Tipping the Scales: Spectroscopic Tools for Intermolecular Energy

Perspective Cite This: J. Phys. Chem. Lett. 2017, 8, 5656-5665

pubs.acs.org/JPCL

Tipping the Scales: Spectroscopic Tools for Intermolecular Energy Balances Anja Poblotzki, Hannes C. Gottschalk, and Martin A. Suhm* Institut für Physikalische Chemie, Universität Göttingen, Tammannstraße 6, 37077 Göttingen, Germany ABSTRACT: Intermolecular energy balances are supramolecular complexes with a nearly degenerate bistable docking structure and low barriers in between, which can be tuned by chemical substitution to prefer one or the other site. The docking preference can be probed by forming the complexes in a supersonic jet expansion and by measuring their spectroscopic signature. Linear spectroscopies are shown to be well suited for this purpose, in particular when they are assisted by more sensitive techniques and by approximate computed photon interaction cross sections. Molecular analogues of conventional beam balances, seesaw balances, and torsional balances are discussed, all based on noncovalent interactions. The discrimination of energy differences down to the sub-kJ/mol level is demonstrated. The correspondence to intramolecular torsional balances in NMR spectroscopy is outlined. Besides highlighting conformational preferences, the results of intermolecular balance experiments can serve as critical benchmarks for an accurate description of intermolecular forces and zero-point vibrational energies.

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energies, a physical chemist is always tempted to resort to relative energies ΔE. After all, most of chemical thermodynamics and reaction kinetics works on that principle, and even the absolute dissociation energy of a complex is obviously an energy difference, comparing to infinitely separated fragments. If a modified challenge is to determine subtle energy differences ΔEB−A between neighboring molecular arrangements A and B within a supramolecular complex, this is not trivial, either. The focus on energies (ΔE0B−A) rather than free energies demands low temperatures, close to absolute zero. Spectroscopy is very good at measuring accurate energy differences as transitions hν between molecular levels, but these transitions rarely involve more than one local minimum structure.7,8 One solution is to simultaneously measure an ensemble of structures prepared in such a way that their abundances cA, cB reflect their relative energy. For molecular complexes, supersonic expansion into vacuum is usually the method of choice. To be close to equilibrium, the slow density decay in slit jet expansions provides an advantage,7,9 whereas the cooling of barrierless degrees of freedom such as rotation is superior in pinhole expansions. However, more relevant in the present context is the cooling across barriers ‡, which separate one local minimum from another. This requires many collisions with suitable collisional cooling partners and most importantly low enough barriers (ΔE‡B→A), to prevent freezing of the ensemble distribution at conformational temperatures Tc close to the nozzle temperature Tn and thus mixing in some entropy information. Pickup in helium nanodroplets often achieves the opposite goal of freezing the free energy landscape at

tructure and energy are the key parameters for a quantitative description of molecular matter. Within the Born−Oppenheimer approximation, their interdependence defines local minima (say A and B) and connecting transition states (‡) as stationary points on a multidimensional potential energy hypersurface. Experimental methods that provide absolute structural and energy information for such local minima are very attractive. Of course, even at low temperatures, zero-point vibrational energy acts as a spoilsport in the direct comparison between theory and experiment, but for many molecular systems, the harmonic approximation or perturbative anharmonic corrections to it are believed to be sufficient. In the field of noncovalent interactions or molecular docking, supramolecular structure and absolute dissociation energy D0 into the molecular units are important goals. The most versatile experimental techniques to tackle these challenges are based on spectroscopy. Microwave spectroscopy features prominently for structure, even more so after the introduction of chirped pulse techniques.1 It only needs a permanent dipole moment to work and if that is missing, rotational coherence spectroscopy can be used in favorable cases.2 Accurate energy information can be more difficult to obtain. D0 measurements often rest on fragment energy analysis and threshold identification.3,4 These are challenging experiments with specific molecular restrictions, which are only practiced by a small number of groups worldwide. There is a substantial need for techniques that provide energy information about noncovalent interactions on a broader basis, extend to larger systems, and assist in the development of improved theoretical methods. The case of many-body dispersion5 and the difficulties in calculating reliable molecule−surface interactions6 underscore this. In the absence of broadly applicable techniques for absolute (dissociation) © 2017 American Chemical Society

Received: September 2, 2017 Accepted: November 2, 2017 Published: November 2, 2017 5656

DOI: 10.1021/acs.jpclett.7b02337 J. Phys. Chem. Lett. 2017, 8, 5656−5665

The Journal of Physical Chemistry Letters

Perspective

Figure 1. Scheme of an intermolecular energy balance, illustrating the quantities introduced in the text.

deposition temperature, which is obviously also attractive.10 Here, we focus on experiments that allow for isomerization down to low temperatures. Figure 1 describes the concept of such barrier-crossing approaches. If the barriers need to be low, the energy differences between the connected isomers cannot be much larger, and the Boltzmann population at low temperature further restricts accessible differences to low values. The goal here is to judge energy differences between isomers of molecular complexes ΔE0B−A on the order of ±0.4 to ±4 kJ/mol, corresponding to effective conformational freezing temperatures Tc between 20 and 200 K, if 10% of a minor isomer can still be detected in the presence of the major one. This follows from a simple Boltzmann distribution in terms of ΔE0B−A and the abundance ratio cB/cA between the excited (B) and the ground state isomer (A):

