Rotational spectra of van der Waals complexes: pyrrole-Ne and pyrrole-Ne₂

Abstract

The van der Waals 1:1 and 1:2 adducts between the aromatic molecule pyrrole (Pyr) and the rare gas atom neon (Ne) have been investigated using a combination of chirped pulse Fourier transform microwave spectroscopy and quantum-chemical calculations. Rotational spectra of two and three isotopologues of Pyr-Ne and Pyr-Ne₂, respectively, arising from the combinations of the ²⁰Ne and ²²Ne isotopes, were identified and a partial r _s structure determined. Unusual spectral intensities have been observed with a significant enrichment of heavier isotopic species in the jet molecular expansion. The observed rotational constants of Pyr-Ne are consistent with a nearly symmetric prolate top with the Ne atom located above the plane of pyrrole. The trimer presents C _2v symmetry with the Ne atoms located one on each side of the ring plane. The experimental ¹⁴N nuclear quadrupole coupling constants have been determined for all the isotopologues of Pyr-Ne and Pyr-Ne₂ complexes. Similar values to those of isolated pyrrole have been found, which suggests that the electrical gradient field of pyrrole does not change much upon complexation. The observed spectroscopic parameters have been compared with those of other aromatic-rare gases complexes.

Introduction

Knowledge of non-covalent intermolecular interactions in aromatic molecules containing van der Waals complexes is of special relevance for the understanding of diverse phenomena such as molecular recognition in biological systems, crystal packing of aromatic molecules, formation of tertiary structure of proteins or base pair stacking in DNA.^1-2 The aromatic π electrons constitute the main driving force for the weak intermolecular bonds and have an important influence on the arrangement of the binding partners.³ The main contribution is the dispersion interaction, which depends on the polarizability of the involved atoms or molecules. One of the simplest models to take account for these interactions consists of an aromatic ring and rare gas atoms.

Jet-cooled Fourier transform microwave (FTMW) spectroscopy of van der Waals molecular complexes has contributed significantly to the fundamental understanding of weak intermolecular interactions^4,5 Several complexes of the type aromatic molecule-rare gas atom have been studied by microwave spectroscopy. The complexes of the prototypical aromatic benzene (Bz) with Ne,^6,7 Ar,^6,8 Kr,⁹ and Xe⁶ have been investigated by FTMW spectroscopy. In the case of pyridine (Py), microwave spectra have been reported for the 1:1 complexes with all rare gases.^10-13 In all the observed complexes, the rare gas atom has been found to be located above the ring plane of the aromatic molecule. Weakly bound trimers containing one aromatic molecule and two rare gas atoms have been also investigated. In spite of two plausible isomers, named [1,1] and [2,0], can exist, only the [1,1] form has been detected for Py-Ar₂,¹⁴ furan-Ar₂ ¹⁵ and Py-Ne₂ ¹⁶ by pure rotational spectroscopy. [1,1] isomer corresponds to the complex where the two rare gas atoms are located above and below of the aromatic ring plane while on the [2,0] form the gas atoms lie on the same side, being energetically less stable than the [1,1] form. The rotationally resolved spectra of two vibronic bands of Bz-Ar₂ complex revealed the formation of the [2,0] isomer as well.^17-18 These trimer complexes are good test cases to illustrate the contribution of three-body non-additive interactions to the overall intermolecular interactions. Additionally, these complexes provide benchmarks for the evaluation of their intermolecular interactions by quantum chemical calculations.

Pyrrole (Pyr) is a five-membered heterocyclic aromatic ring considered as a building block for important biomolecules. Due to its strong polarity, intermolecular interactions in many of its complexes are usually dominated by electrostatic dipole-dipole forces. Interestingly, pyrrole dimer is found to have a T-shaped structure stabilized by dispersion interactions between the aromatic π electrons of the monomers.¹⁹ The complexes of Pyr with rare gas atoms are good candidates to evaluate the balance between the electrostatic and dispersion interactions. In this context, only the study of Pyr-Ar complex²⁰ using FTMW spectroscopy has been reported. The experimentally determined structural parameters locate the Ar atom above the midpoint between the two ring C atoms adjacent to the N atom. Similar results were reported for the furan-Ar complex.²¹ Other rare gas atoms less polarizable such as Ne could shed some light on the significant role of dispersion forces in stabilizing molecular adducts. In addition, since Ne atom is smaller than Ar, the possibility to allocate two atoms on the same side of the aromatic plane in the formation of the trimer would be of interest.

