The spontaneous synchronized dance of pairs of water moleculesLuiz F. Roncaratti, David Cappelletti, and Fernando Pirani Citation: The Journal of Chemical Physics 140, 124318 (2014); doi: 10.1063/1.4869595 View online: http://dx.doi.org/10.1063/1.4869595 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: A new ab initio dipole surface forhigh-temperature applications J. Chem. Phys. 136, 044320 (2012); 10.1063/1.3676406 On equilibrium structures of the water molecule J. Chem. Phys. 122, 214305 (2005); 10.1063/1.1924506 Dipole moments of HDO in highly excited vibrational states measured by Stark induced photofragment quantumbeat spectroscopy J. Chem. Phys. 122, 124312 (2005); 10.1063/1.1864912 Inelastic state-to-state scattering of OH ( Π 3 ∕ 2 2 , J = 3 ∕ 2 , f ) by HCl J. Chem. Phys. 122, 074319 (2005); 10.1063/1.1846692 Infrared absorption by collisional CH 4 +X pairs, with X= He , H 2 , or N 2 J. Chem. Phys. 122, 024301 (2005); 10.1063/1.1829055

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THE JOURNAL OF CHEMICAL PHYSICS 140, 124318 (2014)

The spontaneous synchronized dance of pairs of water moleculesLuiz F. Roncaratti,1,2 David Cappelletti,1,a) and Fernando Pirani11Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, 06123 Perugia, Italy2Instituto de Física, Universidade de Brasília, 70910-900 Brasília, Brazil

(Received 13 February 2014; accepted 13 March 2014; published online 31 March 2014)

Molecular beam scattering experiments have been performed to study the effect of long-rangeanisotropic forces on the collision dynamics of two small polar molecules. The main focus of thispaper is on water, but also ammonia and hydrogen sulphide molecules have been investigated, andsome results will be anticipated. The intermolecular distances mainly probed are of the order of 1 nmand therefore much larger than the molecular dimensions. In particular, we have found that the natu-ral electric field gradient, generated by different spatial orientations of the permanent electric dipoles,is able to promote the transformation of free rotations into coupled pendular states, letting the molec-ular partners involved in the collision complex swinging to and fro around the field direction. Thislong-ranged concerted motion manifested itself as large increases of the magnitude of the total in-tegral cross section. The experimental findings and the theoretical treatment developed to shed lighton the details of the process suggest that the transformation from free rotations to pendular statesdepends on the rotational level of both molecules, on the impact parameter, on the relative collisionvelocity, on the dipole moment product and occurs in the time scale of picoseconds. The conse-quences of this intriguing phenomenon may be important for the interpretation and, in perspective,for the control of elementary chemical and biological processes, given by polar molecules, ions, andfree radicals, occurring in several environments under various conditions. © 2014 AIP PublishingLLC. [http://dx.doi.org/10.1063/1.4869595]

I. INTRODUCTION

The role of molecular orientation is central in molecu-lar sciences1 and is pivotal in the stereodynamics of chemicalreactions.2 Topical issues range from molecular dynamics ofpolar species, the archetypal example being water molecule,3

to non-Arrhenius behavior of elementary processes, includingchemical reactions.4, 5 Historically, the control of molecularorientation has been obtained for polar (symmetric top andlinear) molecules by employing focussing hexapoles and/orstrong external electrostatic fields (brute force approaches),see, i.e., Refs. 6–9. These ideas have been successively ex-tended by exploiting powerful laser beams, whose strongelectric field acting on the molecular polarizability can gen-erate pendular states.10, 11

Herein, we show that molecular orientation processesmay happen spontaneously, i.e., without applied externalfields, when polar molecules interact with themselves at ther-mal energies. We demonstrate that when two water moleculescollide at distances of the order of 1 nm, much larger thantheir dimensions, they engage a synchronous motion for a fewpicoseconds: this sort of molecular dance, driven by the natu-ral electric field gradient generated by the water dipole, is in-duced by the confinement of the molecular complex into cou-pled pendular states. This intriguing phenomenon lasts for afew picoseconds and it affects the behavior of polar moleculesother than water: actually the results obtained are of generalvalidity for all cases where a sufficiently anisotropic long-

a)Author to whom correspondence should be addressed. Electronic mail:david.cappelletti@unipg.it

range interaction is at play. Although dipolar molecules scat-tering was already attempted in the past (see, i.e., Ref. 12),allowing to characterize the role of elastic and inelastic con-tributions to the integral cross sections, no evidences wereobtained on possible alignment/orientation effects at long in-termolecular range. Moreover, these seminal works reportedresults essentially for alkali halides molecules.

