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The Sommerfeld ground-wave limit for a molecule adsorbed at a surface

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Science  11 Jan 2019:
Vol. 363, Issue 6423, pp. 158-161
DOI: 10.1126/science.aav4278

Climbing vibrational levels

Vibrational excitation of molecules adsorbed on a surface is usually limited because the vibrational energy is rapidly transferred into phonons, the vibrational modes of the substrate. Chen et al. found that this is not the case for CO molecules adsorbed on a surface of NaCl. The CO molecules efficiently transferred vibrational energy within groups of molecules from one high excitation state to another until they reached the dissociation limit. This process was possible because of the close proximity of the molecules and the limited transfer of energy to just one phonon mode in the salt surface.

Science, this issue p. 158

Abstract

Using a mid-infrared emission spectrometer based on a superconducting nanowire single-photon detector, we observed the dynamics of vibrational energy pooling of carbon monoxide (CO) adsorbed at the surface of a sodium chloride (NaCl) crystal. After exciting a majority of the CO molecules to their first vibrationally excited state (v = 1), we observed infrared emission from states up to v = 27. Kinetic Monte Carlo simulations showed that vibrational energy collects in a few CO molecules at the expense of those up to eight lattice sites away by selective excitation of NaCl’s transverse phonons. The vibrating CO molecules behave like classical oscillating dipoles, losing their energy to NaCl lattice vibrations via the electromagnetic near-field. This is analogous to Sommerfeld’s description of radio transmission along Earth’s surface by ground waves.

Polar molecules in optical lattices formed by interfering laser beams are platforms for studying quantum magnetism (1), quantum many-body dynamics (2), and quantum computing (3, 4). The electric fields at a crystalline surface are another form of lattice, one capable of orienting and ordering polar molecules. Hence, adsorbing molecules to low-temperature solids might be a complementary and, so far, unexplored approach to studying the lattice dynamics of polar molecules. Unfortunately, dynamical interactions between adsorbates and solid substrates are typically much stronger than those between adsorbed molecules (5, 6). For example, an adsorbate’s vibrational energy may flow to a solid’s electrons within picoseconds (7, 8) or, as a result of intrinsically anharmonic interatomic forces, to lattice vibrations within nanoseconds (9, 10).

One exception (Fig. 1C) is a monolayer of CO adsorbed to NaCl(100). Here, dipole-dipole interactions between CO molecules are stronger than CO-NaCl interactions, and such conditions lead to vibrational energy pooling (VEP). Chang and Ewing (11) observed CO in states with vibrational quantum numbers, v, as high as v = 15 by near-resonant vibration-to-vibration (V-V) energy transfer. Embedded Image(1)Unfortunately, detailed studies were impossible because of the low sensitivity and poor time response of infrared detectors available at that time.

Fig. 1 Structure and infrared spectroscopy of the 13C18O monolayer on NaCl(100).

(A and B) The polarization-dependent monolayer spectrum is observed with Fourier transform infrared (FTIR) absorbance spectroscopy (A) and laser-induced infrared fluorescence (B) by scanning the laser excitation frequency and integrating the total fluorescence signal between 50 and 1050 μs after the laser pulse. The spectra were recorded at a surface temperature of ~7 K. Note that the baseline of the p-polarized spectra is shifted for clarity. The inset in (A) shows that the IR absorption spectrum of the CO monolayer (black) is clearly distinguishable from that of a multilayer (red) for p-polarized light. CO molecules in the multilayer but not in contact with the NaCl surface give rise to a doublet centered at 2042 cm−1 (31, 32). The feature at 2054 cm−1 arises from the CO molecules at the buried NaCl interface (32). The monolayer line intensities have been corrected for an offset of 18° in the polarization of the FTIR spectrometer light source. In (B), the experimental data are represented by square symbols; red lines are Gaussian fits to guide the eye. (C) Structure of the monolayer CO on NaCl(100) (22, 23). The nearest-neighbor CO-CO distance is 3.96 Å. At a surface temperature below 35 K, the CO molecules are tilted with respect to the surface normal by an angle of 25° and are arranged in antiparallel-oriented rows to form a p(2 × 1) unit cell, as depicted by the dashed rectangle.

