1. Acetylene Dynamics at Energies up to 13,000 cm-1
By: Jonathan Martens, David S. Perry
Dept of Chemistry, The University of Akron
Michel Herman, Badr Amyay
Laboratoire de Chimie quantique et Photophysique, Université libre de Bruxelles

2. Computed dynamics based on Michel Herman’s spectroscopic Hamiltonian
Acetylene
Computed dynamics based on Michel Herman’s spectroscopic Hamiltonian
trans bend ν4
cis bend ν5 2
Michael Kellman’s movies:

3. Acetylene Hamiltonian
Badr Amyay
B. Amyay, M. Herman, A. Fayt, L. Fusina, A. Predoi-Cross, Chem. Phys. Lett. 491, (2010) additional lines!
Normal mode basis set: (v1 v2 v3 v4 v5, l4 l5 ) with e/f g/u symmetries
Polyad numbers: Nr = 5v1 + 3v2 + 5v3 + v4 + v5 conserved Ns = v1 + v2 + v not conserved
Vibrational angular momentum: k = l4 + l not conserved
Four coupling types:
Vibrational l-resonance: Δvn = 0, Δl4 = ±2, Δl5 = ∓2, Δk = 0
Anharmonic (e.g., DD4455): Δv4 = ±2, Δv5 = ∓2, Δk = 0
Rotational l-resonance: Δk = ±2, ±4, ~J 2
Coriolis: Δk = ±1, ΔNs = ±1, ~J
Fit included 19,582 lines up to 13,000 cm-1, ~150 off-diagonal parameters
Polyads studied in this work: {Nr, e, g}
{ 8, e, g} – 5682 cm states
{12, e, g} – 8415 cm states
{16, e, g} 10,421 – 11,076 cm states
{18, e, g} 11,808 – 12,379 cm states 3

4. Acetylene: n Coupled Levels
Express zeroth order basis states in terms of eigenstates
Bright state is zeroth order state j = 1
After a coherent excitation of a bright states, calculate the time dependence of the wavefunction.
Project the time-dependent wavefunction onto various zeroth-order states to monitor its time evolution.

5. Acetylene Detailed IVR Dynamics
Δl4 = ±2, Δl5 = ∓2
Badr Amyay
Δv4 = ±2, Δv5 = ∓2
Δk = ±2
Normal Mode Bright State
, 0 0 e g
E = 10,534.7 cm-1
in Polyad {16, e, g}
Δk = ±1, ΔNs = ±1 5

6. Acetylene Detailed IVR Dynamics
J = 2
J = 30
J = 100
ν1+ ν3 = 3
Acetylene Detailed IVR Dynamics
Δl4 = ±2, Δl5 = ∓2
Δv4 = ±2, Δv5 = ∓2
Ns = 3
Δk = ±2
Normal Mode
CH Stretch Bright State
, 0 1 e g
E = 10,421.3 cm-1
in Polyad {16, e, g}
Δk = ±1, ΔNs = ±1
Δk = ±1, ΔNs = ±1 6

7. Acetylene IVR Rates 7

8. Normal Mode Bending States
cis bend 16ν5
cis bend 12n5
cis bend 18ν4
cis bend 8ν5
Wavenumber / cm-1
trans bend 18ν4
trans bend 16ν4
trans bend 12ν4
trans bend 8ν4 8

9. Transformation to DD4455 Eigenstate Basis
Polyad {16, e, g}
DD4455
Eigenstates
Normal Mode
Bright States
counter rotator
cis bend ν5
trans bend ν4
local bender 9

10. Acetylene Computed Spectra
Polyad {16, e, g}; J = 30
Normal Mode Bright States
DD4455 Bright States
cis bend ν5
counter rotator
local bender
trans bend ν4 10

11. Acetylene Detailed IVR Dynamics
Δl4 = ±2, Δl5 = ∓2
Δv4 = ±2, Δv5 = ∓2
Δk = ±2
DD4455 Bright State
10,538.0 cm-1
in Polyad {16, e, g}
Δk = ±1, ΔNs = ±1 11

12. Acetylene IVR Rates
Polyad {16, e, g} 12

13. Acetylene Summary Detailed Dynamics Initial IVR Rates
Hierarchies of sequentially coupled states: 20 fs to 20 ps.
Dramatic enhancement with rotational excitation
Qualitative differences between CH and bending bright states.
Initial IVR Rates
Increase with polyad number
Depend on the nature of the bright state Bend vs CH stretch Normal mode vs local CH, local bender, etc
Faster for interior states than edge states for normal mode bright states
Faster for the local bender than for the counter rotator 13