In the present work, we have studied in details and inwide collision energy range the fundamental case of the waterdimer. The basic point to be addressed here concerns the in-vestigation of stereodynamical effects in absence of externalfields. Under “natural” conditions, as in conventional Boltz-mann distributions, closely related to the present work, thefocus regards the influence that anisotropic intermolecularforces can exert on molecular collisions at long-range, i.e.,in the entrance channels of chemical reactions.

Section II illustrates the experimental technique and themain results obtained. Details of the data analysis follow inSec. III. In Sec. IV, we discuss the results obtained with modelsimulations. Some conclusions follow in Sec. V.

II. EXPERIMENTAL METHOD AND RESULTS

Herein we face the problem with molecular beam (MB)scattering experiments aimed at measuring, under high angu-lar and velocity resolution conditions, orientation effects onthe integral cross sections Q as a function of the selected MBvelocity v. In the thermal velocity range, Q(v) can be given ascombination of an oscillatory pattern �Q(v), due to the gloryquantum interference, over-imposed to an average component

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Q̄(v) which determines the magnitude of the cross section. Ithas been well established13 that these two observables providecomplementary information on the non-covalent intermolec-ular interaction driving the approach of the collision partners:�Q depends on the features of the resulting potential well,while Q̄(v) is directly affected by the strength of the long-range attraction.

The experimental apparatus used in the present workhas been described in detail in previous works.13–15 Briefly,it consists of a set of differentially pumped vacuum cham-bers connected by slits for the MB collimation. The MBemerges through a nozzle (1.0 mm in diameter) from asource, which can operate under nearly effusive or mod-erately supersonic conditions. After mechanical velocityselection, the MB crosses a scattering chamber, which is con-tinuously filled (∼10−3–10−4 mbar) with the target gas andevacuated (∼10−6–10−7 mbar) by an automated procedure.After the scattering region, an electron bombardment ionizerfollowed by a quadrupole mass analyzer detects the on-lineMB intensity. Water and ammonia MBs have been gener-ated by expanding water (ammonia) vapors through a nozzleheated at 500–600 K in order both to suppress cluster forma-tion and to “heat up” the rotational motion of molecules. Wa-ter (ammonia) vapors has been kept in the source both pure,at a stagnation pressure of 5–6 mbar, and in a mixture with He(or H2), always at low total stagnation pressure (<20 mbar), inorder to extend the probed collision velocity range by shiftingthe MB velocity distribution. MB velocity analysis and selec-tion have been achieved by the use of a slotted disk velocityselector with a high resolution (full width at half maximumless than 5%).

At each selected MB velocity v, the measurement of MBattenuation I/I0 (where I and I0 are the MB intensity withand without target gas in the scattering chamber, respectively)permits the determination of the integral cross section Q(v)through the Lambert Beer law

Q(v) = −1/NL log (I/I0),

where N is the gas target density and L is the effective lengthof MB path in the scattering region. In the present experi-ments, the scattering chamber, filled with water, ammonia, orhydrogen sulphide vapors, has been kept at room temperature(about 300 K) in order to increase the rotational temperatureof the target gas molecules and to avoid condensation effectson the chamber walls. The absolute values of Q(v) have beenobtained by an internal calibration of the NL factor,13–15 mea-suring the gas flow in the scattering chamber and on the abso-lute value of the He-Ar cross section.16