However, the population of stiff modes is low even at Tn, and furthermore these stiff modes will be essentially the same for both isomers. For the six newly created, soft intermolecular degrees of freedom, low vibrational temperatures may again be implied. The same is plausible for the effective conformational temperature in the case of low interconversion barriers, as isomerization then becomes a large amplitude variant of intermolecular vibration. Clearly, these simplifying assumptions work better for newly formed complexes from rigid subunits than for conformationally flexible molecules, where a certain persistence of the initial conformational population at the nozzle temperature Tn must be expected. Although the neglected partition functions are accessible from quantum chemical calculations, at least within the rigid rotor and harmonic oscillator approximation, their explicit use suffers from the wide range and difficult measurement of effective temperatures for the various degrees of freedom of jet-cooled molecules. The simplified Boltzmann formula is thus equivalent to neglecting or relaxing any remaining entropy effects under the supersonic jet expansion conditions, except for symmetry factors. The same reasoning applies to zero-point energy contributions, which largely cancel between A and B, except for some of the newly created degrees of freedom and perhaps the directly interacting bonds. Although these are often particularly anharmonic modes, their anharmonicity is expected to change only moderately between A and B.11 Therefore, the harmonic approximation to zero-point energies is less critical for conformational energy differences ΔE0B−A than for dissociation energies D0, where the new vibrations in the complex have rotational and translational counterparts in the separated fragments. Strictly speaking, these assumptions need verification by extended anharmonic calculations, or else by consistent performance across a wide range of similar systems. Note that the population measurement only supplies the ratio of the energy difference to the effective conformational temperature, ΔE0B−A/Tc. If the former is to be quantified explicitly beyond its sign and rough magnitude, some estimate of the latter is needed.

⎛ ΔE 0 ⎞ g cB = B exp⎜ − B − A ⎟ cA gA RTc ⎠ ⎝

If the symmetry for both docking products is the same, their symmetry weights g cancel. This expression follows from the more general statisticalmechanical relationship for gas phase isomerizations in the electronic ground state ⎛ ΔE 0 ⎞ g z rot(T rot)z vib(T vib) cB = B Brot rot Bvib vib exp⎜ − B − A ⎟ cA gA zA (T )zA (T ) RTc ⎠ ⎝

if a few assumptions about effective rotational, vibrational and conformational freezing temperatures are made. The rotational temperature Trot is assumed to be so low (typically 5−20 K for helium slit jet expansions) and uniform that the corresponding partition functions of the docking isomers zrot A,B do not differ much and thus cancel each other. The heavier the acceptor molecule, the better this approximation is expected to be. For vibrational partition functions zvib A,B, such a cancellation is less obvious, as the corresponding temperatures Tvib differ widely among the vibrations, ranging from Trot for soft torsions to the nozzle temperature Tn for stiff intramolecular vibrations. 5657



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contact is rather biased toward one of the interactions, substitution can often tune toward the competing interaction. Ideally, a perfectly balanced situation can be created and probed. This may serve as a sensitive reference case for quantum chemical predictions even if the residual energy difference between the competing isomers cannot be directly measured. The qualitative achievement of a balanced situation can thus be turned into a quantitative test case for quantum chemistry. This strategy is somewhat akin to the Wheatstone bridge as a traditional measurement device for electrical resistances based on a balanced situation which is created by tuning one of the resistors to obtain zero bias.

Assuming for the moment that such techniques for competing docking isomers can be developed and applied, and that the discussed approximations are valid and a conformational temperature Tc can be estimated, what would the resulting energy differences possibly be good for? Energy differences of this magnitude determine whether isolated n-heptadecane exists in a stretched or folded form, due to noncovalent interactions between the chain ends.12 They decide whether the dimer of the peptide bond model Nmethylacetamide engages the N- or the C-terminal lone electron pair of the hydrogen bond acceptor CO group.13 They determine whether a methanol solvent molecule is embedded in the aromatic cleft of the lignin model diphenylether or else forms a classical hydrogen bond with the ether oxygen.14 The same is true for anisoles15 or furans16 as ambivalent docking centers for solvent molecules (Figure 2).

Which spectroscopic tools are most suitable for such intermolecular balance experiments? The key question of this perspective is, Which spectroscopic tools are most suitable for such intermolecular balance experiments and how do they perform in selected cases? For a given donor−acceptor pair, the spectroscopic challenge is 3fold: detection of the isomeric molecular complexes in the cold gas phase, identification of their structures and binding patterns, and finally quantification of their abundance to extract information on the relative stability. For detection, sensitive linear supersonic jet spectroscopy techniques such as Fourier transform infrared (FTIR)19 or spontaneous Raman scattering13 are not very restrictive on the molecular systems, as long as these are volatile enough to realize carrier gas mixtures in the 100 ppm range. Any molecule offers IR and/or Raman active fundamental transitions, but obviously these should be sensitive to aggregation and to the investigated isomerism to be useful. This is typically the case for hydride stretching modes,11 which are strongly affected by hydrogen bonding. However, hydride bending13 and librational,19,20 carbonyl,13 and backbone modes12 have also proven to be quite sensitive to conformation and aggregation, such that monomer signals can be clearly distinguished from those of complexes. Molecular system sizes with interesting docking options have only become accessible to such techniques in recent years.14 Aromatic systems, which are particularly attractive because of their tuneability and π-cloud hydrogen bond options, have only been studied occasionally by such techniques.11 This has to do with the limited heating options for these linear techniques, which in turn is related to their large substance consumption, because continuous13 or very long pulse expansions are typically needed.19 Fortunately, many aromatic systems are accessible to a very rich and powerful set of pulsed UV/IR14,21,22 and stimulated Raman techniques.23 These methods have much lower substance consumption, due to sensitive fluorescence or ionization detection which is synchronized to short gas pulses. They usually allow for size and conformational selectivity by parking the UV laser on a given electronic transition and probing the vibrational spectrum associated with it. It is still meaningful to occasionally probe aromatic systems with linear techniques, because fast processes in the electronically excited state, fragmentation, and other issues of action spectroscopy may sometimes distort the information. Furthermore, any comparison between aromatic and nonaromatic systems profits from a bridging technique which can access both on the same footing. Another powerful technique, only restricted to polar molecules, is microwave

