Interaction of O2 with CH ,CF, and CCl by Molecular Beam ...nunzi/papers/O2_CX4.JPC_A.2016.pdf · Scattering Experiments and Theoretical Calculations David Cappelletti,† Vincenzo

Interaction of O2 with CH4, CF4, and CCl4 by Molecular BeamScattering Experiments and Theoretical CalculationsDavid Cappelletti,† Vincenzo Aquilanti,† Alessio Bartocci,† Francesca Nunzi,†,‡ Francesco Tarantelli,†,‡

Leonardo Belpassi,‡ and Fernando Pirani*,†

†Dipartimento di Chimica, Biologia e Biotecnologie, Universita ̀ di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy‡CNRIstituto di Scienze e Tecnologie Molecolari, Via Elce di Sotto 8, 06123 Perugia, Italy

*S Supporting Information

ABSTRACT: Gas phase collisions of O2 by CH4, CF4, and CCl4 have beeninvestigated with the molecular beam technique by measuring both the integralcross section value, Q, and its dependence on the collision velocity, v. Theadopted experimental conditions have been appropriate to resolve the oscillating“glory” pattern, a quantum interference effect controlled by the features of theintermolecular interaction, for all the three case studies. The analysis of the Q(v)data, performed by adopting a suitable representation of the intermolecularpotential function, provided the basic features of the anisotropic potential energysurfaces at intermediate and large separation distances and information on therelative role of the physically relevant types of contributions to the globalinteraction. The present work demonstrates that while O2−CH4 and O2−CF4are basically bound through the balance between size (Pauli) repulsion anddispersion attraction, an appreaciable intermolecular bond stabilization bycharge transfer is operative in O2−CCl4. Ab initio calculations of the strength ofthe interaction, coupled with detailed analysis of electronic charge displacement promoted by the formation of the dimer, fullyrationalizes the experimental findings. This investigation indicates that the interactions of O2, when averaged over its relativeorientations, are similar to that of a noble gas (Ng), specifically Ar. We also show that the binding energy in the basicconfigurations of the prototypical Ng−CF4,CCl4 systems [Cappelletti, D.; et al. Chem. Eur. J. 2015, 21, 6234−6240] can bereconstructed by using the interactions in Ng−F and Ng−Cl systems, previously characterized by molecular beam scatteringexperiments of state-selected halogen atom beams. This information is fundamental to approach the modeling of the weakintermolecular halogen bond. On the basis of the electronic polarizability, this also confirms [Aquilanti, V.; et al. Angew. Chem.,Int. Ed. 2005, 44, 2356−2360] that O2 can be taken as a proper reference partner for simulating the behavior of some basicnoncovalent components of the interactions involving water. Present results are of fundamental relevance to build up the forcefield controlling the hydrophobic behavior of prototypical apolar CX4 (X = H, F, Cl) molecules.

I. INTRODUCTION

The detailed experimental characterization of strength andnature of the intermolecular interactions in systems involving O2and small hydrogenated and halogenated molecules, such asCH4, CCl4, and CF4, has been the target of this work. The resultsof the present investigation, motivated by the relevance of theweak intermolecular bonds in fields ranging from the chemistryof elementary processes to biochemistry and carried out in aninternally consistent way, are basic for the formulation of reliablemodel potentials able to describe properly both the static and thedynamic properties of these and of more complex aggregates.1−8

In addition to the prototypical CX4−Ng systems (X = H, Cl, Fand Ng = He, Ne, Ar),9 the weakly bound aggregates, formed bythe same polyatomic molecules and O2, have been chosen assystems of interest to be investigated in detail to extend thesystematics. Indeed, previous experimental observations sug-gested that Ar andO2 interacting with the same partner by typicalnoncovalent interactions exhibit a very similar feature.10 Thisevidence emerges when experiments are performed with

rotationally hot O2, scattered by a given target, that is, whenthe diatomic molecule behaves like a spherical projectile, sincethe anisotropy associated with the different orientations of itsmolecular axis is effectively averaged out. Also, scatteringexperiments with fast rotating O2, by measuring integral crosssections and their velocity dependences, permit a bettercharacterization of the “glory” interference effects, with respectto the same experiments with the Ar projectiles. This occursbecause of an improved signal-to-noise ratio and an increasedangular resolution that requires small limiting angle corrections.We performed high-resolution molecular-beam (MB) scatter-

ing experiments that probe with high sensitivity both absolute

Special Issue: Piergiorgio Casavecchia and Antonio Lagana Fes-tschrift

Received: January 28, 2016Revised: March 1, 2016

Article

pubs.acs.org/JPCA

© XXXX American Chemical Society A DOI: 10.1021/acs.jpca.6b00948J. Phys. Chem. A XXXX, XXX, XXX−XXX

scale and anisotropy of the intermolecular potentials for thesegas-phase binary complexes. The analysis of the glory quantuminterference pattern, observable in the velocity dependence ofthe integral cross section, establishes quantitatively the nature ofthe van der Waals (vdW) forces for the intermolecularinteraction in O2−CH4 and CF4 systems, arising from thecombining role of size repulsion and dispersion attraction: anappropriate model potential can accordingly be provided. On theother hand, the same analysis of the measured potential well fromthe O2−CCl4 scattering data reveals the role of a contribution tothe binding energy for some specific geometries of the interactingpartners, additional to the expectation from pure vdW behavior.A similar effect was also observed for Ar−CCl4.

11,12 For this casealso, in order to reproduce the O2−CCl4 experimental data, wehave introduced in the potential formulation a shift of therepulsive wall at shorter distances, accompanied by an increasedrole of the dispersion attraction, and a further stabilizationcomponent, assigned to an emerging charge transfer (CT)contribution.Preliminary analyses, presented in previous papers9,13 and

performed adopting different models, provide only an estimate ofthe averaged strength of the effective radial intermolecularpotential. Here the interaction is formulated in an internallyconsistent way and includes also the angular dependence in orderto extract, from a more complete analysis of the experimentaldata, information on the full intermolecular potential energysurface (PES). In addition, we performed ab initio calculationsaddressed to a proper evaluation of the electron densitymodification, as a consequence of the formation of theaggregates, to correctly define the role of CT through theanalysis of the charge displacement (CD) and to rationalize thesimilarity of O2 (an open-shell molecule) and Ar (a closed-shellatom), when interacting with CF4 and CCl4 molecules.The extended phenomenology has been exploited to isolate

the specific role of F and Cl atoms in these systems containingCF4 and CCl4, where evidence of a weak intermolecular halogenbond is emerging. This has been possible since systems, involvingpolyatomic molecules with high symmetry and bound through alimited number of interaction components, are more easilycharacterizable, electrostatic effects being absent and inductionattraction very weak.

Moreover, with O2, Ar, and H2O having a very similarelectronic polarizability (1.60, 1.64, 1.47 Å3, respectively),14 theobtained results are of relevance to define some basicnoncovalent interactions components determining the hydro-phobic behavior of highly symmetric and apolar CX4 molecules.Section II summarizes the experimental methodology. Section

III describes the formulation of the PES, and section IV presentsthe data analysis. A discussion follows in section V, and someconclusions are given in section VI.