Scattering experiments with water and other hydro-genated molecules have been performed with isotopicallysubstituted and heated projectiles and/or targets, to improveboth signal-to-noise ratio and kinematic conditions, to reducethe probability of cluster formation and the effects of inelasticevents, and to suppress condensation along the gas lines andon the walls of the apparatus, kept at defined temperature. Inthese conditions only single-collisions occur. Molecules showrotations and relative velocities in the thermal energy rangeand measured interactions are found to be insensitive to dis-placements of the molecular center of mass due to isotopic

differences.17 Isotopic effects are expected to play a relevantrole in the quantum dynamics of the hydrogen bonds at shortdistances.18

The experimental strategy has been based on successivemeasurements, carried out in the same operating conditions,looking at collisional pairs with a growing complexity of theintermolecular forces involved, in order to highlights the con-tribution of the different interaction components. In particular,non-covalent interactions, such as those driving the collisionsof water molecules, arise from the critical balance of electro-static Velec, induction Vind, and dispersion Vdisp contributions,which operate at large intermolecular distances R, combinedwith size repulsion Vrep and charge transfer contributions VCT,which emerge at intermediate and short R, being governed bythe overlap of charge densities. We note that the main featuresof Vrep + Vdisp + Vind, namely, the resulting well depth ε, itslocation Rm and the long-range attraction coefficient Ctot, canbe anticipated by correlation formulas given in terms of polar-izability, dipole moment, and charge of involved species.19, 20

As a starting point, we illustrate the case of D2O-Arcompared to O2-Ar. These collisional complexes exhibit avery similar long-range interaction, arising from Vrep + Vdisp

+ Vind (Velec is absent), as confirmed by the measurementof the same Q̄(v) (Fig. 1(a)). This is consistent with thesimilarity of average polarizabilities of water, oxygen, andargon.14, 15, 19, 20 The effective potentials extracted from theexperiments are cast in analytical form using the ImprovedLennard-Jones (ILJ) model13 (Fig. 1(b)).

Adopting the same conditions, the experiments havebeen extended to the water-oxygen and water-water cases(Fig. 1(a)). While water-oxygen behaves as expected, it is eye-catching that water-water shows a completely different Q̄(v):a factor 2.5 larger with respect to that of the other systemssuggesting for water-water an effective long-range attraction afactor ten stronger. In line of principle this is possible becausethe permanent dipoles of water can generate an anisotropicelectrostatic interaction able to orient, even at large R, a frac-tion of the initially random distributed molecules, for a suffi-ciently long time to affect the scattering observable.

III. DATA ANALYSIS

We have extracted from our experimental data thisinformation and also modeled the implications on the molec-ular dynamics. Therefore, while the water-argon and water-oxygen data have been well reproduced by assuming the scat-tering driven by Vrep + Vdisp + Vind, for the water-water case,the fitting of Q(v) has required the introduction of an effectiveelectrostatic component, Velec, which has been expressed as afunction of the product of permanent dipole moments μi, andof the fraction of molecules oriented at long range, c,

V (R) = VILJ (R) − 2cF (R)μ1μ2

4πε0R3, (1)

F(R) is the Fermi function

F (R) = (1 + e

R−R0d

)−1,

which effectively accounts at each R for the spatial averag-ing of Velec over the relative orientation of the two molecules.

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(a)

(b)

FIG. 1. (a) Q(v) for O2-Ar (red), D2O-Ar (green), D2O-O2 (blue), and D2O-D2O (black) reported as a function of MB velocity v. Continuous lines rep-resent cross sections, calculated in the center-of-mass system using the semi-classical JWKB method and then convoluted in the laboratory frame, takinginto account of the average over relative velocity distributions and angularresolutions, for the direct comparison with experimental results. For D2O-D2O, two calculations are reported to show the sensitivity of the experimentaldata to phenomenological long-range attraction (see (c)). (b) Best fit interac-tion potentials V (R). (c) Blow up of the long-range interaction energy, in thedistance interval mainly probed by the absolute value of Q̄(v) for D2O-D2Osystem, compared with that of the other systems. Polarizability values are1.47, 1.60, and 1.64 A3, for water, oxygen, and argon, respectively. 1 meV =0.096485 kJ mol−1.