Figure 2. Examples of intermolecular balances involving ethers and amides with small docking energy differences between the sites indicated by arrows.

In the case of benzofuran,16,17 a triple choice between two π systems and an oxygen atom is well within this energy window for a solvating alcohol. In larger biological systems at room temperature, the relevant free energy differences between docking sites are often somewhat larger due to multiple interactions, and they are also controlled by entropy differences. However, the latter are a source of potential error compensation, and one should only trust computational methods that are also able to correctly describe energy and entropy effects separately, rather than just their sum at a specific temperature. Therefore, there is a definite need for experimental methods that can check theoretical models on their low temperature, low energy difference predictability. The sub-kJ/mol to kJ/mol relative energy window addressed in this work is the typical range in which variations between different basis sets, between different density functionals, between different dispersion corrections, between pairwise and many-body dispersion, between canonical and spincomponent scaled MP2, between CCSD and CCSD(T) or between harmonic and anharmonic zero-point energy treatments happen for intermolecular interactions. This is particularly true if the molecular docking sites differ substantially in their character, such as in oxygen/π-cloud, steric repulsion/dispersion attraction, electrostatics/dispersion, π−π/σ−σ attraction or halogen/hydrogen bonding competitions. Reliable experimental energy sequences also define important reference points to better understand the physical contributions to intermolecular interaction, e.g., provided by symmetry-adapted perturbation theory.18 Such competing situations may be viewed as intermolecular beam balances, which can tip in one or the other direction depending on subtle differences and changes (Figure 1). In the following, we denote the molecule that offers alternative docking sites “acceptor” and the (typically more simple) docking molecule “donor”, irrespective of any hydrogen bond or other donor−acceptor convention involved in the individual interaction. Both the donor and the acceptor can be adjusted to influence this energy balance.15 Therefore, even if the primary 5658



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Figure 3. Schematic levels and transitions involved in the spectroscopic tools to elucidate the different docking isomers A and B and their energy sequence.

spectroscopy based on coherent pulsed excitation.1,14 Its extremely high spectral resolution and the new broadband capabilities even allow one to detect isotopologues of molecular complexes in natural abundance.24 These techniques are schematically summarized in Figure 3. Isomer detection alone is not sufficient for an intermolecular balance experiment. Identification of the docking site at the acceptor molecule is essential and requires different strategies for different spectroscopies. Some of them are purely experimental, others rest on broad experience with related systems and still others use quantum-chemical predictions as a guideline. In linear FTIR and Raman spectroscopy, the spectral resolution is typically not large enough to distinguish moments of inertia and thus different structures in a direct way. For certain interactions, there are still some empirical tools. Directed hydrogen bonds to polar atoms tend to show larger downshifts of the hydride stretch, larger anharmonicities (which are accessible by deuteration and in particular overtone studies), and more librational zero-point energy (which can be tuned by deuteration) than more flexible hydrogen bonds to extended π-systems.11 Cooperative hydrogen bond patterns lead to larger shifts than isolated hydrogen bonds. Furthermore, quantum-chemical harmonic predictions for frequency shifts of hydride stretching fundamentals with different acceptor sites can be quite robust and helpful for assignment. For UV/IR techniques, the complexation shift on the UV chromophore can often tell the difference between docking sites. Dispersed fluorescence can give additional hints by unveiling certain lowfrequency modes of the complex.17 If theoretical predictions for UV and IR differences correlate, they further support an assignment. In microwave spectroscopy, the structure of a complex can in principle be worked out by systematic isotope substitution, but with increasing system size, this soon becomes impractical.24 Microwave/infrared (MW/IR) double resonance experiments could be imagined to correlate the vibrational signature with the rotational signature. Very often, it is sufficient to compare theoretically predicted rotational constants and dipole components with experimental frequen-