II. EXPERIMENTAL METHODS

Scattering experiments have been performed with a MBapparatus, which operates under high angular and velocityresolution conditions.15 The objective has been the measure-ment of the integral cross section Q as a function of the selectedMB velocity v. The apparatus used has been extensively describedelsewhere.15 A sketch is reported in Figure 1 in order to point outthe key features of the experimental arrangement of relevance forthis investigation.The apparatus is composed by a set of differentially pumped

vacuum chambers where the MB, in the present case formed byrotationally hot O2, is produced by the gas expansion from thenozzle, maintained at a temperature that could be varied in a widerange. Under the typical conditions of temperature (500 K) andpressures (in general less than 15 mbar), the O2 MB emergeswith near effusive or moderately supersonic character. It iscollimated by two skimmers and a defined slit and then isanalyzed in velocity by a mechanical selector formed by sixslotted disks. The so formed projectile O2 molecules, flying in theselected slice of the beam velocity distribution, collide with thestationary target gas (CH4, CCl4, or CF4) contained in thescattering chamber and are detected by a quadrupole massspectrometer coupled with an ion counting technique. In theseexperiments the scattering chamber has been filled with the gastarget at ≃10−3−10−4 mbar.The fundamental quantity to be measured at each selected

“nominal” velocity v is the MB attenuation I/I0: I represents theMB intensity detected with the target in the scattering chamberand I0 that without it. From the measurement of the I/I0 ratio it ispossible to determine the value of the integral cross sectionQ(v)through the Lambert−Beer-like law:

Figure 1. In the upper panel a sketch is reported of the experimental apparatus used for the scattering experiments. In the lower panel the relativevelocity distributions f(g,v′) are reported. They are obtained for three specific beam velocities (v′ of 0.6, 1.3, and 2.0 km/s), and assuming as target CCl4or CF4 at room temperature and CH4 at 90 K.

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B

= −Q vNL

II

( )1

log0 (1)

where N is the target gas density and L the path length of thescattering region chamber15 (calibration data are given in refs16−18).The experimental Q(v) value in the laboratory (LAB) frame is

related to the center-of-mass (CM) cross section QCM(g), whichis a function of the relative collision velocity g, through thefollowing relation:15

∫ ∫= ′ ′ ′∞ ∞

Q v R v T v v v Q g f g v g( ) ( ) ( , ) d ( ) ( , ) d0 0

CM

(2)

where R(v) is a factor that limits the value of the measured crosssection because of the finite angular resolution of the experiment.Since R(v) depends on mass and velocity of the projectile, itsvalue is different for the scattering of the O2 and Ar projectiles bythe same target.In eq 2, T(v′,v) describes the transmission function of the

velocity selector, which depends on the transmitted velocity v′,for which the nominal peak value is v, whose full width at half-maximum (fwhm) is lower than 5%. The function f(g,v′) is therelative velocity distribution, providing the proper weight factorin eq 2; it is dependent on the combination of the motion in theforward direction of the velocity selected projectile (flying at v′)with the random motion of the molecular gas target at thermalequilibrium. f(g,v′) takes the form

π′ =

′−

′ −

− −′ +

⎜ ⎟⎛⎝

⎞⎠

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎡

⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥⎫⎬⎪⎭⎪

f g vv

gv

v gv

v gv

( , )1

exp

exp

1/2p

2

p

2

p

2

(3)

where vp is the most probable velocity of the target molecules atthe scattering chamber temperature.In planning this work, a crucial point regarded the choice of the

experimental conditions: because of their relatively high masses,CCl4 and CF4 have been used as targets in order to increase theangular resolution of the experiments, since under suchconditions the R(v) value in eq 2 is approaching 1.0. Moreover,the scattering chamber containing the target has beenmaintainedat room temperature (300 K) in all the measurements in order toavoid condensation phenomena on the walls of the chamber andto exploit a direct comparison of the present scattering data withthose measured under the same conditions and with otherprojectiles.11,12

The obtained results can be directly compared with thosepreviously measured for O2−CH4,

13 where CH4 was confined inthe scattering chamber, cooled at 90 K, in order to increase theenergy resolution by limiting the random thermal motion of thetarget.The features of the f(g,v′) function are crucial for the control of

the obtained velocity resolution conditions: the lower panel ofFigure 1 shows the behavior of f(g,v′) for some selected projectilevelocities, v = v′ = 0.6, 1.3, 2.0 km/s, and using as target at 300 KCCl4 (vp = 0.180 km/s) or CF4 (vp = 0.238 km/s). For the lightertarget CH4, the cooling of the scattering chamber at 90 K reducesstrongly its random motion (vp ≃ 0.306 km/s) and the achievedvelocity resolution is only slighty lower than that for the CF4 case.The width of f(g,v′) (see lower panel of Figure 1) appears to be a

critical quantity, since it directly influences the possibility ofobserving experimentally, in the LAB frame, the oscillatorypatterns in the velocity dependence of Q(v), due to quantuminterference effects.TheQ(v) data, measured for O2−CH4, CF4, and CCl4 systems

as a function of the selectedMB velocity v, are reported in Figures2−4. In all cases, the cross sections are plotted as Q(v)v2/5 to

emphasize and compare, for the present homologous family ofcolliding systems, the well resolved oscillatory patterns due to the“glory” quantum interference. The O2−CH4 and O2−CF4collision complexes show similar trends in the measured data,both in the absolute scale and in the glory interference, while the

Figure 2. Integral cross section, reported as Q(v) v2/5, plotted as afunction of the MB velocity v for the O2−CH4 system. Black circlesymbols are the experimental data. Solid colored lines provide thecontributions from different cuts of the PES. Dashed and dotted blacklines provide the contributions from spherical and anisotropic (IOS)molecular models, respectively. The solid black line considers acombination of these two contributions, according to the differentdynamical regimes discussed in the text.

Figure 3. As in Figure 2 for the O2−CF4 system.

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O2−CCl4 system exhibits a very different behavior, thus revealingsignificant differences in the intermolecular interactions of O2−CCl4 with respect to those of the O2−CH4 and O2−CF4 systems.The analysis of Q(v) (see next sections) provides a

quantitative description of the strength of the intermolecularinteraction combining information both at long range (obtainedfrom the velocity dependence of the average value of Q(v)) andin the potential well region (probed by the glory structure).19,20

During the analysis, the QCM(g) values have been calculatedwithin the semiclassical Jeffreys−Wentzel−Kramers−Brillouin(JWKB) method21 from the assumed intermolecular interactionV (see next section) and then convoluted in the LAB frame (seeeq 2) to make a direct comparison with the measured Q(v).

III. ATOM-BOND PAIRWISE ADDITIVEREPRESENTATION OF THE PES

In the thermal energy range, a small and fast rotating moleculelike O2 behaves as a pseudoatom during the scattering and itseffective interaction can be formulated as determined only by oneinteraction center confined in its CM (see refs 22−24). On theother hand, slowly rotating polyatomic molecular targets areadequately described by considering several interaction centersdistributed on the molecule frame and localized on the chemicalbonds.25 The employed formulation treats the involvedinteraction as determined by a repulsion due to effectivemolecular sizes,10,25 strongly dependent on the molecularorientation, and an attraction determined by the combinationof several pseudoatom−molecular bond contributions.25,26,27,28

A realistic description of the potential energy anisotropy is thenobtained, since such a formulation indirectly accounts for theelectronic charge distribution along the molecular frame. Thisapproach, which exploits the polarizability partition of apolyatomic molecule in bond tensor components, provides arealistic picture of both the repulsion and the attractivecomponents of a vdW interaction and, in addition, effectivelyincludes both three-body and other nonadditive effects.26

Accordingly, in this study the interaction centers (a, b) havebeen localized on the O2 pseudoatom and on each of the four C−X bonds of CX4 molecules, X being H, F, or Cl. Therefore, thevdW intermolecular potential component (VvdW) has been takenas a sum of four pseudoatom−bond interaction terms, VvdW =∑abVab, each one represented by an improved Lennard-Jones(ILJ) function20 of the type

