Intermolecular Dissociation Energies of Dispersively Bound Complexes of Aromatics with Noble Gases and Nitrogen

Abstract We measured accurate intermolecular dissociation energies D0 of the supersonic jet-cooled complexes of 1-naphthol (1NpOH) with the noble gases Ne, Ar, Kr, Xe and with N2, using the stimulated-emission pumping resonant two-photon ionization (SEP-R2PI) method. The ground-state values D0(S0) for the 1NpOH·S complexes with S= Ar, Kr, Xe and N2 were bracketed to within ±3.5 %; they are 5.67 ± 0.05 kJ/mol for S=Ar, 7.34 ± 0.07 kJ/mol for S=Kr, 10.8 ± 0.28 kJ/mol for S=Xe, 6.67 ± 0.08 kJ/mol for isomer 1 of the 1NpOH·N2 complex and 6.62 ± 0.22 kJ/mol for the corresponding isomer 2. For S=Ne the upper limit is D0 < 3.36 kJ/mol. The dissociation energies increase by 1 − 5% upon S0 → S1 excitation of the complexes. Three dispersion-corrected density functional theory (DFT-D) methods (B97D3, B3LYP-D3 and ωB97X-D) predict that the most stable form of these complexes involves dispersive binding to the naphthalene “face”. A more weakly bound Edge isomer is predicted in which the S moiety is H-bonded to the OH group of 1NpOH; however, no Edge isomers were observed experimentally. The B97-D3 calculated dissociation energies D0(S0) of the Face complexes with Ar, Kr and N2 agree with the experimental values within < 5%, but the D0(S0) for Xe is 12% too low. The B3LYP-D3 and ωB97X-D calculated D0(S0) values exhibit larger deviations to both larger and smaller dissociation energies. For comparison to 1-naphthol, we calculated the D0(S0) of the carbazole complexes with S=Ne, Ar, Kr, Xe and N2 using the same DFT-D methods. The respective experimental values have been previously determined to within < 2 %. Again, the B97-D3 results are in the best overall agreement with experiment.


I. INTRODUCTION
Intermolecular London dispersion forces are weak when viewed on a per-atom basis and act at longer range (3-10Å) than chemical bonds, but they are ubiquitous and are always attractive. 1,2 They play a major role in the formation of molecular solids, liquids and solutions and are important for understanding their structures , lattice energies, phonon spectra, melting points, enthalpies and many other properties. [3][4][5][6][7][8][9][10][11][12] Synthetic chemists have recognized that dispersion interactions can be employed as control elements for reactivity and catalysis, in particular, for larger molecules, for which the dispersion energy contributions accumulate. 11 However, the accurate treatment of intermolecular dispersion interactions between polyatomic molecules has proven to be remarkably challenging. Major advances have been achieved by the introduction of dispersion-corrected density functionals, which were tailored to include longrange correlation effects. [12][13][14][15][16][17] However, the parametrization of the widely-used dispersion corrections employed in DFT-D methods is mainly based on calculations. 12,[15][16][17] Furthermore, several databases on which the DFT-D methods have been tested are themselves based on calculations; thus, the well-known S22 database for intermolecular interactions is purely computational. [18][19][20] The non-covalent interaction energy part of the large GMTKN30 database 12,21 is mainly based on calculations: Of the 95 noncovalent interaction energies in GMTKN30, only the six noble-gas gas dimer dissociation energies (the RG6 set) are based on experiment. 22,23 Therefore, more highquality experimental benchmark data for testing dispersion-corrected DFT methods and high-level correlated quantum chemical methods would be highly desirable. 10,[24][25][26][27][28] The intermolecular dissociation energy D 0 of a gas-phase bimolecular complex in its electronic ground state S 0 is such a benchmark observable. However, the number of D 0 (S 0 ) measurements of dispersively bound M·S complexes that are accurate enough to serve as benchmarks is quite limited. 10,[29][30][31][32][33][34][35][36][37] Below we present experimental dissociation energies D 0 (S 0 ) of the aromatic molecule 1-naphthol (1NpOH) complexed to a noble gas atom (Ne, Ar, Kr or Xe) or to N 2 . We chose these nonpolar "solvents" S because (1) they give rise to complexes that are dominantly bound by London dispersion interactions, (2) they are taken from the second to fifth row of the periodic table, so their electronic polarizabilities change over an order of magnitude, (3) they cover a wide range of weak interactions from < 2.5 to about 11 kJ/mol, and (4) their structural simplicity makes them attractive for testing high-level theoretical methods that have a steep dependence of computational time on the system size.
The 1NpOH moiety is small enough to be treated by high-level theoretical methods but large enough to offer two different intermolecular binding sites: The naphthalene ring gives rise to dispersively bound Face structures, [31][32][33][38][39][40][41] while the OH group can act as a nonclassical hydrogenbond donor, giving rise to Edge structures. 35,36,40,42 The 1NpOH·N 2 complex is interesting because its spectrum has been previously interpreted in terms of a Face complex, 43 whereas the closely related phenol·N 2 complex forms an Edge structure. 44 For the complexes investigated here, nearly all the dispersion-corrected DFT calculations predict both Face and Edge structures.
