Interaction of O2 with CH4, CF4, and CCl4 by Molecular Beam

Mar 3, 2016 - Gas phase collisions of O2 by CH4, CF4, and CCl4 have been investigated with the molecular beam technique by measuring both the integral...
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Interaction of O2 with CH4, CF4, and CCl4 by Molecular Beam Scattering Experiments and Theoretical Calculations David Cappelletti,† Vincenzo Aquilanti,† Alessio Bartocci,† Francesca Nunzi,†,‡ Francesco Tarantelli,†,‡ Leonardo Belpassi,‡ and Fernando Pirani*,† †

Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy CNRIstituto 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 been investigated with the molecular beam technique by measuring both the integral cross section value, Q, and its dependence on the collision velocity, v. The adopted experimental conditions have been appropriate to resolve the oscillating “glory” pattern, a quantum interference effect controlled by the features of the intermolecular interaction, for all the three case studies. The analysis of the Q(v) data, performed by adopting a suitable representation of the intermolecular potential function, provided the basic features of the anisotropic potential energy surfaces at intermediate and large separation distances and information on the relative role of the physically relevant types of contributions to the global interaction. The present work demonstrates that while O2−CH4 and O2−CF4 are basically bound through the balance between size (Pauli) repulsion and dispersion attraction, an appreaciable intermolecular bond stabilization by charge transfer is operative in O2−CCl4. Ab initio calculations of the strength of the interaction, coupled with detailed analysis of electronic charge displacement promoted by the formation of the dimer, fully rationalizes the experimental findings. This investigation indicates that the interactions of O2, when averaged over its relative orientations, are similar to that of a noble gas (Ng), specifically Ar. We also show that the binding energy in the basic configurations of the prototypical Ng−CF4,CCl4 systems [Cappelletti, D.; et al. Chem. Eur. J. 2015, 21, 6234−6240] can be reconstructed by using the interactions in Ng−F and Ng−Cl systems, previously characterized by molecular beam scattering experiments of state-selected halogen atom beams. This information is fundamental to approach the modeling of the weak intermolecular 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 basic noncovalent components of the interactions involving water. Present results are of fundamental relevance to build up the force field controlling the hydrophobic behavior of prototypical apolar CX4 (X = H, F, Cl) molecules.

I. INTRODUCTION The detailed experimental characterization of strength and nature of the intermolecular interactions in systems involving O2 and small hydrogenated and halogenated molecules, such as CH4, CCl4, and CF4, has been the target of this work. The results of the present investigation, motivated by the relevance of the weak intermolecular bonds in fields ranging from the chemistry of elementary processes to biochemistry and carried out in an internally consistent way, are basic for the formulation of reliable model potentials able to describe properly both the static and the dynamic properties of these and of more complex aggregates.1−8 In addition to the prototypical CX4−Ng systems (X = H, Cl, F and Ng = He, Ne, Ar),9 the weakly bound aggregates, formed by the same polyatomic molecules and O2, have been chosen as systems of interest to be investigated in detail to extend the systematics. Indeed, previous experimental observations suggested that Ar and O2 interacting with the same partner by typical noncovalent interactions exhibit a very similar feature.10 This evidence emerges when experiments are performed with © XXXX American Chemical Society

rotationally hot O2, scattered by a given target, that is, when the diatomic molecule behaves like a spherical projectile, since the anisotropy associated with the different orientations of its molecular axis is effectively averaged out. Also, scattering experiments with fast rotating O2, by measuring integral cross sections and their velocity dependences, permit a better characterization of the “glory” interference effects, with respect to the same experiments with the Ar projectiles. This occurs because of an improved signal-to-noise ratio and an increased angular resolution that requires small limiting angle corrections. We performed high-resolution molecular-beam (MB) scattering experiments that probe with high sensitivity both absolute Special Issue: Piergiorgio Casavecchia and Antonio Lagana Festschrift Received: January 28, 2016 Revised: March 1, 2016

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Figure 1. In the upper panel a sketch is reported of the experimental apparatus used for the scattering experiments. In the lower panel the relative velocity 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 CCl4 or CF4 at room temperature and CH4 at 90 K.

Moreover, with O2, Ar, and H2O having a very similar electronic polarizability (1.60, 1.64, 1.47 Å3, respectively),14 the obtained results are of relevance to define some basic noncovalent interactions components determining the hydrophobic 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 presents the data analysis. A discussion follows in section V, and some conclusions are given in section VI.

scale and anisotropy of the intermolecular potentials for these gas-phase binary complexes. The analysis of the glory quantum interference pattern, observable in the velocity dependence of the integral cross section, establishes quantitatively the nature of the van der Waals (vdW) forces for the intermolecular interaction in O2−CH4 and CF4 systems, arising from the combining role of size repulsion and dispersion attraction: an appropriate model potential can accordingly be provided. On the other hand, the same analysis of the measured potential well from the O2−CCl4 scattering data reveals the role of a contribution to the binding energy for some specific geometries of the interacting partners, additional to the expectation from pure vdW behavior. A similar effect was also observed for Ar−CCl4.11,12 For this case also, in order to reproduce the O2−CCl4 experimental data, we have introduced in the potential formulation a shift of the repulsive wall at shorter distances, accompanied by an increased role of the dispersion attraction, and a further stabilization component, assigned to an emerging charge transfer (CT) contribution. Preliminary analyses, presented in previous papers9,13 and performed adopting different models, provide only an estimate of the averaged strength of the effective radial intermolecular potential. Here the interaction is formulated in an internally consistent way and includes also the angular dependence in order to extract, from a more complete analysis of the experimental data, information on the full intermolecular potential energy surface (PES). In addition, we performed ab initio calculations addressed to a proper evaluation of the electron density modification, as a consequence of the formation of the aggregates, to correctly define the role of CT through the analysis of the charge displacement (CD) and to rationalize the similarity of O2 (an open-shell molecule) and Ar (a closed-shell atom), 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 containing CF4 and CCl4, where evidence of a weak intermolecular halogen bond is emerging. This has been possible since systems, involving polyatomic molecules with high symmetry and bound through a limited number of interaction components, are more easily characterizable, electrostatic effects being absent and induction attraction very weak.