α ε αα

α

αα

α

=−

−−

α⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥

V rm

n r mr

r

n rn r m

rr

( , ) ( )( , )

( )

( , )( , )

( )

abm

n r

mm

( , )

(4)

where r is the distance of the pseudoatom (localized on O2 CM)from the interaction center on each bond, and α is the angle that rforms with the axis of the considered bond. The parameter m isset equal to 6 for all the pseudoatom−bond interactions. Such asimple formulation provides a realistic picture of both the pairrepulsion (represented by the first term) and the pair attraction(given by the second term), leading to a proper description ofboth equilibrium and nonequilibrium geometries of the weaklybound aggregates.26 It is also given in a form that can beconveniently exploited in molecular dynamics simulations tocalculate static and dynamical properties of clusters formed by avariety of atomic and molecular species (see for instance refs29,30). The parameter n, which defines the ”fall off” of the atom−bond repulsion, depends on β (related to the hardness of thepartners31) and is expressed as a function of both r and α usingthe equation

α βα

= +⎛⎝⎜

⎞⎠⎟n r

rr

( , ) 4( )m

2

(5)

The other potential parameters, i.e., ε and rm (representing,respectively, the well depth and the equilibrium distance of therelevant interaction pair), depend on the atom−bond orientationangle α according to assumed functional forms:26

ε α ε α ε α= +⊥( ) sin ( ) cos ( )2 2(6)

α α α= +⊥r r r( ) sin ( ) cos ( )m m m2 2

(7)

where⊥ and ∥ refer to perpendicular and parallel approach of thepseudoatom-O2 to the bond, respectively. Note that for eachinteracting pair the asymptotic long-range attraction coefficient isequal to ε(α) rm(α)

6 and the global attraction coefficient dependson the sum of such components.As previously,11,12,26,30,32,33 in the present investigation each

interaction center on the polyatomic molecules has beenlocalized for C−H on the middle point of the bond, and forC−F and C−Cl, respectively, at about 60% and 80% of the bondlength toward the halogen atom.11,12

Table 1 reports the values of all the ε, rm potential parametersthat are expected on the basis of the bond polarizability tensorcomponents, which are related to the dimension of the electronic

Figure 4. As in Figure 2 for the O2−CCl4 system.

Table 1. ILJ Potential Parameters (rm in Å, ε and A in meV, β =7.00) for O2−CH, CF, CCl Atom−Bond Pairs Compared toThose of Ar−CH, CF, CCl Bond Pairsa

rm∥ ε∥ rm⊥ ε⊥ A × 105

O2−CH 3.84 4.00 3.63 4.84Ar−CH26 3.85 3.98 3.64 4.81O2−CF 3.89 5.63 3.64 6.33Ar−CF 3.90 5.59 3.64 6.26O2−CCl 4.18 10.98 4.03 10.17 6.5Ar−CCl11,12 4.18 10.98 4.04 10.16 6.5

aThe maximum estimated uncertainty is about 6% for ε, 2% for rm, and10−15% for A.

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charge distribution around each bond34 and are consistent withthe values of the molecular polarizability.35 Such componentshave been combined with the spherical polarizability of O2 (1.6Å3) in the correlation formulas10,25 predicting the VvdWparameters. In obtaining the potential parameters values forO2−CCl4 reported in Table 1, it has been also required that atlong-range they must generate a global average attraction insubstantial agreement with the calculation using the dispersioncoefficient (C6 = 2.08 × 105 meV·Å6) reported by Kumar36 (a C6value of 1.94 × 105 meV·Å6 is obtained from the presentanalysis). As for Ng−CCl4,

11,12,37,38 the rm∥ values have beendecreased by about 4% to account of the “polar flattening” effect,due to the anisotropic distribution of the electronic chargearound the bound Cl halogen atom, and ε∥ adjusted asconsequence. The parameters of Ar−CH, CF, and CCl havebeen also reported for a useful comparison. The dynamicaltreatment used for the data analysis (see next section) haspermitted the satisfatctory reproduction of measured crosssections for O2−CH4 and O2−CF4 simply adopting the atom−bond representation of VvdW. This result represents afundamental test of the employed methodology and confirmsthe reliability of the potential parameters listed in Table 1,indicating the occurrence of a pure vdW component in O2−CH4and O2−CF4. However, although the correct “polar flattening”parameters were used, the same methodology was unable toreproduce the experimental data measured for the O2−CCl4system. As for Ar−CCl4, the reproduction of the glory pattern,observed for such system, has been obtained by introducing afurther modification in the potential formulation, concerning theaddition of an other stabilizing component, emerging atintermediate and short distance.A contribution associated with possible charge-transfer effects

has been included in the potential by adding the term

α= − γ−V A cos ( ) e rCT

4(8)

The value of the exponent γ, which defines the “fall off” of theVCTwith r, has been assumed to be the same adopted for Ng−CCl4.

11,12,39,40 Therefore, during the best fit of cross section data,only the pre-exponential A factor has been adjusted; the finalvalue is given in Table 1 and is coincident with that previouslyobtained for Ar−CCl4.

11

IV. DATA ANALYSIS

As indicated above, in the thermal collision energy range theaverage component of Q(v) and the oscillatory pattern providecomplementary information on the intermolecular interaction,being dependent on collisions at large and intermediate orbitalangular momentum, respectively, which are directly affected bythe strength of the long-range attraction and by the features ofthe well depth, respectively.20,21,41

For the present experiments, carried out with moleculeshaving a broad Boltzmann distribution of rotational states, theexact calculations ofQCM(g) would require a huge computationaleffort. It has been demonstrated42,43 that under the usedconditions the collision dynamics can be treated semiclassically.In particular, the analysis of the integral cross section datameasured with rotationally “hot” molecules, which exhibit aprobability of inelastic events reduced with respect to the samerotationally “cold” molecules, can be safely based on someapproximations in their theoretical treatment,42,43 which makeeasier the cross section calculations and provide insights on thephysical picture.

These approximations apply to collisions occurring atintermediate and large impact parameter (the classical equivalentof the orbital angular momentum), such as those probed by thepresent experiments, with no loss of any relevant information onthe intermolecular interaction. Motivations arise from (i) theexperimental observation of the absence of any appreciable gloryamplitude quenching, due to the interaction anisotropy, whenthe mean molecular rotation time is comparable or shorter thanthe collision time;42−46 (ii) the suggestions, from scatteringexperiments42−47 and theory,42,43 that the interaction anisotropybecomes more effective, generating a more pronunced “glory”amplitude quenching, when the collision velocity overcomes thevalue for which the collision time becomes significantly shorterthan the molecular rotation time. Under such conditions, theprojectile interacts with the molecule suddenly; i.e., theinteracting complex tends to maintain “memory” of a specificconfiguration while collisions evolve.In the present study, the collision dynamics has been then

