Probing the coupling of a dipole-bound electron with a molecular core† †Electronic supplementary information (ESI) available: The calculated wave function of the dipole-bound excited state of C2P–, more experimental details, a description of photoelectron angular distributions and the measured beta 

The spin–orbit coupling of a dipole-bound electron with the neutral core has been studied for the first time.


Introduction
Polar molecules with large enough dipole moments can bind an electron in a diffuse orbital through charge-dipole interactions. Fermi and Teller rst predicted a critical moment of 1.625 D for a stationary dipole to bind a charge. 1 Further theoretical and experimental studies found that a minimum dipole moment of $2.5 D is required for a molecule to form a dipole-bound state (DBS). 2-8 DBSs have been suggested to play an important role as a gateway for anion formation. [9][10][11][12] DBSs can be formed from neutral molecules by Rydberg electron transfer 5,13 and have been investigated using photoelectron spectroscopy (PES). 14,15 Stable anions can have dipole-bound excited states near the electron detachment threshold if the neutral cores have large enough dipole moments. 16,17 Dipole-bound excited states have allowed autodetachment spectroscopy [18][19][20][21][22][23][24] and recently resonantly enhanced PES via vibrational autodetachment, 25 which can yield highly non-Franck-Condon PE spectra and a wealth of spectroscopic information. [26][27][28][29] The electron in a DBS resides in a diffuse orbital far from the neutral core, usually with a very small binding energy on the order of a few to a few tens of meV. The dipole-bound electron is known to have little effect on the structure of the neutral core. However, it is still an open question whether the electron in the diffuse dipole-bound orbital spin-couples with the electrons in the molecular core.
Dipole-bound states can be viewed as the analogues of Rydberg states in neutral molecules. However, it is well known that a Rydberg electron couples strongly with its cation core, particularly in low-n Rydberg states. 30 For example, the Rydberg states of hydrogen halide molecules with a 2 P cationic state have been studied extensively using multi-photon ionization. 31-36 All Hund's cases (a-e) have been considered in these studies to explain the experimental observations, highlighting the importance of the couplings between the Rydberg electron and the cation core. Despite the fact that both the dipole-bound and Rydberg electrons have little effect on the structures of the corresponding molecular cores, they do have major differences. Rydberg states are bound by the À1/r coulombic potential, while DBSs are bound by the À1/r 2 charge-dipole potential. Hence, there are innite Rydberg states in principle, but there is typically only one bound DBS. The weakly bound nature of the DBS raises an interesting question about the coupling of the dipole-bound electron and the electrons in the neutral core or lack thereof. However, to the best of our knowledge, this question has not been addressed.
The dicarbon-phosphorus cluster anion (C 2 P À ) is an ideal candidate to probe the coupling of a dipole-bound electron with the neutral core. Previous spectroscopic studies showed that neutral C 2 P is an open-shell system with a valence electron conguration of 4s 2 5s 2 6s 2 2p 4 7s 2 3p 1 and a 2 P ground state. 37 Spin-orbit coupling splits the ground state into 2 P 1/2 and 2 P 3/2 with the 2 P 1/2 spin-orbit state being lower in energy. The dipole moment of C 2 P was calculated to be 3.241 D, 38 which is large enough to support a DBS. We have recently reported the PE spectra of C 2 P À and measured the electron affinity (EA) of C 2 P to be 2.6328 AE 0.0006 eV. 39 The valence electron conguration of the C 2 P À anion is 4s 2 5s 2 6s 2 2p 4 7s 2 3p 2 with the 3 S + electronic ground state. 39 Hence, C 2 P À is expected to possess a dipolebound excited state with an excitation energy slightly below 2.6328 eV by promoting an electron from the 3p orbital to a dipole-bound orbital. We have indeed found such a diffuse slike orbital computationally, as shown in the ESI (Fig. S1 †). If the dipole-bound electron couples with the open-shell C 2 P core, the DBS could be either in a 1 P state or a 3 P state, based on the 4s 2 5s 2 6s 2 2p 4 7s 2 3p 1 (s DBS ) 1 conguration. The 3 P state would split into three spin-orbit states ( 3 P 0 , 3 P 1 , 3 P 2 ), whereas the 1 P state is spin-forbidden and would be inaccessible in a singlephoton excitation. However, if the dipole-bound electron does not couple with the neutral core, then there should be only two DBSs, which can be denoted as ( 2 P 1/2 )* and ( 2 P 3/2 )*, corresponding to the two spin-orbit states of neutral C 2 P. The purpose of this study is to nd the DBSs in C 2 P À using photodetachment spectroscopy and probe the nature of these diffuse excited states by resonant PES via vibrational autodetachment. [25][26][27][28][29]

Results and discussion
The experiments were carried out using a high-resolution PE imaging system equipped with a laser vaporization cluster source. 40 More experimental details are provided in the ESI. † The non-resonant PE spectra of C 2 P À have been discussed in detail previously 39 and they serve as the reference for the resonant PES in the current study. Additional non-resonant PE spectra have been measured in the current work at 2.6360, 2.6588, and 2.7454 eV, as compared with the 2.9025 eV spectrum reported previously in Fig. 1.