The gas-phase S 0 and S 1 state dissociation energies were measured using the stimulated emission pumping-resonant two-photon ionization (SEP-R2PI) method that was developed in the 1990s [31][32][33]42 and employed to determine the D 0 values of dispersively bound complexes of the aromatic chromophores carbazole [31][32][33][34] and 1NpOH. 35,36,42 We recently determined dissociation energies D 0 (S 0 ) of 1NpOH with cycloalkanes ranging from cyclopropane to cycloheptane, which revealed that the D 0 of these complexes is not simply proportional to the molecular polarizability of the cycloalkane, but saturates with increasing size of the cycloalkane and depends on the details of the structure of the intermolecular complex. 40,41,45 Below, we compare the experimental D 0 values to the binding energies D e and dissociation energies D 0 calculated with the widely-used dispersion-corrected density functional theory (DFT) methods B3LYP-D3, B97-D3 and ωB97X-D. We also calculate the D 0 values of the carbazole complexes with the noble gases and N 2 . The availability of nine experimental dissociation energies that are accurate to ≤ 3.5% allows to compare their dependence on (1) the molecular size of the aromatic, (2) the polarizability of S, and (3) to benchmark the dispersion-corrected DFT calculated values vs. the experimental D 0 energies.

A. The SEP-R2PI Method
Very briefly, a ∼ 5 ns pulsed tunable UV pump laser is fixed at a cold band that originates from the S 0 ; v ′′ = 0 vibrational ground state of the 1NpOH·S complex, exciting it to either the vibrationless S 1 ; v ′ = 0 level (0 0 0 band) or to a low-frequency intermolecular vibrational level. After a short delay of 1 − 3 ns, a tunable dump laser stimulates resonant vibronic transitions back down to vibrationally excited levels (v ′′ i > 0) of the S 0 state. The dump laser is scanned to smaller wavenumber than the 0 0 0 transition; whenever it is resonant with a S 1 ; v ′ = 0 → S 0 ; v ′′ i > 0 downward transition, a large part of the S 1 ; v ′ = 0 population is transferred to a specific vibrationally excited v ′′ i > 0 level. The resulting "microcanonically hot" 1NpOH·S complexes undergo intraand intermolecular vibrational redistribution (IVR) from this v ′′ i level into all other energetically accessible vibrational states. After a long delay (3 − 5 µs) that allows IVR to go to completion, the hot 1NpOH·S complexes are detected by R2PI with a third pulsed UV dye laser, denoted the probe laser. We have previously shown that this delay is long enough to permit all initially prepared S 0 vibrational levels to couple to the intermolecular dissociation coordinates. 41 For the D 0 measurement, the probe laser is fixed to a cold transition between the v ′′ = 0 level and either the v ′ = 0 level (0 0 0 band) or to a low-lying intermolecular vibrational level S 1 (v ′ inter > 0). When scanning the dump laser, the resonant dump transitions are detected as a decrease of the probe laser signal, because the v ′′ = 0 population is additionally depleted via the pump/dump population transfer to v ′′ i > 0 levels. Such a cold-band SEP-R2PI spectrum looks qualitatively similar to the dispersed fluorescence spectrum from the S 1 (v ′ = 0) level of the 1NpOH·S complex, but with negative-going peaks.
Conversely, if the probe laser is fixed at a hot band (or sequence band) that originates from a v ′′ > 0 level, we obtain a positive-going hot-band SEP-R2PI signal. Scanning the dump laser while detecting the hot-band SEP signal gives a hot-band SEP-R2PI spectrum that increases at every resonant dump laser transition, since the hot level being probed is populated via IVR. Hotband SEP signals are only observed as long as the hot 1NpOH·S complex remains bound during the delay time between the dump and probe laser transitions. When the dump laser excites vibrational levels of the 1NpOH moiety that are energetically above than the S 0 dissociation energy of the complex, IVR is followed by efficient 1NpOH ↔ S vibrational predissociation. The hot 1NpOH·S complex is no longer formed, so the hot-band signal is no longer detected with the probe laser.
The ground-state dissociaton energy D 0 (S 0 ) of the complex is then bracketed between the highestwavenumber dump transition that is observed in the hot-band SEP spectrum and the next higher vibration that appears in the cold-band SEP spectrum (or in the fluorescence spectrum) but does not appear in the hot-band SEP spectrum.

B. Experimental
The supersonically cooled 1NpOH·S complexes were produced by co-expanding 1NpOH (Fluka, 99%) and 1% Ar, 0.8% Kr, 0.5% Xe or 1% N 2 which were premixed in Ne carrier gas; the total backing pressure was 1.4 − 1.6 bar. The 1NpOH·Ne complex was produced by expansion in neat Ne. The 1NpOH was heated to 353 K (0.5 mbar vapor pressure). Two frequency-doubled tunable dye lasers (Lambda Physik FL2002 and FL3002, fundamental range 620 − 660 nm) were employed as pump (∼ 0.5 mJ/pulse) and dump (∼ 2 mJ/pulse) lasers. Both were pumped by the same Nd:YAG laser (Quanta Ray DCR3). The probe dye laser (Lambda Physik LPD 3000, ∼ 0.3 mJ/pulse) was pumped by a Continuum Surelite II frequency-doubled Nd:YAG laser. The dye-laser wavelength and bandwidths before frequency doubling were monitored using a HighFinesse WS6 wavemeter; the bandwidths were 0.3 − 0.4 cm −1 . The probe laser was time-delayed by 3 − 5 µs and crossed the molecular beam 3 − 5 mm downstream of the pump and dump lasers, to compensate for the ∼ 950 m/s mean speed of the molecular beam. Other experimental details were reported previously . 40,41 Mass-selective one-color resonant two-photon ionization (R2PI) spectra were recorded using a 120 cm long linear time-of-flight mass spectrometer. Mass-selective ion signals were measured for all complexes. UV/UV hole-burning spectroscopy was performed; for the Ar, Kr and Xe complexes only one ground-state isomer was observed, whereas two ground-state species were observed for the Ne and N 2 complexes.
