Direct detection of polar structure formation in helium nanodroplets by beam deflection measurements
John W. Niman, Benjamin S. Kamerin, Lorenz Kranabetter, Daniel J. Merthe, Jiří Suchan, Petr Slavíček, Vitaly V. Kresin
1 Direct detection of polar structure formation in helium nanodroplets by beam deflection measurements
John W. Niman, [a]
Benjamin S. Kamerin, [a]
Lorenz Kranabetter, [b]
Daniel J. Merthe, [a],†
Jiří Suchan, [c]
Petr Slavíček,* [c,d]
Vitaly V. Kresin* [a] [a]
Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA [b]
Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria [c]
Department of Physical Chemistry, University of Chemistry and Technology, Technická 5, Prague 6, Czech Republic [d]
J. Heyrovský Institute of Physical Chemistry v.v.i., The Czech Academy of Sciences,
Dolejškova 3, 18223 Prague, Czech Republic
Abstract
Long-range intermolecular forces are able to steer polar molecules submerged in superfluid helium nanodroplets into highly polar metastable configurations. We demonstrate that the presence of such special structures can be identified, in a direct and determinative way, by electrostatic deflection of the doped nanodroplet beam. The measurement also establishes the structures’ electric dipole moments. In consequence, the introduced approach is complementary to spectroscopic studies of low-temperature molecular assembly reactions. It is enabled by the fact that within the cold superfluid matrix the molecular dipoles become nearly completely oriented by the applied electric field. As a result, the massive (tens of thousands of helium atoms) nanodroplets undergo significant deflections. The method is illustrated here by an application to dimers and trimers of dimethyl sulfoxide (DMSO) molecules. We interpret the experimental results with ab initio theory, mapping the potential energy surface of DMSO complexes and simulating their low temperature aggregation dynamics. 2
Introduction
Long-range intermolecular forces play an essential role in reactions at sub-Kelvin temperatures (see, e.g., the reviews in refs [1-4). For example, long-range interactions between polar molecules embedded in helium nanodroplets often dominate the outcome of their assembly reactions. This is facilitated by the low internal temperature (370 mK) of the nanodroplet medium as well as by its superfluidity. [5]
As a result, molecular reorientation and intermolecular reactions within nanodroplets are not perturbed by inhomogeneities present in other low-temperature surface and matrix isolation environments, making these “nano-cryo-traps” excellent hosts for exploring the physics and chemistry of cold molecular systems. [6]
A landmark demonstration of the action of long-range forces was furnished by experiments on HCN molecules sequentially picked up by a He nanodroplet beam. [7]
These linear molecules were guided by dipole-dipole forces to self-assemble into long chains aligned head-to-tail inside the nanodroplet. HCCCN was found to behave similarly. [8]
These chains rank among the most polar molecular systems ever observed in a molecular beam. In an “ordinary” environment thermal motion would drive them out of this type of metastable configuration, but within a very cold and inert liquid helium droplet they become long-lived. Data on formic acid, [9] imidazole, [10] and acetic acid [11,12] dimers suggested an analogous alignment mechanism. However, such an outcome is not universal in nanodroplet embedding. For example, two HCl molecules arrange themselves nearly at a right angle to each other [13,14] while water clusters form cyclic structures. [15]
The “decision” by polar molecules how to orient themselves upon approach depends on the strength of their dipoles, on their responsiveness to the mutually reorienting torques (i.e., their rotational constants and their accessible rotational quantum states), and on the directionality and flexibility of their bond formation. That is to say, the outcome depends on the shape of the intermolecular potential energy surface and on the barrier 3 heights encountered on the path to the final configuration. It is therefore interesting and informative to establish whether a molecular formation within a nanodroplet can reach its global energy minimum or finds itself trapped in a polar metastable state. However, often this is not a straightforward determination. The studies cited above based their conclusions on the interpretation of dopant infrared spectra or on inference from electron attachment mass spectrometry. Such assignments grow more difficult and less definitive with increasing size and/or complexity of the embedded molecules and their assemblies. In this work we describe a measurement which directly establishes the polarity of a molecular assembly, as well as determines its dipole moment. It makes use of electrostatic deflection of the doped nanodroplet beam. [16,17]
The technique is based on the fact that polar structures embedded within the superfluid matrix can be made nearly fully oriented by an external static electric field [18] and consequently experience an extremely large deflecting force from the field’s gradient. Such a high degree of orientation is unattainable for bare polyatomic complexes in a molecular beam. Whereas some relatively small and light molecules reach rotational temperatures T rot below 1 K with the use of seeded supersonic expansions and exhibit large deflections (see, e.g., refs [19,20]), this becomes impractical for heavier systems. For the purpose of an estimate, consider the classical Langevin function for the orientation of a molecular rotor in an external field ˆ Ez : coth 1/ z p p x x = − . This is a good approximation [21,22] for k B T rot >> B . Here p is the molecule’s dipole moment, z p is the average projection of this dipole on the field axis, / B rot x p E k T , and B is the rotational constant. For T rot above a few K and practical electric field strengths, the ratio x remains small even for dipole moments of several Debye (D), and in this limit / 3 1 z p p x . Therefore it is only when 4 the rotational temperature becomes very low, as enabled in the present case by helium nanodroplet isolation, that the orientation can approach saturation ( z p p → ). This effect has been taken advantage of in landmark experiments using pendular-state spectroscopy. [18] If the external electric field which orients the nanodroplet-submerged dipoles is designed also to have a strong gradient in the same direction, then these dipoles will experience such a strong sideways force ( ) z z