II. EXPERIMENTAL METHODS Scattering experiments have been performed with a MB apparatus, which operates under high angular and velocity resolution conditions.15 The objective has been the measurement of the integral cross section Q as a function of the selected MB velocity v. The apparatus used has been extensively described elsewhere.15 A sketch is reported in Figure 1 in order to point out the key features of the experimental arrangement of relevance for this investigation. The apparatus is composed by a set of differentially pumped vacuum chambers where the MB, in the present case formed by rotationally hot O2, is produced by the gas expansion from the nozzle, maintained at a temperature that could be varied in a wide range. Under the typical conditions of temperature (500 K) and pressures (in general less than 15 mbar), the O2 MB emerges with near effusive or moderately supersonic character. It is collimated by two skimmers and a defined slit and then is analyzed in velocity by a mechanical selector formed by six slotted disks. The so formed projectile O2 molecules, flying in the selected slice of the beam velocity distribution, collide with the stationary target gas (CH4, CCl4, or CF4) contained in the scattering chamber and are detected by a quadrupole mass spectrometer coupled with an ion counting technique. In these experiments the scattering chamber has been filled with the gas target 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 the MB intensity detected with the target in the scattering chamber and I0 that without it. From the measurement of the I/I0 ratio it is possible to determine the value of the integral cross section Q(v) through the Lambert−Beer-like law: B

DOI: 10.1021/acs.jpca.6b00948 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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1 I log NL I0

critical quantity, since it directly influences the possibility of observing experimentally, in the LAB frame, the oscillatory patterns in the velocity dependence of Q(v), due to quantum interference effects. The Q(v) data, measured for O2−CH4, CF4, and CCl4 systems as a function of the selected MB velocity v, are reported in Figures 2−4. In all cases, the cross sections are plotted as Q(v)v2/5 to

(1)

where N is the target gas density and L the path length of the scattering region chamber15 (calibration data are given in refs 16−18). The experimental Q(v) value in the laboratory (LAB) frame is related to the center-of-mass (CM) cross section QCM(g), which is a function of the relative collision velocity g, through the following relation:15 Q (v ) = R (v )

∫0

∞

T (v′,v) dv′

∫0

∞

QCM(g ) f (g ,v′) dg (2)

where R(v) is a factor that limits the value of the measured cross section because of the finite angular resolution of the experiment. Since R(v) depends on mass and velocity of the projectile, its value is different for the scattering of the O2 and Ar projectiles by the 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 halfmaximum (fwhm) is lower than 5%. The function f(g,v′) is the relative velocity distribution, providing the proper weight factor in eq 2; it is dependent on the combination of the motion in the forward direction of the velocity selected projectile (flying at v′) with the random motion of the molecular gas target at thermal equilibrium. f(g,v′) takes the form ⎡ 2⎧ 1 ⎛⎜ g ⎞⎟ ⎪ ⎢ ⎛⎜ v′ − ⎨exp −⎜ f (g ,v′) = 1/2 π vp ⎝ v′ ⎠ ⎪ ⎢⎣ ⎝ vp ⎩ ⎡ ⎛ v′ + − exp⎢ −⎜⎜ ⎢ ⎝ vp ⎣

g⎞ ⎟⎟ ⎠

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

2⎤

g⎞ ⎥ ⎟⎟ ⎠ ⎥⎦

2 ⎤⎫

⎥⎪ ⎬ ⎥⎪ ⎦⎭

(3)

emphasize and compare, for the present homologous family of colliding systems, the well resolved oscillatory patterns due to the “glory” quantum interference. The O2−CH4 and O2−CF4 collision complexes show similar trends in the measured data, both in the absolute scale and in the glory interference, while the

where vp is the most probable velocity of the target molecules at the 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 the angular resolution of the experiments, since under such conditions the R(v) value in eq 2 is approaching 1.0. Moreover, the scattering chamber containing the target has been maintained at room temperature (300 K) in all the measurements in order to avoid condensation phenomena on the walls of the chamber and to exploit a direct comparison of the present scattering data with those measured under the same conditions and with other projectiles.11,12 The obtained results can be directly compared with those previously measured for O2−CH4,13 where CH4 was confined in the scattering chamber, cooled at 90 K, in order to increase the energy resolution by limiting the random thermal motion of the target. The features of the f(g,v′) function are crucial for the control of the obtained velocity resolution conditions: the lower panel of Figure 1 shows the behavior of f(g,v′) for some selected projectile velocities, v = v′ = 0.6, 1.3, 2.0 km/s, and using as target at 300 K CCl4 (vp = 0.180 km/s) or CF4 (vp = 0.238 km/s). For the lighter target CH4, the cooling of the scattering chamber at 90 K reduces strongly its random motion (vp ≃ 0.306 km/s) and the achieved velocity 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

