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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. +. 1.

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

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  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. + 1 ˜ ACETYLENE IVR IN STATE S X g QM Heff TO CM eff VIA IMPORTANT RESONANCES IN NORMAL MODE BASIS SETS CORRELATION DIAGRAM VISUALIZATIONS OF QUANTUM DYNAMICS BEST BASIS? HEISENBERG’S CORRESPONDENCE PRINCIPLE SURFACES OF SECTION A CAUSE OF SOME BIFURCATIONS ACETYLENEVINYLIDENE ISOMERIZATION CHAOS AND BIFURCATIONS †

  3. EACH TERM IN V(Q) MUST BE IMPORTANT RESONANCES NORMAL MODES NRES = 5v1 +3v2 +5v3 +v4 +v5 NSTRETCH = v1 +v2 +v3 CUBIC TERMS QUARTIC TERMS QiQjQk ΔNRES QiQjQkQ ΔNRES 133 233 122 112 144 155 244 255 345 5 7 1 7 3 3 1 1 3 1,244 1,255 3,245 11,33 44,55 0 0 0 0 0 MOST IMPORTANT INTRAPOLYAD RESONANCES NONE ARE RESONANT!

  4. REPLACE Q, P, H BY DIMENSIONLESS CREATION (a†) ANNIHILATION (a), AND NUMBER (a†a) OPERATORS EXAMPLE quantum numbers constants

  5. Acetylene Bending Effective Hamiltonian

  6. Acetylene Bending Effective Hamiltonian in local mode coordinates

  7. Correlation Diagrams 5,800 5,800 5,600 5,600 Internal Energy (cm–1) 5,400 5,400 5,200 5,200 5,000 5,000 normal mode basis set local mode basis set eigenstates 15,600 15,600 15,200 15,200 14,800 14,800 Internal Energy (cm–1) 14,400 14,400 14,000 14,000 normal mode basis set local mode basis set eigenstates

  8. VISUALIZATIONS OF QUANTUM DYNAMICS Y(t), |Y(t)|2 ARE TOO COMPLICATED. WHY? NEED 1-D VISUALIZATIONS SURVIVAL PROBABILITY TRANSFER PROBABILITY EXCITATION OF ONE MODE RESONANCE OPERATOR TRANSFER RATE OPERATOR

  9. An Unusual Trend in IVR v4 Bright States: (0,0,0,v40,00) Frequency Domain Time Domain y = 0.56 y = 0.16 y = 0.24

  10. † † ai, ai, aiai REDUCED DIMENSION QM Heff CM HeffHexact TRAJECTORIES SURFACES OF SECTION

  11. CLASSICAL MECHANICS CONJUGATE VARIABLES Q, P I, f ACTION, ANGLE IT IS MOST CONVENIENT TO GO FROM QM TO CM VIA THE ACTION, ANGLE REPRESENTATION †

  12. QUANTUM  CLASSICAL HEISENBERG’S CORRESPONDENCE PRINCIPLE Collaboration with C. Jung, UNAM, and H. S. Taylor, USC. CONSERVED NOT CONSERVED

  13. SURFACE OF SECTION WAY OF DISPLAYING STRUCTURE IN EXPLORATION OF PHASE SPACE (Q1, P1;Q2,P2;…Qn,Pn) [Q,P] [Ji,fi] REDUCED DIMENSION VIEW OF CLASSICAL TRAJECTORIES * REGULAR (QUASIPERIODIC) VS. CHAOS * CLASSES OF REGULAR MOTION * BIFURCATIONS APPEARANCE OF NEW CLASSES DISAPPEARANCE OF OLD CLASSES

  14. dfa  0, dt Jb VS. fb PLANE (2–D) AT fa = 0, HCCH PURE BEND PHASE SPACE • 2 2-D BENDS  4-D CONFIGURATION SPACE • 2 GOOD QUANTUM NUMBERS: •  4-2 = 2-D ACCESSIBLE CONFIGURATION SPACE • 2-D CONFIGURATION SPACE  4-D PHASE SPACE • 4–1(ENERGY) = 3-D • TRAJECTORIES IN 3-D PHASE SPACE • (Qi,Pi)  (Ji, fi) ACTION, ANGLE • SURFACE OF SECTION • ONE TRAJECTORY  FAMILY OF POINTS ON s. of s. • SAMPLE MANY TRAJECTORIES NBEND & TOTAL Ja n4 – n5 Jb4 – 5 CHARACTERISTIC PATTERN UNCORRELATED DOTS QUASIPERIODIC CHAOS (Jb, fb, Ja, fa) COLOR CODED INITIAL CONDITIONS “STRUCTURE OF PHASE SPACE” COLOR

  15. Onset of Classical Chaos

  16. Classical Dynamics Near 15,000 cm–1

  17. Effective Frequencies as Means of Identifying Normal/Local Transition 750 + + + + cis bend + counter- rotation Effective Frequencies (weff) 700 + + + + + trans bend 650 local bend 600 0 5 10 15 20 Quanta of Bend Excitation (vb) weff = DE/Dvb

  18. Analysis of IVR: (0,0,0,100,00) Bright State Zero-Order Energies Eigenenergies (and spectrum) v5 (quanta of cis bend) (0,0,0,00,100) l4 = –l5 Internal Energy (cm–1) Bright State v4 (quanta of trans bend)

  19. H :C C H Isomerization Coordinate Energetics 25,000 20,000 15,000 Internal Energy (cm–1) 10,000 5,000 0 Isomerization Coordinate H C H C Dynamics Å Å Halonen, Child, and Carter surface, Mol. Phys. 47, (1982), p. 1097.

  20. Effective Anharmonicities as Means of Identifying Normal/Local Transition 1500 + + + + cis bend + counter- rotation 1400 + E(Nb+1) – E(Nb–1)[cm–1] + + + + trans bend 1300 local bend 1200 0 5 10 15 20 Nb

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