FR16
Multidimensional spectroscopy
A broad infrared peak hides many molecular histories. Three carefully timed pulses connect the frequency a vibration had earlier with the frequency it has later. Follow that connection from a single vibrating bond to photon echoes, signed two-dimensional spectra and tests of molecular memory.
Give the same vibration a second look
A broad peak could come from molecules in different environments or from rapid changes within every molecule. A line drawn on one frequency axis can hide that difference. Short pulses add a controlled interval between preparation and observation. Two frequency axes then show how the earlier and later responses connect.
Start with a bond and a phase arrow. Chapters three and four build the response pathways that create echoes. Chapters five and six connect a few molecular levels to signed spectra reconstructed from complex records. The last pair asks how environmental memory can be inferred, then reads an original paper and reproduces one explicit Gaussian limit.
Shared textbook foundations · Molecular and electronic structure prerequisites · FR16 scope and acceptance
L1 · 1
What one infrared peak can tell us
Start with a vibrating bond, distinguish infrared and Raman selection rules, and see why one frequency axis can hide different molecular histories.
L1 · 2
Why a spectral line broadens
Use phase arrows to distinguish coherence, lifetime and two broadening mechanisms, then derive a Lorentzian line and convert its width into time.
L2 · 3
How three pulses build a third-order response
Introduce populations and coherences through the density matrix, then follow three weak-field interactions into time ordering and phase matching.
L2 · 4
How dispersed phases form a photon echo
Track a static ensemble through a rephasing pathway, calculate echo timing and decay, then select the complex signal with phase cycling.
L3 · 5
How two vibrations meet in a 2D spectrum
Build a weakly anharmonic two-mode Hamiltonian, calculate coupled frequencies, and combine bleaching, emission and excited-state absorption into signed peaks.
L3 · 6
Reconstruct a 2D spectrum from a complex record
Recover field quadratures with a local oscillator, fix Fourier signs for both pathways, and calculate the effects of sampling, bandwidth and noise.
L3 · 7
How a molecule forgets its earlier frequency
Define frequency memory, derive the Gaussian centre-line relation, and distinguish spectral diffusion, chemical exchange and finite-window inference.
L4 · 8
Read a centre-line paper and test frequency memory
Read Fenn and Fayer’s 2011 Figures 1–3, reproduce the Gaussian limit in Eq. (12), and test which inferences survive withheld observations.
Try the connections in an experiment
- Move a pulse and watch an ensemble refocus
- Change coupling and reconstruct a signed 2D spectrum
- Fit frequency memory and predict withheld waits
- Revisit Raman scattering and its selection rules
- Revisit coherent molecular rotation and revivals
The new experiments use original simulated data: a two-level echo reference, a weakly anharmonic two-mode response, and a selected Gaussian frequency-pair band for diffusion inference. Raman scattering and rotational revivals remain distinct physical processes. The paper-reading chapter identifies the exact result reproduced and the observations it does not reanalyse.
Sources and calculation scope
- Andrei Tokmakoff, Nonlinear and Two-Dimensional Spectroscopy (June 2011, v1)
Author lecture notes, nonlinear-spectroscopy section: density-matrix perturbation theory; printed pp. 23–25, Eqs. (51)–(55), for rephasing and nonrephasing; pp. 29–30 for the vibrational harmonic limit. The course examples are new teaching calculations.
- Tokmakoff, Two-dimensional spectroscopy chapter (June 2011)
In the same deposited notes, the section whose printed page numbers restart at 1: pp. 4–5, Eqs. (1)–(3), connect response, Fourier transformation and heterodyne detection; pp. 10–11 discuss coupled-vibration peak pairs. No source figure is redistributed.
- Golonzka et al., Vibrational Anharmonicities Revealed by Coherent Two-Dimensional Infrared Spectroscopy (2001)
Physical Review Letters 86, 2154–2157, published 5 March 2001. Publisher abstract checked for paired features and dipole-angle sensitivity. The full paper was not used for a figure or numerical-data reproduction; the explicit model follows the author lecture notes.
- Fenn and Fayer, Extracting 2D IR frequency-frequency correlation functions from two component systems (2011)
Journal of Chemical Physics 135, 074502, publisher version, DOI 10.1063/1.3625278. Read Figs. 1–3 and Eqs. (1)–(4), (12), (14)–(15). The bounded numerical benchmark is the single-component Gaussian slope relation in Eq. (12), with original synthetic parameters; it is not a fit to the paper’s water measurements.
- Park, Kwak and Fayer, Ultrafast 2D-IR vibrational echo spectroscopy (2007)
Laser Physics Letters 4, 704–718, DOI 10.1002/lapl.200710046. Experimental review: pulse sequence, local oscillator and absorptive phasing in Sections 2–3 and Fig. 3. Its center-line convention uses the inverse slope for the opposite slice direction; the course states its own axes before defining a slope.
- MIT Spectroscopy, Tokmakoff research on hydrogen-bond dynamics
Institutional research description, used for the motivation connecting hydroxyl frequencies to changing hydrogen-bond environments. It supplies no raw data for these Labs.