confined within two different regimes defined by (i) a sphericalmodel, where both molecules behave as “pseudoatoms” and thescattering, mostly elastic, is driven by a central potential close tothe isotropic component (spherical average) of the full PES, and(ii) an anisotropic molecular model, where the cross section isrepresented as a combination of independent contributions fromlimiting configurations of the pseudoatom (O2)−moleculecollision complex. That is, a sort of “infinite order sudden”(IOS) approximation is applied (see for instance refs11,15,42,43). In particular, for the present systems three limitconfigurations, related to three different cuts of the PES, havebeen selected as representative of the interaction anisotropy.They describe the intermolecular interaction potential V whenthe pseudoatom approaches to the vertex (Vv), the face (Vf), andthe edge (Ve) of the tetrahedral molecule. Accordingly, the tworegimes selectively emerge as a function of the ratio between themean rotation time, τM, and the collision time τcoll. Theformer,τM, is the time required to probe an effective potentialclose to the isotropic component of the PES, which can beestimated also as an average among interactions associated withthe limiting configurations of the collision complex; for furtherdetails regarding its estimation see refs 11 and 12 and referencestherein. The latter, τcoll, evaluated according to refs 15 and 43, isfound to be varying between ≃2 and ≃0.5 × 10−12 s with thebeam velocity at v = 0.5 and 2.2 km/s, respectively. Thecomparison of times suggests that the CCl4 molecules can beconsidered as rotating sufficiently fast during the collisions onlyat low v (v ≤ 0.80 km/s),11,12 while for CF4 and CH4 the samelimit occurs for v≤ 1.1 km/s. Therefore, in the low velocity limit,the collisions have been considered exclusively elastic and mainlydriven by an “effective” radial potential V(R) (R is theintermolecular distance defined as the separation between theCM of two partners) related to the isotropic component of thePES, obtained at each R by averaging the interaction over all theangular coordinates. At higher velocity, i.e., when τcoll < τM, theanisotropic molecular regime sets in. In this case, at each v, theindividual cross sections, calculated from Vv, Vf, and Ve, havebeen combined according to the following normalizationpreserving relation:

=+ +

Q vQ Q Q

( )4 6 4

14v e f

(9)

where the numerical coefficients represent the degeneracy of thelimiting configurations.

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The final theoretical Q(v) values, to be compared with theexperimental data, have been then calculated within the sphericalmodel at low v and according to the anisotropic molecular modelat high v. At intermediate v, the switch between the dynamics ofthe spherical model and that of the anisotropic molecular modelhas been obtained as a weighted sum, depending on v,15,48

according to the procedure detailed in refs 11 and 12.Cross sections, calculated according to the potential

parameters of Table 1, are compared with the experimentaldata in Figures 2−4, showing a very good description of all theinterference patterns.More in detail, cross sections calculated from the selected cuts

of the PES and from the spherical component are reported,together, with those obtained combining them, according to thedifferent dynamical regimes introduced above, in order toprovide a better comparison with the experimental data. Thecomplete calculations reproduce both the amplitude andfrequency of the observed glory pattern.Figure 5 displays, for each O2−CX4 systems, the total potential

energy V as a function of the intermolecular distance R for boththe selected cuts of the PES and for the spherical component.

V. DISCUSSION

The systems investigated in this paper can be considered assuitable reference cases for modeling the leading VvdWcomponent and other possible additional contributions to theinteractions in prototypical aggregates involving symmetricapolar molecules.Isotropic and Anisotropic Components of the Inter-

action. The analysis of theQ(v) data for O2−CH4 and O2−CF4,measured in the thermal collision energy range and showing wellresolved glory patterns, has been carried out with a semiclassicalmethod. The PESs so characterized are fully describable as sumof contributions, VvdW =∑abVab, where each Vab is formulated asindividual pseudoatom−bond interaction components.11,12 Inthese two systems, the strength of the average (isotropic)component is similar, as effectivelly exhibited by the closeness ofthe measured absolute values of Q(v). Regarding the anisotropyof the interactions, experimentally pointed out by the quencingof the glory oscillations, it appears slightly larger for CF4 than forCH4, as expected for the C−F bond being longer with respect to

the C−H one. From this viewpoint, because of the smallerdimensions, the methane molecule behaves as a more sphericalpartner than CF4.The O2−CCl4 system shows a quite different behavior with

respect to the previous two cases: the average interaction isstronger both at long-range and in the potential well region, asexpected because of the increased molecular polarizability α(10.48 Å3 for CCl4 with respect to 2.78 and 2.60 Å

3 for CF4 andCH4, respectively; for both CCl4 and CF4 the contribution of theindividual halogen atoms represents more than the 80% of theoverall α value). Also the anisotropy manifests a differentbehavior. Specifically, the interaction in the vertex configurationis significantly stabilized by an additional short-range compo-nent.A similar additional stabilization effect by CT was charac-

terized in the analysis of He, Ne, Ar−CCl4 systems.11,12 For O2−

CCl4, theQ(v) data have been measured under increased angularresolution conditions with respect to similar experimentsperformed on Ar−CCl4, leading to the observation of a betterresolved glory pattern, with a consequent more accurate probe ofthe interaction.The present analysis confirms the validity of the model

potential previously used, which includes explicitly the role of CTin the formulation of the interaction only in the aggregatesinvolving CCl4 molecule.In order to properly rationalize the experimental findings for

CF4 and CCl4 interacting with various partners, we found ituseful to focus on two aspects, concerning (i) the analysis of theelectron density distribution in complexes as O2−CF4, CCl4,with O2 being an open shell 3Σg

− paramagnetic species, and itscomparison with that in Ar−CF4, Ar−CCl4, with Ar being aclosed shell 1S0 atom; and (ii) the characterization of the specificrole of the halogen atoms within the CF4 and CCl4 moleculeswhen interacting with various partners.

Charge Displacement Analysis and Charge TransferContribution by High-Level ab Initio Calculations. Inorder to clearly define the role of the CT contribution in theO2(Ar)−CX4, X = F, Cl interacting systems, we first carried outconstrained geometry optimizations on the vertex configurationby high-level ab initio calculations; see Supporting Informationfor further details. Afterward, we analyzed the electron density

Figure 5.Total potential energy (V) of the O2−CX4 systems plotted as a function of the intermolecular distance (R) between the CM of O2 and of CX4for three selected cuts of the PES (solid color lines), together with the spherical component (dashed line) of the same PES.

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changes due to the interaction between CX4 and O2 (Ar) in thevertex configuration by means of the charge displacement (CD)function, Δq(z). This function gives at each point (z), chosen

along an axis joining the two interacting fragments, the netelectronic charge that, upon formation of the complex, has beendisplaced from right to left across the plane perpendicular to the

Figure 6. CD curves for the vertex configuration of the O2−CCl4 system in the collinear (a) and perpendicular (b) orientations of the O−O bond andfor the Ar−CCl4 system (c). The insets show 3D isodensity plots of the electron density change due to the intermolecular interaction. The isodensitysurfaces are for Δρ = ±0.05 me/bohr3 (negative values in red, positive in blue). (d) CD curves for the O2−CCl4 system in the collinear (red) andperpendicular (blue) orientations and that obtained as weighted average in the ratio 1:2 (curve with dashed line), according to their degeneracy, arecompared with the CD curve of the Ar−CCl4 system. The dots correspond to the positions of nuclei on the z axis, which is here the axis joining the C−Clbond with the CM of O2 (Ar). The axis origin is at the CM of CCl4. The vertical dashed lines mark the isodensity boundaries between the fragments.

Figure 7.CD curves for the O2−CF4 system in the collinear (a) and perpendicular (b) orientations. The insets show 3D isodensity plots of the electrondensity change accompanying bond formation. The isodensity surfaces are forΔρ =±0.05me/bohr3 (negative values in red, positive in blue). The dotscorrespond to the positions of nuclei on the z axis, which is here the axis joining the C−F bond with the CM of O2. The axis origin is at the CM of CF4.The vertical dashed lines mark the isodensity boundaries between the fragments.

