Microhydration of Tertiary Amines: Robust Resonances in Red-Shifted Water

Tertiary amines are strong hydrogen bond acceptors. When a water molecule donates one of the OH groups, its in-phase stretching vibration wavenumber is decreased to such an extent that it comes close to the water bending overtone. This gives rise to anharmonic phenomena such as classical Fermi resonance, resonance with multiple-quantum dark states, or combination transitions with low-frequency intermolecular modes. These effects, which contribute to the spectral breadth of room-temperature hydrogen-bonded amine complexes, are disentangled by Fourier transform infrared spectroscopy in pulsed supersonic slit jet expansions. Monohydrates of the amines quinuclidine, N-methylpyrrolidine, N-methylpiperidine, and dimethylcyclohexylamine exhibit systematic mode coupling signatures. These suggest relatively fast energy flow out of the excited OH stretching fundamental into intra- and intermolecular degrees of freedom of the hydrogen-bonded water molecule. Trimeric complexes are spectroscopically separated from the amine monohydrates.


Experiment 1.Investigated compounds
Tab. S1 gives detailed information about the chemicals used for the study and introduces the codes for the chemical names that are also used in the main document.

Experimental details
The experimental setup for the FTIR measurements is introduced in great detail in [1] and more information on the recorded spectra can be found in Tab.S2.
Table S2: Spectroscopic details of the figures 1, 4 and 5 in the main document.The partial pressures of the amine (p A ), water (p w ), as well as the carrier gases helium (p He ) and neon (p Ne ) and the total stagnation pressure of the expansion (p s ) are given.The spectra were obtained by averaging # FTIR scans during a 133 ms gas pulse through a 700 mm×0.2 mm slit nozzle with a Bruker VERTEX 70v FTIR spectrometer in double-sided mode at 140 kHz scanning speed.A 20 W tungsten light source, an InSb/HgCdTe sandwich detector and an optical filter (wavenumber range <4000 cm −1 ) were used.The date of the spectrum being recorded is given in a dd/mm/yyyy format and in the last column it is indicated in which figure in the main publication the corresponding spectrum is shown.The molecular structures of N555, MN4, MN5 and MMCN were optimized by using three-body-inclusive D3-dispersioncorrected [2,3] B3LYP with the def2-TZVP basis set [4][5][6] (B3LYP/TZ) on Orca 5.0.3 [7][8][9][10] with the keywords ABC DEFGRID3 VERYTIGHTSCF VERYTIGHTOPT FREQ.One water was then attached to the monomers using Chemcraft version 1.8 and the generated monohydrates were preoptimized using Crest [11,12] .After that, the 2-4 lowest energy structures were reoptimized using B3LYP-D3/def2-TZVP on Orca 5.0.
Table S8: Relative electronic ∆E el and zero point corrected ∆E 0 energy and lowest wavenumber ν(imaginary/real) for different conformers using B3LYP-D3/ma-def2-TZVP.These conformers structures are shown in Fig. S1

Example input
For convenience, an example input for a relaxed coordinate scan is given in Tab.S10.
Table S10: Example input for relaxed surface scan in the ORCA 5.0.3 calculations at the B3LYP level of computation.In the input file, x x x x is needed to define the name of atoms HO...NC for torsion.type of calculation input Relaxed surface scan !B3LYP D3BJ ABC ma-def2-TZVP SlowConv VeryTightOpt VeryTightSCF defgrid3 Mass2016 %geom Scan D x x x x = 0, 360, 72 # Attention ORCA starts counting atom from 0 end end %pal nprocs 8 end %Maxcore 3000 xyzfile 0 1 axstart.xyz

Integration methods
To calculate the coupling constants for the postulated resonance between OHb and b2 (Model A, described in the main text and next section) or the pairwise resonances between OHb, b2 and b2ON (Model B, described in the main text and next section), the experimental fractional intensities r of OHb, b2 and b2ON are required.The intensities in the range 3000 -3380 cm −1 of the spectra shown in the Fig. 1 of the main text are evaluated.The fractional intensities are determined by four different integration methods and the mean values r as well as a measure for the scatter across the four methods ∆s (vide infra) of these independent methods are taken as realistic estimates and uncertainties for the analysis of the resonance.The four integration methods (I, II, III, IV) are described below and the resulting fractional intensities r and uncertainties ∆r of each method are given in Tab S11.All four methods are largely based on the NoisySignalIntegration method by Nils O. B. Lüttschwager [14], which allows for different settings of the integration windows and their variation.In brief, the program analyzes the noise in a given wavenumber range of the spectrum and uses this to simulate additional noise with the same characteristics to many samples before the integration is performed.The uncertainty ∆r is estimated as a 95% confidence interval of the resulting integral distributions and listed together with r in Tab.S11.

