Do Hyung
Kang
,
Jinwoo
Kim
and
Sang Kyu
Kim
*
Department of Chemistry, KAIST, Daejeon 34141, Republic of Korea. E-mail: sangkyukim@kaist.ac.kr
First published on 4th February 2022
Real-time autodetachment dynamics of the loosely bound excess electron from the vibrational Feshbach resonances of the dipole-bound states (DBS) of 4-bromophonoxide (4-BrPhO−) and 4-chlorophenoxide (4-ClPhO−) anions have been thoroughly investigated. The state-specific autodetachment rate measurements obtained by the picosecond time-resolved pump-probe method on the cryogenically cooled anions exhibit an exceptionally long lifetime (τ) of ∼823 ± 156 ps for the 11′1 vibrational mode of the 4-BrPhO− DBS. Strong mode-dependency in the wide dynamic range has also been found, giving τ ∼ 5.3 ps for the 10′1 mode, for instance. Though it is nontrivial to get the state-specific rates for the 4-ClPhO− DBS, the average autodetachment lifetime of the 19′120′1/11′1 mode has been estimated to be ∼548 ± 108 ps. Observation of these exceptionally slow autodetachment rates of vibrational Feshbach resonances strongly indicates that the correlation effect may play a significant role in the DBS photodetachment dynamics. Fermi's golden rule has been invoked so that the correlation effect is taken into account in the form of the interaction between the charge and the induced dipole where the latter is given by the polarizable counterparts of the electron-rich halogenated compound and the diffuse non-valence electron. This report suggests that one may measure, from the real-time autodetachment dynamics, the extent of the correlation effect contribution to the stabilization and/or dynamics of the excess non-valence electron among many different types of long-range interactions of the DBS.
The lower threshold of the dipole moment for holding the excess electron was firstly proposed to be 1.625 D,20 although it has been refined repeatedly after the correction of the Born–Oppenheimer approximation,21,22 for instance. More practically, however, it seems to be widely accepted now, as a rule of thumb, that the DBS may exist when the dipole moment of the neutral core exceeds 2.5 D.23,24 Although the long-range interaction of the dipole moment of the neutral core with the excess non-valence electron has been considered to be the most critical factor in the electron binding/unbinding dynamics, many theoretical studies have suggested that the (especially dispersive) electron correlation effect should be largely responsible for the excess electron binding to the neutral core in the DBS.4,25–27 The significant contribution of the electron correlation effect to the binding energy of the DBS has been theoretically demonstrated by quantum-mechanical calculations using the 2nd-order Møller–Plesset perturbation (MP2), the coupled cluster singles and doubles (CCSD) theory, or the quantum Monte Carlo method.28–31 In the same context, it is notable that the critical value of the dipole-moment for the existence of the π-type DBS is still in dispute.32–34 Although the extent of the correlation effect is highly anticipated to be strongly dependent on individual chemical systems, the importance of the correlation effect in the DBS seems to be well received in the scientific community. Apparently, however, it is nontrivial to experimentally identify the correlation effect in terms of the static and/or dynamic role in the DBS. Even though the electron binding energy of the DBS is often expected to be proportional to the dipole-moment magnitude of the neutral core, it does not necessarily mean that the electron binding of the DBS is governed by the dipole moment only, as many different factors related to the long-range interaction potential could be cancelled out or added up depending on the chemical details.35 For example, the smaller (or lager) binding energy does not necessarily mean the smaller (or larger) contribution of the correlation effect, and vice versa.
In this aspect, we have here found that the correlation effect may be reflected in the dynamic property of the DBS rather than in the static binding energy. For example, two different DBS chemical systems of similar binding energies could be quite different in terms of the extent of the correlation-effect. Herein, we argue that the autodetachment dynamics could reveal the nature of the electron binding in terms of the dynamic role of the correlation effect in the electron binding/unbinding dynamics of the DBS. We have investigated the picosecond (ps) time-resolved autodetachment dynamics of the DBS vibrational Feshbach resonances prepared by the one-photon photoexcitation of the cryogenically-cooled 4-bromophenoxide (4-BrPhO−) and 4-chlorophenoxide (4-ClPhO−) anions. The exceptionally slow autodetachment dynamics observed in some vibrational Feshbach resonances of these anions have been analyzed from the new perspective that the correlation effect may play a significant role in the autodetachment dynamics.
