The dynamics of molecular functional group plays an important role during a chemical process, chemical bond forming and breaking, energy transfer and other dynamics happens within picoseconds domain. It is very difficult to study such fast processes directly, for decades scientists can only learn from theoretical calculations, lacking experimental methods.

However, with the development of ultrashort pulsed laser enable experimental study of molecular functional group dynamics. With ultrafast laser technologies, people develop a series of measuring methods, among which, pump-probe technique is widely used to study the molecular functional group dynamics. Here we concentrate on how to use pump-probe experiment to measure functional group vibrational lifetime. The principle, experimental setup and data analysis will be introduced.

For every function group within a molecule, such as the C≡N triple bond in phenyl selenocyanate (C₆H₅SeCN) or the C-D single bond in deuterated chloroform (DCCl₃), they have an individual infrared vibrational mode and associated energy levels. For a typical 3-level system (Figure 1), both the 0 to 1 and the 1 to 2 transition are near the probe pulse frequency (they don't necessarily need to have exactly the same frequency).

Figure 1: Schematic representation of a typical three level system.

In a pump-probe experiment, we use the geometry as is shown in Figure 2. Two synchronized laser beams, one of which is called pump beam (E_pu) while the other probe beam (E_pr). There is a delay in time between each pulse. The laser pulses hit the sample, the intensity of ultrafast laser (fs or ps) is strong enough to generated 3^rd order polarization and produce 3^rd order optical response signal which is use to give dynamics information of molecular function groups. For the total response signals we have Equation 1, where µ₁₀ µ₂₁ are transition dipole moment and E₀, E₁, and E₂ are the energies of the three levels, and t₃ is the time delay between pump and probe beam. The delay t₃ is varied and the response signal intensity is measured. The functional group vibration life time is determined from the data.

Figure 2: The geometry of the pump-probe experiment.

(1)

The optical layout of a typical pump-probe setup is schematically displayed in Figure 3. In the setup, the output of the oscillator (500 mW at 77 MHz repetition rate, 40 nm bandwidth centered at 800 nm) is split into two beams (1:4 power ratio). Of this, 20% of the power is to seed a femtosecond (fs) amplifier whose output is 40 fs pulses centered at 800 nm with power of ~3.4 W at 1 KHz repetition rate. The rest (80%) of the seed goes through a bandpass filter centered at 797.5nm with a width of 0.40 nm to seed a picosecond (ps) amplifier. The power of the stretched seed before entering the ps amplifier cavity is only ~3 mW. The output of the ps amplifier is 1ps pulses centered at 800 nm with a bandwidth ~0.6 nm. The power of the ps amplifier output is ~3 W. The fs amplifier is then to pump an optical parametric amplifier (OPA) which produces ~100 fs IR pulses with bandwidth of ~200 cm^-1 that is tunable from 900 to 4000 cm^-1. The power of the fs IR pulses is 7~40 mW, depending on the frequencies. The ps amplifier is to pump a ps OPA which produces ~900 fs IR pulses with bandwidth of ~21 cm^-1, tunable from 900 - 4000 cm^-1. The power of the fs IR pulses is 10 ~ 40 mW, depending on frequencies.

Figure 3: Schematic representation of the optical layout for a pump-probe experiment.

In a typical pump-probe setup, the ps IR beam is collimated and used as the pump beam. Approximately 1% of the fs IR OPA output is used as the probe beam whose intensity is further modified by a polarizer placed before the sample. Another polarizer is placed after the sample and before the spectrograph to select different polarizations of the signal. The signal is then sent into a spectrograph to resolve frequency, and detected with a mercury cadmium telluride (MCT) dual array detector. Use of a pump pulse (femtosecond, wide band) and a probe pulse (picoseconds, narrow band), scanning the delay time and reading the data from the spectrometer, will give the lifetime of the functional group. The wide band pump and spectrometer described here is for collecting multiple group of pump-probe combination.

Data analysis

For a typical pump-probe curve shown in Figure 4 life time t is defined as the corresponding time value to the half intensity as time zero.

Figure 4: A typical pump-probe curve.

Table 1 shows the pump-probe data of the C≡N triple bond in a series of aromatic cyano compounds: n-propyl cyanide (C₃H₇CN), ethyl thiocyanate (C₂H₅SCN), and ethyl selenocyanate (C₂H₅SeCN) for which the ν_C≡N for each compound (measured in CCl₄ solution) is 2252 cm^-1), 2156 cm^-1, and ~2155 cm^-1, respectively.

Table 1: Pump-probe intensity data for C≡N stretching frequency in n-propyl cyanide, ethyl thiocyanate, and ethyl selenocyanate as a function of delay (ps).

Delay (ps)	C3H7CN	C2H5SCN	C2H5SeCN
0	-0.00695	-0.10918	-0.06901
0.1	-0.0074	-0.10797	-0.07093
0.2	-0.00761	-0.1071	-0.07247
0.3	-0.00768	-0.10545	-0.07346
0.4	-0.0076	-0.10487	-0.07429
0.5	-0.00778	-0.10287	-0.07282
0.6	-0.00782	-0.10286	-0.07235
0.7	-0.00803	-0.10222	-0.07089
0.8	-0.00764	-0.10182	-0.07073
0.9	-0.00776	-0.10143	-0.06861
1	-0.00781	-0.10099	-0.06867
1.1	-0.00745	-0.10013	-0.06796
1.2	-0.00702	-0.10066	-0.06773
1.3	-0.00703	-0.0989	-0.06767
1.4	-0.00676	-0.0995	-0.06638
1.5	-0.00681	-0.09757	-0.06691
1.6	-0.00639	-0.09758	-0.06696
1.7	-0.00644	-0.09717	-0.06583
1.8	-0.00619	-0.09741	-0.06598
1.9	-0.00613	-0.09723	-0.06507
2	-0.0066	-0.0962	-0.06477
2.5	-0.00574	-0.09546	-0.0639
3	-0.0052	-0.09453	-0.06382
3.5	-0.00482	-0.09353	-0.06389
4	-0.0042	-0.09294	-0.06287
4.5	-0.00387	-0.09224	-0.06197
5	-0.00351	-0.09009	-0.06189
5.5	-0.00362	-0.09084	-0.06188
6	-0.00352	-0.08938	-0.06021
6.5	-0.00269	-0.08843	-0.06028
7	-0.00225	-0.08788	-0.05961
7.5	-0.00231	-0.08694	-0.06065
8	-0.00206	-0.08598	-0.05963
8.5	-0.00233	-0.08552	-0.05993
9	-0.00177	-0.08503	-0.05902
9.5	-0.00186	-0.08508	-0.05878
10	-0.00167	-0.0842	-0.0591
11	-0.00143	-0.08295	-0.05734

A plot of intensity versus time for the data from TABLE is shown Figure 5. From these curves the C≡N stretch lifetimes can be determined for C₃H₇CN, C₂H₅SCN, and C₂H₅SeCN as ~5.5 ps, ~84 ps, and ~282 ps, respectively.

Figure 5: The C≡N stretch lifetimes for benzyl cyanide, phenyl thiocyanate, and phenyl selenocyanate.

From what is shown above, the pump-probe method is used in detecting C≡N vibrational lifetimes in different chemicals. One measurement only takes several second to get all the data and the lifetime, showing that pump-probe method is a powerful way to measure functional group vibrational lifetime.