Ultrafast coherence transfer in DNA-templated silver nanoclusters

DNA-templated silver nanoclusters of a few tens of atoms or less have come into prominence over the last several years due to very strong absorption and efficient emission. Applications in microscopy and sensing have already been realized, however little is known about the excited-state structure and dynamics in these clusters. Here we report on a multidimensional spectroscopy investigation of the energy-level structure and the early-time relaxation cascade, which eventually results in the population of an emitting state. We find that the ultrafast intramolecular relaxation is strongly coupled to a specific vibrational mode, resulting in the concerted transfer of population and coherence between excited states on a sub-100 fs timescale.


Constructing the cross-peak specific map
The amplitude of a feature in the 2D map is a function of not only the transition moment strengths of the involved transitions, but also their relative angles. In the following analysis we consider the map as a grid of "two-colour pump-probe" experiments -each spectral point is the result of "pumping" one transition at some ω1 frequency, and "probing" another (or the same in the case of the diagonal features) along some ω3 frequency. The general expression for the signal amplitude resulting from a sequence of four polarized pulses en interacting with four transition moments qn in isotropic solution has been derived by Hochstrasser and coworkers 3,4,5 .
We consider only features resulting from two (or one) distinct transition moments. Further, we are interested in static and energy-transfer signals rather than coherent signals, and thus consider signals resulting from interactions where q1 = q2 and q3 = q4.
The transition q1 can be decomposed into two spectral projections: qz parallel to the "probe" q3, and qx perpendicular to q3. The signal amplitude in Eq. 1 then appears as: Using the pulse polarization sequences = 〈0,0,0,0〉 and = 〈 2 , 2 , 0,0〉 yields the signal amplitudes: eq 3. = 2 3 2 ( 2 + 3 2 ) ; = 2 3 2 (2 2 + 2 ) These signal amplitudes can be used to generate the 2D analogue to the pump-probe (or fluorescence) anisotropy in terms of the spectral projections Applying the normalization condition 2 + 2 = 1 and reorganizing allows the construction of expressions for these squared dipole moment projections (i.e. oscillator strengths) in terms of the experimentally measurable anisotropy: eq 5. These expressions can be multiplied by the magic angle spectrum to generate the full 2D spectra containing only the projections into the "probe" direction (i.e. parallel to the diagonal), and the projection perpendicular to the diagonal. This latter projection, shown in the manuscript Figure   2B, in particular is of interest as it entirely eliminates the diagonal features from the spectrum, allowing clearer view of many cross-peaks due to significant reduction in spectral congestion. It should be noted that this projection is formally equivalent to the "cross-peak specific" spectrum SVV-3SVH used by Fleming and coworkers 6, 7 . showing where beats will appear, and with which frequency sign, after Fourier transforming total real data. c: The total QB response separated into individual GSB and SE components. The QB amplitude "patterns" for GSB and SE contributions are identical in total real data.

Three-state system
The Ag20NC electronic structure involve (at least) three excited electronic levels: L, and the two H levels, schematically shown in Supplementary Figure 7. A number of coherent pathways analogous to the ones observed in the displaced two-state oscillator may be expected. For low vibrational frequencies these will contribute around the diagonal features, essentially giving the response of two displaced oscillators at different energies. In addition to these "trivial" coherent pathways, coherences can be induced in one state and probed in the other. In particular, ground state vibrational coherences induced by excitation into e.g. Hcould possibly be observable around L in the case of a shared ground-state. Importantly, these pathways will still appear with the 2 frequency sign of a ground-state coherence (negative in rephasing, positive in non-rephasing). The experimental observation is however equal amplitude quantum beats in positive and negative frequencies; induced by excitation in H and probed around L. This is clear evidence for excited state coherence. In Supplementary Figure 7 we show the Feynman diagrams involving the creation of coherence in the H states, followed by rapid (relative to the period) transfer to vibrational coherence in L. In Supplementary Figures 8 and 9 we schematically show the spectral positions where these pathways are expected to contribute, and compare this to the experimental data.
Overall we find excellent agreement, lending strong support to the idea of ultrafast coherence transfer in Ag20NC.

DNA-AgNC purification
The synthesized IR silver nanoclusters were purified by HPLC purification to remove all remaining DNA and unwanted silver nanoclusters. An analytical HPLC Dionex UltiMate 3000 system with a Dionex UltiMate 3000 fluorescence detector and Phenomenex Germini C18 column (5μm, 110Å, 50 × 4.6 mm) was used for purification. The mobile phase in the HPLC purification consisted of 35mM triethylammonium acetate (TEAA) in water (solvent A) and methanol (solvent B) at pH 7. A linear solvent gradient was used with an increase of solvent B from 5-50% over 10 minutes followed by 5 minutes wash at 95% methanol. After purification the samples were concentrated ~5x by centrifugal filtration using Pur-A-Lyzer maxi 1200 dialysis kit with a capacity of 0.1-3 mL and a molecular weight cut-off at 12-14 kDa (SigmaAldrich).