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

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The Journal of Physical Chemistry A ⎡ ⎛ rm(α) ⎞n(r ,α) m Vab(r ,α) = ε(α)⎢ ⎜ ⎟ ⎢⎣ n(r ,α) − m ⎝ r ⎠ −

m⎤ n(r ,α) ⎛ rm(α) ⎞ ⎥ ⎜ ⎟ n(r ,α) − m ⎝ r ⎠ ⎥⎦

(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 r forms with the axis of the considered bond. The parameter m is set equal to 6 for all the pseudoatom−bond interactions. Such a simple formulation provides a realistic picture of both the pair repulsion (represented by the first term) and the pair attraction (given by the second term), leading to a proper description of both equilibrium and nonequilibrium geometries of the weakly bound aggregates.26 It is also given in a form that can be conveniently exploited in molecular dynamics simulations to calculate static and dynamical properties of clusters formed by a variety of atomic and molecular species (see for instance refs 29,30). The parameter n, which defines the ”fall off” of the atom− bond repulsion, depends on β (related to the hardness of the partners31) and is expressed as a function of both r and α using the equation

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

O2−CCl4 system exhibits a very different behavior, thus revealing significant 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 intermolecular interaction combining information both at long range (obtained from the velocity dependence of the average value of Q(v)) and in the potential well region (probed by the glory structure).19,20 During the analysis, the QCM(g) values have been calculated within the semiclassical Jeffreys−Wentzel−Kramers−Brillouin (JWKB) method21 from the assumed intermolecular interaction V (see next section) and then convoluted in the LAB frame (see eq 2) to make a direct comparison with the measured Q(v).

⎛ r ⎞2 n(r ,α) = β + 4⎜ ⎟ ⎝ rm(α) ⎠

(5)

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

III. ATOM-BOND PAIRWISE ADDITIVE REPRESENTATION OF THE PES In the thermal energy range, a small and fast rotating molecule like O2 behaves as a pseudoatom during the scattering and its effective interaction can be formulated as determined only by one interaction center confined in its CM (see refs 22−24). On the other hand, slowly rotating polyatomic molecular targets are adequately described by considering several interaction centers distributed on the molecule frame and localized on the chemical bonds.25 The employed formulation treats the involved interaction as determined by a repulsion due to effective molecular sizes,10,25 strongly dependent on the molecular orientation, and an attraction determined by the combination of several pseudoatom−molecular bond contributions.25,26,27,28 A realistic description of the potential energy anisotropy is then obtained, since such a formulation indirectly accounts for the electronic charge distribution along the molecular frame. This approach, which exploits the polarizability partition of a polyatomic molecule in bond tensor components, provides a realistic picture of both the repulsion and the attractive components of a vdW interaction and, in addition, effectively includes both three-body and other nonadditive effects.26 Accordingly, in this study the interaction centers (a, b) have been localized on the O2 pseudoatom and on each of the four C− X bonds of CX4 molecules, X being H, F, or Cl. Therefore, the vdW intermolecular potential component (VvdW) has been taken as a sum of four pseudoatom−bond interaction terms, VvdW = ∑abVab, each one represented by an improved Lennard-Jones (ILJ) function20 of the type

ε(α) = ε⊥ sin 2(α) + ε cos2(α)

(6)

rm(α) = rm ⊥ sin 2(α) + rm cos2(α)

(7)

where ⊥ and ∥ refer to perpendicular and parallel approach of the pseudoatom-O2 to the bond, respectively. Note that for each interacting pair the asymptotic long-range attraction coefficient is equal to ε(α) rm(α)6 and the global attraction coefficient depends on 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 been localized for C−H on the middle point of the bond, and for C−F and C−Cl, respectively, at about 60% and 80% of the bond length toward the halogen atom.11,12 Table 1 reports the values of all the ε, rm potential parameters that are expected on the basis of the bond polarizability tensor components, which are related to the dimension of the electronic 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 to Those of Ar−CH, CF, CCl Bond Pairsa O2−CH Ar−CH26 O2−CF Ar−CF O2−CCl Ar−CCl11,12

rm∥

ε∥

rm⊥

ε⊥

A × 105

3.84 3.85 3.89 3.90 4.18 4.18

4.00 3.98 5.63 5.59 10.98 10.98

3.63 3.64 3.64 3.64 4.03 4.04

4.84 4.81 6.33 6.26 10.17 10.16

6.5 6.5

a The maximum estimated uncertainty is about 6% for ε, 2% for rm, and 10−15% for A.

D

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The Journal of Physical Chemistry A charge distribution around each bond34 and are consistent with the values of the molecular polarizability.35 Such components have been combined with the spherical polarizability of O2 (1.6 Å3 ) in the correlation formulas10,25 predicting the V vdW parameters. In obtaining the potential parameters values for O2−CCl4 reported in Table 1, it has been also required that at long-range they must generate a global average attraction in substantial agreement with the calculation using the dispersion coefficient (C6 = 2.08 × 105 meV·Å6) reported by Kumar36 (a C6 value of 1.94 × 105 meV·Å6 is obtained from the present analysis). As for Ng−CCl4,11,12,37,38 the rm∥ values have been decreased by about 4% to account of the “polar flattening” effect, due to the anisotropic distribution of the electronic charge around the bound Cl halogen atom, and ε∥ adjusted as consequence. The parameters of Ar−CH, CF, and CCl have been also reported for a useful comparison. The dynamical treatment used for the data analysis (see next section) has permitted the satisfatctory reproduction of measured cross sections for O2−CH4 and O2−CF4 simply adopting the atom− bond representation of V vdW . This result represents a fundamental test of the employed methodology and confirms the reliability of the potential parameters listed in Table 1, indicating the occurrence of a pure vdW component in O2−CH4 and O2−CF4. However, although the correct “polar flattening” parameters were used, the same methodology was unable to reproduce the experimental data measured for the O2−CCl4 system. As for Ar−CCl4, the reproduction of the glory pattern, observed for such system, has been obtained by introducing a further modification in the potential formulation, concerning the addition of an other stabilizing component, emerging at intermediate and short distance. A contribution associated with possible charge-transfer effects has been included in the potential by adding the term VCT = −A cos 4(α) e−γr