Vibrational features for the two spin-orbit states of C 2 P are denoted by black ( 2 P 1/2 ) and red ( 2 P 3/2 ) colors in Fig. 1. All three vibrational modes were observed for each spin-orbit state, i.e., the C-C stretching (n 1 ), C-P stretching (n 2 ), and the bending mode (n 3 ). ‡ For the bending mode, only levels with even quanta (3 2 0 ) were observed. It should be pointed out that the Renner-Teller effect splits the bending levels in each spin-orbit state of C 2 P, which have been analyzed in detail previously. 37 The vibronic levels, their symmetries, and known energies for the rst three bending quanta are given in Fig. 2, according to ref. 37. The more intense 0 0 0 peak for the 2 P 3/2 state in Fig. 1b and the 2 1 0 peak in Fig. 1c are due to a threshold enhancement effect, while the spectrum in Fig. 1d at 2.9025 eV photon energy represents the normal Franck-Condon transitions. The 0 0 0 peak for the 2 P 1/2 state yielded a detachment threshold of 2.6328 AE 0.0006 eV, which dened the EA of neutral C 2 P. 39 Features below the threshold are due to vibrational hot-bands from the anions. The same vibrational features for the two spin-orbit states are characterized by similar relative intensities in the non-resonant PE spectra, except for the threshold enhancement.
We searched for the DBS of C 2 P À experimentally using photodetachment spectroscopy by measuring the total electron yield, while scanning the detachment laser from 2.62 to 2.88 eV, as shown in Fig. 3. Electron signals appeared promptly at the detachment threshold of 2.6328 eV (indicated by a long arrow). The photodetachment cross section was expected to smoothly increase with the photon energy and exhibit steps as new Fig. 1 Non-resonant photoelectron spectra of C 2 P À at four different photon energies. The spectrum at 2.9025 eV is from ref. 39 and is presented for comparison. The spectra in (a), (b), and (c) were recorded at photon energies corresponding to the short arrows in the photodetachment spectrum shown in Fig. 3. detachment channels (electronic or vibrational) opened up. In addition, several resonant peaks were observed and marked with numbers 1À7 or an asterisk in Fig. 3. These peaks indicated the presence of a dipole-bound excited state, representing autodetachment from vibrationally excited levels of the DBS of C 2 P À . No other resonant peaks were observed in this energy range; the spikes in the gure were due to the relatively poor signal-to-noise ratios as a result of the weak and sometimes unstable C 2 P À mass signals. The excitation energies of the observed resonant peaks and their assignments are given in Table 1. The ground vibrational level of the DBS should be just below the detachment threshold and could only be observed via resonant two-photon detachment, which was usually very weak. [25][26][27][28][29] The overall weak signals for the C 2 P À anions prevented us from observing the resonant two-photon transition. However, the ground vibrational state of the DBS can be deduced from resonant PE spectra (vide infra).