Now, by employing the ps pump-probe scheme, we could measure the state-specific autodetachment rates of vibrational Feshbach resonances for both 4-BrPhO− and 4-ClPhO−, Fig. 2. The autodetachment rate has been determined by the transient taken by monitoring the low kinetic energy electron as a function of the delay-time between the pump and probe laser pulses. The pump laser wavelength is tuned at the particular DBS vibrational band while the spatially overlapped non-resonant probe laser pulse (791 nm) is given at different delay times. At the zero delay-time, the DBS is most efficiently depopulated to give a spike19 with the pump-probe cross-correlation width of ∼2.88 ps. With the increase of the pump-probe delay, the transient signal shows the apparent recovery (which is equivalent to the decay in the transients shown in Fig. 2) due to the autodetachment process, giving the lifetime of the DBS Feshbach resonance from the exponential fit to the experiment.
The peak-I transient of 4-BrPhO− shows the bi-exponential behavior with two distinct lifetimes, Fig. 2. The faster decaying component gives the lifetime (τ) of ∼8.3 ± 2.6 ps whereas the lifetime of the slow-decaying component is found to be extremely long, giving τ ∼ 823 ± 156 ps. As the fundamental 11′1 and 20′130′1 combinational modes are expected to be co-excited within the ps pump laser spectral window, two distinct lifetimes are ascribed to the autodetachment of two different vibrational modes. For the appropriate matches between the individual vibrational modes and their associated lifetimes, the time-resolved velocity-map photoelectron images have been taken at the pump wavelength of the peak-I. The photoelectron spectra give the nature of the DBS band as the propensity rule of Δv = −1 is strictly obeyed. Accordingly, in the photoelectron spectrum (Fig. 2) taken from the peak-I, the −ν11 band represents the autodetachment of the 11′1 mode whereas the −ν20 or −ν30 photoelectron band is the consequence from the autodetachment of the 20′130′1 combination mode via the wobbling associated with the ν20 or ν30 mode, respectively. The time constants of the 11′1 or 20′130′1 mode, obtained from the integration over the corresponding distinct energetic windows in the time-resolved photoelectron images (see ESI†) are estimated to be ∼534 ± 87 ps (253–500 cm−1 for −ν11) or ∼61 ± 34 ps (25–130 cm−1 for −ν20), respectively. Although the time constants do not exactly match, this strongly supports that the exceptionally long lifetime of ∼ 823 ps shown in the upper trace of Fig. 2(a) represents the autodetachment from the 11′1 mode whereas the faster decaying component with τ ∼ 8.3 ps should be ascribed to the autodetachment from the 20′130′1 combinational mode. It should be noted that the time constants extracted from the low kinetic energy photoelectron transients taken by the continuous scan of the pump-probe delay time (Fig. 2) are taken to be more reliable here compared to those from the time-resolved photoelectron images as the experimental conditions are hardly kept identical for all images in the latter. Interestingly, whereas the autodetachment lifetime of the 20′130′1 mode sounds reasonable in terms of the order of magnitudes,19 the lifetime of the 11′1 mode seems to be extraordinarily long for the vibrational autodetachment process. It should be noted though that the estimated lifetime of 823 ps of the 11′1 mode has a somewhat large uncertainty due to the narrow temporal window (0–2.2 ns) of the present experimental conditions. Nonetheless, it is quite remarkable that the autodetachment rate of the 11′1 mode of the 4-BrPhO− DBS is ∼25 times slower compared to that of the 11′1 mode of the PhO− of which the lifetime has been measured to be ∼33.5 ps.19 Considering that the infrared intensity of the ν11 mode of the 4-BrPhO is only two times weaker than the ν11 mode of the PhO (vide infra), the retardation of the DBS autodetachment of the former compared to the latter by more than one order of magnitude is quite exceptional. The somewhat similar analysis for the 11′2/10′1 band (peak-II) of 4-BrPhO− has also been carried out in order to discriminate closely-lying 11′2 and 10′1 modes (ESI†), giving τ ∼ 82 or 5.3 ps for the 11′2 or 10′1 mode, respectively. The autodetachment rate of the 11′2 mode of 4-BrPhO− (τ ∼ 82 ps) is also quite slow compared to that of the 11′2 mode of PhO− (τ ∼ 12 ps),19 supporting the experimental finding of the extremely slow autodetachment rate for the 11′1 mode of 4-BrPhO−.