To study VEP in detail, we detected time- and wavelength-resolved laser-induced infrared fluorescence with a superconducting nanowire single-photon detector (SNSPD) (12, 13). Kinetic Monte Carlo (kMC) simulations (1418) of our observations reveal V-V energy transfer occurring between CO molecules separated by more than eight lattice sites and show that the excess energy represented by Δε(v + 1) in Eq. 1 is selectively absorbed by NaCl’s transverse phonons. Surprisingly, the vibrating CO molecules behave like classical oscillating dipoles, losing their energy to NaCl lattice vibrations via the electromagnetic near-field. These rates are quantitatively described by a theory (19, 20) that has its origins in Sommerfeld’s 1909 description of a radio transmitter interacting with Earth forming damped electromagnetic surface waves (21). This is a weak coupling limit where the anharmonic interatomic forces that are normally important to energy flow can be completely neglected.

Figure 1 shows infrared spectra of CO adsorbed to NaCl obtained in absorption (Fig. 1A) and with laser-induced infrared fluorescence (Fig. 1B). The spectrum of the CO monolayer is composed of a doublet centered at 2052 cm−1, where the intensity pattern is polarization-sensitive. The feature at 2055 cm−1 results from the symmetric stretching of the two coupled CO molecules in the 2 × 1 unit cell (shown as a dashed rectangle in Fig. 1C) (22, 23). The 2049 cm−1 line observed with s- and p-polarization arises from the antisymmetric stretch vibration. For comparison, Fig. 1B shows the laser-induced infrared fluorescence excitation spectrum obtained from a CO monolayer for both p- and s-polarization. There can be no doubt that the laser-induced fluorescence results from the excitation of CO molecules in the monolayer.

Figure 2, A and B, shows the experimentally obtained fluorescence emission spectrum (in black) compared to kMC simulations (in red). All features in these spectra result from the first-overtone emission of vibrationally excited CO; the emitting vibrational state is indicated by combs. Intensity peaks reflecting enhanced vibrational populations are seen near v = 7, 16, and 25; hereafter, we refer to vibrational states near these three values of v as base-camp 1, 2, and 3, respectively.

The red curve in Fig. 2A shows a kMC simulation under our experimental conditions where only nearest-neighbor V-V energy transfer is permitted, an assumption used in previous work (1418). This approach yields a peak in population at v ~ 8 (base-camp 1), strongly resembling figure 3 of (14) and (15) but markedly different from experiment. Note that a single molecule with only four nearest neighbors can still reach v = 8 because the nearest neighbors can transport vibrational quanta from more distant molecules by process 2:Embedded Image(2)Population in states higher than v ~ 8 is prevented by a one-phonon energy cutoff (14, 15) that is reached when Δε(v + 1), the rightmost term in Eq. 1, exceeds the energy of the highest-frequency phonon of the NaCl substrate. Clearly, the nearest-neighbor assumption in these kMC simulations fails to describe the experiment.

To produce molecules in higher vibrational states, long-distance interactions between vibrationally excited molecules are needed. When VEP is modeled including V-V exchange over an area of ~1000 Å2, kMC simulations reproduce the experiment well (Fig. 2B, red curve). In this case, vibrationally excited molecules in base-camp 1 states can interact with one another even though they are not likely to be nearest neighbors. For example, processes such asEmbedded Image(3)allow molecules in base-camp 1 states to climb to base-camp 2, where again the one-phonon energy cutoff slows further pooling. Subsequently, molecules in base-camp 2 climb to base-camp 3 by even longer-range interactions. Vibrational states higher than v = 27 are not seen as energy transfer to the lowest-lying excited electronic states becomes possible (V-E energy transfer). The temporal sequence of base-camp formation can also be seen by taking snapshots of the vibrational distribution in the kMC simulations at different times (see Fig. 2C). This shows that base-camp 1 forms within 100 ns, base-camp 2 within 0.1 to 1 μs, and base-camp 3 only after 10 to 100 μs.