The three short arrows in Fig. 3 indicate the photon energies used to obtain the non-resonant PE spectra presented in Fig. 1. Resonantly enhanced PE spectra were recorded at the photon energies corresponding to peaks 1-7 and *, as shown in Fig. 4, where the non-resonant spectrum at 2.9025 eV is also given for comparison in Fig. 1 to show the normal Franck-Condon intensities. The resonant peaks in Fig. 3 correspond to excitations to vibrational levels of the DBS, followed by autodetachment, which obeys the Dv ¼ À1 propensity rule due to the similarity of the neutral core of the DBS and the neutral nal state. 41,42 Hence, the resonant PE spectra are highly non-Franck-Condon and one or more peaks are enhanced in each spectrum, compared to the non-resonant PE spectrum (Fig. 1d). The resonantly enhanced peaks are labeled in boldface in Fig. 4; the vibrational levels for the 2 P 1/2 spin-orbit state are labeled in black and those for the 2 P 3/2 state are given in red. In addition to the photon energy used, the resonant peak number from Fig. 3 and the DBS vibrational level (indicated by an apostrophe ') are also given in Fig. 4. The 0 0 0 transition of the 2 P 1/2 state is enhanced in Fig. 4a and c, while the 0 0 0 and 2 1 0 transitions of the 2 P 1/2 state are enhanced in Fig. 4d. The 0 0 0 transition of the 2 P 3/2 state is enhanced in Fig. 4e and f. In addition, a new peak assigned to the 3 1 0 (m 2 D 3/2 ) vibronic level of the 2 P 1/2 state (see Fig. 2) is observed in Fig. 4e. In Fig. 4f, the intense 2 1 0 peak of the 2 P 1/2 state is due to threshold enhancement similar to that observed in Fig. 1c. The 0 0 0 and 2 1 0 levels of the 2 P 3/2 state are resonantly enhanced in Fig. 4g, where the intense 1 1 0 peak of the 2 P 1/2 state is again due to threshold enhancement. Finally, the enhanced peak in Fig. 4b (134 cm À1 above the 0 0 0 peak) is due to the 3 1 0 (m 2 S) vibronic level of the 2 P 1/2 state, and is very close to the 0 0 0 peak of the 2 P 3/2 state (Fig. 2). To understand the spectral assignments and the resonant PE spectra, we need to consider the electronic selection rule for autodetachment, in addition to the Dv ¼ À1 vibrational propensity rule. For the linear C 2 P À molecule, electron detachment should follow the DJ ¼ AE1/2 selection rule. If the dipole-bound electron in C 2 P À couples with the core Fig. 3 Photodetachment spectrum of C 2 P À obtained by measuring the total electron yield as a function of photon energy. The electron detachment threshold at 2.6328 eV (ref. 39) is denoted by the long arrow. The short arrows indicate the photon energies used for the non-resonant photoelectron spectra presented in Fig. 1. The numbers (1-7) and the asterisk indicate resonant vibrational autodetachment peaks from dipole-bound excited states of C 2 P À . Table 1 Photon energies (in nm, eV, and cm À1 ) and assignments of the observed resonant peaks in the photodetachment spectrum of C 2 P À shown in Fig. 2 Peak The shi is calculated as the difference between the photon energy of the resonant peak and the detachment threshold of the corresponding neutral spin-orbit states. b Vibrational energy levels of the corresponding neutral C 2 P states from ref. 37. See also Fig. 5. c The deduced binding energy of the dipole-bound electron, calculated as the difference between the neutral vibrational level and the corresponding shi. The vibrational frequencies and levels of the dipole-bound states are assumed to be the same as those of neutral C 2 P. The average binding energy is computed to be 37 AE 6 cm À1 . electrons, the DBS should be a 3 P J state with three spin-orbit components, J ¼ 0, 1, 2. Hence, we would expect the 3 P 0 spinorbit DBS to autodetach only to the 2 P 1/2 state of C 2 P, the 3 P 2 DBS to the 2 P 3/2 state only, and the 3 P 1 DBS to both the 2 P 1/2 and 2 P 3/2 states of C 2 P. However, if the dipole-bound electron in C 2 P À is not coupled with the electrons in the C 2 P core, we would