F p E z = that the massive doped droplets, comprised of tens of thousands of helium atoms, will be significantly deflected in their entirety. Thus, our procedure involves comparing the deflection profile of a singly-doped nanodroplet beam with that of a beam composed of multiply-doped nanodroplets. If, for example, the droplets containing two (or three, etc.) molecules show negligible deflection, we can immediately conclude that the dimer (trimer, etc.) has settled into a nonpolar configuration. A strongly deflected profile, on the other hand, immediately attests to the formation of a polar structure, and the magnitude of the deflection translates into the magnitude of this formation’s total dipole moment. This is a conveniently unambiguous measurement applicable to a wide range of molecules, from diatomic to polyatomic (including biological). Practically any molecular species that can be brought into the vapor phase with a pressure of only 10 -6 -10 -4 mbar can be picked up by the nanodroplet beam and thermalized within the inert viscosity-free medium. The thermalization proceeds by evaporative cooling: the molecules’ translational and internal energies are transferred to the superfluid matrix which has a very high thermal conductivity, and released via evaporation of surface helium atoms, promptly bringing the nanodroplet back to the original temperature. [5] Here we apply the deflection method to monomers, dimers and trimers of the dimethyl sulfoxide molecule (“DMSO,” (CH ) SO, molecular mass 78 Da). The molecule is nearly an oblate symmetric top, with rotational constants of [23,24] -1 , 0.231 cm -1 , and 0.141 cm -1 [25] p =4.0 D. The measurement clearly reveals the presence of highly polar dimers and trimers, i.e., the formation of metastable polar configurations abetted by the cryogenic nanodroplet environment. To our knowledge, this is the first direct non-spectroscopic identification of such a cold polar molecular assembly. Results and Discussion
Deflection profiles.
The experimental setup has been described in detail elsewhere. [16,17,26]
A nanodroplet beam is formed by cold nozzle expansion of pure helium gas. It passes first through a pick-up cell filled with DMSO vapor, and then between two high-voltage electrodes which create an electric field and a collinear field gradient directed perpendicular to the beam axis. Downstream, the beam enters through a slit into an electron-impact ionizer, and the intensities of the resulting molecular ions are recorded by a quadrupole mass spectrometer in synchronization with a beam chopper. The deflection induced by the electric field is determined by comparing the beam’s “field-on” and “field-off” spatial profiles which are mapped out by translating the detector chamber, with its entrance slit, on a precision linear stage. Molecules are picked up by helium nanodroplets via successive collisions in a Poisson process. [5]
Therefore it is important to correlate measured beam deflections with the specific number of molecules embedded in the droplet. In other words, when mapping out the deflection profile of a dopant ion peak in the mass spectrum, we need to ensure that it is not a fragment of a larger agglomerate. This is done by gradually increasing the vapor pressure in the pick-up cell and monitoring the mass spectrum for the appearance of molecular ions characteristic of progressively larger entities. For example, monomer ionization produces a strong (DMSO) + signal [27] at m =78 Da, hence if we measure beam profiles with the mass spectrometer set to this mass peak but with the vapor pressure low enough to suppress the corresponding characteristic 6 (DMSO) peak at m =156 Da, then we can be confident that the deflection principally corresponds to droplets carrying the monomer. Similarly, profiles measured at m =156 Da but before the appearance of the trimer’s signal must derive from the dimer, etc. Representative mass spectra are shown in the Supporting Information (SI). Fig. 1 shows the deflection profiles of helium nanodroplets containing one, two, and three DMSO molecules. The deflections are substantial despite the fact that the droplets are truly massive (~1×10 –3×10 He atoms, as described in the caption). Therefore we are immediately and directly informed by Fig. 1(b) that (DMSO) settles into a strongly polar configuration and not into its global minimum structure, because the latter would be symmetric with a zero dipole moment. [28] In order to assign an absolute value of the dipole moment to the dopant, we must keep in mind that the host nanodroplets are not all of the same size. The size distribution produced by the nozzle expansion is log-normal, and this translates into a convolution of pick-up cross sections, deflection angles, and ionization efficiencies. Our procedure [16,17] is to start with the profile corresponding to a single DMSO dopant molecule whose dipole moment is known. A fit to the deflected profile (by a Monte Carlo simulation of the pick-up, evaporation, deflection, and detection steps) is used to calibrate the droplet size distribution. Then by repeating the deflection measurement and its simulation with doubly- and triply-doped nanodroplets produced and detected under the same conditions, we can deduce the electric dipole moments corresponding to the dimer and the trimer. 7
Figure 1.
Profiles of (DMSO) n -doped helium nanodroplet beams. Blue: zero-field profiles, orange: deflection by a field of 82 kV/cm strength and 338 kV/cm gradient. Symbols: experimental data, lines: fits of the deflection process, as described in the text. The monomer profile mapped for a particular temperature T and stagnation pressure P of the He N beam source is used to determine the average N and width Δ N of the nanodroplet size distribution, and then fits to the dimer and trimer profiles for the same source conditions yield these dopants’ dipole moments. In (b) P=
80 bar, T= N , in (c) P=
80 bar, T= N . z p , i.e., the degree of orientation induced by the applied field. For the DMSO monomer this is carried out by diagonalizing the rotational Stark effect matrix (cf. ref [29]) using the components of the molecule’s dipole moment. [24] For the heavier dimer and trimer the classical Langevin-Debye formula is sufficiently accurate. [30]
In calculating the monomer’s Stark spectra one should keep in mind that rotational coupling to the superfluid [31] enhances the moments of inertia of the heavier molecular rotors by an average factor of ~2.5-3 compared with their gas phase value.