These approximations apply to collisions occurring at intermediate and large impact parameter (the classical equivalent of the orbital angular momentum), such as those probed by the present experiments, with no loss of any relevant information on the intermolecular interaction. Motivations arise from (i) the experimental observation of the absence of any appreciable glory amplitude quenching, due to the interaction anisotropy, when the mean molecular rotation time is comparable or shorter than the collision time;42−46 (ii) the suggestions, from scattering experiments42−47 and theory,42,43 that the interaction anisotropy becomes more effective, generating a more pronunced “glory” amplitude quenching, when the collision velocity overcomes the value for which the collision time becomes significantly shorter than the molecular rotation time. Under such conditions, the projectile interacts with the molecule suddenly; i.e., the interacting complex tends to maintain “memory” of a specific configuration while collisions evolve. In the present study, the collision dynamics has been then confined within two different regimes defined by (i) a spherical model, where both molecules behave as “pseudoatoms” and the scattering, mostly elastic, is driven by a central potential close to the isotropic component (spherical average) of the full PES, and (ii) an anisotropic molecular model, where the cross section is represented as a combination of independent contributions from limiting configurations of the pseudoatom (O2)−molecule collision complex. That is, a sort of “infinite order sudden” (IOS) approximation is applied (see for instance refs 11,15,42,43). In particular, for the present systems three limit configurations, related to three different cuts of the PES, have been selected as representative of the interaction anisotropy. They describe the intermolecular interaction potential V when the pseudoatom approaches to the vertex (Vv), the face (Vf), and the edge (Ve) of the tetrahedral molecule. Accordingly, the two regimes selectively emerge as a function of the ratio between the mean rotation time, τM, and the collision time τcoll. The former,τM, is the time required to probe an effective potential close to the isotropic component of the PES, which can be estimated also as an average among interactions associated with the limiting configurations of the collision complex; for further details regarding its estimation see refs 11 and 12 and references therein. The latter, τcoll, evaluated according to refs 15 and 43, is found to be varying between ≃2 and ≃0.5 × 10−12 s with the beam velocity at v = 0.5 and 2.2 km/s, respectively. The comparison of times suggests that the CCl4 molecules can be considered as rotating sufficiently fast during the collisions only at low v (v ≤ 0.80 km/s),11,12 while for CF4 and CH4 the same limit occurs for v ≤ 1.1 km/s. Therefore, in the low velocity limit, the collisions have been considered exclusively elastic and mainly driven by an “effective” radial potential V(R) (R is the intermolecular distance defined as the separation between the CM of two partners) related to the isotropic component of the PES, obtained at each R by averaging the interaction over all the angular coordinates. At higher velocity, i.e., when τcoll < τM, the anisotropic molecular regime sets in. In this case, at each v, the individual cross sections, calculated from Vv, Vf, and Ve, have been combined according to the following normalization preserving relation:

(8)

The value of the exponent γ, which defines the “fall off” of the VCT with 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 final value is given in Table 1 and is coincident with that previously obtained for Ar−CCl4.11

IV. DATA ANALYSIS As indicated above, in the thermal collision energy range the average component of Q(v) and the oscillatory pattern provide complementary information on the intermolecular interaction, being dependent on collisions at large and intermediate orbital angular momentum, respectively, which are directly affected by the strength of the long-range attraction and by the features of the well depth, respectively.20,21,41 For the present experiments, carried out with molecules having a broad Boltzmann distribution of rotational states, the exact calculations of QCM(g) would require a huge computational effort. It has been demonstrated42,43 that under the used conditions the collision dynamics can be treated semiclassically. In particular, the analysis of the integral cross section data measured with rotationally “hot” molecules, which exhibit a probability of inelastic events reduced with respect to the same rotationally “cold” molecules, can be safely based on some approximations in their theoretical treatment,42,43 which make easier the cross section calculations and provide insights on the physical picture.

Q (v ) =

4Q v + 6Q e + 4Q f 14

(9)

where the numerical coefficients represent the degeneracy of the limiting configurations. E

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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 CX4 for three selected cuts of the PES (solid color lines), together with the spherical component (dashed line) of the same PES.

The final theoretical Q(v) values, to be compared with the experimental data, have been then calculated within the spherical model at low v and according to the anisotropic molecular model at high v. At intermediate v, the switch between the dynamics of the spherical model and that of the anisotropic molecular model has 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 experimental data in Figures 2−4, showing a very good description of all the interference 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 the different dynamical regimes introduced above, in order to provide a better comparison with the experimental data. The complete calculations reproduce both the amplitude and frequency 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 both the selected cuts of the PES and for the spherical component.

