The 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, Italy
‡CNR - Istituto di Scienze e Tecnologie Molecolari, Via Elce di Sotto 8, 06123 Perugia,
Italy
E-mail: [email protected]
1
Computational details
The Charge Displacement (CD) Function, 1 was successfully employed in several diverse contexts to investigate both the chemical bonding and the intermolecular weak interactions. 2–6
Briefly, the CD function 1 is defined as:
∫
∫
∞
∆q(z) =
dx
−∞
∫
∞
z
dy
−∞
∆ϱ(x, y, z ′ ) dz ′ i
(1)
−∞
where ∆ϱ is the electron density difference between the interacting complex and the isolated
constituent fragments (in the present case, CX4 and the molecular oxygen or Ar atom) placed
in the same positions. z is a suitably chosen axis, which here is the one joining the CM of
the two fragments. At each point along z, ∆q measures the net electron charge that, upon
formation of the complex, has been displaced from right to left across the plane perpendicular
to the axis at that point (thus, where ∆q is negative, electron charge has correspondingly
moved from left to right).
The CD function provides a useful snapshot of the features of the interaction across the
whole molecular region, especially insightful to compare different interaction geometries.
The CT in the interacting system can be evaluated by considering the CD function value at
a specific point along z between the fragments. Our choice has been the point along z where
the electron densities of the non-interacting fragments become equal (isodensity boundary).
This choice is reasonable especially for small weakly interacting systems.
All calculations were performed with the MOLPRO program. 7 The geometry optimizations of the interacting systems involving the O2 (Ar)−molecule interactions were performed
at the unrestricted (restricted) coupled-cluster level of theory, with single, double and perturbatively included triple excitations UCCSD(T) (CCSD(T)), 8–10 with the augmented correlation consistent polarized valence basis set aug-cc-pVTZ (AVTZ). 11
The relatively weak interactions with O2 (Ar) leave the geometries of CCl4 and CF4
essentially unaffected. Thus, during all the calculations, the C−Cl, C−F and O−O bonds
S2
were kept rigid at their equilibrium distances (1.776, 1.315 and 1.207 Å, respectively). 12–14
With frozen-geometry fragments and with additional constraint that O2 (Ar) is allowed to
move only along the CX4 symmetry axis and pointing directly to the halogen atom (vertex
configuration), the geometry of O2 (Ar)−CX4 is defined in terms of the distance R between
the molecular CM of O2 (Ar) and CX4 (located at the C atom). We focus on those cuts of
the PES shown to be relevant for the anisotropic behavior of the O2 (Ar)-CX4 interaction,
i.e. the vertex configuration; the O2 molecule approaching the CX4 molecule is taken both
in a collinear and in a perpendicular orientation, that can be unambiguously defined by
considering the angle between the O−O bond axis and the C3 symmetry axis of CX4 , being
180◦ and 90◦ , respectively.
In this context, we resort to compute the electron densities employed in the CD analysis
at the Restricted Hartree-Fock (RHF) level of theory with AVTZ basis set. It is well known
that RHF poorly describes the electron correlation in weakly interacting systems. However,
we verified by means of a systematic investigation on the benchmark Ar−CCl4 system that
the CD function computed on the CCSD(T)/AVTZ optimized geometries are only slightly
affected by the level of theory employed for the single point calculations, both of the isolated
partners and their aggregates. In particular, we carried out a CCSD, a Quadratic Configuration Interaction SD (QCISD) and an HF single point calculation with the AVTZ basis
set on a fixed geometry (assuming for the R distance the experimental value of 5.3Å in the
vertex configuration, see Ref. 5 ).
The CD curves reported in Figure S1 clearly show that the HF/AVTZ level of theory
adequately describes the CT from Ar to CCl4 partner, with slight differences between the
highly correlated and the HF methods.
The optimized intermolecular distance (R) and the corresponding interaction energies
(E) for O2 −CX4 and Ar−CX4 (X = F, Cl) are reported in Table S1. The perpendicular
orientation shows an equilibrium distance R shorter than the parallel configuration by 0.5 Å
both in O2 −CF4 and O2 −CCl4 , likely because of a minor Pauli repulsion contribution. As
S3
8
6
4
∆q (me)
2
0
Cl
C
Cl
Ar
−2
−4
−6
−8
−10
−4
−2
0
2
4
6
8
10
z (Å)
Figure S1: CD curves for the Ar−CCl4 system computed on a fixed geometry (R = 5.3 Å)
at various level of theory (red line, HF; blue line QCISD; black line CCSD) with the AVTZ
basis set. The insets show 3D isodensity plots of the electron density change accompanying bond formation computed at the CCSD level of theory. The isodensity surfaces are for
∆ρ=±0.05me/bohr3 (negative values in red, positive in blue). The dots on the ∆q curves
correspond to the positions of nuclei on the z axis, which is here the axis joining the C−Cl
bond with Ar. The axis origin is at the CM of CCl4 . The vertical dashed lines mark the
isodensity boundaries between the fragments.
S4
discussed in details in Ref. 5 , the calculation of accurate interaction energies for these weakly
interacting systems is highly challenging and require the use of extended basis set. Even if the
interaction energies computed at the (U)CCSD(T)/AVTZ level of theory are overestimated
with respect to the experimental data, they consistently reproduce the relative stabilities of
the investigated systems. In particular, the O2 -CCl4 system is computed 6.7 and 9.2 meV
more stable in energy than the O2 -CF4 system respectively in the perpendicular and collinear
orientation, to be compared with a value of 10 meV obtained from the experimental data
(see Figure 5). Interestingly, in the O2 -CF4 system the interaction energy E is computed as
1.5 meV higher in the perpendicular vs the collinear orientation, while in the O2 -CCl4 system
the collinear orientation is stabler than the perpendicular one by 1.0 meV. In agreement with
the experimental findings, the computed R and E values describe an interaction strength of
molecular oxygen with CX4 almost close to that of Ar atom. In particular, the computed
equilibrium distance R in Ar-CX4 (4.7 and 5.4 Å for X = F and Cl, respectively) fall
within the R values computed for the O2 −CX4 systems in the collinear and perpendicular
orientations (4.8 and 5.6 Å for X = F and 4.3 and 5.1 for X = Cl, respectively). As shown in
Table S1, the interaction energies in O2 -CF4 (O2 −CCl4 ) are computed to be only 5-6 (2-3)
meV higher than in Ar−CF4 (Ar−CCl4 ).
Table S1: Computed geometrical parameters R (Å) and interactione energy E (meV) of
O2 −CX4 both in the collinear and perpendicular orientations and of Ar−CX4 (X = Cl, F)
computed at the (U)CCSD(T)/AVTZ levl of theory.
R
E
O2 collinear
5.6
31.9
R
E
O2 collinear
4.8
22.7
CCl4
O2 perpendicular
5.1
30.9
CF4
O2 perpendicular
4.3
24.2
Ar
5.4
28.7
Ar
4.7
17.6
S5
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