In the one-color R2PI process, the ionization laser (with the same photon energy as the excitation laser) may deposit sufficient energy in the ground state of the ionized complex to induce dissociation in the ion state. Larger 1NpOH·S n clusters were present in small relative amounts.
The R2PI spectra of the 1NpOH·S n (n = 2, 3) clusters were also measured to evaluate the possibility of fragmentation in the ion state into the respective (n − 1) + ion channels. No evidence was found to suggest that this occurs to a significant degree. S 1 → S 0 dispersed fluorescence spectra were measured by exciting the respective 0 0 0 band or intermolecular fundamental excitation (in some cases). The fluorescence was collected with fused silica optics and detected in the second order of a SOPRA UHRS F1500 1.5 m monochromator using a Hamamatsu R928 photomultiplier. The slit width was 200 µm, equivalent to a bandpass of 28 pm; the spectra were scanned in 2.5 pm steps.

C. Computational
The geometrical structures, harmonic vibrational wavenumbers, binding energies (D e ) and dissociation energies (D 0 ) of the 1NpOH·S and carbazole·S complexes were calculated using the B97 density functional with the D3 dispersion correction 16,17 (B97-D3) and the def2-TZVPP basis set, using Gaussian 16 (Rev. A). 46 B97-D3 exhibits one of the smallest total mean absolute deviations (MAD) between experiment and calculation for the noncovalent interaction part of the GMTKN30 test set. 12 The B97-D3 method also predicts that Ne 2 is a bound molecule, in contrast to the dispersion-corrected GGA functionals BP86-D3, BPBE-D3, and BOP-D3. 12 This property is important, since we experimentally investigate the 1NpOH·Ne complex. Also, the B97-D3 dissociation energies of the previously measured 1NpOH·cycloalkane complexes agreed with the experimental values to within ≤ 1.1%. 40,41 For comparison, additional calculations were performed with the B3LYP-D3 method and the def2-TZVPP basis set, and with the ωB97X-D method 15 (which employs the D2 dispersion correction) and the 6-311++G(d,p) basis set for all complexes except for the Xe complex, for which the def2-TZVPP basis set was used. For Xe, the def2-TZVPP basis set 47 models the inner shell electrons with the small-core effective-core potential ECP-28, 48 which represents the core AOs from 1s to 3d. The counterpoise method for correcting D e values for basis-set superposition error is not recommended if the D3 method is used, 16 and thus it was not employed with B97-D3 and B3LYP-D3. The ωB97X-D results were counterpoise corrected.
The structure optimizations were unconstrained. The threshold for SCF convergence was set to 10 −9 a.u., the convergence threshold for RMS Force to 10 −6 a.u., maximum Force to 2x10 −6 a.u., the RMS displacement to 4x10 −6 a.u. and the maximum displacement to 6x10 −6 a.u. (corrresponding to the VERYTIGHT option in Gaussian16). 46 The optimized minima were checked for the absence of imaginary vibrational frequencies. The Cartesian coordinates of the ground state geometries of 1-naphthol and of all the Face and Edge complexes optimized with all three DFT methods are given in Tables S1-S33 (supplementary material, SI).

III. RESULTS
A. R2PI spectra Figure 1 shows the one-color R2PI spectra of bare 1-naphthol and the 1-naphthol·S complexes in the region of their S 0 → S 1 0 0 0 bands. The spectra of the complexes, Figure 1(b-g), exhibit weak bands corresponding to low-frequency intermolecular vibrational fundamentals and their overtones or combinations. These give valuable information about the intermolecular frequencies and VZPEs and will be discussed in section IV D.
The 0 0 0 bands of the complexes are shifted relative to the 0 0 0 of bare 1-naphthol (at 31455 cm −1 ) by the spectral shift δν. Assuming that the S 0 → S 1 electronic excitation is localized on the 1NpOH moiety, the spectral shift corresponds to the difference of ground-and excited-state dissociation energies, δν = D 0 (S 0 ) − D 0 (S 1 ). [31][32][33]35,42 The R2PI spectra of 1NpOH·Ar and 1NpOH·N 2 have been measured previously by Zierhut et al, 43 who reported spectral red shifts of δν = −15 cm −1 for S=Ar and −14 cm −1 for S=N 2 . 43 The spectral shift of the of 1NpOH·S complexes also indicates their binding topology: If cyclopropane is dispersively adsorbed as a Face complex, the spectral shift is small or even to the blue (δν = +1.9 cm −1 ), while in the hydrogen-bonded OH· · ·cyclopropane Edge complex, the spectral shift is large and to the red (δν = −71.5 cm −1 ). 40 The small spectral shifts of the complexes reported here imply that the noble gas or N 2 is adsorbed in a Face geometry.