In an attempt to broaden the structural information of such complexes, we report here the first high-resolution rotational spectroscopic study of Pyr-Ne_n (n=1,2) complexes in the 2-8 GHz frequency range. We provide rotational, centrifugal distortion and ¹⁴N nuclear quadrupole coupling constants of Pyr-Ne and Pyr-Ne₂ as well as information about the molecular geometry of both complexes. Furthermore, we have carried out a parallel computational study of Pyr-Ne_n complexes in order to establish which of the most commonly employed, in rotational spectroscopy studies, levels of theory provides the best overall results for the prediction of the rotational spectrum.

Experimental

The details of the broadband microwave instrument employed in this work have been described elsewhere.²² Pyrrole (stated purity ≥ 98%) was purchased from Sigma Aldrich and used without further purification. The pyrrole sample was placed in a reservoir on a section of tubing outside of the vacuum chamber. The carrier gas neon (3 bar backing pressure) was allowed to flow over pyrrole at room temperature, and the mixture was expanded into the vacuum chamber using a pulse nozzle (0.8 mm diameter, Parker General Valve, Series 9). For each gas pulse, the ensemble of molecules was polarized with a series of 4 microwave chirps of 5μs duration spanning 2 → 8 GHz using the fast-frame option of our oscilloscope. The radio frequency chirp (0.2-1 GHz) was generated with an arbitrary waveform generator (Tektronix AWG 70002A), amplified to 20 W with a solid state MW amplifier and broadcast perpendicular to the propagation of the jet expansion through a horn antenna. A molecular transient emission spanning 20 μs was then detected through a second horn and amplified by a low noise MW signal amplifier. A total of 1100k FIDs were co-added and Fourier transformed with a Kaiser-Bessel window function to give the broadband rotational spectrum in the 2-8 GHz frequency domain. The estimated accuracy of frequency measurements is better than 25 kHz.

Quantum Chemical Calculations

Geometry optimizations for the Pyr-Ne and Pyr-Ne₂ complexes were carried out in order to predict the rotational parameters necessary to interpret their rotational spectra. Quantum chemical calculations were carried out using several levels of theory including density functional theory (DFT)²³ methods; B3LYP²⁴ hybrid density functional with and without the Becke-Johnson D3(BJ) damping function³², the hybrid meta exchange-correlation functional M06-2X²⁵, the Grimme’s functional including dispersion B97D,²⁶ the long-range corrected hybrid density functional wB97XD²⁷. Møller-Plesset (MP2)²⁸ perturbation theory in the frozen core approximation method and the coupled cluster singles and doubles (CCSD)²⁹ correlated method were also employed. These methods have been combined with five different basis set named; Pople triple-ζ basis set (6-311++G(d,p)) and (6-311++G(2d,p)),³⁰ the Dunning’s correlation consistent polarized valence triple-ζ (cc-pVTZ) and the augmented diffuse (aug-cc-pVTZ) basis sets,³¹ and Ahlrich´s triple-ζ basis set with diffuse functions (def2-TZVPP)³³. In order to check the reliability of our calculations, we carried out optimization calculations using the same methods of already investigated analogue species such as Py-Ne and Pyr-Ar complexes (Tables S2 and S3). The calculations were carried out using the Gaussian 16³⁴ and Molpro 2018.1³⁵ program packages.

