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Vibrational Anharmonicity and Multilevel Vibrational Dephasing from Vibrational Echo Beats K

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Vibrational Anharmonicity and Multilevel Vibrational Dephasing from Vibrational Echo Beats K Vibrational anharmonicity and multilevel vibrational dephasing from vibrational echo beats K. D. Rector, A. S. Kwok,a) C. Ferrante,b) and A. Tokmakoffc) Department of Chemistry, Stanford University, Stanford, California 94305 C. W. Rella Hansen Experimental Physics Laboratory, Stanford University, Stanford, California 94305 M. D. Fayerd) Department of Chemistry, Stanford University, Stanford, California 94305 ~Received 22 January 1997; accepted 21 March 1997! Vibrational echo experiments were performed on the IR active CO stretching modes 21 (;2000 cm ) of rhodium dicarbonylacetylacetonate @Rh~CO!2acac# and tungsten hexacarbonyl @W~CO!6# in dibutylphthalate and a mutant of myoglobin-CO ~H64V-CO! in glycerol–water using ps IR pulses from a free electron laser. The echo decays display pronounced beats and are nonexponential. The beats and nonexponential decays arise because the bandwidths of the laser pulses exceed the vibrational anharmonicities, leading to the excitation and dephasing of a multilevel coherence. From the beat frequencies, the anharmonicities are determined to be 14.7, 21 13.5, and 25.4 cm , for W~CO!6,Rh~CO!2acac, and H64V-CO, respectively. From the components of the nonexponential decays, the vibrational dephasing at very low temperature of both the v50–1 and v51 – 2 transitions are determined. At the lowest temperatures, T2'2T1 , so the v52 lifetimes are obtained for the three molecules. These are found to be significantly shorter than the v51 lifetimes. Although the v51 lifetimes are similar for the three molecules, there is a wide variation in the v52 lifetimes. © 1997 American Institute of Physics. @S0021-9606~97!02324-6# I. INTRODUCTION tional pump–probe spectroscopy.1,2 In this method, the v50 1 transition is pumped with an intense ps IR pulse. The measurement of vibrational spectra using Fourier On a→ time scale short compared to the vibrational lifetime, a transform infrared ~FTIR! spectroscopy provides a wealth of second IR probe, generally having a wide bandwidth, is information about the equilibrium structures of molecules passed through the sample and spectrally resolved. The and the effects of solvents on normal modes. However, im- v51 2 transition appears as an absorption of the probe portant types of measurements, i.e., vibrational homoge- that is→ not present in the absence of the pump. This method neous linewidth and the vibrational anharmonicity, are either has been successfully applied,1,2 but it requires two ps IR difficult or impossible to perform with ordinary linear tech- pulses with different characteristics, i.e., wavelength and niques. Measurements of vibrational anharmonicities provide bandwidth. information about the shape of the vibrational potential sur- An alternative approach is to perform a vibrational face. Vibrational anharmonicities are not readily obtained us- echo3–6 using pulses having sufficiently wide bandwidth to ing a conventional FTIR because the v50 2 transition is establish a multilevel coherence among the v50, 1, and 2 → forbidden, and, therefore, the absorption at the frequency states.7 The multilevel coherence results in a vibrational echo corresponding to the v50 2 transition is weak. In addi- decay with beats. The beats occur at the frequency of the → tion, the spectral region around a v50 2 transition is fre- difference between the v50 1 and v51 2 transition en- → quently congested with combination bands, making it diffi- ergies, i.e., at the frequency→ of the vibrational→ anharmonic cult to identify the correct peak. A direct measurement of the splitting. This is not a conventional quantum beat. In a quan- v51 2 transition is not usually feasible for the higher fre- tum beat, a state is coupled by the radiation field directly to → 2 quency modes (1000– 4000 cm 1) because the thermal two other states that fall within the bandwidth of the pulse. population at ambient temperatures of the v51 state is down In the vibrational echo anharmonic beat ~VEB! experiment, five to twenty factors of e compared to the v50 state. the radiation field couples v50 1 and then v51 2. Another technique for measuring vibrational anharmo- There is no direct coupling between→v50 2. → nicity involves the use of time resolved, two color vibra- In addition to measuring the vibrational→ anharmonicity through the echo decay beat frequency, the echo decay pro- a!Permanent address: Department of Physics, Franklin and Marshall College, vides the homogeneous dephasing time ~homogeneous line- Lancaster, PA 17604. width! of both the v50–1 and v51 – 2 transitions. The b!Present address: Department of Chemistry, University of Munich, 80290 homogeneous linewidth provides information on the dynami- Munich Germany. c! cal interactions of a vibration with its environment. Vibra- Present address: Department of Chemistry, University of Chicago, Chi- 4,5 4,5 cago, IL 60637. tional echo experiments on liquids, glasses, and d!Author to whom correspondence should be sent. proteins6,8 have shown that vibrational spectra may be J. Chem. Phys. 106 (24), 22 June 1997 0021-9606/97/106(24)/10027/10/$10.00 © 1997 American Institute of Physics 10027 Downloaded¬31¬Jul¬2002¬to¬171.64.123.74.