In order to explain the experiment, we have invoked Fermi's golden rule which has been widely used for the autodetachment rate.39–42
(1) |
(2) |
(3) |
Here, ϕi and ϕf are the initial and final total wavefunctions, respectively, whereas vi (ei) or vf (ef) is the initial or final vibrational (electronic) wavefunction, respectively. ρ is the density of states which is the function of the electron kinetic energy (KEe). U is the charge–dipole interaction potential for the excess electron whereas Q is the normal mode coordinate associated with the particular vibrational mode. When the electron binding potential is confined to the interaction between the charge and permanent-dipole moment (μ0), F(Q) is proportional to the magnitude of the derivative of μ0 with respect to Q, ∂μ0/∂Q. As the infrared (IR) intensity is proportional to (∂μ0/∂Q)2, it is approximately regarded as the quantitative measure of the relative autodetachment rate of the corresponding vibrational mode.39,43 Actually, the mode-dependent behavior of the autodetachment rate of the PhO− DBS could be quite successfully explained by the relative IR intensities of the individual vibrational modes as well as the Franck–Condon derivative factor for the overtone band.19 In this regard, the more than one order of magnitude increase of the lifetime of the 11′1 mode of 4-BrPhO− compared to that of the 11′1 PhO− mode cannot be explained by the simple application of the conventional Fermi's golden rule, especially as the IR intensity of the former is only two times weaker than that of the latter (vide supra).
It should be emphasized that the autodetachment rate is little influenced by the amount of the electron-binding energy. Rather, the loosely-bound electron is shaken off by the dynamic change of the interaction potential induced by the vibrational wobbling motion.44 In this regard, one may invoke the aforementioned electron correlation effect into the autodetachment dynamics for the explanation of the large discrepancy of the experiment from the conventional Fermi's golden rule, especially as the electron-rich halogen atomic moiety is expected to be strongly correlated with the non-valence electron at the positive end of the dipole. Instead of the quantum-mechanical Hamiltonian, we have brought a simple physical model where the interaction potential in Fermi's golden rule is modified to include the interaction between the charge and the (newly-added) induced dipole moment (ind). The effective dipole moment (eff) is then the sum of the permanent and the induced dipole-moments. The induced dipole moment can be expressed by the relation of
(4) |
Here, is assumed to be independent of Q. At the equilibrium position, as heads from the neutral core to the dipole-bound electron, the neutral core is polarized so that the oxygen moiety is negatively charged whereas the opposite-positioned bromine moiety should be positively charged according to The resultant induced-dipole, therefore, points the same direction as the permanent dipole (Fig. 3(a)). And yet, the autodetachment process is not determined by the static property of the dipole. Rather, it is governed by the dynamic interplay between the instant changes of the permanent- and induced-dipoles with respect to the particular vibrational normal mode (Q). Accordingly, the directions of ∂μ0/∂Q and vectors (the positive or negative slope with respect to Q) determine whether or not the correlation effect expedites or impedes the autodetachment process. Namely, if both ∂μ0/∂Q and have the positive (or negative) slopes with respect to Q, then the autodetachment rate would increase, indicating that the correlation effect facilitates the autodetachment process. And yet, if the slope of ∂μ0/∂Q is positive (or negative) while the slope of is negative (or positive), then the magnitude of the vector sum diminishes to give the decrease of the autodetachment rate. In this case, the autodetachment should be retarded due to the correlation effect. It should be noted that, when the dipole-bound electron is regarded as a point-charge lying on the molecule-fixed z-axis (Fig. 1 and 3), all the in-plane vibrational modes of PhO− or 4-BrPhO− end up with the instant changes of dipole moments along the z-axis.
In order to verify the physical model, we have calculated the ∂μ0/∂Q and ∂α/∂Q terms for the ν11 modes of 4-BrPhO and PhO, Fig. 3(b). For ∂μ0/∂Q, μ0 is identical to the z-component of the permanent dipole moment (μz) (vide supra). Regarding ∂α/∂Q, the derivative of the isotropic polarizability (αiso) or that of the polarizability along the molecular z-axis (αzz) has been separately calculated with respect to the ν11 mode coordinate, and thus we denote α as either αiso or αzz. It should be emphasized again that the ν11 modes of two different neutral cores of 4-BrPhO and PhO have their own normal-mode characteristics in terms of the detailed nuclear displacements. Remarkably, whereas the signs of ∂μ0/∂Q and ∂α/∂Q are the same for the ν11 mode of PhO, it has been found that the slope of ∂μ0/∂Q has the opposite sign from that of ∂α/∂Q for the ν11 mode of 4-BrPhO. Apparently, the latter is the consequence from the reduction of the permanent dipole moment of 4-BrPhO with the positive displacement of the ν11 mode whereas the polarizability along the z-axis instantly increases by the same displacement (Fig. 3). Substitution of the electronegative Br atom on the para position should be responsible for the opposite behavior of the dipole-moment change with ν11, compared to that of PhO. Therefore, it is most likely that the correlation effect embodied in the charge-induced dipole interaction should impede the autodetachment of the 11′1 mode of 4-BrPhO− whereas it expedites that of the 11′1 mode of PhO−. Though the quantitative comparison is nontrivial, it gives the rational explanation why the autodetachment rate could be exceptionally slow for the 11′1 mode of 4-BrPhO−. Notably, the magnitude of ∂α/∂Q could be larger for 4-BrPhO− compared to that of PhO− because of the lager polarizability of the former than the latter although the more sophisticated calculation is highly desirable (ESI†).