1-Naphthol·Ne: UV/UV spectral holeburning experiments on the Ne complex revealed a contribution from a minor species whose S 0 → S 1 0 0 0 band is slightly blue-shifted relative to that of 1NpOH. Figure 1(b) shows the spectrum of the major 1NpOH·Ne species in the jet, the spectral contribution of the minor species has been removed by UV/UV hole-burning. The spectrum is dominated by the 0 0 0 band, which is shifted by δν = −2 cm −1 . The small shift implies a small change between the S 0 -and S 1 -state dissociation energies and leads us to assign this species as a Face isomer. Weak intermolecular excitations are observed at 0 0 0 + 11 cm −1 and 0 0 0 + 37 cm −1 . Their low Franck-Condon factors imply a small change of geometry between the S 0 and S 1 state for the Ne complex. The B97-D3 frequency calculations in Table I predict the three intermolecular fundamental vibrations at 8.5 cm −1 (in-plane long-axis ν X ), 13.2 cm −1 (in-plane short-axis vibration ν Y ) and at 39.8 cm −1 (perpendicular ν Z vibration). Given the small change in geometry and dissociation energy, we expect the calculated S 0 state harmonic wavenumbers to be similar to the calculated S 1 values. Indeed, the observed bands at 11 and 37 cm −1 agree well with the calculated ν X and ν Z wavenumbers. The experimental and calculated S 0 state harmonic wavenumbers of the intermolecular vibrations are compared in Table I.
Since the spectrum of the minor species overlaps extensively with that of the major species it is hard to separate cleanly; the total 1NpOH·Ne R2PI spectrum and the partially separated UV/UV-holeburned spectra are shown in Figure S1 (supplementary material). The minor species could either be a second ground-state Face isomer or residual population of S 0 state ν X = 1 level.
Assuming a typical vibrational temperature T vib ∼ 10 K in the supersonic jet expansion, we would expect a relative population of 20 − 30 % in v X = 1, which agrees nicely with the observed intensity of the minor species.
1-Naphthol·Ar: The R2PI spectrum in Figure 1(c) shows an intense S 0 → S 1 electronic origin band at 31440 cm −1 and five intermolecular vibronic transitions. The UV/UV holeburning measurements reveal that all bands originate from one single isomer. The 0 0 0 band is shifted by δν = −14.8 cm −1 relative to 1NpOH, very close to the value reported previously. 43 The bands at 7.3, 19.8 and 46.1 cm −1 above the origin are assigned to the three intermolecular fundamental vibrations ν ′ X , ν ′ Y and ν ′ Z , based on the calculated intermolecular B97-D3 frequencies in Table I. The experimental ν ′ X wavenumber is only 65 % of the calculated ν X value. However, the ν ′ Y and ν ′ Z wavenumbers agree withing 3 − 5 % with the calculated values, see Table I. The two bands at 14.8 and at 37.2 cm −1 are assigned to the 2ν ′ X and 2ν ′ Y overtone transitions.

1-Naphthol·Kr:
The 1NpOH·Kr spectrum is shown in Figure 1 Table I shows, the agreement of the experimental and calculated wavenumbers is good, the ν ′ X value being in better agreement with calculation than in the Ne and Ar complexes; also, ν ′ Z is 1.8 cm −1 higher than calculated. The two bands at 16.7 and 36.2 cm −1 are assigned to 2ν ′ X and 2ν ′ Y . The latter lies 5 cm −1 below the value expected for a harmonic overtone 2ν ′ Y = 40.8 cm −1 . Since this value nearly coincides with the calculated B97-D3 ν ′ Z = 40.6 cm −1 wavenumber, one expects that these two levels may give rise to a 2:1 Fermi resonance, leading to downward and upward frequency shifts of the 2ν ′ Y and ν ′ Z levels relative to the uncoupled harmonic values.
1-Naphthol·Xe: Figure 1(e) shows the R2PI spectrum of 1NpOH·Xe. The intense 0 0 0 band at 31420 cm −1 is red-shifted by δν = −35 cm −1 relative to bare 1NpOH. The bands at 10.5, 22.5 and 37.5 cm −1 above the origin are assigned to the intermolecular vibrational fundamentals ν ′ X , ν ′ Y and ν ′ Z , by comparison with the B97-D3 calculated values, given in Table I. The agreement of the calculated harmonic ν X and ν Y wavenumber with experiment is very good; the experimental where a weak band is indeed observed. We suggest that the 2ν ′ Y ↔ ν ′ Z Fermi resonance interaction is smaller than in the 1NpOH·Kr complex, since the the Y 2 0 band is much less intense than the Z 1 0 band.