cies and relative intensities to distinguish two isomers.14 It should be noted that all techniques must also carefully differentiate 1:1 complexes from higher aggregates and homoaggregates of the components, but there is usually sufficient evidence for that by tuning the concentration, analyzing the ion mass, or looking at the rotational constants. Once the docking isomers have been identified by one or more of the techniques described above, quantification is needed to judge their abundance ratio which forms the core of the Boltzmann analysis for the energy balance. Sometimes, the estimation of a similar abundance of both isomers within a factor of 2 or 3 is sufficient for the judgment of computational predictions, in particular at low conformational temperature. This can be achieved in all discussed methods, by simply using approximate (empirical or theoretical) evidence for UV, IR, Raman or MW transition strengths. If a more accurate quantification is desired, it is almost unavoidable to resort to theoretical predictions of photon−molecule interaction cross sections σ (Figure 1). As these transition strength predictions are only weakly correlated with relative energy predictions, it is legitimate to use the former as input in order to judge the latter by the output.15 This assumes that the transition strengths are sufficiently robust, which is usually the case if they are large. A large oscillator strength, dipole derivative, polarizability derivative or dipole component is likely to remain relatively large upon refinement of the calculation, whereas small transition moments can be extremely sensitive to perturbations and variations. When applicable, linear IR or Raman spectroscopies can thus have a distinct advantage, because large dipole and polarizability derivatives are a precondition for observability. Ratios of such transition moments between isomers σB/ σA computed at the same level are even more reliable, because methodical deficiencies tend to cancel. Furthermore, all signals IA, IB are recorded simultaneously such that source fluctuations cancel out. In UV/IR, one needs reliable predictions for two unrelated transition moments and has to carefully check for nonlinear saturation effects and source stability before interpreting depletion effects quantitatively. In coherent MW 5659



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Before addressing the essential triad of isomer detection, identification, and quantification for a single molecular balance system, one normally has to screen different donors and acceptors for suitably balanced and sufficiently low barrier cases. This is best done by a combination of linear spectroscopies and exploratory calculations. It may not appear meaningful to spend much time on isomeric pairs with large (>2 kJ/mol) energy separation. They will only provide spectral signatures of a single isomer and cannot challenge any but the poorest quantum chemical models.15 However, they can still be very useful to calibrate the IR or Raman signature and to validate some of the assumptions implicit in the balance concept, such as the presence of sufficiently low interconversion barriers. Assume a system that is predicted to have only one isomer within a 4 kJ/mol window but shows two spectral features that are not due to anharmonic resonance or different degrees of aggregation. This clearly indicates kinetic trapping behind high or broad barriers,15 which is undesirable in this context. After identifying and quantifying an interesting molecular balance case that is well described by theory, it is mandatory to start exploring the chemical space around it to see whether the agreement persists. Any quantum chemical model can be successful in reproducing a single data point, simply based on fortuitous error compensation. If the donor and acceptor systems are systematically varied by substitution and derivatization and the theoretical model follows all the induced balance changes, the likelihood of a fundamentally correct description can be increased by orders of magnitude. Again, this calls for linear spectroscopy as a routine exploration tool and for support by MW and UV/IR spectroscopy focused on limiting, contradicting, or otherwise decisive systems. Once the numerous data sets of experimental populations as a function of predicted energy differences fall on a reasonably smooth curve that goes through equipopulation at zero energy difference, two things are achieved: The theoretical model is

excitation spectra, line intensities are also not easy to analyze quantitatively, in particular for narrow cavity resonances, but the modern broadband techniques have the advantage of recording different transitions simultaneously, and intensities are generally more robust. Summarizing, in favorable cases, linear spectroscopies can be used for all three steps of the intermolecular balance experiment once supplemented with some guiding theoretical predictions, which do not have to offer relative energy accuracy better than a few kJ/mol. An example is the M06-2X functional, which provides grossly wrong energetics of the OH-π to OH-O competition in methanol−anisole complexes15 and also not the best structural predictions, but still provides quite reasonable IR intensity ratios to be used in the translation from signal strength to approximate abundance. However, there are other cases where additional input from MW and UV/IR spectra is definitely needed for the correct conclusions.14 Standalone balance experiments based on UV/IR or MW spectra are most feasible for qualitative conclusions on nearly perfect balance situations.17 As MW assignments can be demanding and systematic UV/IR measurements are rather time-consuming, it is anyway better to start with a linear vibrational spectroscopy investigation, if the volatility is sufficiently high to provide enough signal strength for these intrinsically less sensitive methods. Intermolecular balance experiments thus provide fertile ground for multiexperimental approaches toward the testing of quantum chemical performance.

If the systems are systematically varied, the likelihood of a fundamentally correct quantum chemical description can be increased by orders of magnitude.

Figure 4. Experimental fraction cπ/(cO+cπ) of π-docking versus the calculated (three-body-inclusive dispersion-corrected B3LYP25) energy difference for dimers of methanol with different acceptor molecules. The gray comfort zone accounts for up to 20% kinetic trapping of the less stable structure in the experiment and up to 0.5 kJ/mol error in the harmonically evaluated zero-point energy difference. 5660



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Figure 5. Infrared spectra of 2-t-butylfuran/methanol at two different methanol concentrations.