Since DMSO’s specific renormalization factor is not known, it was set to 2.6 in our data fitting procedure. We found that the inclusion of this factor had practically no effect on the deduced dipole of the dimer but shifted that of the trimer upward by n orientations within an applied 82 kV/cm field were found to be 86%, 97%, and 98% for n= Dipole moments.
From analysis of the measurements, we assign effective electric dipole moments of 7.2 D to (DMSO) and 8.6 D to (DMSO) , with an estimated accuracy of ±0.2 D and ±0.6 D, respectively. These values, which can be compared with the ground state moments of 0 D for the aforementioned symmetric dimer and 4.2 D for the trimer [28] (essentially a nonpolar dimer plus an unpaired monomer), establish the presence of highly polar metastable structures. In the cold superfluid environment these structures are steered into formation by the long-range intermolecular forces and are then unable to overcome the potential barrier leading to the global minimum configuration. Modeling of molecular complex formation.
To facilitate the interpretation of the above results, we supplemented the experiments with ab initio modeling of DMSO condensation. We optimized the geometry of DMSO dimers and trimers with the B3LYP functional with the aug-9 cc-pVDZ basis set. The DMSO complexes are dominantly bound by electrostatic forces but the dispersion interactions still play a non-negligible role. We have therefore used the D2 correction of Grimme. [32]
The approach was tested against the CCSD(T)/aug-cc-pVTZ method for the DMSO dimer, yielding similar energetics (see the SI). All calculations were performed in the gas phase: by considering complexes with helium atoms or within a dielectric continuum we found that the helium environment had a negligible effect on the structure and energetics. The potential energy surfaces (PES) were pre-screened with molecular mechanics (MM)-based metadynamics simulations [33] and the structures were then recalculated at the DFT level (see the SI for further information). The process of DMSO dimer formation was modeled with molecular dynamics (MD) simulations within the canonical ensemble. We used the Nosé-Hoover thermostat with a rather small value of = 0.01 ps. This corresponds to fast draining of extra energy from the system, so that at each time it essentially remains in equilibrium. A temperature of 5 K was chosen in order to accelerate the simulations. It is higher than in the experiment but the difference is small compared with the PES accuracy. We started with two DMSO molecules positioned at a distance of 20 Å between the two sulphur atoms with a random orientation. We then performed molecular mechanics simulations with the MM force field. [34] The molecules gradually approached each other while aligning their dipole moment. Since the MM force field does not reproduce the energetics of the minima sufficiently well, at the intermolecular distance of 10 Å we reset the simulations, switching from the force field to the more accurate semiempirical density functional tight binding (DFTB) method [35] with D3 dispersion correction. [36,37]
The system then continued to evolve in time for another 500 ps with a time step of 1 fs, using the velocity Verlet integrator. Dipoles along the path were recalculated at the B3LYP/aug-cc-pVDZ level. 10 The DFT and CCSD(T) calculations were performed in Gaussian09. [38]
Molecular dynamics simulations were performed in GROMACS 2018.4 [39] and the DFTB simulations in the DFTB+ 18.2 code. [35]
We also utilized our in-house MD code ABIN. [40]
Results of modeling.
Fig. 2 shows several low-lying minima of the DMSO dimer obtained from extensive mapping of its potential energy surface. The structures are divided into two classes of minima: non-polar and polar. The global minimum (complex D1) of (DMSO) has a symmetrical configuration with a zero dipole moment, consistent with the aforementioned work. [28] Structures D2 and D3 also belong to the low dipole manifold. Complexes D4 and D5 represent polar type structures. The experimental data suggest that the highly polar structure D5, with an almost orthogonal arrangement of dipoles, predominantly forms within nanodroplets. It is separated from the global minimum by a barrier of 0.08 eV (see the SI), which is more than sufficient to prevent a D5 → D1 transition. Structure formation under cryogenic conditions is therefore likely to proceed as follows. At large separation the dominant force is the dipole-dipole interaction which aligns the two DMSO molecules. As described in the SI, there is a barrierless pathway between this structure and the D5 minimum. Therefore the molecules approach each other gradually within the helium environment to which all excess energy is almost immediately drained. The (DMSO) ends up trapped within the basin of complex D5. 11 Figure 2.
Energy minima of the DMSO dimer, with their corresponding binding energies and dipole moments.
We support this scenario by molecular dynamics (MD) simulations of the binary encounter under conditions of very efficient energy transfer. At the start the two dipoles are assigned a random relative orientation, but the trajectory shown in Fig. 3 demonstrates that it becomes correlated already at large distances. At closer approach the total dipole moment transiently increases. The molecular dipoles at that point are still parallel, hence the bump in the dipole moment is caused by mutual induction. Finally, the dimer quenches into one of the potential minima. In accord with the experiment, no formation of a zero dipole structure is found. The majority of the trajectories end up in the D5 minimum with a dipole of 6.4 D, some of them end up in the D4 minimum with a somewhat lower dipole moment than detected in the experiment. 12
Figure 3 . Dipole moment of DMSO dimer complex along the intermolecular approach coordinate, as illustrated by a molecular dynamics simulation.