1-Naphthol·N 2 :
The one-color R2PI spectrum of the 1NpOH·N 2 complex is shown in Figure S2(a) (SI); it differs from those of the noble-gas complexes in that the most intense band at 31441 cm −1 is not at lowest wavenumber; two additional bands are observed further to the red. A similar 1C-R2PI spectrum of 1NpOH·N 2 complex was measured and discussed by Zierhut et al., 43 who assigned the most intense band at 31441 cm −1 as the 0 0 0 , but did not discuss the lower-lying bands. They performed UV/UV holeburning experiments (not shown there) and reported that it was "difficult to extract detailed information". 43 Our UV/UV holeburning experiments revealed separate spectral contributions from two species that we denote isomer 1 and 2; their UV-holeburned spectra are shown in Figure 1 We assign the intense band at 31441 cm −1 as the 0 0 0 band of isomer 1. It is shifted by δν = −14.4 cm −1 to the red of the 1NpOH origin, close to the value reported by Zierhut et al., 43 and also similar to the shift of the Ar complex, see Figure 1(c). The spectral shift of the 0 0 0 band of isomer 2 is δν = −28 cm −1 , which is close to twice that of red shift of isomer 1. This might suggest that the species 2 actually arises from n = 2 → 1 fragmentation of the n = 2 cluster (or cluster ion), the corresponding spectral signal then appearing in the n = 1 ion channel. This was investigated by measuring the 1C-R2PI spectra of 1NpOH and the 1NpOH·(N 2 ) n clusters with n = 1−3 at the same time. No spectroscopic signature of the n = 1 → 0 fragmentation appears in the mass channel of bare 1NpOH + and at the same time, the spectrum measured in the n = 2 ion mass channel is completely different from that measured in the n = 1 mass channel. In order to attribute the spectrum of species 2 to the n = 2 cluster we would have to assume that n = 2 → 1 fragmentation is 100 % efficient while both the n = 1 → 0 and n = 3 → 2 fragmentation processes are highly inefficient. This seems very improbable, so we remain with the assignment to a second, structurally distinct Face isomer of the n = 1 N 2 complex.
The UV-holeburned spectra of isomers 1 and 2 exhibit similar four-to five-membered vibrational progressions with slightly unequal spacings of about 7 − 9 cm −1 . The lowest harmonic intermolecular frequency of the N 2 complexes calculated with the B97-D3 method is 25 cm −1 for the long-axis in-plane vibration ν X , the other modes are calculated to have even higher frequencies up to 93 cm −1 , see Table I. However, the N 2 complex has one intermolecular vibrational degree of freedom that corresponds to internal rotation of the N 2 about an axis perpendicular to its internuclear axis and parallel to the surface normal of the naphthalene ring, similar to the internal rotation modes of the complexes of N 2 with aniline, 49 , benzene, 50 and p-difluorobenzene. 51 In the benzene·N 2 complex there is a low (0.05 cm −1 ) sixfold V 6 barrier to this motion, so the internal rotation about the C 6 axis is essentially free. 50 In the aniline·N 2 and p-difluorobenzene·N 2 complexes, the lower symmetry of the substrate leads to twofold barriers, but these are also low Assuming that internal rotation is nearly free in 1NpOH·N 2 , one expects to observe level ener- Fermi resonance between the ν X vibrational level, which we assign to the transition at 25 cm −1 , and the l = ±3 level; this pushes the two states apart. The weak band at 0 0 0 + 34.5 cm −1 nicely agrees with to the l = ±4 internal-rotation transitions that are expected at 32 cm −1 .
Thus, three low-frequency bands in the R2PI spectrum of 1NpOH·N 2 that cannot be interpreted in terms of the calculated intermolecular normal-mode frequencies are nicely compatible with the hypothesis that internal rotation of the N 2 moiety is only unhindered or slightly hindered in the S 1 states of isomers 1 and 2. A consequence of the internal-rotation character of this mode is that its contribution to the VZPE is close to zero, in contrast to the normal-mode value of 72.6/2 = 36.3 cm −1 at the B97-D3 level. As discussed in section IV D, we expect the anharmonic VZPE of the N 2 complexes to differ by 0.4 − 0.5 kJ/mol from the calculated harmonic VZPE.

B. Excited-state lifetimes and intersystem crossing
In the SEP-R2PI process, the S 1 (v ′ = 0) → S 0 dump laser transition competes with three other excited-state processes of the 1NpOH chromophore, the S 1 → S 0 internal conversion (IC), S 1 → T n intersystem crossing (ISC) to the energetically accessible triplet states, and S 1 → S 0 spontaneous fluorescence, with rate constants denoted k IC , k ISC and k rad , respectively. Changing the chemical identity of S leads to dramatic changes in the ISC kinetics of the 1-naphthol chromophore, which we briefly discuss in this section.
We measured the fluorescence lifetimes τ f l of 1NpOH and the complexes at their respective 0 0 0 bands, see above. Laser stray light was eliminated by measuring the fluorescence through the monochromator. Table II shows the experimental lifetimes and the fluorescence quantum yields of the complexes, relative to that of bare 1NpOH. The experimental lifetime of 1NpOH at its Upon complexation of 1NpOH with N 2 , the fluorescence lifetime remains the same within the experimental error bars. The lifetime of the Ne complex could not be measured because of the spectral overlap of its 0 0 0 band with that of bare 1NpOH, whose emission swamps that of the 1NpOH·Ne complex. For the Ar complex a lifetime shortening by 25 % is observed, for Kr the lifetime decreases by a factor of 10 and for Xe by a factor of 30 or more.