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp 10028 Rector et al.: Vibrational dephasing from vibrational echo beats inhomogeneously broadened, even at room temperature. the first pulse and initiates rephasing of the inhomogeneous Therefore, vibrational echo experiments are necessary to ex- contributions to the vibrational spectral line. This rephasing tract the homogeneous linewidth from the observed spectro- results in a macroscopic polarization that is observed as an scopic line. The VEB experiment makes it possible to com- echo pulse at time 2t. The echo emerges from the sample at pare the homogeneous linewidths of the v50–1 and v an angle 2u with respect to the first beam due to wave vector 51 – 2 transitions. At the polarization level for Lorentzian matching conditions. The integrated intensity of the echo homogeneous lines, the echo decay is a bi-exponential pulse is measured as a function of t. squared with beats. One exponential corresponds to the de- For the case in which the laser bandwidth is narrow with cay of the v51 – 2 coherence and the other exponential cor- respect to the vibrational anharmonicity, such that the vibra- responds to the decay of the v50 – 1 coherence. Therefore, tional coherence involves only the v50 – 1 transition, the the VEB experiment allows both the homogeneous line- experiment is modeled well by a two level system. For a widths and the vibrational anharmonicity to be experimental Lorentzian homogeneous lineshape with linewidth observables. G51/pT2 , the echo decays as In this paper, VEB experiments on CO stretching modes of three molecules are presented: rhodiumdicarbonylacety- I~t!5I0 exp~24gt!, ~1! lacetonate @Rh~CO!2acac# and tungsten hexacarbonyl @W~CO! # in dibutylphthalate ~DBP!, and CO bound to the 6 where g51/T for the v50 – 1 transition. The homogeneous active site of a myoglobin protein in a 95:5 mixture of glyc- 2 dephasing time has contributions from the pure dephasing erol:water. The myoglobin protein is a mutant of wild type time, T* , and the vibrational lifetime, T , myoglobin in which the distal histidine ~position 64! is re- 2 1 placed with a valine ~H64V-CO!.6 The protein pocket around 1 1 1 the CO in H64V is markedly different than either of the 5 1 . ~2! inorganic compounds. In the protein, the CO is bound to an pT2 pT2* 2pT1 octahedral Fe which has four bonds to a large aromatic mac- rocycle. The last bond of the Fe is to the proximal histidine There can also be a contribution from orientational ~position 93!. relaxation.5 However, the experiments reported here were The vibrational echo experiments on Rh~CO!2acac are conducted in low temperature glassy solvents, so the contri- the first for this molecule. Vibrational echo studies of bution from orientational relaxation is negligible. The life- W~CO!6 in several liquid and glassy solvents have been time can be measured with a pump–probe experiment, and 3,5 reported, including the first observation of vibrational echo when combined with a vibrational echo measurement of 7 anharmonic beats on W~CO!6 in DBP. Further, extensive T2 , the pure dephasing contribution to the homogeneous vibrational echo studies and lifetime measurements of the linewidth can be determined. For the systems studied here, v50 – 1 transition have been presented previously for the lifetime components of the homogeneous lines are only 6,8 Mb–CO and H64V-CO. slightly temperature dependent. The pure dephasing compo- In the following, Rh~CO!2acac data is presented as a nents are more strongly temperature dependent. function of the excitation frequency. As the frequency is de- When the laser bandwidth is similar to the anharmonic- creased, the beats become more pronounced. These results ity, short pulse excitation will create a three level coherence are compared to an approximate theoretical calculation, and involving the v50, 1, and 2 vibrational levels. Previous the- the trends are found to be in accord. The v50–1 and oretical work on a three level echo described an equally v51 – 2 dephasing times and the anharmonicity are also ob- spaced system.9 The derivation of the VEB signals for three tained. For H64V-CO, the anharmonicity is much greater level systems has a large contribution from experiments and than in the two organometallic compounds. By tuning to theory studying coherent oscillations in semiconductor lower frequencies than the v50 1 transition, beats are ob- structures.10,11 The echo signal can be described for an un- → served although the pulse bandwidth is insufficient to pro- equally spaced three-level system using a semiclassical dia- duce beats when centered on the v50 1 line. Again, the grammatic perturbation theory treatment of the third-order → v50–1 and v51 – 2 dephasing times and the anharmonic- nonlinear polarizability.12,13 ~See Appendix for details.! The ity are obtained.
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