The structures are more diverse for the trimer (Fig. 4). The lowest energy structure is cyclic with a dipole moment of 4.25 D (complex T1). Its formation is kinetically hindered. Indeed, as mentioned above, it represents the global dimer minimum to which the third molecule is added; since in the nanodroplets the former structure is not formed, neither will the cyclic trimer. We have located linear structures (T6, T7) with a much higher dipole close to 10 D. There are multiple other minima with intermediate dipoles. It follows from our simulations that a rather complex mixture of these metastable structures may be formed under the experimental conditions, and its precise assignment is beyond the reach of theory. The effective dipole moment of Figure 4.
Energy minima of DMSO trimers, with their corresponding binding energies and dipole moments.
Conclusion
In summary, we have demonstrated that the presence of peculiar polar structures, formed by sequential embedding of polar molecules into superfluid helium nanodroplets, can be clearly and directly detected by electrostatic deflection of the doped nanodroplet beam. In an 14 application of this method to DMSO molecules we found that they form dipole-aligned dimer and trimer structures, steered by long-range electrostatic interactions. The formation mechanism and the magnitudes of the dipole moments are in good agreement with calculations describing molecular interactions and structure formation in the viscosity-free cryogenic environment. In future applications it will be interesting to extend this approach, for example, to a study of interactions between polar amino acids or between prototype solute and solvent molecules, as well as between molecules in photoinduced polar conformations. It is also interesting to inquire whether transfer of angular momentum between the impurities and the quantum-fluid bath, a phenomenon predicted to have the potential to screen the impurity – electric field interaction, [41] may be able to measurably affect the dynamics of molecular assembly within nanodroplets.
Acknowledgments
This work was supported by the U. S. National Science Foundation under Grant No. CHE-1664601. L.K. acknowledges a scholarship from the Austrian Marshall Plan Foundation and support from the Austrian Science Fund under project FWF W1259. J.S. and P.S. thank the Czech Science Foundation for support under Project number 18-16577S. J.S. is an International Max Planck Research School for Many Particle Systems in Structured Environments student. We would like to thank Jiahao Liang and Atef Sheekhoon for assistance. References [1] M. T. Bell, T. P. Softley,
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Phys. Rev. Lett. , , 085302. -1 S UPPORTING I NFORMATION FOR
Direct detection of polar structure formation in helium nanodroplets by beam deflection measurements
John W. Niman, [a]
Benjamin S. Kamerin, [a]
Lorenz Kranabetter, [b]
Daniel J. Merthe, [a]
Jiří Suchan, [c]
Petr Slavíček, [c,d]
Vitaly V. Kresin [a] [a]
Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA [b]
Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria [c]
Department of Physical Chemistry, University of Chemistry and Technology, Technická 5, Prague 6, Czech Republic [d]
J. Heyrovský Institute of Physical Chemistry v.v.i., The Czech Academy of Sciences,
Dolejškova 3, 18223 Prague, Czech Republic
Contents I. (DMSO) n ion mass spectra II. Ab initio calculations: Benchmarking III. Mapping of the (DMSO) and (DMSO) potential energy surfaces IV. Transition between two dimers at a distance and D5 V. Transition between the D5 and D1 minima VI. Two dimensional free energy surface VII. Force field parameters VIII. Cartesian coordinates of all structures References -2 I. (DMSO) n ion mass spectra As described in the main text, deflection profiles of droplets doped with DMSO monomers, dimers, or trimers were acquired by setting the mass spectrometer to the masses of (DMSO) + , (DMSO) and (DMSO) ions, respectively, and maintaining the pickup vapor pressure at a level such that the mass peak of interest would be dominant over the next higher one. This is illustrated in Fig. S1. The mass spectrometer is a Balzers QMG-511 crossed-beam quadrupole analyzer with its electron impact ionization source set to 90 eV impact energy. Figure S1.
Representative mass spectra corresponding to deflection measurements on (DMSO) n -doped nanodroplets. The mass spectrometer was set to the masses of intact ions: (a) 78 Da for the monomer, (b) 156 Da for the dimer, (c) 234 Da for the trimer. -3 II. Ab initio calculations: Benchmarking
The potential energy surface was explored with the B3LYP(D2)/aug-cc-pVDZ method. The dipole moment of the isolated DMSO molecule in its equilibrium geometry calculated with this approach was 4.3 D, which is consistent with the tabulated value [S1] of 4.0 D within the expected accuracy of DFT. [S2]
We validated this approach against the high-level CCSD(T)/aug-cc-pVTZ method. Basis set superposition error (BSSE) correction was used for all structures. The agreement is very good for all cluster structures, see Table S1. We also show the energetics of the respective minima at the DFTB/D3 level used for exploratory simulations. The DFT and CCSD(T) calculations were performed in the Gaussian 09, rev. D01 package, [S3] the DFTB results were calculated in the DFTB+ 18.2 program. [S4]
Table S1.
Comparison of DMSO dimer binding energies at the CCSD(T), B3LYP(D2) and DFTB(D3) levels. The BSSE correction was accounted for in the CCSD(T) and B3LYP(D2) calculations.