These decreases reflect the external heavy-atom effect (EHAE) in dispersively bound complexes, first observed by Jortner and co-workers in complexes of tetracene and pentacene with no-ble gas atoms. [55][56][57][58][59] Mackenzie and co-workers have later studied the EHAE in p-difluorobenzene·S and toluene·S complexes and compared the measured lifetimes to calculated S 1 ↔ T 1 spin-orbit coupling (SOC) matrix elements. 60,61 Based on these results, we suggest that the observed lifetime decrease by a factor of about 30 arises from the spatial proximity of the noble gas atoms with large SOC matrix elements (Ar and especially Kr and Xe) that increase the ISC rate of the 1-naphthol chromophore. This in turn strongly affects the efficiency of the SEP-R2PI experiment and leads to considerably lower signal/noise ratios in the S=Kr and Xe spectra, as will be seen below.  Table III. 1-Naphthol·Kr: Figure 4(a) shows the hot-band probed SEP-R2PI spectra of the 1NpOH·Kr complex, with the pump laser set to the the intermolecular excitation at 0 0 0 + 36 cm −1 [see Figure  1(d)] and the probe laser set to 0 0 0 − 34 cm −1 , where an intense hot-band signal is observed after dumping. The corresponding R2PI spectrum is shown in Figure S4 (supplementary information).  and 620 cm −1 in Figure 4(c) bracket the D 0 (S 0 ) of the 1NpOH·Kr complex as 614 ± 6 cm −1 , see Table III. From the spectral shift δν of 1NpOH·Kr we obtain the excited-state dissociation energy D 0 (S 1 ) = 636 ± 65 cm −1 , see also Table III. 1-Naphthol·Xe: As discussed in section III. B, the Xe complex has a very short fluorescence decay lifetime of τ f l ≤ 3 ns, due to the heavy-atom induced ISC, which becomes the most effective nonradiative pathway, see Table II. For this reason, the stimulated-emission step is much less efficient and both the dump spectrum and the origin-probed SEP-R2PI spectrum exhibited a much lower S/N ratio compared to the other complexes. Despite the the low fluorescence quantum yield, the best information on the S 0 state vibrations could be obtained from the fluorescence spectrum, which is shown in Figure 5(b).
The hot-band detected SEP spectrum was measured 19 cm −1 below the 0 0 0 band, where a weak signal increase occures upon dumping to the S 0 state. A corresponding R2PI spectrum is shown in Figure S5 (supplementary information). The highest-wavenumber transition in this spectrum is observed at 880 cm −1 , see Figure 5(a). It clearly correlates with the intense band at 880 cm −1 in the fluorescence spectrum. The next higher band in the fluorescence spectrum at 927 cm −1 is not observed in the hot-band SEP spectrum, nor are any of the higher energy fluorescence bands. This brackets the D 0 (S 0 ) of the 1NpOH·Xe complex between these two bands as 904 ± 24 cm −1 , see Table III. The excited-state dissociation energy is D 0 (S 1 ) = 939 ± 24 cm −1 , see also Table III. 1-Naphthol·N 2 : As discussed above, two isomers of the 1NpOH·N 2 complex were observed by UV/UV holeburning. The top panel of Figure 6 shows two hot-band probed SEP-R2PI spectra of isomer 1. The red spectrum (a) was excited at an intermolecular vibrational combination band at 0 0 0 +34.5 cm −1 , as indicated with a vertical arrow in Figure 1(f). The black spectrum in Figure 6(b) is the hot-band probed SEP-R2PI spectrum following excitation at the 0 0 0 band. In both cases the probe laser was set to 0 0 0 − 53 cm −1 . While the black spectrum exhibits better signal/noise, the highest vibronic excitation that is clearly above the noise is at 545 cm −1 , while spectrum (a) shows the highest-energy band at 558 cm −1 , thereby significantly increasing the lower limit of D 0 (S 0 ). For the upper D 0 limit we compare to the fluorescence spectrum in Figure 6(c), the lowest-wavenumber band that is not observed in spectrum (b) lies at 571 cm −1 . These two values bracket the D 0 (S 0 ) of isomer 1 of the N 2 complex as 565 ± 7 cm −1 , given also in Table III.
The corresponding spectra for isomer 2 of the 1NpOH·N 2 complex are shown in the lower panel of Figure 6. We could only measure the hot-band SEP spectrum excited at the 0 0 0 band, Figure 6(d), which is compared to the fluorescence spectrum of isomer 2, shown in Figure 6(e).
This spectrum is less well resolved than that of isomer 1, because of the lower concentration of isomer 2 in the supersonic jet. The D 0 of isomer 2 is bracketed between the highest-energy band in the hot-band probed SEP-R2PI (at 535 cm −1 ) and the next higher-energy band in the fluorescence spectrum, see Figure 6(e) at 571 cm −1 , giving D 0 (S 0 ) = 553 ± 18 cm −1 .
As Table III shows, the dissociation energies of the two N 2 isomers overlap within their respective brackets. If we assume typical supersonic-jet vibrational temperatures in the range T vib = 10 − 15 K, the ∼ 30% intensity of isomer 2 relative to isomer 1 (see Figure 1) implies that the D 0 of isomer 2 is about 8−12 cm −1 smaller than that of isomer 1. This estimate is compatible with the difference of ∼ 12 cm −1 between the two interpolated D 0 values. Due to the larger spectral shift δν of isomer 2 relative to that of isomer 1, the S 1 state dissociation energies of the two isomers become very similar, being D 0 (S 1 ) = 579 cm −1 for isomer 1 and 581 cm −1 for isomer 2, see also Table III.

