DENOMINATOR “RESONANCE” * RESONANCES ARE USUALLY SYSTEMATIC * RESONANCES HAVE PROMINENT EFFECTS ON THE SPECTRUM AND THE EARLY TIME DYNAMICS MOST NON-RESONANT k ijk and k ijk l CAN BE IGNORED!

Slide #5 POLYADS EXAMPLE: SELECTION RULE:  v 1 = ±1,  v 2 = ±2, 0 SCALING: NEAR DEGENERATE GROUPS OF BASIS STATES P=4POLYAD v 1 v 2 P=2v 1 +v 2 E 000  011  102  022  113  033  204  124  044  ALL POLYADS EXPRESSED IN TERMS OF  AND K P = 10 POLYAD? HINT: 6 BASIS STATES RESONANCE COUPLING TERM (20) (12) (04)

Slide #6 BRIGHT AND DARK STATES CHANGE IN GEOMETRY Let MODE 1 BE F–C DARK, MODE 2 F-C BRIGHT ELECTRONIC TRANSITION: FRANCK-CONDON FACTORS q v,v  EIGENSTATES: ONLY 1 BRIGHT STATE IN EACH  1  2  2 POLYAD P = 4 POLYAD

Slide #7 Acetylene Polyad Structure Polyad Quantum Numbers N s = v 1 + v 2 + v 3 “quanta of stretching excitation” N res = 5v 1 + 3v 2 + 5v 3 +v 4 + v 5 “approximate energy” = “total vibrational angular momentum” v 1 = sym. CH stretch v 2 = CC stretch v 3 = anti-sym. CH stretch v 4 = trans bend v 5 = cis bend 4 / 5 = vib. ang. momentum [Fried and Ezra, JCP 86 (1987) 6270; Kellman and Chen, JCP 95 (1991) 8671] H = = bright state  0,v 2,0,v 4,0 0  0 

Slide #8 NOW FOR THE REAL WORLD ENERGY LEVEL PATTERNS FROM DIFFERENT POLYADS OVERLAP INTER-POLYAD MIXING? CAN OVERLAPPING POLYADS BE DISENTANGLED? HIGH RESOLUTION: SEP PUMP DUMP LOW RESOLUTION: DF FLUORESCE PUMP

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Slide #13 INTRINSICALLY UNASSIGNABLE? E J(J+1) VIBRATIONAL LEVELS EXIST? OR SCATTER PLOT? STATISTICAL TESTS LEVEL SPACING DISTRIBUTION INTENSITY DISTRIBUTION QUANTUM CHAOS ! ? OR NOT ? !

Slide #14 origin 3 33   3   3 42,000 cm –1 16,000 cm –1 pump C C H H S1S1 S0S0 :C C H H 2 = CC stretch 3 = trans bend ** 2 = CC stretch 4 = trans bend ** FRANCK-CONDON PLUCK Dispersed Fluorescence Spectroscopy from S 1 State of Acetylene C C H H Dispersed fluorescence spectra recorded from J=1 levels of 5 S 1 -State vibrational levels. Dispersed emission recorded on an intensified Charge Coupled Device (ICCD) at 16 cm –1 and 7 cm –1 resolution. Frequency calibration (good to ~3 cm –1 ) accomplished using Hg, Ne, Kr, Xe, Th, Fe, and Ar frequency standards. Intensity calibration (good to ~20%) accomplished using Standard of Spectral Irradiance (quartz tungsten lamp).

Slide #15 How do we make sense of these spectra? Internal Energy (cm –1 ) JCP (1997) XCC Our Approach: Numerical Pattern Recognition Based on two (good) approximations: 1. The acetylene effective Hamiltonian is block diagonal (polyads) 2.There is one bright state per polyad.

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Slide #20 Selected Eigenstates at E vib ≈ 14,500 cm –1 “local bend”“counter-rotation”???

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Slide #24 ASSIGNABILITY WHAT DOES IT MEAN TO “ASSIGN” A SPECTRUM ? RIGOROUSLY CONSERVED QUANTITIES [H,A] = 0 BORING APPROXIMATELY CONSERVED QUANTITIES [H (0),A] = 0PATTERNS [H (1),A]  0DYNAMICS SEVERAL CHOICES OF PARTITIONINGS OF H INTO H (0) + H (1) RISKY EARLY TIME DYNAMICS “THE PLUCK” MECHANISM