Dimer complex
Binding energy [eV]
CCSD(T)/aug-cc-pVTZ B3LYP/aug-cc-pVDZ D2 DFTB D1 D2 D3 D4 D5 -4 III. Mapping of the (DMSO) and (DMSO) potential energy surfaces The potential energy surfaces (PES) of DMSO complexes are rather rich and we mapped them in the following way. First, we performed accelerated molecular dynamics simulations with the molecular mechanics (MM) force field, [S5] using the so-called metadynamics method. [S6]
Here, an additional potential is added along a preselected coordinate so that we can quickly overcome barriers along these coordinates. These simulations then also provide the free energy as a function of the selected coordinate [potential of mean force (PMF) or free energy surface (FES)]. We then selected different structures with distinct dipole moments from these metadynamical trajectories and performed further B3LYP optimization. Metadynamics simulations were performed at 100 K to reveal the regions of interest in the dipole moment coordinate. This temperature is much higher than the experimental conditions, yet we opted for it to avoid ergodicity problems. Note that these simulations are only auxiliary, serving as a starting point for minimizations or MD simulations. The minimum on the PMF is found for a small yet non-zero dipole moment due to entropic reasons. The force field overestimates the dipole moment by 20% with respect to the ab initio value. The final PMFs for the dimer and trimer complexes are displayed in Fig. S2. By clustering structures with similar dipoles together and performing 100 subsequent optimizations with Gaussian 09, for both the dimer and trimer structures, we were then able to map their PES landscapes. The metadynamics parameters were as follows. The dimer simulation length was 100 ps, leap-frog stochastic integrator was utilized, the temperature was set to 100 K with a thermostat constant of τ =1.0 ps. For the trimer the simulation length was increased to 300 ps. The collective variable (CV) is the total dipole moment. An additional Gaussian potential was added every 100 steps. The Gaussian height was 0.015 kJ/mol and the CV gaussian width was 1.2 Debye. MD simulations were performed with GROMACS 2018.4 code [S7] coupled with PLUMED 2.5 code [S8] for the FES simulations. Figure S2.
PMF for DMSO dimer and trimer complexes for the dipole moment coordinate at 100K. -5 IV. Transition between two dimers at a distance and D5
Nudged elastic band (NEB) optimization [S9] was performed to find energy barriers between two DMSO molecules a distance apart (13.5 Å; in the minimal geometry at that separation the two DMSO molecules have aligned dipoles) and complex D5. Fig. S3 shows that the connection is barrierless. The simulations were carried out in the TeraChem code [S10,S11] using the B3LYP(D2)/aug-cc-pVDZ method with 14 molecular images between the two structures. The images were generated by constrained minimization.
Figure S3.
NEB calculations connecting the long-distance configuration to the D5 minimum. -6 V. Transition between the D5 and D1 minima
We also performed NEB calculation connecting the D5 minimum with the global D1 minimum. The final energy curve is shown in Fig. S4.
Figure S4.
NEB calculations connecting the minima D1 and D5. -7 VI. Two dimensional free energy surface
Additional insight into the topology of the multidimensional PES of DMSO aggregates can be brought about via modeling of free energy surfaces (FES). We evaluated the FES (i.e., the two dimensional version of the PMF in Fig. S2) as a function of two coordinates: the aggregate dipole moment and the interatomic S-S distance, see Figs. S5-S8. The graphs were once again generated using the metadynamics method and the temperature of 100 K to avoid convergence issues. It is clear that at large intermolecular distance the system prefers the high-dipole configuration, as mentioned above. At close distances one observes a number of minima separated by barriers. The 2D metadynamics parameters were as follows. As before, for the dimer the simulation length was 100 ps, leap-frog stochastic integrator was utilized, the temperature was set to 100 K with thermostat constant τ =1.0 ps. The first collective variable, CV1, was defined as the S-S interatomic distance between the DMSO monomers. An additional Gaussian potential was added at every 1000 steps. The Gaussian height was 0.015 kJ/mol and the CV1 Gaussian width was 0.1 nm. The second collective variable was the dipole moment with the same deposition parameters as CV1 and Gaussian width of 1.2 D. Upper energetic walls for CV1 were applied at 2 nm in order to keep the molecule in the area of interest. For the trimer the simulation length was increased tenfold to 1000 ps, with the other parameters fixed. CV1 was redefined as the sum of S-S interatomic distances due to the presence of the third DMSO molecule, the other variables remained the same. The upper energetic walls for CV1 were shifted to 6.0 nm. Figure S5.
FES for the DMSO dimer at 100 K. -8 Figure S6 . FES heatmap for the DMSO dimer at 100 K. Contour spacing 0.01 eV.
Figure S7.
FES for the DMSO trimer at 100 K. -9 Figure S8.
FES heatmap for the DMSO trimer at 100 K. Contour spacing 0.01 eV. -10
VII. Force field parameters
The MM simulations were performed with parameters taken from ref S5. The parameters are summarized in Tables S2 and S3.
Table S2.
Atomic type parameters for DMSO.
Atom Charge ε (kJ/mol) σ (nm) O -0.556 0.50242 0.30291 S 0.312 1.46537 0.35636 C -0.148 0.32657 0.36348 H 0.090 0.10048 0.23876
Table S3.
Intermolecular parameters for DMSO.