the C−H one. From this viewpoint, because of the smaller dimensions, the methane molecule behaves as a more spherical partner than CF4. The O2−CCl4 system shows a quite different behavior with respect to the previous two cases: the average interaction is stronger both at long-range and in the potential well region, as expected because of the increased molecular polarizability α (10.48 Å3 for CCl4 with respect to 2.78 and 2.60 Å3 for CF4 and CH4, respectively; for both CCl4 and CF4 the contribution of the individual halogen atoms represents more than the 80% of the overall α value). Also the anisotropy manifests a different behavior. Specifically, the interaction in the vertex configuration is significantly stabilized by an additional short-range component. A similar additional stabilization effect by CT was characterized in the analysis of He, Ne, Ar−CCl4 systems.11,12 For O2− CCl4, the Q(v) data have been measured under increased angular resolution conditions with respect to similar experiments performed on Ar−CCl4, leading to the observation of a better resolved glory pattern, with a consequent more accurate probe of the interaction. The present analysis confirms the validity of the model potential previously used, which includes explicitly the role of CT in the formulation of the interaction only in the aggregates involving CCl4 molecule. In order to properly rationalize the experimental findings for CF4 and CCl4 interacting with various partners, we found it useful to focus on two aspects, concerning (i) the analysis of the electron density distribution in complexes as O2−CF4, CCl4, with O2 being an open shell 3Σg− paramagnetic species, and its comparison with that in Ar−CF4, Ar−CCl4, with Ar being a closed shell 1S0 atom; and (ii) the characterization of the specific role of the halogen atoms within the CF4 and CCl4 molecules when interacting with various partners. Charge Displacement Analysis and Charge Transfer Contribution by High-Level ab Initio Calculations. In order to clearly define the role of the CT contribution in the O2(Ar)−CX4, X = F, Cl interacting systems, we first carried out constrained geometry optimizations on the vertex configuration by high-level ab initio calculations; see Supporting Information for further details. Afterward, we analyzed the electron density

V. DISCUSSION The systems investigated in this paper can be considered as suitable reference cases for modeling the leading V vdW component and other possible additional contributions to the interactions in prototypical aggregates involving symmetric apolar molecules. Isotropic and Anisotropic Components of the Interaction. The analysis of the Q(v) data for O2−CH4 and O2−CF4, measured in the thermal collision energy range and showing well resolved glory patterns, has been carried out with a semiclassical method. The PESs so characterized are fully describable as sum of contributions, VvdW = ∑abVab, where each Vab is formulated as individual pseudoatom−bond interaction components.11,12 In these two systems, the strength of the average (isotropic) component is similar, as effectivelly exhibited by the closeness of the measured absolute values of Q(v). Regarding the anisotropy of the interactions, experimentally pointed out by the quencing of the glory oscillations, it appears slightly larger for CF4 than for CH4, as expected for the C−F bond being longer with respect to F

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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 and for the Ar−CCl4 system (c). The insets show 3D isodensity plots of the electron density change due to the intermolecular interaction. The isodensity surfaces 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) and perpendicular (blue) orientations and that obtained as weighted average in the ratio 1:2 (curve with dashed line), according to their degeneracy, are compared 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−Cl bond 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 electron density change accompanying bond formation. The isodensity surfaces are for Δρ = ±0.05me/bohr3 (negative values in red, positive in blue). The dots correspond 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.

along an axis joining the two interacting fragments, the net electronic charge that, upon formation of the complex, has been displaced from right to left across the plane perpendicular to the

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

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The Journal of Physical Chemistry A axis and passing through that point z (see Supporting Information for a detailed description).49 This approach has been successfully employed in several diverse contexts to investigate charge fluxes both in transition-metal compounds50−52 and in weak intermolecular systems.11,12,24,32,33 The results of the CD analysis for O2(Ar)−CX4, X = F, Cl, are reported in Figures 6 and 7. While the insets show the isosurfaces of the electronic density difference, the main panels display, on the same horizontal scale, the CD curves. We considered the O2 molecule approaching the CX4 molecule in both a collinear and perpendicular orientation, which can be unambiguously defined by the angle between the O−O bond and the C3 symmetry axis of CX4, 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 shows that CCl4 strongly polarizes the electron cloud of the O2 molecule both in the collinear (a) and in the perpendicular (b) orientations. The charge polarization is similar in both cases: the O2 molecule undergoes a charge depletion (red color) in the region opposite to Cl and a charge accumulation (blue color) toward the halogen atom. A certain amount of charge rearrangement is present also on the CCl4 partner. The analysis of the corresponding Δq curve returns a quantitative picture of the interaction between O2 and CCl4 molecules. In particular, the electronic charge starts flowing toward the CCl4 moiety from the right side of the O2 molecule so that the Δq presents the maximum value close to the O2 CM. Further to the left, the CD function value decreases reaching a minimum but remaining positive. Subsequently, the charge starts to reaccumulate (at the right side of Cl), the CD function increases 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 interacting systems, we can conclude that a net CT occurs from O2 to CCl4 independent from the relative orientation of the interacting partners. A numerical value of CT can be estimated by considering the CD function value at a specific point between the fragments along the z axis. Our choice has been the point along z where the electron densities of the noninteracting fragments become equal (isodensity boundary). This choice is reasonable, especially for small weakly interacting systems.22 The position of the minimum on the CD curve is close to this isodensity boundary, located at 3.5 Å from the carbon atom and 1.6 (2.1) Å from O2 in the perpendicular (collinear) orientation. At this point, the Δq value, which we take as an estimate of CT from O2 to CCl4, is equal to 0.6 me in the perpendicular orientation and 1.1 me in the collinear one. The analysis of CD curves for the collinear and perpendicular orientation in the O2− CCl4 complex clearly shows that the anisotropy of the O2 molecule does not qualitatively affect the nature of the intermolecular interaction. Also, the comparison of the CD function curves points out that the CT from O2 to CCl4 is slightly more efficient in the collinear rather than in the perpendicular orientation. The CD analysis of the Ar−CCl4 system is reported in Figure 6c for comparison. The inset shows the isosurfaces of the density deformation of the Ar−CCl4 complex, which closely resembles the 3D isodensity plot of the O2−CCl4 system, with a large density accumulation lobe on the side toward the Cl atom and depletion when opposite to it, accompanied by a sizable amount of charge rearrangement on the CCl4 moiety. As described above for the O2−CCl4 system, the CD function curve for Ar−CCl4 is invariably positive over all the complex and at the isodensity