Figure 6. Example of a carbonyl group balance that allows one to judge theoretical predictions on a sub-kJ/mol scale.

there is evidence that the conformational freezing temperature drops with dilution and heavier carrier gases, this still needs systematic exploration16 and the effects of dilution are rather subtle. We are just at the start of such screening/detection/ identification/quantification/variation sequences, which promise to provide significant constraints on the quality of quantum chemical methods in describing noncovalent interactions for families of commonly observed interactions. An important family started with methanol−anisole, where the π-docking isomer was hardly detectable in competition with O-docking.11

validated and approximately uniform conformational freezing temperatures Tc across the experimental data sets may be assumed. An example of such a curve is illustrated in Figure 4. If Tc were below 30 K (the value used for the limiting Boltzmann curves), more data points would follow the 0% and 100% π fraction horizontal lines and the ΔE = 0 vertical line, i.e., a step function as a function of the energy difference. If conformational freezing happened already close to room temperature, data points would tend to fill the 20−80% π fraction band. Partial outliers such as the point at −3 kJ/mol actually find plausible explanations due to unusually broad barriers.15 While 5661



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Intermolecular balances are not restricted to scale-like systems, where one interaction “pulls” more than the other. Intermolecular torsional balances in analogy to Cavendish’s two centuries old gravitational balance can be imagined. Two molecules connected via an XH-Y hydrogen bond have multiple interaction minima along the torsion coordinate, in which Y is rotated more or less around the hydrogen bond axis at fixed X. Small complexes like methanol dimer usually find a single preferred torsional angle (within zero-point motional amplitude) along this nearly barrierless coordinate, but for more bulky species X and Y, there could be bistability and a high sensitivity to substitution. Methanol−ethene is an archetypical example, where the ethene unit rotates almost freely around the hydrogen bond.29 Any substitution at the alkene acceptor and optionally also at the alcohol donor introduces imbalances and a corrugated torsional potential to be predicted by quantum chemical calculations. If these imbalances generate at least two minima along the torsional path, they can be probed by spectroscopy. A recent example is the dimer of hexafluoroisopropanol after N2 decoration.30 Finally, such energy balances are not restricted to dimers. Rod-like isolated molecules like n-alkanes12 or oligoglymes can assume stretched and folded conformations and the folding penalty may or may not be overcome by nonbonded attraction between the chain ends. Another example is the cis/trans isomerism of amide bonds, which can be manipulated by adding substituents to the C- and N-terminus,13 which may interact through space in repulsive or attractive ways. Such bistable rod-hairpin systems may be considered as intramolecular torsion balances. The driving forces are just the same as in intermolecular balances, but the interacting ends are covalently attached to each other at the torsion link. In both cases, the isomerization barriers are substantially higher, moving them further away from energy control into the regime of kinetic trapping.31 Alkane or amide folding may also be viewed as a very simplified version of the ingenious Wilcox torsion balance,32 which is used in solution phase to measure free energies of interaction between two ends of a molecule and has recently been extended to aryl−aryl and N−aryl torsion.33 Like the examples discussed previously, it requires at least “two gently restricted conformational states”32 to work. Unlike the examples discussed previously, a Wilcox torsional balance in solution also involves sizable solvation and entropy effects, which are not always easy to separate from the isolated molecule energy trends.34 Therefore, the gas phase energy balances presented here form a useful and important complement to the solution phase free energy balances which are typically probed by NMR.32,33,35,36 However, a definite advantage of torsional balances in solution is the much higher tolerance to sizable interconversion barriers.37 In supersonic jets, these quickly lead to kinetic trapping and thus complicate the interpretation or even lead to free energy control at the preexpansion temperature. Therefore, the old problem in protein folding, whether a native conformation corresponds to the global minimum or to a kinetically stabilized form, re-emerges at a much lower temperature scale.

A large number of substituted anisoles followed, some of them bringing π-docking closer in energy or even exceeding the stability of the O-docking alternative. This allowed clear separation of poor from acceptable methods for the description of the balance between these two types of hydrogen bond, which have different dispersion contributions along the hydrogen bond and besides it.15 Currently, we are exploring variations of the donor molecule. A second family of compounds that looks promising are furans.26 Their balanced docking behavior has been pioneered by the Nibu group using UV/IR techniques, studying benzofuran in combination with methanol.17 We have confirmed that result and extended it to furans without an attached benzene ring.16 Due to the strong delocalization of oxygen electron density into the aromatic furan ring, a close competition of oxygen- and carbon-docking was observed. A recent study of different popular density functional approaches to the basic furan−methanol case underscores that energy balance experiments are very important for this system. Predicted docking energy differences range from −3 to +5 kJ/mol, spanning more than 50% of the total binding energy of this dimer.27 A double-blind benchmark on a small family of increasingly methylated furans was initiated to identify theoretical methods which are able to describe this kind of interactions properly (www.goebench.net). They shall then be further tested by extending the sample size. Figure 5 contains the newest result for methanol docking on 2-t-butylfuran, which is predicted and found to clearly prefer the π site. Due to the importance of relative peak intensities of docking isomers for benchmarking, we go through major efforts to achieve lower temperatures and to avoid contamination from larger clusters. In the case of 2,5-dimethylfuran,16 the best IO/Iπ intensity ratio in diluted helium expansions is now 2.0(1) for methanol and 2.4(2) for methanol-d1. These values are included in Figure 4. Deuterium favors the more localized docking site, which is already predicted in the harmonic approximation. Currently, we are exploring the suitability of the two lone electron pairs of carbonyl groups as a molecular balance toward hydrogen bond donors. Depending on the two substituents of the >CO group and the structure of the donor, there could be nearly isoenergetic situations. Indeed, the dimer of Nmethylacetamide13 shows such a nearly isoenergetic isomerism with clearly distinct fundamental N−H stretching wavenumbers. A potential disadvantage of this seesaw-type balance28 is that there will be no important relative assignment clues from deuteration, as the two docking sites are similar in their electrostatics and anisotropy, and zero-point-corrected energy differences ΔE0 will differ little from electronic ones, ΔEel. Steric repulsion can help to differentiate the isomers, as the hydride stretching wavenumber is sensitive to the angle of approach to the carbonyl group. The complex of methanol with acetophenone provides a reference case (FTIR spectra in Figure 6). It shows a 3-fold higher concentration for carbonyl docking on the methyl side, which may be assigned to the more downshifted signal due to the ideal hydrogen bond angle. Deuteration of the OH group is only used to rule out carbonyl overtone interference, but does not provide additional assignment hints. The theoretical prediction is consistent with Tc ≈ 70 K. Anharmonic zero-point energy corrections are likely small as the harmonic ones do not exceed 0.2 kJ/mol. By substituting the acetophenone and/or the alcohol, interactions between the different organic residuals can be probed very sensitively.