Bond b (nm) f c (kJ mol -1 nm -2 ) H-C 0.111 134724.8 C-S 0.180 100416.0 S-O 0.153 225936.0
Angles θ (nm) f c (kJ mol -1 rad -2 ) H-C-H 108.400 148.5320 H-C-S 111.300 192.8824 C-S-O 106.750 330.5360 C-S-C 95.000 142.2560
Dihedrals φ (deg) f c (kJ mol -1 ) X H-C-S-O 0.0 0.8368 3 H-C-S-C 0.0 0.8368 3 -11
VIII. Cartesian coordinates of all structures
Geometries of the optimal structures presented in Figs. 2 and 4 of the main text are listed below, with all coordinates in Angstroms.
Monomer 10 C 1.390750 0.279323 -0.278296 S 0.072728 -0.679506 0.585004 C -1.342363 0.171624 -0.236526 O 0.075720 -0.189227 2.044957 H 1.346127 0.069130 -1.356470 H 1.227420 1.344812 -0.066434 H 2.347951 -0.053762 0.141464 H -1.314193 -0.035613 -1.315827 H -2.257159 -0.235280 0.211752 H -1.256995 1.246897 -0.028367 D1 20 C 1.391830 0.296071 -0.267191 S 0.073035 -0.689518 0.555023 C -1.343411 0.188626 -0.225497 O 0.078854 -0.256270 2.047129 H 1.379923 0.056354 -1.339642 H 1.179380 1.359143 -0.087564 H 2.341205 -0.018939 0.183566 H -1.345350 -0.050790 -1.298081 H -2.251051 -0.199163 0.253587 H -1.209576 1.265306 -0.051326 S -0.073081 3.587139 1.938615 O -0.078682 3.153903 0.446506 C -1.391839 2.601376 2.760682 C 1.343385 2.709142 2.719264 H -1.380080 2.841096 3.833135 H -2.341208 2.916257 2.309824 H -1.179218 1.538334 2.581077 H 1.345162 2.948483 3.791865 H 1.209699 1.632459 2.545001 H 2.251033 3.097074 2.240313 -12 D2 20 O 8.826895 8.110270 10.400227 S 9.972464 7.608129 9.483674 C 11.539269 7.974326 10.379345 H 12.382316 7.730081 9.717863 H 11.525836 9.039717 10.646509 H 11.551024 7.328890 11.266521 C 10.186293 8.892506 8.183524 H 11.035534 8.602394 7.548535 H 9.256912 8.900193 7.600878 H 10.362717 9.852789 8.687985 O 10.697510 11.161246 10.536141 S 9.253455 11.346438 11.076378 C 9.145789 10.330797 12.600760 H 8.213528 10.584098 13.124409 H 9.133390 9.289859 12.256910 H 10.027135 10.559985 13.215271 C 9.274676 12.983721 11.916622 H 8.313117 13.137349 12.426572 H 10.112562 12.992963 12.626663 H 9.422581 13.740250 11.136213 D3 20 C -6.599507 -9.935427 -8.808258 S -6.050826 -8.220930 -8.418528 C -7.587463 -7.381111 -8.969174 O -4.975044 -7.895873 -9.486073 H -7.454125 -10.195223 -8.167596 H -6.867985 -9.974321 -9.872589 H -5.748550 -10.596439 -8.602335 H -8.424339 -7.741197 -8.354184 H -7.407231 -6.311806 -8.806702 H -7.734957 -7.620273 -10.031201 S -4.736135 -4.653480 -8.965041 O -5.810347 -4.978975 -7.896071 C -4.188088 -2.938502 -8.576590 C -3.198394 -5.492320 -8.416137 H -3.333958 -2.678643 -9.217880 H -5.039455 -2.277959 -8.782326 H -3.918996 -2.898989 -7.512438 H -2.362832 -5.133640 -9.033730 H -3.048402 -5.251363 -7.354870 H -3.379470 -6.561814 -8.576431 -13 D4 20 O 10.770543 12.406453 7.172925 S 10.996603 12.217603 8.692035 C 12.663048 11.452412 8.865018 H 12.827871 11.198932 9.921240 H 12.692858 10.559951 8.226519 H 13.389878 12.202747 8.531247 C 10.042817 10.713973 9.163143 H 10.255542 10.475201 10.214216 H 8.982319 10.960304 9.031380 H 10.346341 9.897937 8.494552 O 11.783311 8.009573 5.181466 S 11.481115 9.357691 5.867285 C 12.445813 10.642888 4.970928 H 12.145669 11.622494 5.364081 H 13.505277 10.435700 5.167309 H 12.228607 10.534564 3.900118 C 9.828399 9.903572 5.270228 H 9.653478 10.918986 5.647899 H 9.840437 9.858877 4.173228 H 9.097072 9.191144 5.672183 D5 20 C 0.832083 0.053205 0.687160 S -0.018838 0.529481 -0.873482 S 1.568387 -2.573673 -1.989863 C 0.721902 -2.067199 -3.541948 C -1.624708 -0.272902 -0.470355 O -0.252453 2.053432 -0.806970 O 0.449839 -2.770887 -0.938584 C 2.024752 -4.266109 -2.547539 H 0.867295 -1.043176 0.726962 H 1.838413 0.487869 0.644560 H 0.262499 0.486055 1.520395 H -1.455444 -1.355871 -0.418903 H -1.978107 0.143628 0.482340 H -2.317341 -0.012725 -1.280529 H 2.733390 -4.189503 -3.384114 H 2.491453 -4.765940 -1.690035 H 1.103863 -4.786018 -2.843846 H 1.450590 -2.071775 -4.364292 H -0.098565 -2.774219 -3.724319 H 0.340792 -1.054444 -3.366810 -14 T1 30 O 18.325573 19.811653 21.617481 S 19.721884 20.312996 21.169378 C 20.228323 21.608815 22.376809 H 21.215482 21.985848 22.075579 H 19.485068 22.415686 22.369997 H 20.289383 21.113897 23.353709 C 19.440363 21.463757 19.758658 H 20.418372 21.838813 19.426676 H 18.968548 20.870817 18.965678 H 18.799604 22.289633 20.091628 O 18.271096 24.146530 21.392567 S 17.718310 25.601134 21.478337 C 16.938575 25.747636 23.136233 H 16.505635 26.754394 23.216988 H 16.166283 24.969074 23.217754 H 17.742714 25.618895 23.871189 C 16.151632 25.602873 20.517245 H 15.714781 26.608754 20.587075 H 16.422965 25.376776 19.478677 H 15.486136 24.843390 20.952583 O 14.642326 23.527870 22.517495 S 15.116812 22.043647 22.457649 C 16.675088 21.971241 23.424806 H 17.142014 20.993610 23.248081 H 17.321498 22.778503 23.058847 H 16.399735 22.113636 24.476868 C 15.887654 21.824953 20.806281 H 16.405169 20.856910 20.796220 H 15.074819 21.866766 20.071118 H 16.603161 22.645493 20.671394 T2 30 C 19.978371 22.960022 19.710536 S 19.735892 23.242403 21.510328 C 20.388685 21.613064 22.058900 O 18.198954 23.189838 21.745112 C 15.358815 23.917374 20.096399 S 14.121084 23.111607 21.194225 C 15.047600 23.377434 22.762579 O 14.190395 21.590951 20.897064 S 17.054341 20.556144 20.208772 C 15.942352 19.217124 19.628149 -15 O 18.501515 20.064915 19.893824 C 16.827935 20.251673 22.004302 H 21.059208 22.936455 19.512556 H 19.496985 22.004570 19.454354 H 19.514939 23.811524 19.197357 H 21.467010 21.591478 21.848409 H 20.210845 21.552465 23.139753 H 19.850741 20.831749 21.503192 H 15.760191 20.345461 22.229074 H 17.216281 19.244890 22.206490 H 17.413863 21.021960 22.516917 H 14.919373 19.492859 19.911972 H 16.052332 19.168894 18.537795 H 16.267612 18.274891 20.088960 H 15.332881 24.997756 20.296283 H 16.349231 23.496971 20.310933 H 15.040118 23.707847 19.068112 H 15.045690 24.454363 22.980238 H 14.504377 22.828117 23.541197 H 16.073387 23.010200 22.639216 T3 30 C 19.318080 22.762136 22.418743 S 18.401131 21.379365 21.618767 C 18.852818 21.822207 19.888771 O 16.894078 21.701134 21.778298 O 19.025390 25.162225 20.116170 S 18.978878 26.478380 19.285963 C 18.218864 27.737277 20.375610 C 20.695828 27.130948 19.340978 C 16.290257 24.915699 22.126303 S 15.070039 25.136098 20.770491 C 15.850747 23.953991 19.603056 O 15.323351 26.555016 20.184537 H 20.393691 22.575593 22.293887 H 19.028486 23.706104 21.941314 H 19.045684 22.740531 23.480909 H 19.921248 21.605360 19.751253 H 18.245550 21.181412 19.238001 H 18.646287 22.887366 19.725303 H 20.713003 28.127033 18.877545 H 21.008893 27.173273 20.392785 H 21.324967 26.432136 18.776249 H 18.326517 28.718024 19.891996 H 17.157993 27.455148 20.467183 -16 H 18.745592 27.706182 21.339379 H 16.277900 23.860237 22.428986 H 17.274927 25.192098 21.728825 H 15.980785 25.581780 22.940796 H 15.862931 22.963479 20.077728 H 15.245255 23.967205 18.688986 H 16.872837 24.307564 19.416185 T4 30 C 5.071517 -0.034670 -3.655985 S 4.287297 -0.194668 -1.997307 C 5.830416 -0.559251 -1.075361 O 3.893217 1.257561 -1.611793 S -0.020529 2.540318 0.295084 C 1.283159 3.066414 -0.885371 O 0.572434 2.732177 1.715202 C 3.644181 1.756288 1.598188 S 2.617946 0.269497 1.276626 C 1.964214 0.086045 2.982365 O 3.615924 -0.905124 1.078908 H 1.323627 0.953582 3.183548 H 1.388114 -0.847471 2.998202 H 2.818493 0.022048 3.669544 H 2.968760 2.565559 1.900207 H 4.362207 1.495270 2.386815 H 4.148555 1.979398 0.651252 H 0.822989 3.182558 -1.876460 H 1.688760 4.020594 -0.522132 H 2.057413 2.289562 -0.920766 H 5.497260 -1.005416 -3.946611 H 4.282043 0.264332 -4.356496 H 5.846821 0.740863 -3.594728 H 6.247662 -1.502562 -1.454190 H 6.520679 0.279922 -1.237121 H 5.523931 -0.655551 -0.027295 C -1.126902 3.988674 0.041019 H -1.509237 3.972861 -0.989222 H -1.948976 3.889460 0.760368 H -0.546405 4.899313 0.241051 -17 T5 30 O 