Method I
The more or less symmetric integration window around the band maximum is chosen so narrow that the signal remains consistently above the noise level.The integration boundaries are allowed to vary by 1 cm −1 .To give an example for the main band of the MN4 monohydrate, the low integration boundary is sampled in the 3285-3286 cm −1 range and the high boundary in the 3312-3313 cm −1 range.

Method II
The more or less symmetric integration window is larger, including significant noise traces beyond the wings of the signal, whose contributions should cancel on average for an ideal baseline.The integration boundaries are allowed to vary by 3 cm −1 .In the MN4 example, the boundaries are chosen from the ranges 3275-3278 cm −1 and 3320-3323 cm −1 .

Method III
The integration boundaries are allowed to vary between the extreme values of methods I and II.Staying with the MN4 example, the integration is carried out from 3275-3286 cm −1 to 3312-3323 cm −1 .

Method IV
The integration is based on a symmetric window between 30 and 40 cm −1 in size around the band maximum.For the main band of MN4, the maximum is at 3299cm −1 and the sampled integration window ranges from 3279-3284 cm −1 to 3314-3319 cm −1 .

Average intensity fraction
The fractional intensities from the four integration methods are averaged to obtain the estimated intensity fraction r listed in Tab.S11 for each band.To estimate the associated uncertainty due to the method used, the probability distribution histograms of all four integration methods are drawn together and the uncertainty ∆s is calculated as one half of the span between the higher 1σ deviation of the highest histogram and the lower 1σ deviation of the lowest histogram.These results are depicted in Tab.S11.

Model A
In model A, there is only a 1:2 Fermi resonance between the bound OH stretching vibration of water (OHb) and the bending overtone of water (b2), explained in detail in the main text.The coupling constant W 2 is calculated using equation S1 with the ratio of the intensity fractions of OHb and b2 and the results are given in Tab.S12.The anharmonic peak position of OHb for Fig. 1 in the main text (dashed arrow) is derived from the equation S2.
Table S11: Experimental intensity ratio r and an error margin ∆r of four integration methods and the average realistic intensity fraction r and uncertainty error ∆s for b2, OHb and b2ON of amine-water complexes.The last column provides full widths at half maximum (FWHW) in cm −1 for the bands which are integrated.

Figure S1 :Figure S2 :
Figure S1: The torsional scan of N555+water with the basis set ma-def2-TZVP giving the relative energy of the torsion of the free OH bond of the water molecule over the amine rotating along the H-bond between water and nitrogen.As N555 is symmetric, three equivalent local minimum structures for N555 are found in the 360°torsional scan.

Figure S3 :Figure S4 :Figure S5 :Figure S6 :
Figure S3: The torsional scan of MN5+water with the basis set ma-def2-TZVP giving the relative energy of the torsion of the free OH bond of the water molecule rotating along the H-bond between water and nitrogen over the amine.There is only one local minimum structure for MN5 monohydrate according to energy diagram.

Table S1 :
Table of investigated chemicals, the introduced code names (supplement and main document), their CAS number, the supplier, purity and Lot#.

Table S3 :
Harmonic DFT predictions on B3LYP/TZ level of theory of low wavenumber modes for the four investigated amines (monomers and monohydrates).The monohydrate modes with intermolecular motion character which may modulate the water Fermi resonance or appear as OHb combination bands are marked with different colors and labeled in the empty monomer field with an arrow.The soft in plane (ip) bending motion is given in green and the out of plane (op) bending motion in orange, the torsion (t) of the free OH of the water is shown in violet, the movement changing the distance between water and amine (ON) is depicted in brown, the in plane libration (Lip) is given in blue and the out of plane libration (Lop) in magenta.The other vibrations (black) are amine-specific (see Fig.2in the main text).If an intermolecular mode harmonically mixes with an amine mode, both are labeled in the corresponding color in both rows. ) amine modes are shown in the Tab.S3 to recognize six newly generated vibrations in monohydrates.

Table S5 :
xyz coordinates of MN4 water structure in Å optimized at the B3LYP/TZ level on ORCA 5.0.3.The non-pairwise C-H of the methyl group is pointing away from the water unit.

Table S6 :
xyz coordinates of MN5 water structure in Å optimized at the B3LYP/TZ level on ORCA 5.0.3.The non-pairwise C-H of the methyl group is pointing away from the water unit.

Table S7 :
xyz coordinates of MMCN water structure in Å optimized at the B3LYP/TZ level on ORCA 5.0.3.