F(R) tends to zero for randomly oriented and freely rotat-ing molecules. These can behave as free rotors at very largeR (where F(R) = 0) or can be trapped in pendular states(at the distances of the closest approach, where F(R) �= 0).The parameters of the Fermi function, R0 and d, charac-terize when and how fast the transition occurs. The best-fitcross sections (Fig. 1(a)) have been obtained with c = 0.16,R0 = 1.05 nm, and d = 0.08 nm, suggesting that an ap-preciable fraction of the collision pairs is oriented at longrange in order to influence so strongly Q̄(v). In the regionmanly probed by Q̄(v) of water-water, Velec is the leadinginteraction component and shows an average strength in the−0.25/−1 meV (−0.025/−0.1 KJ/mol) range (Fig. 1(b)). Theprobed attraction is comparable to the rotational quantumof water molecule and therefore it confirms the possibility

FIG. 2. Total integral collision cross sections Q(v), as a function of the colli-sion velocity v, for the D2O-D2O, D2O-ND3, D2O-H2S, and ND3-H2S polarpairs.21 Dashed lines are QILJ(v) calculated for the reference pairs, Ar-Ar(black), Ar-Kr (green), Ar-Xe (blue), and Kr-Xe (red) and convoluted in thelaboratory frame under the same conditions. Polarizability values are 2.16,2.49, 378, and 4.04 A3, for ammonia, krypton, hydrogen sulphide, and xenon,respectively (see Fig. 1).

of molecular pair trapping (polarization) during the single-scattering event. We associate this effect, emerging in theneighborhood of the distance of closest approach, where themost part of the partial wave phase shifts relevant to the quan-tum scattering is accumulated,13 to the transformation of freerotations into pendular states (hindered rotations).

How general is this phenomenon? Our analysis impliesthat the insurgence of pendular states at long range shouldbe a common phenomenon for polar species, depending onthe product of the electric dipole moments of the collisionpair. In order to validate this hypothesis, more scattering ex-periments (Fig. 2) have been performed with NH3 and H2S(and water).21 Best fit Q(v) have been obtained by exploit-ing the effective potential formulation of Eq. (1). Also, in thefigure have been reported QILJ(v) of four reference systems(Ar-Ar, Ar-Kr, Ar, Xe, and Kr-Xe), chosen on the basis oftheir polarizabilities,19, 21 and having VILJ terms (but not Velec)similar to those of the corresponding polar pairs. A plot ofQ(v)-QILJ(v) (Fig. 3) shows a clear linear trend as a functionof the product of the dipole moments of the polar pair andtherefore it provides a robust support to the present results.The observed trend suggests that, under the present condi-tions, formation of the pendular states is ineffective for dipolemoment products lower than one square Debye.

IV. MODEL SIMULATIONS

What are the consequences of the presence, at long range,of an effective orienting field? To answer this central ques-tion, we have carried out a dynamical treatment by usingwell-known electrostatic equations to define the force fieldthat each molecule feels within the collisional complex. Forthe sake of simplicity, we have assumed rectilinear trajecto-ries for the molecular motion during collisions at large impactparameters, which are those determining the observed Q̄(v).

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FIG. 3. Difference between cross sections, Q, of each polar pair versus those,QILJ, of the relative reference system.21 Data are averaged over MB velocityv and plotted as a function of the permanent dipole moment, μ, product ofthe polar pairs. μ(D2O) = 1.85 D; μ(ND3) = 1.47 D; μ(H2S) = 0.98 D;1 D (Debye) = 3.336 × 10−30 C m.