16.634857 24.592189 18.933949 S 17.819686 24.188608 19.842340 C 18.546611 25.748060 20.487096 H 19.438384 25.480875 21.069767 H 18.776646 26.394312 19.630220 H 17.780785 26.213377 21.119207 C 19.237765 23.746631 18.763679 H 20.096423 23.565749 19.425082 H 18.955755 22.836787 18.219781 H 19.417204 24.574596 18.065138 O 20.209226 23.485765 22.163446 S 18.877554 23.104769 22.864853 C 19.254372 22.812446 24.636229 H 18.324234 22.468296 25.107880 H 20.058270 22.067975 24.708308 H 19.577739 23.772502 25.056335 C 18.574534 21.347602 22.430705 H 17.751416 20.981712 23.056223 H 18.299881 21.331231 21.369829 H 19.512448 20.803987 22.601658 O 15.856035 22.403783 23.805490 S 15.408064 22.687282 22.347855 C 15.384240 24.514743 22.152187 H 15.163099 24.748814 21.101020 H 14.647435 24.936357 22.847504 H 16.395863 24.844707 22.412702 C 13.585634 22.453003 22.322482 H 13.200021 22.813677 21.358789 H 13.395364 21.379488 22.440968 H 13.163459 23.017678 23.164279 T6 30 O 18.248791 19.538962 25.445555 S 18.177691 19.442715 26.988687 C 18.433034 21.156221 27.613792 H 18.496857 21.127477 28.710183 H 19.356533 21.546423 27.166533 H 17.561677 21.740741 27.294830 C 19.813685 18.792657 27.529990 H 19.853766 18.804080 28.627823 H 19.884199 17.765020 27.153619 H 20.593531 19.428978 27.091708 -18 O 22.122928 22.013981 19.259183 S 22.029013 21.907157 20.795300 C 22.263129 23.603652 21.467768 H 22.337954 23.520943 22.560161 H 23.173825 24.017982 21.015392 H 21.385740 24.187672 21.162752 C 23.639059 21.242274 21.387621 H 23.636418 21.292751 22.484521 H 23.704654 20.207811 21.027740 H 24.435317 21.852934 20.941810 O 22.288179 21.938705 24.307074 S 21.002813 21.173364 24.716842 C 20.992990 19.611911 23.748124 H 20.049272 19.097423 23.964572 H 21.091252 19.874277 22.687275 H 21.857084 19.027672 24.087681 C 19.609864 21.978664 23.829299 H 18.704772 21.397957 24.043202 H 19.535878 22.999435 24.224070 H 19.855097 21.990158 22.759892 T7 30 C 0.472180 -0.265895 0.733682 S -0.136458 0.321670 -0.898489 O -0.384447 1.846400 -0.754727 C -1.785515 -0.482541 -0.798695 O 0.359320 -2.893610 -1.176365 S 1.641205 -2.693731 -2.021010 C 2.115524 -4.372107 -2.603230 C 1.077057 -2.055772 -3.650613 H 0.551026 -1.358283 0.675742 H 1.451728 0.200982 0.892637 H -0.247228 0.058360 1.495983 H -1.625451 -1.566818 -0.828784 H -2.261186 -0.155086 0.134675 H -2.355211 -0.137931 -1.670337 H 2.951015 -4.283369 -3.311612 H 2.420451 -4.939134 -1.715311 H 1.234961 -4.831777 -3.071533 H 1.927235 -2.048859 -4.346467 H 0.268384 -2.708093 -4.006330 H 0.713231 -1.036965 -3.472756 S -2.320128 1.993864 2.169713 O -3.154515 2.294445 3.432453 C -3.077491 2.942538 0.787412 -19 C -0.788980 3.007148 2.285051 H -2.419933 2.841894 -0.086210 H -4.064898 2.499581 0.606587 H -3.180753 3.985061 1.116591 H -0.254575 2.912504 1.330540 H -1.090007 4.041603 2.496975 H -0.204794 2.601451 3.120616 T8 30 O 22.134918 25.903523 23.940447 S 23.041269 24.808338 24.561304 C 22.070844 24.071469 25.935851 H 22.726180 23.402398 26.509576 H 21.686789 24.890733 26.558087 H 21.251172 23.507444 25.474200 C 24.246540 25.712157 25.614598 H 24.837479 24.984221 26.187314 H 24.891884 26.286350 24.938904 H 23.682050 26.382530 26.276309 O 18.026224 22.657810 23.136880 S 19.327282 23.413547 23.474273 C 18.847931 25.002640 24.270183 H 19.769957 25.568621 24.458552 H 18.190563 25.554032 23.588146 H 18.338681 24.736761 25.204821 C 19.960394 24.149959 21.912549 H 20.865655 24.718669 22.164650 H 20.186067 23.308764 21.246021 H 19.190316 24.810736 21.496604 O 18.606089 27.152941 21.810753 S 19.594310 28.340832 21.800217 C 21.206535 27.678398 21.199666 H 21.938315 28.498325 21.206754 H 21.524346 26.861633 21.859709 H 21.033168 27.327994 20.175000 C 20.127602 28.590982 23.547016 H 20.862715 29.407639 23.569519 H 19.226795 28.869318 24.107320 H 20.565929 27.657234 23.920780 -20
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