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axis and passing through that point z (see SupportingInformation for a detailed description).49 This approach hasbeen successfully employed in several diverse contexts toinvestigate charge fluxes both in transition-metal com-pounds50−52 and in weak intermolecular systems.11,12,24,32,33

The results of the CD analysis for O2(Ar)−CX4, X = F, Cl, arereported in Figures 6 and 7. While the insets show the isosurfacesof the electronic density difference, the main panels display, onthe same horizontal scale, the CD curves. We considered the O2molecule approaching the CX4 molecule in both a collinear andperpendicular orientation, which can be unambiguously definedby the angle between theO−Obond and the C3 symmetry axis ofCX4, being 180° and 90°, respectively.Figure 6, top of the panel, reports the CD analysis of the O2−

CCl4 system. The 3D plot of the isodensity deformation showsthat CCl4 strongly polarizes the electron cloud of the O2molecule both in the collinear (a) and in the perpendicular (b)orientations. The charge polarization is similar in both cases: theO2 molecule undergoes a charge depletion (red color) in theregion opposite to Cl and a charge accumulation (blue color)toward the halogen atom. A certain amount of chargerearrangement is present also on the CCl4 partner.The analysis of the corresponding Δq curve returns a

quantitative picture of the interaction between O2 and CCl4molecules. In particular, the electronic charge starts flowingtoward the CCl4 moiety from the right side of the O2 molecule sothat the Δq presents the maximum value close to the O2 CM.Further to the left, the CD function value decreases reaching aminimum but remaining positive. Subsequently, the charge startsto reaccumulate (at the right side of Cl), the CD functionincreases and than remains almost stable in the region of the C−Cl bond, decreasing to zero at the left side of the CCl4 moiety.Since the Δq curve is distinctly positive in the whole interactingsystems, we can conclude that a net CT occurs from O2 to CCl4independent from the relative orientation of the interactingpartners. A numerical value of CT can be estimated byconsidering the CD function value at a specific point betweenthe fragments along the z axis. Our choice has been the pointalong z where the electron densities of the noninteractingfragments become equal (isodensity boundary). This choice isreasonable, especially for small weakly interacting systems.22 Theposition of the minimum on the CD curve is close to thisisodensity boundary, located at 3.5 Å from the carbon atom and1.6 (2.1) Å from O2 in the perpendicular (collinear) orientation.At this point, the Δq value, which we take as an estimate of CTfrom O2 to CCl4, is equal to 0.6 me in the perpendicularorientation and 1.1 me in the collinear one. The analysis of CDcurves for the collinear and perpendicular orientation in the O2−CCl4 complex clearly shows that the anisotropy of the O2molecule does not qualitatively affect the nature of theintermolecular interaction. Also, the comparison of the CDfunction curves points out that the CT fromO2 to CCl4 is slightlymore efficient in the collinear rather than in the perpendicularorientation.The CD analysis of the Ar−CCl4 system is reported in Figure

6c for comparison. The inset shows the isosurfaces of the densitydeformation of the Ar−CCl4 complex, which closely resemblesthe 3D isodensity plot of the O2−CCl4 system, with a largedensity accumulation lobe on the side toward the Cl atom anddepletion when opposite to it, accompanied by a sizable amountof charge rearrangement on the CCl4 moiety. As described abovefor the O2−CCl4 system, the CD function curve for Ar−CCl4 isinvariably positive over all the complex and at the isodensity

boundary the CT (in the direction from Ar to CCl4) is equal to0.31 me.Our preliminary analysis confirms the occurrence of an

appreciable electron transfer from O2 and Ar to CCl4 partner.However, theΔq is computed larger in O2−CCl4 with respect toAr−CCl4 (for further details see Supporting Information), whilethe analysis of the experimental data suggests that the role of CTis expected to be similar in the two systems (see section III).This can be rationalized by taking into account that the

experiments are affected by all the configurations and the mainlyprobed distances occur at shorter values with respect to thatoptimized in the vertex configuration.11 As outlined in theprevious sections, in the MB scattering experiments the O2molecules are fast rotating and behave almost as sphericalprojectiles, with molecular anisotropy averaged over all theorientations.This behavior can be roughly mimicked by means of a

weighted average of the CD function of the limiting collinear andperpendicular orientations of O2−CCl4 according to their one-to-two degeneracy, thus allowing a more reliable comparisonwith the CD of Ar−CCl4. As shown in Figure 6d, Ar−CCl4 andO2−CCl4 weighted average CD curves are close all over theentire interacting system, thus suggesting that electron densityfluctuations of the same magnitude occur in the complexesinvolving O2 and Ar partners, despite the presence of twounpaired electrons in the O2 molecule with respect to the closedshell Ar system. The similarity in the interaction can be related tothe value of the α polarizability of O2 and Ar, i.e., 1.60 and 1.64Å3, respectively.Finally, the CD curves for the O2−CF4 complex (collinear and

perpendicular orientations), together with the 3D plot of theisodensity deformation as insets, are reported in Figure 7. Asalready discussed for the Ng−CX4 series, X = F, Cl,9,11,12 thepattern of the CD function in O2−CF4 is completely differentfrom that in the O2−CCl4 complex. In particular, by comparingFigures 6 and 7, it is evident that the polarization of the O2molecule induced by CF4 is opposite that exerted by CCl4 forboth considered orientations. Indeed, the CD function isnegative at the O2 molecule, suggesting a charge shift from theleft to the right of the O2 molecule. Afterward, the CD functionassumes very small positive values in the region between themolecules and remains very close to zero in the whole region ofCF4. It even shows a change of sign in the middle of the distancebetween partners; thus the contribution of CT to theintermolecular halogen bond, if present, becomes hardlydiscernible and its role is expected to be negligible. A similarbehavior has been observed for the Ar−CF4 system. We cantherefore conclude that the CT component does not play aneffective role in the O2−CF4 complex (as already observed in theanalyzed Ng−CF4 systems),

11,12 with the attraction determinedsolely by the dispersion forces, and this result is independentfrom the relative orientation of the fragments.Therefore, our calculations support the experimental findings,

allowing an estimation of the CT interaction in the formation ofweak intermolecular halogen bonds and suggesting that the O2molecule behaves like a spherical projectile, as well as Ar atom,despite its O−O bond anisotropy and its open shell nature.

Specific Role of F and Cl Atoms in HalogenatedMethanes. The aggregates formed by CF4 and CCl4 moleculeswith noble gases, recently investigated with the same method-ology,11,12 must be considered as prototype systems for theformulation of models describing the weak intermolecularhalogen bond. In particular, the absence of the electrostatic

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and induction contributions favors the proper characterization ofthe other few effective interaction components. In addition to theimportance of modeling systems of increasing complexity, wehave found it remarkable to discover possible relations betweenthe basic features of the obtained PES in Ng−CF4 and Ng−CCl4and those of the interaction in noble-gas fluorides (NgF)53,54 andnoble-gas chlorides (NgCl)55−57 weakly bound dimers. Thelatter has been experimentally investigated by utilizing similarcollisional experiments, performed with fine structures stateselected F(2Pj) andCl(

2Pj) atomic beams scattered byNg targets.The data analysis permitted the characterization of the basicterms V0(r) (spherical component) and V2(r) (anisotropiccomponent),58−60 whose combination provides the VΣ(r) andVΠ(r) potential,53,54,56−58 namely, the interaction energiesassociated with molecular quantum states arising from differentalignment of the half-filled orbital of the halogen atom withrespect to the interatomic axis.The investigation of such weakly bound compounds

demonstrated that while V0(r) and VΠ(r) terms show asubstantial vdW character, VΣ(r) is selectively stabilized by aCT contribution (the ground neutral Ng−F, Cl and the ionicstate of the excimer Ng+−F−, Cl− having the same symmetry);the effect is an increase along the Ng family from He to Xe: thedecrease of the ionization potential of Ng induces a moreefficient coupling (configuration interaction) between neutraland ionic states.We have attempted to reproduce the binding energy in Ng−