The molecular parameters predicted from our calculations for Pyr-Ne and Pyr-Ne₂ complexes are shown in Tables 1 and 2 and also in Table S1 of the ESI. These parameters are the rotational and ¹⁴N nuclear quadrupole coupling constants and the electric dipole moment components. It is common to describe the structure of the complex between an aromatic molecule and a rare gas atom with the R and θ structural parameters. R measures the distance between the center of mass of the aromatic monomer, pyrrole, and the rare gas atom, Ne, while θ is the angle between R and the principal axis a of isolated pyrrole. Hence, the values for these parameters are also indicated in Tables 1 and 2 because they help to make a picture of the relative location of pyrrole and Ne in the complexes.

Table 1.

Rotational constants, nuclear quadrupole coupling constants (all in MHz) and dipole moment components (in Debye) for the Pyr-Ne complex at different levels of theory. The structural parameters R and θ (in Angstrom and degree, respectively) are also indicated, see text.

	B3LYP	B3LYP-D3BJ	B97D	wB97XD	MP2	CCSD
	6-311++G(d,p)	6-311++G(d,p)	def2-TZVPP	aug-cc-pVTZ	6-311++G(2d,p)	def2-TZVPP
A	5114.1	4681.9	4647.9	4640.1	4674.8	4638.1
B	1751.7	2287.0	2142.8	2077.7	2198.5	2117.3
C	1683.3	2259.8	2123.3	2074.6	2177.7	2108.7
χaa	−1.76	−2.62	−2.55	−2.56	−2.40	−2.50
χbb	1.37	1.37	1.28	1.24	1.18	1.23
|μa|	0.99	0.58	0.56	0.30	0.34	0.41
|μc|	1.59	1.76	1.79	1.84	1.84	1.84
R	3.889	3.285	3.421	3.494	3.364	3.449
θ	64.67	77.85	78.72	82.96	78.38	81.36

Table 2.

Rotational constants, nuclear quadrupole coupling constants (all in MHz) and dipole moment components (in Debye) for the Pyr-Ne₂ complex at different levels of theory. The structural parameters R and θ (in Angstrom and degree, respectively) are also indicated, see text.

	B3LYP	B3LYP-D3BJ	B97D	wB97XD	MP2	CCSD
	def2-TZVPP	def2-TZVPP	aug-cc-pVTZ	aug-cc-pVTZ def2-TZVPP	def2-TZVPP
A	3604.9	4367.7	4270.8	4364.7	4335.9	4322.7
B	860.5	1040.4	961.1	938.6	1006.5	973.9
C	818.3	1028.5	947.7	927.7	993.1	961.0
χaa	−2.80	−2.83	−2.86	−2.73	−2.40	−2.67
χbb	1.56	1.59	1.55	1.51	1.31	1.40
|μb|	1.88	1.87	1.80	1.92	1.94	1.85
R	3.817	3.310	3.461	3.521	3.379	3.443
θ	72.97	82.18	81.64	82.23	81.71	81.63

Figure 1 shows the optimized structures for the Pyr-Ne and Pyr-Ne₂ at CCSD/6-311++G(d,p) level of theory together with the principal inertial axes system. As it can be seen for Pyr-Ne₂ complex, both Ne atoms are located on different sides, above and below, of the pyrrole ring plane. The isomer in which both Ne atoms are allocated on the same side of the pyrrole plane is less stable (around 190 cm^-1, see Table S4 of ESI). As it can be seen in the Fig. 1, Ne atoms are considerably shifted towards the N atom, probably attracted by the higher electronic density around it. Isolated pyrrole structure is also depicted in Figure 1 to show the permutation of the principal axes in going from the isolated molecule to the dimer and trimer complexes. For the Pyr-Ne complex, the Ne atom is very close to the c axis of pyrrole resulting in an upward translation of the center of mass and switching of the a and c inertial axis. Passing from Pyr-Ne to Pyr-Ne₂ induces the downward move of the center of mass, being close to that for the pyrrole monomer, and the exchange of the b and c inertial axis. This has greatest impact on the moments of inertia about the b and c axes which is reflected in the values of B and C rotational constants of both complexes. Thus, while A constant for Pyr-Ne₂ differs by -10% from that of the Pyr-Ne, the B and C values vary > 50 %.

Figure 1.

