Switching Hydrogen Bonding to π-Stacking: The Thiophenol Dimer and Trimer

We used jet-cooled broadband rotational spectroscopy to explore the balance between π-stacking and hydrogen-bonding interactions in the self-aggregation of thiophenol. Two different isomers were detected for the thiophenol dimer, revealing dispersion-controlled π-stacked structures anchored by a long S–H···S sulfur hydrogen bond. The weak intermolecular forces allow for noticeable internal dynamics in the dimers, as tunneling splittings are observed for the global minimum. The large-amplitude motion is ascribed to a concerted inversion motion between the two rings, exchanging the roles of the proton donor and acceptor in the thiol groups. The determined torsional barrier of B2 = 250.3 cm–1 is consistent with theoretical predictions (290–502 cm–1) and the monomer barrier of 277.1(3) cm–1. For the thiophenol trimer, a symmetric top structure was assigned in the spectrum. The results highlight the relevance of substituent effects to modulate π-stacking geometries and the role of the sulfur-centered hydrogen bonds.


Chirp-pulsed Fourier transform microwave spectroscopy
The experimental investigation was conducted with supersonic-jet chirped-pulsed Fourier-transform microwave (CP-FTMW) spectroscopy, 1,2,3 using instruments in Valladolid 4 and Hamburg 5,6 which covered the region 2-8 GHz. The spectrometers use a direct-digital design following Pate. 7 In this technique a short (1 s) linear microwave chirp excites the rotational resonances of an expanding molecular jet. The chirp pulse is synthesized digitally with an arbitrary waveform generator, amplified to 20 -200 W, and broadcasted into the jet through a horn antenna, perpendicular to the vertically moving jet. The jet is generated by a pulsed solenoid valve (Parker, series 9), which injects a gaseous mixture into the expansion chamber through a mm-size circular nozzle. The gas expands against an ultimate vacuum pressure of ca. 10 -7 hPa produced with an oil diffusion pump and a primary rotary pump. Gas pulses were typically of 500-900 s duration and contained a small amount of sample highly diluted in a carrier gas. Thiophenol (99%) was obtained commercially and used without further purification. The sample is liquid at room temperature (m.p. -15°C, b.p. 169°C), so it was heated inside a reservoir nozzle (60°C) to increment the vapor pressure (1.4 mm Hg at 20°C), while the stream of the carrier gas (neon or argon at stagnation pressures of 1-3 bar) was flowed over the sample. The pulsed expansion leads to effective cluster generation at the nozzle exit, followed by non-collisional propagation and effective internal cooling (rotational temperatures ca. 2 K). Following the transient excitation the spectrometer records the time-domain free-induction decay caused by rotational dephasing, using a receiving horn antenna, low-noise amplifiers and a digital oscilloscope. Typical acquisition times were of 40 s. Normally a single gas pulse is probed several times to increase the signal level. The final time-domain data are Fourier transformed using a Kaisser-Bessel window, resulting in linewidths of ca. 100 kHz. 8 Frequency uncertainties for the experimental measurements are estimated as 10 kHz. For the present purposes ca. 1 M spectral averages were acquired at a repetition rate of 5 Hz.

Conformational search and molecular models
An initial set of starting structures was generated using Molecular Mechanics 9 and conformational searching routines implemented in MacroModel. 10 This calculation was followed by molecular orbital calculations using Kohn-Sham density-functional-theory (DFT), 11 which included full reoptimizations and vibrational frequency calculations. Following previous experiences four DFT methods were chosen, including hybrid (B3LYP, 12 B97X-D 13 ), double-hybrid (B2PLYP 14 ) and composite (PBEh-3c 15 ) functionals. The Becke's three-parameter functional was supplemented with two-body Grimme's D3(BJ) dispersion 16 corrections with Becke-Johnson 17 damping, while Head-Gordon's B97X-D includes D2 empirical dispersion. 18 Becke's methods were combined with the Alrich's triple- def2-TZVP basis set, 19 while Dunning's cc-pVTZ 20 was chosen for B97X-D. In addition to the rovibrational and electric parameters needed for spectroscopic analysis (Tables 1-2 and S1-S4 below) we calculated the complexation energies relative to the monomers in the cluster geometries (including basis set superposition errors) and Gibbs energies in the range 50 K -300 K. DFT calculations were implemented in Gaussian16. 21 PBEh-3c was implemented in ORCA. 22