CF4 and Ng−CCl4 systems in the limiting vertex and faceconfigurations, as combination of the experimentally determinedNg−F and Ng−Cl interaction potentials. The results of thisattempt are that for Ng−CF4, both in the vertex (see Table 2)

and in the face configurations (see Table 3), the moreappropriate combination is always that involving the V0component, each one scaled for the different distance of Fatoms in CF4 from Ng, leading to a binding energy of≃4V0. Thisconfirms the vdW character of the interaction in all the basicconfigurations of Ng−CF4 adducts.The comparison performed on Ng−CCl4 systems suggests

that the combination of 4V0 is suitable for the face configuration(see Table 3), but it underestimates the interaction in the vertex(see Table 2), for which it appears to be more appropriate to use3V0 + VΣ(r), where 3V0 refers to the contribution of the threemost distant Cl atom and VΣ(r) to the closer one.

Therefore, the proper combination of phenomenologicalpotentials, derived with different methods of analysis, provides astrong confirmation of the selective role of CT in systemsinvolving CCl4, which is instead practically absent in CF4.

VI. CONCLUSIONS

The results of the present investigation, carried out in aninternally consistent way on the O2−CX4 systems, are importantfrom several points of view, and specifically:

(1) to characterize the features and to quantify strength andanisotropy in the VvdW component;

(2) to assess the selective binding stabilization energy, arisingfrom CT effects;

(3) to understand and cast light on the specific role of thebound halogen F and Cl atom in CF4 and CCl4, whichassumes a different (F) and a similar (Cl) character withrespect to the isolate case. In particular, the open-shellnature of the isolated F atom is completely loosen in themolecule while that of Cl is partially mantained, assuggested by the need for introducing corrections in thepotential formulation, due to polar flattening effects andCT contributions as O2 approaches CCl4 along the vertexconfiguration (see also previous section and next point);

(4) to attribute differences in the experimental findings to thedifferent electronic charge distribution of the halogenatom bound in the molecule. Such differences were mostlyascribed to the change in sp-hybridization degree of F andCl atoms when forming the C−F and C−Cl bonds,respectively.61 In particular, the separation in the s and patomic orbital energies, smaller for F than Cl, favors theformation of C−F bonds with increased sp hybridizationdegree with respect to C−Cl.

In conclusion, the present investigation can contribute toassess the role of the vdW component in determining thehydrophobic behavior of prototypical CX4 molecules. Thepresent results are then of relevance to build up models for theintermolecular halogen bond occurring on aggregates of highercomplexity. Moreover, we demonstrated that O2, exhibiting anelectronic polarizability similar not only to Ar but also to H2O,can be used as suitable reference to cast light on the differencesand similarities in the peculiar nature of the interaction insystems involving water, oxygen, and argon with the samepartners (see refs 62−64 and references therein).

Table 2. Binding Energy (in meV) for Ng−CF4 and Ng−CCl4Systems in the Vertex Configuration, Obtained from theFormulation of the Interaction Discussed in the Texta

system model potential 4V0 3V0 + VΣ

He−CF4 2.85 2.50 2.80Ne−CF4 5.20 4.90 8.80Ar−CF4 9.50 6.90 15.60He−CCl4 3.60 3.00 3.70Ne−CCl4 9.30 2.00 8.20Ar−CCl4 19.30 8.70 19.3

aA comparison is reported with the values obtained as combination ofthe interaction components (the spherical term V0, of vdW type, andthe VΣ potential, stabilized by the CT contribution) in F(2Pj)−Ng andCl(2Pj)−Ng atom−atom systems, provided by a previous analysis ofscattering data measured with state selected open shell atombeams.53,54,56−58

Table 3. Binding Energy (in meV) for Ng−CF4 and Ng−CCl4Systems in the Face Configurationa

system model potential 4V0

He−CF4 6.30 5.90Ne−CF4 12.20 12.20Ar−CF4 19.00 20.00He−CCl4 6.20 6.10Ne−CCl4 13.30 13.70Ar−CCl4 33.50 36.70

aFor such configuration, the values obtained as combination of thespherical component V0

53,54,56−58 (see text and also Table 2)reproduce the model potential values (the use of VΣ componentprovides an overestimated binding energy).

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■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpca.6b00948.

Detailed description of the employed computationalmethods and the equilibrium structures and energeticstability of the investigated systems (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis paper has been supported by Italian Ministry for Education,University and Research, MIUR, (PRIN 2010−2011, Grant 2010ERFKXL_002 and SIR 2014 [RBSI14U3VF]) and byFondazione Cassa di Risparmio Perugia (Contract2015.0331.021).

■ REFERENCES(1) Arunan, E. Hydrogen bond seen, halogen bond defined and carbonbond proposed: intermolecular bonding, a field that is maturing! Curr.Sci. 2013, 105, 892−894.(2) Shahi, A.; Arunan, E. Hydrogen bonding, halogen bonding andlithium bonding: an atoms in molecules and natural bond orbitalperspective towards conservation of total bond order, inter-and intra-molecular bonding. Phys. Chem. Chem. Phys. 2014, 16, 22935−22952.(3) Goodnough, J. A.; Goodrich, L.; Farrar, T. C. Dynamics of DiluteWater in Carbon Tetrachloride. J. Phys. Chem. A 2007, 111, 6146−6150.(4) Chang, T.-M.; Dang, L. X. Computational Studies of Liquid Waterand Diluted Water in Carbon Tetrachloride. J. Phys. Chem. A 2008, 112,1694−1700.(5) Mierzwicki, K.; Mielke, Z.; Saldyka, M.; Coussan, S.; Roubin, P.Structure, spectra and stability of a tetrafluoromethane-water complex.Phys. Chem. Chem. Phys. 2008, 10, 1292−1297.(6) Caminati, W.; Maris, A.; Dell’Erba, A.; Favero, P. G. DynamicalBehavior and Dipole-Dipole Interactions of Tetrafluoromethane-Water.Angew. Chem. 2006, 118, 6863−6866.(7) Feng, G.; Evangelisti, L.; Gasparini, N.; Caminati, W. On the Cl−NHalogen Bond: A Rotational Study of CF3Cl-NH3. Chem. - Eur. J. 2012,18, 1364−1368.(8) Chandler, D. Hydrophobicity: Two faces of water. Nature 2002,417, 491−491.(9) Cappelletti, D.; Candori, P.; Pirani, F.; Belpassi, L.; Tarantelli, F.Nature and Stability of Weak Halogen Bonds in the Gas Phase:Molecular Beam Scattering Experiments and Ab Initio ChargeDisplacement Calculations. Cryst. Growth Des. 2011, 11, 4279−4283.(10) Cambi, R.; Cappelletti, D.; Liuti, G.; Pirani, F. GeneralizedCorrelations in Terms of Polarizability for Van der Waals InteractionPotential Parameter Calculations. J. Chem. Phys. 1991, 95, 1852−1861.(11) Bartocci, A.; Belpassi, L.; Cappelletti, D.; Falcinelli, S.;Grandinetti, F.; Tarantelli, F.; Pirani, F. Catching the role of anisotropicelectronic distribution and charge transfer in halogen bonded complexesof noble gases. J. Chem. Phys. 2015, 142, 184304−184314.(12) Cappelletti, D.; Bartocci, A.; Grandinetti, F.; Falcinelli, S.;Belpassi, L.; Tarantelli, F.; Pirani, F. Experimental Evidence of ChemicalComponents in the Bonding of Helium and Neon with NeutralMolecules. Chem. - Eur. J. 2015, 21, 6234−6240.(13) Liuti, G.; Pirani, F. Molecular Beam Study of the Interaction ofAtomic and Molecular Oxygen with Methane. J. Chem. Phys. 1987, 87,5266−5271.(14) Olney, T.; Cann, N.; Cooper, G.; Brion, C. Absolute ScaleDetermination for Photoabsorption Spectra and the Calculation of