expect to have only two DBSs, which can be denoted as ( 2 P 1/2 )* and ( 2 P 3/2 )*, corresponding to the two neutral spinorbit states, respectively. Each of the DBSs would autodetach only to the corresponding neutral spin-orbit state: ( 2 P 1/2 )* / 2 P 1/2 + e À and ( 2 P 3/2 )* / 2 P 3/2 + e À . The observed resonant PE spectra shown in Fig. 4 are consistent with the latter, i.e., there are only two DBSs in C 2 P À . In each resonant PE spectrum, only the vibrational levels of one spin-orbit component are enhanced. We did not observe any resonances in the photodetachment spectrum that led to simultaneous enhancement of the same vibrational levels of the two spinorbit states. In addition to the Dv ¼ À1 propensity rule, vibrational autodetachment is also mode-selective, [25][26][27][28][29] i.e., a vibrational level v 0 x n of mode v 0 x of the DBS preferentially autodetaches to the v x nÀ1 vibrational level of the same mode of the neutral species (the apostrophe ' is used to indicate the same vibrational mode for the DBS). As shown recently, the vibrational frequencies of the DBS are the same as those of the neutral species. [25][26][27][28][29] Using the vibrational propensity rule and the known vibrational levels of neutral C 2 P ( Fig. 2 and 5, and Table  1), we can understand the resonant PE spectra, assign the resonant peaks in Fig. 3, and deduce the DBS vibrational ground state. The 0 0 0 peak of the 2 P 1/2 spin-orbit state of C 2 P is enhanced in the resonant PE spectra in Fig. 4a, c and d, which were recorded at photon energies corresponding to resonant peaks 1 (2.6446 eV), 4 (2.7315 eV), and 6 (2.8326 eV), respectively. These resonant peaks should correspond to fundamental vibrational excitations in the ( 2 P 1/2 )* DBS to obey the Dv ¼ À1 propensity rule. The excitation energies of resonant peaks 1, 4, and 6 are 0.0118 eV (95 cm À1 ), 0.0987 eV (796 cm À1 ), and 0.1998 eV (1611 cm À1 ) above the detachment threshold of 2.6328 eV, respectively. As shown in Fig. 5, peaks 1, 4, and 6 should correspond to the 3 0 1 0 (m 2 S), 2 0 1 0 , and 1 0 1 0 vibrational levels of the ( 2 P 1/2 )* DBS, respectively, which autodetach to the 0 0 0 level of the 2 P 1/2 spin-orbit state of C 2 P via transfer of one vibrational quantum to the dipole-bound electron. Since the vibrational frequencies of the DBS are the same as those of the corresponding neutral states, peaks 1, 4, and 6 indicate a vibrational ground state for the ( 2 P 1/2 )* DBS, which is on average 37 cm À1 (AE6 cm À1 ) below the detachment threshold of the 2 P 1/2 state of C 2 P, i.e., the binding energy of the DBS. There also appears to be some enhancement of the 2 1 0 level in Fig. 4d and this is likely due to the proximity of the 2 0 2 0 (1677.7 cm À1 ) and 1 0 1 0 (1644.3 cm À1 ) vibrational levels (Fig. 5). The 0 0 0 peak of the 2 P 3/2 spin-orbit state of C 2 P is enhanced in the resonant PE spectra in Fig. 4e-g, which were recorded at photon energies corresponding to resonant peaks 2 (2.6639 eV), 5 (2.7490 eV), and 7 (2.8550 eV), respectively. These resonant peaks should correspond to fundamental vibrational excitations in the ( 2 P 3/2 )* DBS to obey the Dv ¼ À1 propensity rule. The excitation energies of the resonant peaks 2, 5, and 7 are 0.0136 eV (110 cm À1 ), 0.0987 eV (796 cm À1 ), and 0.1997 eV (1611 cm À1 ) above the detachment threshold of 2.6503 eV for the 2 P 3/2 spin-orbit state of C 2 P, respectively. As shown in Fig. 5, peaks 2, 5, and 7 should correspond to the 3 0 1 0 ðk 2 D 5=2 Þ, 2 0 1 0 , and 1 0 1 0 vibrational levels of the ( 2 P 3/2 )* DBS, respectively, which autodetach to the 0 0 0 level of the 2 P 3/2 spin-orbit state of C 2 P. The vibrational ground state of the ( 2 P 3/2 )* DBS is also deduced on average to be 37 cm À1 (AE6 cm À1 ) below the 2 P 3/2 state of C 2 P (Fig. 5). Again, the enhancement of the 2 1 0 level in Fig. 4g is likely due to the proximity of the 2 0 2 0 and 1 0 1 0 vibrational levels (Fig. 5).