Topological analysis of the electron density and binding energy decomposition
The analysis of the non-covalent interactions in the dimer used a calculation of the reduced gradient (= 1 2(3 2 ) 1/3 |∇ | 4/3 ) of the electronic density , as implemented in NCIPlot. 23,24 A categorization of the physical forces stabilizing the thiophenol dimer was obtained from a symmetry-adapted perturbation theory 25,26 (SAPT) analysis implemented in PSI4, 27 producing a binding energy decomposition. This perturbative calculation used second-order intramonomer correlation corrections and up to thirdorder intermonomer dispersion corrections denoted SAPT2+(3) 28 and a double- aug-cc-pVDZ 20 basis set. The interaction energy is decomposed into electrostatic (Eelec), inductive (multipole interactions/charge transfer, Eind), exchange repulsion (Eexch) and dispersion (Edisp) energy terms.

Meyer's flexible model calculations
The potential energy function describing the concerted internal rotation of the two thiol groups in isomer II (PD2-cis) of the thiophenol dimer was first calculated from the experimental torsional splitting E10 (= 8.8698(51), Table 1) using Meyer's flexible model. 29 The determination of two-fold internal rotation barriers using semirigid formalisms has been discussed elsewhere. 30,31 The Meyer's flexible model, which has been extensively used to treat the MW data of molecular complexes, 32 is designed to numerically calculate energies and wavefunctions of vibrational and rotational states for 1-or 2-dimensional (1D, 2D) vibrational problems. This model can be applied to any type of internal motion of any non-linear molecule, with the advantages that it allows for structural relaxation, has no symmetry restrictions, and works efficiently for few mesh points. In the case of a 1D problem, if we consider  as the parameter to describe the motion (for example the correlated SH internal rotation coordinate in isomer II), the relaxations of any structural parameter can be taken into account as a function of . We assumed the following double minimum potential energy function to be appropriate for our problem: where 2 is the barrier at = 0° and 0 is the equilibrium value of the inversion angle. Since the HS-CC dihedral angles at the energy minimum are slightly different for the two thiol groups, we fixed 0 to their average value (63°) and adjusted 2 in order to reproduce the experimental E10 splitting.
We needed to take into account the structural relaxations of at least three structural parameters as  With these structural conditions we found that 2 = 250.3 cm -1 leads to a torsional splitting of E10 = 8.88 MHz, i.e., it reproduces the experimental value. In the flexible model calculations, the coordinate has been considered in the ±110° range and solved into 79 mesh points.

Torsional effective Hamiltonian
The torsional potential and tunneling splitting in the thiophenol dimer II were also predicted computationally with the following procedure. Initially, geometry optimizations for two equivalent minima were performed using the DFT method PBEh-3c, 15 followed by harmonic frequency calculations. The minimal energy path (MEP) between these minima was then computed using the nudged elastic band (NEB) algorithm 33 , with k enumerating all the nuclei, m and r being atomic masses and Cartesian coordinates, and ·, ×, and ⊗ denoting scalar, vector, and outer products.
The parameters of Hamiltonian given by equation M9 were computed using the following algorithm.
• All the MEP structures were oriented to yield least mass-weighted deviation of the coordinates from the structure best approximating transition state (with smallest |ξ|).
Hessians were transformed accordingly.
• The Cartesian coordinates of atoms along LAM coordinate were approximated with splines, this approximation was used to obtain derivatives .
• Seven degrees of freedom (transnational, rotational, and LAM) were removed from the Hessians, the resulting harmonic vibrational problem was solved yielding effective ZPVE correction. LAM direction was given by vectors.
• The effective structures outside the minima in the direction opposite to transitional state (the walls of the potential) were extrapolated from the coordinates of the minima via linear Taylor expansion as ( ) ≈ ( ) + ( ) ⋅ ( − ) with index "eq" denoting the minimal energy (equilibrium) structure. Electronic energies of these structures were estimated from the harmonic potential of the equilibrium structure, ZPVE of these structures was the ZPVE of the equilibrium structure.
• Effective masses ( ) = −1 ( ) were computed from MEP and extrapolated structures by the formulas given above.
• All the resulting Hamltonian parameters were symmetrized with respect to ξ=0, and then extrapolated using cubic splines. The resulting curves are given in Figures S5 and S6.
• The effective 1D Schrödinger equation was solved using the sinc-DVR method. 36 The resulting tunneling splittings and potential barriers are given in Table S9.          Table S3) of the thiophenol trimer.           (5)