The relative energy information provides a further dimension for the critical evaluation of computational methods. 5662



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conformational temperature in the experiment remains as unknown as the precise experimental energy difference and will depend sensitively on (and scatter with) the height and width of the interconversion barrier. A method that symmetrically overestimates docking energy differences by a fixed factor will not necessarily fail the test, as it will just mimick a systematically lower conformational temperature. A method that systematically overestimates a certain docking position by a fixed amount will be disqualified by its curve shift, but might still serve to support a choice of systems with uniform barriers, if the prediction is smooth. A method which yields widely scattered data in Figure 4 is either poor or else indicates a wide variation or large size of interconversion barriers. Only the combination of many systems and several computational methods will allow for safe conclusions. As in any new concept, the validity range of the underlying approximations such as degree of equilibration and cancellation of partition functions has to be explored by as many different case studies as possible. We document examples for classical scale balances and seesawtype balances, and we propose torsion balances, all for intermolecular interactions. Linear FTIR or Raman spectroscopy, often complemented by UV/IR and MW spectroscopy, provides convenient access to these energy balances. Together with intramolecular torsion balances in the gas phase, they form an energy-focused complement to the free-energy intramolecular torsion balances probed by NMR in solution. In particular, they are much closer to computationally feasible and still accurate quantum chemistry predictions and can thus serve as energy-only benchmarks for such methods, without the complicating influence of entropy. For selected cases, it will be interesting to compare our findings for energy differences to absolute dissociation energy measurements,4 to see whether they are consistent. Finally, this is a call to supramolecular spectroscopists, either experimental or theoretical, to search for and to report close intermolecular docking competitions with distinct vibrational signatures connected by low barriers.

All these energy balances must be distinguished from another popular measure of the strength of an intermolecular interaction, in particular a hydrogen bond. The vibrational downshift of a hydride stretching fundamental vibration upon hydrogen bonding is often correlated with the bond energy. To stay within the balance metaphor, this would be a kind of spring balance, where the interaction partner stretches the hydride spring and lowers its spring constant. However, it has to be emphasized that this downshift can also be influenced by compression or distortion of the hydrogen bond due to other interactions between the molecules. In that sense, it is a local bond property that is affected by external constraints. The binding energy between two molecules, on the other hand, is an intrinsically global property involving all atoms of the interacting molecules and a compromise between attractive and repulsive forces of different directionality. Such an interplay of different contributions is best analyzed by energy decomposition schemes like SAPT.18,38 However, the goal of the present article was to discuss spectroscopic methods to determine observable energy differences. One may argue that for the benchmarking of quantum chemical methods, relative vibrational frequency information is much more suitable than energy information, because it can be determined orders of magnitude more precisely than relative conformational energy in most spectroscopic methods. However, energy is the primary quantity, whereas vibrational frequencies are second derivatives, which are very sensitive to structural deficiencies and challenging anharmonic effects. Therefore, spectroscopists are often satisfied with empirically scaled harmonic frequencies in reasonable agreement with experiment. Furthermore, the relative energy information derived from intermolecular balance experiments provides a further and rather independent dimension for the critical evaluation of computational methods, once such balance experiments can be broadly established. This is illustrated in Figure 7 (see also ref 30).

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Martin A. Suhm: 0000-0001-8841-7705 Notes

The authors declare no competing financial interest. Biographies

Figure 7. Advocating multiobservable approaches: Adding an energy dimension ΔE in the assessment of quantum chemical predictions A− H for two docking isomers discriminates more exclusively between poor (red) and satisfactory (blue) agreement than the relative spectral frequency dimension Δν alone does. Similar to the exploration of the chemical space, the spectroscopic space removes fortuitous success.30

In summary, we advocate the use of balanced, bistable docking situations between a multifunctional acceptor and a solvating donor in the adiabatically cooled gas phase to extract information on their relative energy order on a low to sub-kJ/ mol scale. Through systematic chemical modification, the performance of quantum chemical methods in predicting these docking energy differences can be tested, although the exact

Anja Poblotzki graduated from the University of Göttingen in 2014 and is currently working on her PhD under the supervision of Martin 5663