D. Calculated Structures
The B97-D3, B3LYP-D3 and ωB97X-D calculated structures of the 1NpOH·S complexes are very similar to each other. Since the dissociation energies calculated with B97-D3 are on average closer to the experimental ones than those calculated by the other methods, we only show the B97-D3 structures here. The calculated Cartesian coordinates of all the complexes using all three methods are given in Tables S1-S33 (SI). Figure 7 shows the calculated Face structures. The noble-gas atoms and the N 2 molecule are adsorbed above the naphthalene ring at R ⊥ = 3.44Å for Ne, 3.56Å for Ar, 3.62Å for Kr, 3.75Å for Xe, 3.13Å for N 2 isomer (1) and 3.13Å for isomer 2. Regarding the X/Y coordinates of the structures, the Ne atom is adsorbed directly above the central C8-C9 bond of the naphthalene moiety and is very slightly shifted towards the OH group. With increasing van-der-Waals radius the larger noble gas atoms shift progressively away from the central C8-C9 bond and towards the center of the OH-carrying benzene ring.
With the exception of the Xe complex calculated with the B3LYP-D3 method and the Ar and Xe complexes calculated with the ωB97X-D method, all three DFT methods also predict Edge isomers, 40 in which the -OH group of 1NpOH forms a non-conventional OH· · ·S hydrogen bond to the noble-gas atom or N 2 molecule, which now lies in the 1NpOH plane. These Edge structures are shown in the supplementary Figure S6 1NpOH·Ar and 1NpOH·N 2 complexes, respectively, and considered the Ar or N 2 moiety to be adsorbed on the aromatic face of 1NpOH. 43 We have previously noted that the Face isomer of 1NpOH·cyclopropane exhibits a small spectral shift to the blue, δν = +2 cm −1 , 40 while the spectral shift of the Edge isomer of 1NpOH·cyclopropane shows a much larger spectral red shift of −71.5 cm −1 . 40 Since the spectral shifts of the noble gas complexes lie between −2 and −35 cm −1 , we assign them to Face complexes.
We expect that the Edge isomers predicted by the DFT calculation would show larger red shifts than the Face isomers. However, we have not observed any strongly red-shifted bands, see Figure 1. We therefore conclude that even if such locally stable Edge isomers are formed during the supersonic-jet expansion, they easily isomerize to the more stable Face counterparts.

B. Experimental dissociation energies
We complement the experimental D 0 values of the 1NpOH·S complexes with those of the carbazole·S complexes. These have been measured earlier to within ±0.05 kJ/mol, using the same SEP-R2PI technique. [31][32][33][34] This doubles the size of the benchmark set and allows interesting comparisons. The experimental D 0 values of the carbazole complexes are given in Table V and are graphically compared to the 1NpOH·S dissociation energies in Figure 8.
For the carbazole·Ne complex only an upper limit to D 0 could be measured, but since the lowest optically active vibration in carbazole is lower than in 1-naphthol, this value of < 2.56 kJ/mol is about 1 kJ/mol lower than for the 1NpOH complex. Figure 8 shows that D 0 s of the carbazole complexes with S=Ar, Kr and N 2 are uniformly 12% larger than those of the corresponding 1naphthol complexes. This agrees with expectations, since carbazole (C 12 H 9 N) has two secondrow atoms more than 1-naphthol (C 10 H 8 O), thereby increasing the number of valence electrons and electronic polarizability.  Table IV gives the dissociation energies of the 1-naphthol·S complexes that were calculated using the three dispersion-corrected DFT methods; those of the corresponding carbazole complexes are given in Table V. We compare the experimental D 0 values to the calculated ones in Figure 9.
Starting with the 1-naphthol·Ne complex, one sees that the experimental upper D 0 limit is larger than all the calculated values, so the experiment is compatible with all calculations, but does not test them. The D 0 of 1NpOH·Ar is closest to the B97-D3 value, the B3LYP-D3 calculated D 0 being 13% too high, while the ωB97X-D D 0 is 9% too low. For the N 2 complex we compare the calculated and experimental values for isomer 1 because of the narrower experimental brackets for this complex. The experimental D 0 is closest to the ωB97X-D value, with B97-D3 being 5% larger and B3LYP-D3 about 9% larger. As for Ar, the D 0 of 1NpOH·Kr is also closest to the B97-D3 value, however, the ωB97X-D value is now the second closest, being only 4% too high, while the B3LYP-D3 D 0 is 15% too high. 1NpOH·Xe is the only complex for which all the DFT calculated D 0 values fall below the experimental value, with B97-D3 predicting the lowest D 0 (−12%), ωB97X-D being closer (−8%) and B3LYP-D3 closest (−4%). Overall, the B97-D3 D 0 values exhibit the smallest mean average deviation (MAD) relative to experiment, followed by the D 0 values calculated by the ωB97X-D and by B3LYP-D3 methods.