This approximation is substantiated by the fact that the mea-sured interaction attraction is much smaller than the transla-tional kinetic energy, which covers the range 50–200 meV.The used coordinate system and all quantities relevant for thesimulations are illustrated in Fig. 4. The electric field �Ei gen-erated by a molecular dipole �μi , the crucial quantity drivingthe molecular dance, is given by

�Ei = 1

4πε0

3( �μi · R̂)R̂ − �μi

R3. (2)

This equation allows the evaluation of both the average valueof the electric field, felt by another molecule with dipole mo-ment �μ j placed at R, and the field gradient induced by a vari-ation of R and/or of the dipole orientation. The moleculartorque �τ j i exerted by �Ei on �μ j drives the trapping of free ro-

tors in pendular states, and is given by �τ j i = �μ j × �Ei , whilethe effective potential energy Velec probed in the experimentis given by the average value of Velec = − �μ j · �Ei .

In particular, the explicit expression of Velec corre-sponds to the well-known description of the dipole-dipole

FIG. 4. Coordinate systems used in the present model simulations.

interactions,22 whose angular part, averaged over anisotropicdistributions of molecular orientations during the collision,has been tested to play the form of a Fermi function.

For all the selected impact parameter and collision ve-locity, we have carried more than 10 000 simulations to mapthe role of different initial in plane and off plane configu-rations. Although we have carried out classical mechanicssimulations, where a continuous range of angular momen-tum is allowed, we sampled the “quantum cases” by settingthe initial angular velocities of each water molecule equal toω = (¯/I)(J(J+1))1/2.

The model described above has been applied to a widevariety of initial conditions (rotational states J = 0–10, im-pact parameters b = 0.8–1.2 nm, relative collision velocitiesg = 1.0–2.0 km/s, and a manifold of initial relative orienta-tions), in order to evaluate the emergence and development ofpendular states, the influences of the forces driving this trans-formation, the role of rotational states and, finally the charac-teristic time-scale of this process.

The population of the rotational states has been definedusing Boltzmann distributions: a temperature of 300 K is as-sumed for water molecules in the scattering chamber andof 300–100 K for water in the MBs, since in the later casethey show a near effusive or a moderate supersonic charac-ter. Some illustrative examples of outcomes of the model arereported in the following figures.

In Fig. 5, three examples of coplanar molecular collisionsevents are visually illustrated by evaluating both the local co-ordinates of the two dipole moments and their electrostaticinteraction energy as a function of the time t. The system isdefined before the collision by a negative t, after the colli-sion by a positive t and the turning point, i.e., the distance ofclosest approach, by t = 0. At the beginning, the moleculesare both in J = 0 (see panel (a)) and after the collision bothmolecules slowly rotate. Panel (b) describes an elastic colli-sion between molecules both in J = 1. In panel (c), an elas-tic collision between J = 3 and J = 5 molecules is depicted.In all cases the coupling induces a local modification of themolecular modes, clearly evidenced when the relative motionof the two dipoles are projected on the Y-t plane. The dynam-ics of the collision complex is driven by a resulting Velec, wellevident in the first two cases, following the system evolutionon the Velec-t plane, where it exhibits a negative (attractive)contribution. Most part of its influence manifests in the timescale from −1 to +1 ps. In the third case, the coupling tendsto be less effective, since at the same time scale, Velec exhibitsseveral oscillations from positive to negative values, with anaverage effect tending to zero.

A second example of the outcomes of the model is re-ported in Fig. 6. Herein, the chosen case refers to the approachof two water molecules with the dipole vectors rotating in per-pendicular planes. Also in this case the collision event is vi-sualized by plotting the local coordinates of the two dipolemoments in successive time-frames. In the central time-frame(lasting 4 ps), the two molecules dance tightly oriented one re-spect to the other, driven by Velec, plotted in the bottom panel.