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(2) Felker, P. M. Rotational Coherence Spectroscopy: Studies of the Geometries of Large Gas-Phase Species by Picosecond Time-Domain Methods. J. Phys. Chem. 1992, 96, 7844−7857. (3) Rocher-Casterline, B. E.; Ch’ng, L. C.; Mollner, A. K.; Reisler, H. Communication: Determination of the Bond Dissociation Energy (D0) of the Water Dimer, (H2O)2, by Velocity Map Imaging. J. Chem. Phys. 2011, 134, 211101. (4) Maity, S.; Ottiger, P.; Balmer, F. A.; Knochenmuss, R.; Leutwyler, S. Intermolecular Dissociation Energies of Dispersively Bound 1Naphthol·Cycloalkane Complexes. J. Chem. Phys. 2016, 145, 244314. (5) Reilly, A. M.; Tkatchenko, A. Van der Waals Dispersion Interactions in Molecular Materials: Beyond Pairwise Additivity. Chem. Sci. 2015, 6, 3289−3301. (6) Wellendorff, J.; Silbaugh, T. L.; Garcia-Pintos, D.; Nørskov, J. K.; Bligaard, T.; Studt, F.; Campbell, C. T. A Benchmark Database for Adsorption Bond Energies to Transition Metal Surfaces and Comparison to Selected DFT Functionals. Surf. Sci. 2015, 640, 36−44. (7) Farrell, J. T.; Suhm, M. A.; Nesbitt, D. J. Breaking Symmetry with Hydrogen Bonds: Vibrational Predissociation and Isomerization Dynamics in HF−DF and DF−HF Isotopomers. J. Chem. Phys. 1996, 104, 9313−9331. (8) Kisiel, Z.; Dorosh, O.; Maeda, A.; Medvedev, I. R.; de Lucia, F. C.; Herbst, E.; Drouin, B. J.; Pearson, J. C.; Shipman, S. T. Determination of Precise Relative Energies of Conformers of nPropanol by Rotational Spectroscopy. Phys. Chem. Chem. Phys. 2010, 12, 8329−8339. (9) Zischang, J.; Lee, J. J.; Suhm, M. A. Communication: Where Does the First Water Molecule Go in Imidazole? J. Chem. Phys. 2011, 135, 061102. (10) Skvortsov, D. S.; Vilesov, A. F. Using He Droplets for Measurements of Interconversion Enthalpy of Conformers in 2Chloroethanol. J. Chem. Phys. 2009, 130, 151101. (11) Heger, M.; Altnöder, J.; Poblotzki, A.; Suhm, M. A. To π or Not to π − How Does Methanol Dock onto Anisole? Phys. Chem. Chem. Phys. 2015, 17, 13045−13052. (12) Lüttschwager, N. O. B.; Suhm, M. A. Stretching and Folding of 2-Nanometer Hydrocarbon Rods. Soft Matter 2014, 10, 4885−4901. (13) Forsting, T.; Gottschalk, H. C.; Hartwig, B.; Mons, M.; Suhm, M. A. Correcting the Record: the Dimers and Trimers of trans-NMethylacetamide. Phys. Chem. Chem. Phys. 2017, 19, 10727−10737. (14) Medcraft, C.; Zinn, S.; Schnell, M.; Poblotzki, A.; Altnöder, J.; Heger, M.; Suhm, M. A.; Bernhard, D.; Stamm, A.; Dietrich, F.; et al. Aromatic Embedding Wins over Classical Hydrogen Bonding − a Multi-Spectroscopic Approach for the Diphenyl Ether−Methanol Complex. Phys. Chem. Chem. Phys. 2016, 18, 25975−25983. (15) Gottschalk, H. C.; Altnöder, J.; Heger, M.; Suhm, M. A. Control over the Hydrogen-Bond Docking Site in Anisole by Ring Methylation. Angew. Chem., Int. Ed. 2016, 55, 1921−1924. (16) Poblotzki, A.; Altnöder, J.; Suhm, M. A. Subtle Solvation Behaviour of a Biofuel Additive: the Methanol Complex with 2,5Dimethylfuran. Phys. Chem. Chem. Phys. 2016, 18, 27265−27271. (17) Sasaki, H.; Daicho, S.; Yamada, Y.; Nibu, Y. Comparable Strength of OH-O versus OH-π Hydrogen Bonds in HydrogenBonded 2,3-Benzofuran Clusters with Water and Methanol. J. Phys. Chem. A 2013, 117, 3183−3189. (18) Jansen, G. Symmetry-Adapted Perturbation Theory Based on Density Functional Theory for Noncovalent Interactions. WIREs Comput. Mol. Sci. 2014, 4, 127−144. (19) Suhm, M. A.; Kollipost, F. Femtisecond Single-Mole Infrared Spectroscopy of Molecular Clusters. Phys. Chem. Chem. Phys. 2013, 15, 10702−10721. (20) Andersen, J.; Heimdal, J.; Wugt Larsen, R. The Influence of Large-Amplitude Librational Motion on the Hydrogen Bond Energy for Alcohol−Water Complexes. Phys. Chem. Chem. Phys. 2015, 17, 23761−23769. (21) Mons, M.; Robertson, E. G.; Simons, J. P. Intra- and Intermolecular π-Type Hydrogen Bonding in Aryl Alcohols: UV and IR−UV Ion Dip Spectroscopy. J. Phys. Chem. A 2000, 104, 1430− 1437.

A. Suhm. Her research interests include the control of dispersion interactions studied by multispectroscopical approaches.

Hannes C. Gottschalk is a PhD student in the group of Martin A. Suhm. He received his M.Sc. from the University of Göttingen in 2015. His research focusses on benchmarking intermolecular interactions using linear FTIR spectroscopy.