The fast autodetachment rate (τ ∼ 8.3 ps) observed for the 20′130′1 mode of 4-BrPhO− is probably due to the cooperation effect of the combination mode in the wobbling motion as demonstrated previously for PhO− (ESI†).19 Regarding the 11′2 overtone mode of 4-BrPhO−, its lifetime of 82 ps is much longer than the lifetime of 12 ps measured for the 11′2 mode of PhO−. According to the derivative Franck–Condon factor in eqn (2), the autodetachment rate of the overtone mode is anticipated to be ∼4 times faster than that of the fundamental mode.19 In that sense, if the lifetime of the 11′1 mode of 4-BrPhO− is taken to be 823 ps, the lifetime of ∼200 ps is expected for the 11′2 mode. In the same context, if the lifetime of 82 ps is taken for the 11′2 mode, the autodetachment lifetime of the 11′1 mode is expected to be ∼330 ps, which is already quite long for the vibrational autodetachment lifetime. Therefore, although the lifetime measurement of 823 ps is subject to the further refinement, it seems to be quite certain that the autodetachment rate of the 11′1 mode of 4-BrPhO− is exceptionally slow. The fast autodetachment rate of the 10′1 mode of 4-BrPhO− with τ ∼ 5.3 ps is mainly attributed to the much stronger IR intensity of the ν10 mode which is ∼30 times larger than that of ν11, although Fermi's golden rule could not give the quantitative explanation of the experiment (ESI†). It is interesting to note that the magnitude of ∂α/∂Q is much smaller than that of ∂μ0/∂Q for the 10′1 mode of 4-BrPhO−, Fig. 3, suggesting that the dynamics of the corresponding mode is little influenced by the correlation effect.
Similar analysis has also been carried out for 4-ClPhO−. For the peak-III in Fig. 1, the 19′120′1/11′1 DBS band undergoes the autodetachment process via −ν19 (or −ν20) from the 19′120′1 combination mode whereas the autodetachment from the 11′1 mode is responsible for the −ν11 peak. The relative ratio of the former to the latter in the peak-III is estimated to be 0.86:0.14. The peak-IV of 4-ClPhO− (Fig. 1) is assigned to the 11′119′120′1/11′2 band. In the photoelectron spectrum, the photoelectron peak populated by the autodetachment via the ν20 or ν19 mode is found to be quite small. Similar to the case of peak-III, the relative contribution of the 11′119′120′1 and 11′2 mode to the peak-IV is estimated to be 0.86:0.14. Unfortunately, however, it turns out to be nontrivial to extract two different lifetimes from the transient of peak-III or peak-IV by the bi-exponential fit, mainly due to the relatively poor S/N ratio, Fig. 2. Instead, the single exponential fit to the experiment give the averaged autodetachment lifetime of ∼548 ± 108 or 50.0 ± 8.5 ps for the peak-III or peak-IV, respectively. Overall, the autodetachment rate of the 4-ClPhO− DBS is also estimated to be quite slow compared to that of PhO−, indicating that the correlation effect on the electron-binding dynamics could also be quite significant in 4-ClPhO−. The overall autodetachment rate of the 4-BrPhO− DBS seems to be slower than that of the 4-ClPhO− 11′1, though it should be noted that the autodetachment dynamics is strongly mode-dependent. This could be partially due to the larger polarizability of the former (159.3 Bohr3) compared to the latter (138.1 Bohr3), though it is subject to the further investigation. It should also be emphasized that the autodetachment dynamics is expected to be strongly dependent on the individual chemical systems, and thus the theoretical analyses for individual chemical systems should be carried out case by case.
It is interesting to note that the highest occupied molecular orbital (HOMO) of the 4-BrPhO− or 4-ClPhO− is delocalized over the entire body including the p-type lobe of the halogen atomic moiety at the positive end of the dipole (Fig. 4). The excess non-valence electron is diffuse and polarizable whereas it could exert the local electric field to influence the electrons in the neutral core.45 In this aspect, the relative geometrical orbital arrangements of the neutral-core with respect to the excess electron of which its own arrangement is given by the molecular geometry could be quite critical in the role of the correlation effect in static and dynamic properties of the DBS, which is subject to further investigation in the near future.
Footnote |
† Electronic supplementary information (ESI) available: Details of the photoelectron spectra deconvolution, vibrational modes of each molecule, and dipole or polarizability change upon the associated molecular vibration were described. See DOI: 10.1039/d1sc05481c |
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