boundary the CT (in the direction from Ar to CCl4) is equal to 0.31 me. Our preliminary analysis confirms the occurrence of an appreciable electron transfer from O2 and Ar to CCl4 partner. However, the Δq is computed larger in O2−CCl4 with respect to Ar−CCl4 (for further details see Supporting Information), while the analysis of the experimental data suggests that the role of CT is 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 mainly probed distances occur at shorter values with respect to that optimized in the vertex configuration.11 As outlined in the previous sections, in the MB scattering experiments the O2 molecules are fast rotating and behave almost as spherical projectiles, with molecular anisotropy averaged over all the orientations. This behavior can be roughly mimicked by means of a weighted average of the CD function of the limiting collinear and perpendicular orientations of O2−CCl4 according to their oneto-two degeneracy, thus allowing a more reliable comparison with the CD of Ar−CCl4. As shown in Figure 6d, Ar−CCl4 and O2−CCl4 weighted average CD curves are close all over the entire interacting system, thus suggesting that electron density fluctuations of the same magnitude occur in the complexes involving O2 and Ar partners, despite the presence of two unpaired electrons in the O2 molecule with respect to the closed shell Ar system. The similarity in the interaction can be related to the value of the α polarizability of O2 and Ar, i.e., 1.60 and 1.64 Å3, respectively. Finally, the CD curves for the O2−CF4 complex (collinear and perpendicular orientations), together with the 3D plot of the isodensity deformation as insets, are reported in Figure 7. As already discussed for the Ng−CX4 series, X = F, Cl,9,11,12 the pattern of the CD function in O2−CF4 is completely different from that in the O2−CCl4 complex. In particular, by comparing Figures 6 and 7, it is evident that the polarization of the O2 molecule induced by CF4 is opposite that exerted by CCl4 for both considered orientations. Indeed, the CD function is negative at the O2 molecule, suggesting a charge shift from the left to the right of the O2 molecule. Afterward, the CD function assumes very small positive values in the region between the molecules and remains very close to zero in the whole region of CF4. It even shows a change of sign in the middle of the distance between partners; thus the contribution of CT to the intermolecular halogen bond, if present, becomes hardly discernible and its role is expected to be negligible. A similar behavior has been observed for the Ar−CF4 system. We can therefore conclude that the CT component does not play an effective role in the O2−CF4 complex (as already observed in the analyzed Ng−CF4 systems),11,12 with the attraction determined solely by the dispersion forces, and this result is independent from the relative orientation of the fragments. Therefore, our calculations support the experimental findings, allowing an estimation of the CT interaction in the formation of weak intermolecular halogen bonds and suggesting that the O2 molecule 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 Halogenated Methanes. The aggregates formed by CF4 and CCl4 molecules with noble gases, recently investigated with the same methodology,11,12 must be considered as prototype systems for the formulation of models describing the weak intermolecular halogen bond. In particular, the absence of the electrostatic H

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The Journal of Physical Chemistry A and induction contributions favors the proper characterization of the other few effective interaction components. In addition to the importance of modeling systems of increasing complexity, we have found it remarkable to discover possible relations between the basic features of the obtained PES in Ng−CF4 and Ng−CCl4 and those of the interaction in noble-gas fluorides (NgF)53,54 and noble-gas chlorides (NgCl)55−57 weakly bound dimers. The latter has been experimentally investigated by utilizing similar collisional experiments, performed with fine structures state selected F(2Pj) and Cl(2Pj) atomic beams scattered by Ng targets. The data analysis permitted the characterization of the basic terms V0(r) (spherical component) and V2(r) (anisotropic component),58−60 whose combination provides the VΣ(r) and VΠ(r) potential,53,54,56−58 namely, the interaction energies associated with molecular quantum states arising from different alignment of the half-filled orbital of the halogen atom with respect to the interatomic axis. The investigation of such weakly bound compounds demonstrated that while V0(r) and VΠ(r) terms show a substantial vdW character, VΣ(r) is selectively stabilized by a CT contribution (the ground neutral Ng−F, Cl and the ionic state of the excimer Ng+−F−, Cl− having the same symmetry); the effect is an increase along the Ng family from He to Xe: the decrease of the ionization potential of Ng induces a more efficient coupling (configuration interaction) between neutral and ionic states. We have attempted to reproduce the binding energy in Ng− CF4 and Ng−CCl4 systems in the limiting vertex and face configurations, as combination of the experimentally determined Ng−F and Ng−Cl interaction potentials. The results of this attempt are that for Ng−CF4, both in the vertex (see Table 2)

Table 3. Binding Energy (in meV) for Ng−CF4 and Ng−CCl4 Systems in the Face Configurationa

system

model potential

4V0

3V0 + VΣ

2.85 5.20 9.50 3.60 9.30 19.30

2.50 4.90 6.90 3.00 2.00 8.70

2.80 8.80 15.60 3.70 8.20 19.3

model potential

4V0

He−CF4 Ne−CF4 Ar−CF4 He−CCl4 Ne−CCl4 Ar−CCl4

6.30 12.20 19.00 6.20 13.30 33.50

5.90 12.20 20.00 6.10 13.70 36.70

a

For such configuration, the values obtained as combination of the spherical component V0 53,54,56−58 (see text and also Table 2) reproduce the model potential values (the use of VΣ component provides an overestimated binding energy).

Therefore, the proper combination of phenomenological potentials, derived with different methods of analysis, provides a strong confirmation of the selective role of CT in systems involving CCl4, which is instead practically absent in CF4.