Extensive computations clearly confirm that the phe-nomenon arises at large R; it becomes particularly evi-dent when projectile and target molecules are both in low

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124318-5 Roncaratti, Cappelletti, and Pirani J. Chem. Phys. 140, 124318 (2014)

(a)

(b)

(c)

FIG. 5. Examples of coplanar molecular collisions at relative velocity g = 1.0 km/s and impact parameter b = 1.0 nm (see text).

rotational states; it is more efficient when the rotation fre-quencies closely match, favoring a sort of “resonance” (seealso Ref. 12); it is less active when the rotational energy in-creases, but the effect persists even after averaging over ther-

mal rotational Boltzman distributions; the coupling occurs ina time scale of picoseconds, being this time scale comparableboth with the period of low lying-rotational states and alsowith the collision time. The average electric field felt by each

FIG. 6. Two water molecules initially in the rotational level J = 1 and with the dipole vectors rotating in perpendicular planes colliding at a relative collisionvelocity g = 1.5 km/s and impact parameter b = 1.0 nm. In the initial −6 ps < t < −2 ps time-frame, both molecules freely rotate but at approximately 4 nmdistance (t = −2 ps), they start to interact, as indicated by the slight distortion of their motion; the –2 ps < t < 2 ps time-frame shows the insurgence of apendular state and the associated coupled motion occurring in the neighborhood of the turning point (R = 1.0 nm; t = 0); further on (2 ps < t < 6 ps) at R > 4nm, the molecules return to the free rotor condition but with a change of the relative orientation of J.

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124318-6 Roncaratti, Cappelletti, and Pirani J. Chem. Phys. 140, 124318 (2014)

water molecule at R = 1.0 nm (the distance mainly probedby the present experiments), as derived from the measured in-teraction energy (see Fig. 1(b)), amounts to 130 kV/cm. Thisresult represents an average over all accessible configurationswithin the collision complexes and it is expected to increasewith the decrease of distance. Not surprisingly, this value islarger than fields typically used with the brute force technique(20 kV/cm).

V. CONCLUSIONS

In the present paper, we presented new high resolutionscattering results and their analysis showing for the first timeand for the most important and ubiquitous molecule, wa-ter, a previously unnoticed stereodynamical effect emergingat long-range and having a major influence on the value ofthe experimental observable we measure, the total scatteringcross section. The combined analysis of these and other scat-tering data, obtained under the same conditions, by means ofsuitable theoretical models, suggests as crucial the dialogueat large distance between the two colliding water molecules,leading to a sort of spontaneous, synchronized dance withinthe collision complex. Specifically, we demonstrated that thelong-range electrostatic (permanent dipole-permanent dipole)interaction acting between the two water molecules is thedriving force of the observed stereodynamical effect and pro-motes the selective transformation of rotational motions intospecific pendular states. The dynamical treatment developedallowed us to verify that this natural orienting field is at leastof the same order of magnitude then those exploited in thebrute force technique and that the generated pendular mo-tions survive for the few picoseconds, which are typical ofthe collisional times. Moreover, the simulation showed thatthis effect affects a wide range of rotational states and occursfor several collisional energies. Therefore, due to the abun-dance of water in the atmosphere, this must be a commonnatural phenomenon, even if never noticed previously at thepresent level of detail. Finally, we have demonstrated experi-mentally that the emergence of these pendular states is com-mon to molecules other than water, such as ammonia and hy-drogen sulfide, the presence of permanent dipole moments (oreven quadrupole moments) being the only prerequisite.

We conclude with some considerations on possible im-pacts to and/or relationships with other phenomena of greatinterest. The experimental findings presented here representa clear evidence of molecular polarization that can emergein gas phase but is related to all cases where sufficientlyanisotropic non-covalent interactions are at play, as for in-stance at the gas–surface interfaces23 or even in liquid water.24

The insurgence of long-range pendular states can be also con-nected to the formation in early stages of aligned moleculesin one dimension water wires,3 a process known to af-fect structure and dynamics of naturally occurring biologi-cal systems.25 Finally, the present results must relate withthe stereodynamics of elementary chemical processes, involv-

ing open shell atoms,26 free radicals,8, 27 and ionic species,28

where anisotropic non-covalent intermolecular interactionscontrol the selective trapping of reagents in the entrance chan-nels of bimolecular chemical reactions.

ACKNOWLEDGMENTS

This work has been supported by the Italian Ministerodell’Istruzione, della Ricerca e dell’Universitá (PRIN 2010-2011, Grant No. 2010ERFKXL_002). L.F.R. acknowledgesthe Conselho Nacional de Pesquisa (CNPq).

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