1 / 24

IT’S WHAT YOU PLUCK! A TUTORIAL ON INTRAMOLECULAR DYNAMICS

THE STIMULATED EMISSION PUMPING AND DISPERSED FLUORESCENCE SPECTRA OF ACETYLENE ARE NOT INTRINSICALLY UN ASSIGNABLE. 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.

rafael
Download Presentation

IT’S WHAT YOU PLUCK! A TUTORIAL ON INTRAMOLECULAR DYNAMICS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 Heff TO A CLASSICAL MECHANICAL Heff: VIEWS OF INTRAMOLECULAR DYNAMICS

  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] total [83] BY PERTURBATION THEORY V(Q)E(V)

  3. PERTURBATION THEORY AND “RESONANCE” DEFINE “ZERO-ORDER” BASIS SET ( 0 ) Y ( 0 ) = ( 0 ) Y ( 0 ) H E n n n ( 1 ) H kn Y = Y ( 0 ) + y ( 0 )  n n k ( 0 ) ( 0 ) - E E  k n n k 2 ( 1 ) H  kn ( 0 ) ( 1 ) = + + E E H n n nn ( 0 ) ( 0 ) - E E k n  n k (1) H OTHERWISE “RESONANCE” kn > VALID IF 1 (0) (0) - E E n k MUST DIVIDE BASIS STATES INTO QUASI-DEGENERATE GROUPS VAN VLECK TRANSFORM AND DIAGONALIZE EACH †

  4. IS RESONANCE BAD NEWS? CAN’T USE NONDEGENERATE PERTURBATION THEORY CAN’T DERIVE SIMPLE ENERGY LEVEL FORMULAS “x-k RELATIONSHIPS” A FEW kijk AND kijkl 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 kijk and kijkl CAN BE IGNORED!

  5. v v P=2v +v E 1 2 1 2 0 0 0 (3/2+ 0 )w (3/2+ 1 )w 0 1 1 1 0 2 (3/2+ 1 )w (3/2+ 2 )w 0 2 2 1 1 3 (3/2+ 3 )w (3/2+ 3 )w 0 3 3 2 0 4 (3/2+ 4 )w (3/2+ 4 )w 1 2 4 0 4 4 (3/2+ 4 )w POLYADS EXAMPLE: RESONANCE COUPLING TERM SELECTION RULE: v1 = ±1, v2 = ±2, 0 SCALING: NEAR DEGENERATE GROUPS OF BASIS STATES P=4 POLYAD (20) (12) (04) ALL POLYADS EXPRESSED IN TERMS OF wAND K P = 10 POLYAD? HINT: 6 BASIS STATES

  6. BRIGHT AND DARK STATES ELECTRONIC TRANSITION: FRANCK-CONDON FACTORS qv¢,v CHANGE IN GEOMETRY Let MODE 1 BE F–C DARK, MODE 2 F-C BRIGHT EIGENSTATES: P = 4 POLYAD ONLY 1 BRIGHT STATE IN EACH w1  22 POLYAD

  7. Acetylene Polyad Structure Polyad Quantum Numbers Ns = v1 + v2 + v3 “quanta of stretching excitation” Nres = 5v1 + 3v2 + 5v3 +v4 + v5 “approximate energy”  = 4 + 5 “total vibrational angular momentum” v1 = sym. CH stretch v2 = CC stretch v3 = anti-sym. CH stretch v4 = trans bend v5 = 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,v2,0,v4,00 0 †

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

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

  10. Dispersed Fluorescence Spectroscopy from S1 State of Acetylene H C C H H :C C H H H C C n3 n3 n2 = CC stretch n3 = trans bend n3 42,000 cm–1 n3 S1 ** origin 16,000 cm–1 pump S0 n2 = CC stretch n4 = trans bend ** FRANCK-CONDON PLUCK • Dispersed fluorescence spectra recorded from J¢=1 levels of 5 S1-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).

  11. How do we make sense of these spectra? Internal Energy (cm–1) 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. JCP 107 8349 (1997)XCC

  12. Selected Eigenstates at Evib ≈ 14,500 cm–1 “local bend” ??? “counter-rotation”

  13. 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

More Related