VI. CONCLUSIONS The results of the present investigation, carried out in an internally consistent way on the O2−CX4 systems, are important from several points of view, and specifically: (1) to characterize the features and to quantify strength and anisotropy in the VvdW component; (2) to assess the selective binding stabilization energy, arising from CT effects; (3) to understand and cast light on the specific role of the bound halogen F and Cl atom in CF4 and CCl4, which assumes a different (F) and a similar (Cl) character with respect to the isolate case. In particular, the open-shell nature of the isolated F atom is completely loosen in the molecule while that of Cl is partially mantained, as suggested by the need for introducing corrections in the potential formulation, due to polar flattening effects and CT contributions as O2 approaches CCl4 along the vertex configuration (see also previous section and next point); (4) to attribute differences in the experimental findings to the different electronic charge distribution of the halogen atom bound in the molecule. Such differences were mostly ascribed to the change in sp-hybridization degree of F and Cl atoms when forming the C−F and C−Cl bonds, respectively.61 In particular, the separation in the s and p atomic orbital energies, smaller for F than Cl, favors the formation of C−F bonds with increased sp hybridization degree with respect to C−Cl. In conclusion, the present investigation can contribute to assess the role of the vdW component in determining the hydrophobic behavior of prototypical CX4 molecules. The present results are then of relevance to build up models for the intermolecular halogen bond occurring on aggregates of higher complexity. Moreover, we demonstrated that O2, exhibiting an electronic polarizability similar not only to Ar but also to H2O, can be used as suitable reference to cast light on the differences and similarities in the peculiar nature of the interaction in systems involving water, oxygen, and argon with the same partners (see refs 62−64 and references therein).

Table 2. Binding Energy (in meV) for Ng−CF4 and Ng−CCl4 Systems in the Vertex Configuration, Obtained from the Formulation of the Interaction Discussed in the Texta He−CF4 Ne−CF4 Ar−CF4 He−CCl4 Ne−CCl4 Ar−CCl4

system

a

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

and in the face configurations (see Table 3), the more appropriate combination is always that involving the V0 component, each one scaled for the different distance of F atoms in CF4 from Ng, leading to a binding energy of ≃4V0. This confirms the vdW character of the interaction in all the basic configurations 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 use 3V0 + VΣ(r), where 3V0 refers to the contribution of the three most distant Cl atom and VΣ(r) to the closer one. I

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Molecular Properties Using Dipole Sum Rules. Chem. Phys. 1997, 223, 59−98. (15) Cappelletti, D.; Bartolomei, M.; Pirani, F.; Aquilanti, V. Molecular Beam Scattering Experiments on Benzene-Rare Gas Systems: Probing the 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 with the rare gases at thermal energies. J. Chem. Phys. 1976, 65, 4751−4755. (17) Nenner, T.; Tien, H.; Fenn, J. B. Total Cross Section Measurements for the Scattering of Argon by Aliphatic Hydrocarbons. J. Chem. Phys. 1975, 63, 5439−5444. (18) Pirani, F.; Vecchiocattivi, F. Absolute Total Elastic Cross Sections for 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 Semiclassical Calculation 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 and accurate potential function probed by high resolution scattering data useful 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 by Molecular 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 Beam Scattering Experiments and Ab-Initio Calculations. J. Phys. Chem. A 2014, 118, 6440−6450. (25) Pirani, F.; Cappelletti, D.; Liuti, G. Range, Strength and Anisotropy of Intermolecular Forces in Atom-Molecule Systems: an Atom-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 Intermolecular Potential 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 Intermolecular Interaction Energy: The Case of Weakly Bound N2-H2 and N2-N2 Complexes. 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 Ground State Potential Energy Surfaces for N2-H2 and N2-N2 van der Waals Dimers. Chem. Phys. Lett. 2007, 445, 99−107. (29) Alberti, M.; Amat, A.; De Angelis, F.; Pirani, F. A Model Potential for 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 of the 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 Model Potentials for Collision Integral Calculations of Interest for Planetary Atmospheres. 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 the CH4−Ar, CH4−Xe, CH4−H2O and CH4−H2S Complexes: Insights into 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

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b00948. Detailed description of the employed computational methods and the equilibrium structures and energetic stability of the investigated systems (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This paper has been supported by Italian Ministry for Education, University and Research, MIUR, (PRIN 2010−2011, Grant 2010 ERFKXL_002 and SIR 2014 [RBSI14U3VF]) and by Fondazione Cassa di Risparmio Perugia (Contract 2015.0331.021).

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REFERENCES

(1) Arunan, E. Hydrogen bond seen, halogen bond defined and carbon bond proposed: intermolecular bonding, a field that is maturing! Curr. Sci. 2013, 105, 892−894. (2) Shahi, A.; Arunan, E. Hydrogen bonding, halogen bonding and lithium bonding: an atoms in molecules and natural bond orbital perspective towards conservation of total bond order, inter-and intramolecular bonding. Phys. Chem. Chem. Phys. 2014, 16, 22935−22952. (3) Goodnough, J. A.; Goodrich, L.; Farrar, T. C. Dynamics of Dilute Water in Carbon Tetrachloride. J. Phys. Chem. A 2007, 111, 6146−6150. (4) Chang, T.-M.; Dang, L. X. Computational Studies of Liquid Water and 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. Dynamical Behavior 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−N Halogen 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 Charge Displacement Calculations. Cryst. Growth Des. 2011, 11, 4279−4283. (10) Cambi, R.; Cappelletti, D.; Liuti, G.; Pirani, F. Generalized Correlations in Terms of Polarizability for Van der Waals Interaction Potential 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 anisotropic electronic distribution and charge transfer in halogen bonded complexes of 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 Chemical Components in the Bonding of Helium and Neon with Neutral Molecules. Chem. - Eur. J. 2015, 21, 6234−6240. (13) Liuti, G.; Pirani, F. Molecular Beam Study of the Interaction of Atomic and Molecular Oxygen with Methane. J. Chem. Phys. 1987, 87, 5266−5271. (14) Olney, T.; Cann, N.; Cooper, G.; Brion, C. Absolute Scale Determination for Photoabsorption Spectra and the Calculation of J