The spectrum in Fig. 4b was recorded at the photon energy of resonant peak 3 (2.6662 eV). The 3 1 0 (m 2 S) vibronic level of the 2 P 1/2 spin-orbit state of C 2 P was enhanced, suggesting that the autodetaching state was from the 3 0 0 2 (m 2 P 3/2 ) vibronic level of the ( 2 P 1/2 )* DBS (Fig. 5), in agreement with the dipole selection rule of the vibronic transition. In Fig. 4e, the 3 1 0 (m 2 D 3/2 ) vibronic peak of the 2 P 1/2 spin-orbit state of C 2 P is also enhanced, in addition to the enhancement of the 0 0 0 peak of the 2 P 3/2 spinorbit state. This was because of the near degeneracy of the 3 0 1 0 ðk 2 D 5=2 Þ vibronic level (287.0 cm À1 ) of the ( 2 P 3/2 )* DBS and the 3 0 2 0 ðm 2 P 1=2 Þ vibronic level (282.0 cm À1 ) of the ( 2 P 1/2 )* DBS (Fig. 2). Dipole selection rules allow for only one autodetachment transition from the 3 0 2 0 ðm 2 P 1=2 Þ resonant state to the 3 1 0 (m 2 D 3/2 ) neutral vibronic state (Fig. 5), which is observed to be 176 cm À1 above the ground vibrational level of the 2 P 1/2 spinorbit state of C 2 P, in good agreement with the previous measurement. 37 Finally, the resonant PE spectrum corresponding to the resonant peak labeled as * (2.7430 eV) in Fig. 3 is shown in Fig. 4h. The intense 2 1 0 peak is likely due to threshold enhancement, similar to that shown in Fig. 1c. Clearly, the 0 0 0 peak and possibly the 3 1 0 peak of the 2 P 1/2 spin-orbit state of C 2 P are enhanced, suggesting the excitation to a vibrational level of the ( 2 P 1/2 )* DBS. The resonant energy at 2.7430 eV is 0.1102 eV (889 cm À1 ) above the EA of C 2 P, indicating a DBS vibrational level at 926 cm À1 (889 + 37 cm À1 ). This could correspond to a higher bending vibronic level of the ( 2 P 1/2 )* DBS, according to ref. 37. However, we cannot assign this resonance denitively without precise knowledge of the vibronic levels of C 2 P at around 926 cm À1 . The angular distributions of all the observed peaks in the resonant and nonresonant PE spectra are shown in Fig. S2. † The nearly isotropic distributions of the resonantly enhanced peaks provide further conrmation of our assignments because the lifetime of a DBS is typically much longer than the rotational period of a molecule. [43][44][45] Conclusions It is now clear that there are only two dipole-bound excited states in C 2 P À , ( 2 P 1/2 )* and ( 2 P 3/2 )*, each autodetaching only to a single spin-orbit state of neutral C 2 P ( 2 P). The binding energy of each DBS is 37 AE 6 cm À1 . This observation suggests that the spin of the dipole-bound electron is not coupled with the electrons in the neutral C 2 P core. Hence, the electron in the dipolebound excited states of C 2 P À can be viewed as a quasi-free electron. This conclusion raises some interesting questions. Does the uncoupling between the dipole-bound electron and the electrons in the molecular core depend on the binding energy of the DBS, i.e., the magnitude of the dipole moment, or is it universal for DBSs? Does this observation mean that the electron spin is not conserved during excitation from the anion ground state to the dipole-bound excited states? The current study further demonstrates that resonant PES via vibrational two dipole-bound excited states of C 2 P À and their autodetachment to the two spin-orbit states of neutral C 2 P. The detachment thresholds of the 2 P 1/2 ground spin-orbit state of C 2 P and the 2 P 3/2 excited state are given, as well as the deduced binding energy (37 AE 6 cm À1 ) of the DBSs. The vibrational levels and energies for neutral C 2 P are from ref. 37 and 39. The vibronic symmetries of the bending levels are given in parentheses.
autodetachment is a powerful technique to probe the nature of dipole-bound excited states.

Conflicts of interest
There are no conicts to declare.