Turning to the carbazole·Ne complex in Figure 9(b), again only an upper limit of D 0 < 2.56 kJ/mol is known. 33 Table V shows that the ratios of ∆VZPE to D e are very similar. This result is in agreement with the London model for dispersive interactions between closed-shell atoms. 1,2 For N 2 the linear correlation of D 0 (S 0 ) with α is only good if we plot against the longaxis (parallel) polarizability α zz of N 2 , the correlation of D 0 with the perpendicular polarizability α xx is unsatisfactory. Note that for cycloalkane admolecules, which have larger polarizabilities, the D 0 values do not scale linearly with the α of S but increase much more slowly and depend on details of the structure of the admolecule. 41 The structures, binding energies D e , vibrational frequencies and changes of vibrational zeropoint energy (∆VZPE) were calculated using the dispersion-corrected density functional methods B97-D3, B3LYP-D3 and ωB97X-D. All methods predict that Face structures are most stable, in which the adatom/molecule is adsorbed above and close to the center of the naphthalene frame, similar to the 1-naphthol·cyclopropane Face isomer. 40 All three DFT-D methods also predict Edge isomers in which the S moiety forms a nonconventional H-bond to the OH group of 1-naphthol, similar to the 1-naphthol·cyclopropane Edge isomer. 40 While B97-D3 predicts stable Face and Edge minima for all complexes, the B3LYP-D3 and ωB97X-D methods predict index-1 saddle points for some adatoms. The calculated dissociation energies of the Edge isomers are smaller than those of the Face isomers, although for the Ne complex the difference is small (0.1 − 0.25 kJ/mol).
For the larger adatoms/-molecule, the differences increase to 1 − 2.5 kJ/mol.
Based on the small spectral shifts, we assign the observed R2PI and UV holeburning spectra to Face complexes. We searched for signals of Edge isomers, but did not observe any red-shifted bands with significant intensity. This implies that the Edge→ Face isomerization barriers are low for these complexes. Using UV/UV holeburning, we were able to separate two spectra for the 1NpOH·N 2 . The DFT-D calculations indeed predict two separate Face isomers with the N 2 is adsorbed above either of the benzene rings of 1-naphthol. For the Ne complex, UV holeburning allowed to partially separate the spectrum of a minor species that is blue-shifted by a few cm −1 from the 0 0 0 band of the major species. Since all the DFT-D calculations predict a only single S 0 state isomer for the Ne complex, we interpret the minor species in terms of residual population of the S 0 state v x = 1 level.
We extended the calculations to the analogous Ne, Ar, Kr, Xe and N 2 complexes of the planar aromatic carbazole which were previously measured using the SEP-R2PI method. [31][32][33][34]63 Again all three DFT-D methods predict Face and Edge complexes. The Face complexes are predicted to be more stable, in agreement with the relatively small experimental spectral shifts. The comparison of the experimental D 0 values of 1-naphthol·Xe and carbazole·Xe revealed that both values lie within the (larger) bracketing limits of the 1-naphthol·Xe D 0 , whereas the D 0 trend of the Ne-Kr complexes suggests that the D 0 of carbazole·Xe 33 should be ∼ 1 kJ/mol larger than that of 1-naphthol·Xe. This difference needs to be checked in the future.
Based on the nine experimental dissociation energies for the complexes of two different aromatic molecules, we evaluated and compared the predictions of the three DFT methods: Overall, the B97-D3 method reproduced the experimental D 0 values best, with a mean absolute difference (MAD) of 0.37 kJ/mol and a maximum difference of 1.27 kJ/mol (for 1-naphthol·Xe). This predictive performance is encouraging, but the MAD is significantly larger than the experimental bracketing width, which is ±0.10 kJ/mol, when averaged over the same nine complexes. The The calculated ∆VZPE is 18 − 25 % of the D e , depending on the DFT method. The in-plane internal-rotation mode of the N 2 complexes is very poorly described by the normal-mode treatment: The predicted harmonic frequency is ∼ 70 cm −1 , while experimentally this vibration is a (slightly) hindered internal rotation, whose lowest excitation lies at 2 − 3 cm −1 . For this mode the calculated and experimental VZPE differ by about 0.4 kJ/mol. The out-of-plane internal-rotation mode of the N 2 moiety was not detected experimentally, so no overall evaluation of the VZPE could be made. We suspect that the relatively good agreement of experimental and calculated D 0 s for the N 2 complexes is be due to fortuitous cancellation of errors in the calculated D e and the calculated ∆VZPE values.
We believe that the nine experimental D 0 values presented above -especially in combination with the experimental D 0 values of the 1NpOH·cycloalkane complexes 40,41 and those of other intermolecular complexes discussed in the literature 10,37 -can serve as experimental benchmarks for testing both highly correlated ab initio calculations and density functional methods, as well as for improving our understanding and modelling of intermolecular interactions.

Supplementary Material
See supplementary material for additional UV/UV-hole-burning and probe laser spectra ( Figures   S1 to S5), structures of the Edge complexes ( Figure S6) and tables of Cartesian coordinates of the 1-naphthol and carbazole complexes optimized by the DFT methods (Tables S1 to S33).   The calculated D 0 that agrees best with experiment is given in bold.  1   2  3  4  5  5  2  3  6  7  5  2  3  6  8  5  2  3  6  6  5  2  3  6  9  5  2  3  6  5  5  2  3  2  7  5 :  Table I. In panels (c,d) and (f), the intermolecular vibronic excitations employed for the D 0 determination are marked with an upward arrow. The lowest-energy vibronic transition in the dump laser spectrum (b) is at 281.4 cm −1 ; since no corresponding transition is observed in (a), this is the upper limit of the ground-state dissociation energy D 0 (S 0 ).