DOI: 10.1021/acs.jpca.6b00948 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Charge Transfer Effects in Coordination Chemistry. J. Chem. Phys. 2015, 142, 084112. (53) Aquilanti, V.; Luzzatti, E.; Pirani, F.; Volpi, G. G. Molecular Beam Studies of Weak Interactions for Open-Shell Systems: the Ground and Lowest 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 Interactions with 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: the Ground and Lowest Excited States of Rare-Gas Chlorides. J. Phys. Chem. 1993, 97, 2063−2071. (56) Aquilanti, V.; Cappelletti, D.; Pirani, F. Magnetically Selected Beams of Atomic Chlorine: Measurement of Long-Range Features of the Chlorine-Hydrogen and Chlorine-Methane Potential Energy Surfaces. 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-Range Interactions 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 by Charge Transfer: Role in Bond Stabilization for Open-Shell Systems and Ionic Molecules and in Harpooning and Proton Attachment Processes. Mol. Phys. 2000, 98, 1749−1762. (60) Aquilanti, V.; Cappelletti, D.; Pirani, F. Bond Stabilization by Charge Transfer: the Transition from Van der Waals Forces to the Simplest Chemical Bonds. Chem. Phys. Lett. 1997, 271, 216−222. (61) Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. Halogen Bonding: 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-Gas interactions: The Birth of the Hydrogen Bond. Angew. Chem., Int. Ed. 2005, 44, 2356−2360. (63) Roncaratti, L. F.; Cappelletti, D.; Pirani, F. The Spontaneous Synchronized 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.

H2S−CH4 Complexes: a Direct Comparison through Molecular Beam Experiments and ab initio calculations. Phys. Chem. Chem. Phys. 2015, 17, 30613−306231. (34) Denbigh, K. G. The polarisabilities of bondsI. Trans. Faraday Soc. 1940, 36, 936−948. (35) Olney, T. N.; Cann, N.; Cooper, G.; Brion, C. Absolute Scale Determination for Photoabsorption Spectra and the Calculation of Molecular Properties Using Dipole Sum Rules. Chem. Phys. 1997, 223, 59−98. (36) Kumar, A. Reliable Isotropic Dipole Properties and Dispersion Energy 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 in Biomolecular Halogen Bonds. J. Phys. Chem. B 2015, 119, 9140−9149. (39) Pirani, F.; Giulivi, A.; Cappelletti, D.; Aquilanti, V. Coupling by Charge Transfer: Role in Bond Stabilization for Open-Shell Systems and Ionic Molecules and in Harpooning and Proton Attachment Processes. Mol. Phys. 2000, 98, 1749−1762. (40) Aquilanti, V.; Cappelletti, D.; Pirani, F. Bond Stabilization by Charge Transfer: the Transition from Van der Waals Forces to the Simplest Chemical Bonds. Chem. Phys. Lett. 1997, 271, 216−222. (41) Pirani, F.; Vecchiocattivi, F. A Fast and Accurate Semiclassical Calculation of the Total Elastic Cross Section in the Glory Energy Range. Mol. Phys. 1982, 45, 1003−1013. (42) Aquilanti, V.; Beneventi, L.; Grossi, G.; Vecchiocattivi, F. Coupling Schemes for Atom-Diatom Interactions and an Adiabatic Decoupling Treatment of Rotational Temperature Effects on Glory Scattering. 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 the Kr-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 Calculations 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 Elastic Cross Sections for O2-Rare Gases Scattering. Mol. Phys. 1977, 34, 1279− 1286. (46) Pirani, F.; Vecchiocattivi, F.; van den Biesen, J. J. H.; van den Meijdenberg, C. J. N. Effect of Rotational Temperature on the Glory Undulations 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. A Molecular Beam Scattering Investigation of Methanol-Noble Gas Complexes: Characterization of the Isotropic Potential and insights into 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 the Acetylene-Argon Complex: Experiments and Calculations on a New Potential Energy Surface. J. Phys. Chem. A 2005, 109, 8471−8480. (49) Belpassi, L.; Infante, I.; Tarantelli, F.; Visscher, L. The Chemical Bond between Au(I) and the Noble Gases. Comparative Study of NgAuF and NgAu+ (Ng = Ar, Kr, Xe) by Density Functional and Coupled Cluster Methods. J. Am. Chem. Soc. 2008, 130, 1048−1060. (50) Salvi, N.; Belpassi, L.; Tarantelli, F. On the Dewar-ChattDuncanson Model for Catalytic Gold(I) Complexes. Chem. - Eur. J. 2010, 16, 7231−7240. (51) Bistoni, G.; Belpassi, L.; Tarantelli, F. Disentanglement of Donation and Back-Donation Effects on Experimental Observables: A Case Study of Gold-Ethyne Complexes. Angew. Chem., Int. Ed. 2013, 52, 11599−11602. (52) Bistoni, G.; Rampino, S.; Tarantelli, F.; Belpassi, L. ChargeDisplacement Analysis Via Natural Orbitals for Chemical Valence: K

DOI: 10.1021/acs.jpca.6b00948 J. Phys. Chem. A XXXX, XXX, XXX−XXX