Molecular Properties Using Dipole Sum Rules. Chem. Phys. 1997, 223,59−98.(15) Cappelletti, D.; Bartolomei, M.; Pirani, F.; Aquilanti, V. MolecularBeam Scattering Experiments on Benzene-Rare Gas Systems: Probingthe Potential Energy Surfaces for the C6H6−He, −Ne, and −Ar Dimers.J. Phys. Chem. A 2002, 106, 10764−10772.(16) Aquilanti, V.; Liuti, G.; Pirani, F.; Vecchiocattivi, F.; Volpi, G. G.Absolute total elastic cross sections for collisions of oxygen atoms withthe rare gases at thermal energies. J. Chem. Phys. 1976, 65, 4751−4755.(17) Nenner, T.; Tien, H.; Fenn, J. B. Total Cross SectionMeasurements for the Scattering of Argon by Aliphatic Hydrocarbons.J. Chem. Phys. 1975, 63, 5439−5444.(18) Pirani, F.; Vecchiocattivi, F. Absolute Total Elastic Cross Sectionsfor Collisions of He with Ne, Ar, Kr, and Xe. J. Chem. Phys. 1977, 66,372−373.(19) Pirani, F.; Vecchiocattivi, F. A Fast and Accurate SemiclassicalCalculation of the Total Elastic Cross Section in the Glory Energy range.Mol. Phys. 1982, 45, 1003−1013.(20) Pirani, F.; Brizi, S.; Roncaratti, L. F.; Casavecchia, P.; Cappelletti,D.; Vecchiocattivi, F. Beyond the Lennard-Jones model: a simple andaccurate potential function probed by high resolution scattering datauseful for molecular dynamics simulations. Phys. Chem. Chem. Phys.2008, 10, 5489−5503.(21) Child, M. Molecular Collision Theory; Claredon Press, Oxford,U.K., 1974.(22) Cappelletti, D.; Ronca, E.; Belpassi, L.; Tarantelli, F.; Pirani, F.Revealing Charge-Transfer Effects in Gas-Phase Water Chemistry. Acc.Chem. Res. 2012, 45, 1571−1580.(23) Pirani, F.; Cappelletti, D.; Belpassi, L.; Tarantelli, F.Intermolecular Interaction in the NH3-H2 and H2O-H2 Complexes byMolecular Beam Scattering Experiments: The Role of Charge Transfer.J. Phys. Chem. A 2013, 117, 12601−12607.(24) Bartocci, A.; Cappelletti, D.; Pirani, F.; Tarantelli, F.; Belpassi, L.Intermolecular Interaction in the H2S-H2 Complex. Molecular BeamScattering Experiments and Ab-Initio Calculations. J. Phys. Chem. A2014, 118, 6440−6450.(25) Pirani, F.; Cappelletti, D.; Liuti, G. Range, Strength andAnisotropy of Intermolecular Forces in Atom-Molecule Systems: anAtom-Bond Pairwise Additivity Approach. Chem. Phys. Lett. 2001, 350,286−296.(26) Pirani, F.; Alberti, M.; Castro, A.; Teixidor, M. M.; Cappelletti, D.Atom-Bond Pairwise Additive Representation for IntermolecularPotential Energy Surfaces. Chem. Phys. Lett. 2004, 394, 37−44.(27) Cappelletti, D.; Pirani, F.; Bussery-Honvault, B.; Gomez, L.;Bartolomei, M. A Bond-Bond Description of The IntermolecularInteraction Energy: The Case of Weakly Bound N2-H2 and N2-N2Complexes. Phys. Chem. Chem. Phys. 2008, 10, 4281−4293.(28) Gomez, L.; Bussery-Honvault, B.; Cauchy, T.; Bartolomei, M.;Cappelletti, D.; Pirani, F. Global Fits of New Intermolecular GroundState Potential Energy Surfaces for N2-H2 and N2-N2 van der WaalsDimers. Chem. Phys. Lett. 2007, 445, 99−107.(29) Alberti, M.; Amat, A.; De Angelis, F.; Pirani, F. A Model Potentialfor Acetonitrile: from Small Clusters to Liquid. J. Phys. Chem. B 2013,117, 7065−7076.(30) Alberti, M.; Castro, A.; Lagana’, A.; Pirani, F.; Porrini, M.;Cappelletti, D. Properties of an Atom-Bond Additive Representation ofthe Interaction for Benzene-Argon Clusters. Chem. Phys. Lett. 2004, 392,514−520.(31) Capitelli, M.; Cappelletti, D.; Colonna, G.; Gorse, C.; Laricchiuta,A.; Liuti, G.; Longo, S.; Pirani, F. On the Possibility of Using ModelPotentials for Collision Integral Calculations of Interest for PlanetaryAtmospheres. Chem. Phys. 2007, 338, 62−68.(32) Bartocci, A.; Frati, F.; Roncaratti, L. F.; Cappelletti, D.; Tarantelli,F.; Belpassi, L.; Pirani, F. An ab initio Electronic Density Study of theCH4−Ar, CH4−Xe, CH4−H2O and CH4−H2S Complexes: Insightsinto the Nature of the Intermolecular Interaction.Mol. Phys. 2015, 113,3992−3999.(33) Cappelletti, D.; Bartocci, A.; Frati, F.; Roncaratti, L. F.; Belpassi,L.; Tarantelli, F.; Lakshmi, P. A.; Arunan, E.; Pirani, F. H2O−CH4 and