Fig. 2 Base-camp pooling mechanism operating for a monolayer of CO on NaCl(100).

(A and B) Experimentally observed emission spectrum (black solid lines) and simulated spectra using kMC methods (red solid lines). The insets represent the CO lattice; the red shaded areas visualize the interaction distance around a given CO molecule (black dot) used in each kMC simulation. In (A), the simulation allows only nearest-neighbor V-V exchange, an assumption that was also made in (1416). In (B), the simulation includes molecular interactions out to a distance of 34 Å. In each case, the monolayer feature at 2055 cm−1 (Fig. 1B) was excited with a narrowband infrared laser and the emission was dispersed through a monochromator and detected with a SNSPD integrating the signal counts between 50 and 250 μs after the laser pulse. (C) Snapshots in the experimentally derived and simulated population distributions showing sequential formation of the base-camps. The red dashed line corresponds to the population distribution at 100 ns.

The distance dependence of dipole-dipole interactions explains the sequential formation of base-camps. From the kMC simulations of Fig. 2B, we find that the average distance between pooling molecules forming base-camp 1 is 4.1 Å (~1 lattice constant), whereas for base-camp 2 this distance is 11.7 Å, and for base-camp 3 it is 17.6 Å. One-phonon–assisted V-V rates scale with distance as R–8 (24), meaning that base-camp 1 is formed 103 times faster than base-camp 2, which is formed 102 times faster than base-camp 3. This hierarchy of rates is consistent with our experimental observations.

VEP selectively excites transverse NaCl phonons. The left panel of Fig. 3 shows four kMC simulations (red, blue, green, and brown) of emission spectra using different assumptions about the solid’s phonon density of states (DOS) and compares them to experiment (black). (The assumed phonon DOS used in each simulation appears in the right panel.) Although all four simulations resemble experimental results, we find best agreement with experiment when only transverse phonons are allowed to accept energy in the ladder-climbing process. Indeed, only here do we see the formation of three base-camps.

Fig. 3 Selective excitation of NaCl transverse phonons during energy pooling.

The experimental emission spectrum (black solid line) is compared to kMC simulations assuming various NaCl phonon DOSs. In each simulation, the CO-to-CO interaction distance extends up to 34 Å. Each pooling step has an energy release to phonons of the solid; the probability depends on the phonon DOS at that energy. Shown are the results for a Debye DOS (brown) and three DFT-based DOSs: projection of the bulk DOS for NaCl onto the motion of the Na ions in the (100) plane (blue), longitudinal contribution to the projected DOS (green), and transverse contribution to the projected DOS (red).

Under conditions of this work, VEP rapidly produces CO in many vibrationally excited states. Relaxation of the system back to vibrational equilibrium proceeds more slowly, as in Fig. 4A, where we show measurements of the time-resolved infrared fluorescence (open symbols) from seven vibrational states. Asymptotically, they all exhibit exponential decay (solid lines) with effective lifetimes, shown as open circles with error bars in Fig. 4B. For kMC simulations of the asymptotic exponential fall-off, we include three elementary processes: V-V energy transfer between CO molecules, Embedded Image(4)spontaneous radiative emission,Embedded Image(5)and vibrational energy transfer to the NaCl lattice vibrations.Embedded Image(6)For process 4, we use the same approach that allowed successful simulation of the data of Figs. 2 and 3 (24). For process 5, we use the known radiative emission rate constants for gas-phase CO(v′). For process 6, we have tested two models of vibrational energy transfer. The solid squares in Fig. 4B are the effective lifetimes that result from implementation of the Skinner-Tully (ST) model (14, 24), where anharmonic coupling of CO vibration to NaCl phonons is mediated via the CO-NaCl surface bond (1418). The predicted effective lifetimes are in poor agreement with experiment, and they exhibit a vibrational quantum number dependence that is far too strong. (Note the logarithmic scale.)