Martin A. Suhm is a professor of Physical Chemistry at the University of Göttingen since 1997. He is interested in the study of noncovalent interactions and dynamics, as revealed by linear vibrational spectroscopy techniques. A current focus is on experimental benchmarks for quantum-chemical methods in this field. For this purpose, one-of-itskind supersonic jet spectrometers are developed and applied in his group.

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ACKNOWLEDGMENTS We acknowledge financial support by the German Research Foundation (Su 121/5) in the context of the priority program SPP 1807, where intermolecular energy balances with particular focus on London dispersion effects are explored. We also thank our experimental cooperation partners Markus Gerhards, Samuel Leutwyler, Melanie Schnell, and Timothy Zwier for fruitful collaborations beyond linear vibrational spectroscopy. We profit from theoretical input by Georg Jansen and Ricardo Mata. Furthermore, we are grateful to Thomas Forsting, Robert Medel, Katharina Meyer, and Sönke Oswald for exploring different kinds of intermolecular energy balances as well as Sebastian Bocklitz for intramolecular chain-folding versions.

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REFERENCES

(1) Brown, G. G.; Dian, B. C.; Douglass, K. O.; Geyer, S. M.; Shipman, S. T.; Pate, B. H. A Broadband Fourier Transform Microwave Spectrometer Based on Chirped Pulse Excitation. Rev. Sci. Instrum. 2008, 79, 053103. 5664



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(22) Schwing, K.; Gerhards, M. Investigations on Isolated Peptides By Combined IR/UV Spectroscopy in a Molecular Beam − Structure, Aggregation, Solvation and Molecular Recognition. Int. Rev. Phys. Chem. 2016, 35, 569−677. (23) Golan, A.; Mayorkas, N.; Rosenwaks, S.; Bar, I. Raman Spectral Signatures as Conformational Probes of Gas Phase Flexible Molecules. J. Chem. Phys. 2009, 131, 024305. (24) Pérez, C.; López, J. C.; Blanco, S.; Schnell, M. Water-Induced Structural Changes in Crown Ethers from Broadband Rotational Spectroscopy. J. Phys. Chem. Lett. 2016, 7, 4053−4058. (25) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (26) Kumar, S.; Pande, V.; Das, A. π-Hydrogen Bonding Wins over Conventional Hydrogen Bonding Interaction: A Jet-Cooled Study of Indole···Furan Heterodimer. J. Phys. Chem. A 2012, 116, 1368−1374. (27) Jiang, X.; Liu, S.; Tsona, N. T.; Tang, S.; Ding, L.; Zhao, H.; Du, L. Matrix Isolation FTIR Study of Hydrogen-Bonded Complexes of Methanol with Heterocyclic Organic Compounds. RSC Adv. 2017, 7, 2503−2512. (28) Yamada, S.; Yamamoto, N.; Takamori, E. Synthesis of Molecular Seesaw Balances and the Evaluation of Pyridinium-π Interactions. J. Org. Chem. 2016, 81, 11819−11830. (29) Heger, M.; Mata, R. A.; Suhm, M. A. Soft Hydrogen Bonds to Alkenes: The Methanol-Ethene Prototype under Experimental and Theoretical Scrutiny. Chem. Sci. 2015, 6, 3738−3745. (30) Oswald, S.; Suhm, M. A. Experimental Reference Data for Hexafluorinated Propanol by Exploring an Unusual Intermolecular Torsional Balance. Angew. Chem., Int. Ed. 2017, 56, 12672−12676. (31) Zhang, D.; Blodgett, K. N.; Zhu, X.; Zwier, T. S. Single Conformation Spectroscopy of Suberoylanilide Hydroxamic Acid: A Molecule Bites Its Tail. J. Phys. Chem. A 2017, 121, 986−997. (32) Paliwal, S.; Geib, S.; Wilcox, C. S. Molecular Torsion Balance for Weak Molecular Recognition Forces. Effects of “Tilted-T” Edge-toFace Aromatic Interactions on Conformational Selection and SolidState Structure. J. Am. Chem. Soc. 1994, 116, 4497−4498. (33) Lypson, A. B.; Wilcox, C. S. Synthesis and NMR Analysis of a Conformationally Controlled β-Turn Mimetic Torsion Balance. J. Org. Chem. 2017, 82, 898−909. (34) Biedermann, F.; Schneider, H.-J. Experimental Binding Energies in Supramolecular Complexes. Chem. Rev. 2016, 116, 5216−5300. (35) Yang, L.; Adam, C.; Nichol, G. S.; Cockroft, S. L. How Much do van der Waals Dispersion Forces Contribute to Molecular Recognition in Solution? Nat. Chem. 2013, 5, 1006−1010. (36) Hwang, J.; Li, P.; Smith, M. D.; Shimizu, K. D. DistanceDependent Attractive and Repulsive Interactions of Bulky Alkyl Groups. Angew. Chem., Int. Ed. 2016, 55, 8086−8089. (37) Mati, I. K.; Cockroft, S. L. Molecular Balances for Quantifying Non-Covalent Interactions. Chem. Soc. Rev. 2010, 39, 4195−4205. (38) Sherman, M. C.; Ams, M. R.; Jordan, K. D. Symmetry-Adapted Perturbation Theory Energy Analysis of Alkyl Fluorine−Aromatic Interactions in Torsion Balance Systems. J. Phys. Chem. A 2016, 120, 9292−9298.

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Tipping the Scales: Spectroscopic Tools for Intermolecular Energy

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