The Journal of Physical Chemistry A Article

DOI: 10.1021/acs.jpca.6b00948J. Phys. Chem. A XXXX, XXX, XXX−XXX

J

H2S−CH4 Complexes: a Direct Comparison through Molecular BeamExperiments and ab initio calculations. Phys. Chem. Chem. Phys. 2015, 17,30613−306231.(34) Denbigh, K. G. The polarisabilities of bondsI. Trans. FaradaySoc. 1940, 36, 936−948.(35) Olney, T. N.; Cann, N.; Cooper, G.; Brion, C. Absolute ScaleDetermination for Photoabsorption Spectra and the Calculation ofMolecular Properties Using Dipole Sum Rules. Chem. Phys. 1997, 223,59−98.(36) Kumar, A. Reliable Isotropic Dipole Properties and DispersionEnergy Coefficients for CCl4. J. Mol. Struct.: THEOCHEM 2002, 591,91−99.(37) El Kerdawy, A.; Murray, J. S.; Politzer, P.; Bleiziffer, P.; Heelmann,A.; Gorling, A.; Clark, T. Directional Noncovalent Interactions:Repulsion and Dispersion. J. Chem. Theory Comput. 2013, 9, 2264−2275.(38) Scholfield, M. R.; Ford, M. C.; Vander Zanden, C.M.; Billman, M.M.; Ho, P. S.; Rappe’, A. K. Force Field Model of Periodic Trends inBiomolecular Halogen Bonds. J. Phys. Chem. B 2015, 119, 9140−9149.(39) Pirani, F.; Giulivi, A.; Cappelletti, D.; Aquilanti, V. Coupling byCharge Transfer: Role in Bond Stabilization for Open-Shell Systems andIonic Molecules and in Harpooning and Proton Attachment Processes.Mol. Phys. 2000, 98, 1749−1762.(40) Aquilanti, V.; Cappelletti, D.; Pirani, F. Bond Stabilization byCharge Transfer: the Transition from Van der Waals Forces to theSimplest Chemical Bonds. Chem. Phys. Lett. 1997, 271, 216−222.(41) Pirani, F.; Vecchiocattivi, F. A Fast and Accurate SemiclassicalCalculation of the Total Elastic Cross Section in the Glory EnergyRange. Mol. Phys. 1982, 45, 1003−1013.(42) Aquilanti, V.; Beneventi, L.; Grossi, G.; Vecchiocattivi, F.Coupling Schemes for Atom-Diatom Interactions and an AdiabaticDecoupling Treatment of Rotational Temperature Effects on GloryScattering. J. Chem. Phys. 1988, 89, 751−761.(43) Aquilanti, V.; Ascenzi, D.; Cappelletti, D.; de Castro, M.; Pirani, F.Scattering of aligned molecules. The potential energy surfaces for theKr-O2 and Xe-O2 systems. J. Chem. Phys. 1998, 109, 3898−3910.(44) Roncaratti, L. F.; Belpassi, L.; Cappelletti, D.; Pirani, F.; Tarantelli,F. Molecular-Beam Scattering Experiments and Theoretical Calcu-lations Probing Charge Transfer in Weakly Bound Complexes of Water.J. Phys. Chem. A 2009, 113, 15223−15232.(45) Luzzatti, E.; Pirani, F.; Vecchiocattivi, F. Absolute Total ElasticCross Sections for O2-Rare Gases Scattering.Mol. Phys. 1977, 34, 1279−1286.(46) Pirani, F.; Vecchiocattivi, F.; van den Biesen, J. J. H.; van denMeijdenberg, C. J. N. Effect of Rotational Temperature on the GloryUndulations in the Atom-Diatom Total Collision Cross Section. J.Chem. Phys. 1981, 75, 1042−1043.(47) Cappelletti, D.; Candori, P.; Falcinelli, S.; Alberti, M.; Pirani, F. AMolecular Beam Scattering Investigation of Methanol-Noble GasComplexes: Characterization of the Isotropic Potential and insightsinto the Nature of the Interaction. Chem. Phys. Lett. 2012, 545, 14−20.(48) Cappelletti, D.; Bartolomei, M.; Sabido, M.; Pirani, F.; Blanquet,G.; Walrand, J.; Bouanich, J.-P.; Thibault, F. Collision Cross Sections,Pressure-Broadening Coefficients and Second Virial Coefficients for theAcetylene-Argon Complex: Experiments and Calculations on a NewPotential Energy Surface. J. Phys. Chem. A 2005, 109, 8471−8480.(49) Belpassi, L.; Infante, I.; Tarantelli, F.; Visscher, L. The ChemicalBond between Au(I) and the Noble Gases. Comparative Study ofNgAuF and NgAu+ (Ng = Ar, Kr, Xe) by Density Functional andCoupled Cluster Methods. J. Am. Chem. Soc. 2008, 130, 1048−1060.(50) Salvi, N.; Belpassi, L.; Tarantelli, F. On the Dewar-Chatt-Duncanson Model for Catalytic Gold(I) Complexes. Chem. - Eur. J.2010, 16, 7231−7240.(51) Bistoni, G.; Belpassi, L.; Tarantelli, F. Disentanglement ofDonation and Back-Donation Effects on Experimental Observables: ACase Study of Gold-Ethyne Complexes. Angew. Chem., Int. Ed. 2013, 52,11599−11602.(52) Bistoni, G.; Rampino, S.; Tarantelli, F.; Belpassi, L. Charge-Displacement Analysis Via Natural Orbitals for Chemical Valence:

Charge Transfer Effects in Coordination Chemistry. J. Chem. Phys.2015, 142, 084112.(53) Aquilanti, V.; Luzzatti, E.; Pirani, F.; Volpi, G. G. Molecular BeamStudies of Weak Interactions for Open-Shell Systems: the Ground andLowest Excited States of ArF, KrF, and XeF. J. Chem. Phys. 1988, 89,6165−6175.(54) Aquilanti, V.; Candori, R.; Cappelletti, D.; Luzzatti, E.; Pirani, F.Scattering of Magnetically Analyzed F(2P) Atoms and their Interactionswith He, Ne, H2 and CH4. Chem. Phys. 1990, 145, 293−305.(55) Aquilanti, V.; Cappelletti, D.; Lorent, V.; Luzzatti, E.; Pirani, F.Molecular Beam Studies of Weak Interactions of Open-Shell Atoms: theGround and Lowest Excited States of Rare-Gas Chlorides. J. Phys. Chem.1993, 97, 2063−2071.(56) Aquilanti, V.; Cappelletti, D.; Pirani, F. Magnetically SelectedBeams of Atomic Chlorine: Measurement of Long-Range Features ofthe Chlorine-Hydrogen and Chlorine-Methane Potential EnergySurfaces. J. Chem. Soc., Faraday Trans. 1993, 89, 1467−1474.(57) Aquilanti, V.; Cavalli, S.; Pirani, F.; Volpi, A.; Cappelletti, D.Potential Energy Surfaces for F−H2 and Cl−H2: Long-RangeInteractions and Nonadiabatic Couplings. J. Phys. Chem. A 2001, 105,2401−2409.(58) Pirani, F.; Maciel, G. S.; Cappelletti, D.; Aquilanti, V.Experimental Benchmarks and Phenomenology of Interatomic Forces:Open-Shell and Electronic Anisotropy Effects. Int. Rev. Phys. Chem.2006, 25, 165−199.(59) Pirani, F.; Giulivi, A.; Cappelletti, D.; Aquilanti, V. Coupling byCharge Transfer: Role in Bond Stabilization for Open-Shell Systems andIonic Molecules and in Harpooning and Proton Attachment Processes.Mol. Phys. 2000, 98, 1749−1762.(60) Aquilanti, V.; Cappelletti, D.; Pirani, F. Bond Stabilization byCharge Transfer: the Transition from Van der Waals Forces to theSimplest Chemical Bonds. Chem. Phys. Lett. 1997, 271, 216−222.(61) Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. HalogenBonding: the σ-hole. J. Mol. Model. 2007, 13, 291.(62) Aquilanti, V.; Cornicchi, E.; Teixidor, M.; Saendig, N.; Pirani, F.;Cappelletti, D. Glory-Scattering Measurement of Water-Noble-Gasinteractions: The Birth of the Hydrogen Bond. Angew. Chem., Int. Ed.2005, 44, 2356−2360.(63) Roncaratti, L. F.; Cappelletti, D.; Pirani, F. The SpontaneousSynchronized Dance of Pairs of Water Molecules. J. Chem. Phys. 2014,140, 124318.(64) Pirani, F.; Maciel, G. S.; Cappelletti, D.; Aquilanti, V.Experimental Benchmarks and Phenomenology of Interatomic Forces:Open-Shell and Electronic Anisotropy Effects. Int. Rev. Phys. Chem.2006, 25, 165−199.

The Journal of Physical Chemistry A Article

DOI: 10.1021/acs.jpca.6b00948J. Phys. Chem. A XXXX, XXX, XXX−XXX

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