Fig. 4 Relaxation of CO to the NaCl solid follows the CPS model.

(A) Representative temporal profiles of wavelength-resolved infrared fluorescence (open symbols); the emitting vibrational state’s quantum number is indicated. The long-time relaxation exhibits an exponential decay (black solid lines). Note that the y axis is logarithmic and that the data are offset from one another along the y axis for clarity. (B) The effective exponential lifetime obtained from these (and other) fits (black open circles with error bars). Error bars denote SD (1σ) from three measurement results. The kMC simulations also exhibit long-time exponential behavior. The corresponding effective lifetimes are shown as solid symbols for two different vibrational relaxation models: the Skinner-Tully model (squares) and the CPS model (circles).

We also tested a model developed by Chance, Prock, and Silbey (CPS) (19, 20), shown as solid circles in Fig. 4B (24). The agreement with experiment is striking. CPS was developed to describe fluorescence lifetimes of dye molecules interacting through an inert spacer layer with an absorbing and reflecting solid (2530). Here, coupling occurs through electromagnetic fields. The fact that CPS accurately reproduces the observations of this work suggests that CO vibrational relaxation to NaCl lattice vibration also occurs through the electromagnetic near-field, even though there is a surface bond.

We emphasize that the weak vibrational quantum number dependence of the effective lifetime is indicative of coupling via the electromagnetic field; ST predicts a change in effective lifetime of four orders of magnitude over the same range of v where CPS predicts a change of less than an order of magnitude. Although an ab initio treatment of the coupling to the solid’s phonon bath is still lacking, we expect the strong v-dependence to be retained (24). Referring to Fig. 4B, we speculate that the steeper slope above v ~ 23 indicates a transition to ST behavior.

Normally, we consider energy flow within an ensemble of oscillators to be a consequence of interatomic anharmonicity. This work shows that we can bind a molecule to a solid with sufficient strength to create samples that are stable over long periods of time without any influence of anharmonicity on the vibrational energy relaxation. In this Sommerfeld ground-wave limit, vibrational relaxation occurs exclusively via the electromagnetic field obeying the CPS model. Here, the strength of coupling scales with the solid’s imaginary index of refraction and the square of the molecule’s transition dipole moment (24). Besides CO on NaCl, other similar systems are to be expected. CO on KCl and N2 on NaCl are both interesting possibilities in which CPS coupling would be even weaker than seen here. For dipolar adsorbates that find themselves within this limit, the solid’s crystalline lattice can be exploited to produce spatial registry and orientational order while the strength of dipole-dipole interactions between the adsorbate molecules still far exceeds the adsorbate coupling to the solid. Systems like the one described here appear to be promising for the study of quantum lattice dynamics.

Supplementary Materials

www.sciencemag.org/content/363/6423/158/suppl/DC1

Materials and Methods

Figs. S1 to S6

References (3349)

References and Notes

  1. See supplementary materials.
Acknowledgments: We thank S. A. Corcelli for sharing his kMC simulation code, A. Kandratsenka for helpful discussions, and F. Heidrich-Meisner for providing helpful suggestions after reading an early version of this manuscript. Funding: Supported by Netherlands Organization for Scientific Research (NWO) Vidi grant 723.014.009 (J.M.). Author contributions: L.C. carried out experiments with the SNSPD-based spectrometer, analyzed data, and contributed to the manuscript; J.A.L. analyzed data, implemented and carried out the kMC calculations, and contributed to the manuscript; D.S. built and commissioned the SNSPD-based spectrometer, supervised experimentation, and contributed to the manuscript; J.M. implemented and carried out the calculations for the projected phonon DOS and contributed to the manuscript; V.B.V. developed the SNSPD devices for these experiments and reviewed drafts of the manuscript; and A.M.W. conceived the experiment and wrote the paper. Competing interests: None declared. Data and materials availability: There are no restrictions on materials used in this work. All data needed to evaluate the conclusions in the paper are present in the paper or the supplementary materials.
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