Molecular structures for the Pyr-Ne and Pyr-Ne₂ complexes in their principal inertial axis system calculated at CCSD/6-311++G(d,p) level of theory. Pyrrole monomer is also shown to illustrate the permutation of the principal axes in going from the isolated molecule to the complexes.

Results

Pyrrole-Ne

The broadband rotational spectrum recorded for Pyr-Ne and Pyr-Ne₂ species is shown in Figure 2. On first inspection the broadband rotational spectrum is dense with lines corresponding to several species previously identified, including pyrrole monomer³⁶,³⁷ and its ¹³C and ¹⁵N isotopic species,³⁸ pyrrole dimer,¹⁹ and pyrrole-water complexes.³⁹ After removing the known lines from the spectrum, two strong c-type lines consistent with the ¹⁴N nuclear quadrupole hyperfine pattern expected for the 1₁₀←0₀₀ transitions were firstly assigned to the Pyr-²⁰Ne and Pyr-²²Ne species. The intensity ratio Pyr-²⁰Ne/ Pyr-²²Ne was found to be 1.4, which is far from that expected, 9.75, taking into account the natural abundances of ²⁰Ne (~ 90.5%) and ²²Ne (~ 9.3%) isotopic species. A second c-type R-branch 2₀₂←1₁₀ transition and two Q-branch (ΔK_a = 1←0 and 2←1) series were quickly found for both isotopologues. Most of the assigned transitions displayed a hyperfine structure well resolved (see Figure 2) while some Q-branch transitions exhibit very small splittings not well resolved. In these cases, the averages of the line frequencies are taken as the center frequencies. In addition to the c-type transitions, a very week a-type transition, 1₀₁←0₀₀, was measured for both isotopic species. This a-type transition is the only one for Pyr-Ne complex in the 2-8 GHz frequency range. A total of 51 and 54 hyperfine components of Pyr-²⁰Ne and Pyr-²²Ne, respectively (see Tables S8 and S9, ESI) were fitted⁴⁰ using Watson’s S-reduced Hamiltonian⁴¹ for asymmetric top molecules, with the following form: H = H_R + H_Q where H_R contains rotational and centrifugal distortion parameters while H_Q describes the quadrupole coupling terms. The experimentally determined rotational and centrifugal distortion constants, as well as ¹⁴N nuclear quadrupole coupling constants for Pyr-²⁰Ne and Pyr-²²Ne species are collected in Table 3. A deeper inspection of the spectrum allowed us to observe the 1₁₀←0₀₀ rotational transition for the two ¹³C and the ¹⁵N isotopic species in natural abundance for both Pyr-²⁰Ne and Pyr-²²Ne isotopomers. Unfortunately, additional lines could not be measured with accuracy due to the low intensity of the signals.

Figure 2.

Broadband spectrum of Pyr-Ne and Pyr-Ne₂ complexes in the 2–8 GHz frequency region. Lines for other known species, see text, have been removed for clarity. a) A section of the broadband spectrum showing the 1₁₁-0₀₀ rotational transition for the three isotopic species of Pyr-Ne₂, illustrating the anomalous intensities in isotopic species with ²²Ne, see text. b) 1₁₁-0₀₀ rotational transition for Pyr-²⁰Ne species showing its hyperfine structure completely resolved with the typical intensity pattern of 5/9, 3/9 and 1/9 for the hyperfine components F″←F′ = 2←1, 1←1 and 0←1, respectively.

Table 3.

Experimental rotational and nuclear quadrupole coupling constants, all in MHz, for the pyrrole-Ne complex.

	Pyrrole-20Ne	Pyrrole-22Ne
A	4654.5380(60)a	4652.7314(46)
B	2101.6705(51)	1990.1525(39)
C	2099.3956(54)	1988.3777(41)
DJ	0.03272(80)	0.0294(60)
DJK	0.13554(31)	0.1244(20)
DK	−0.1429(12)	−0.1308(87)
χaa	−2.498(12)	−2.5190(85)
χbb	1.231(14)	1.255(10)
N b	51	54
σ c	17.3	13.4

^aValues in parentheses denote 1σ errors, applied to the last digit.

^bNumber of hyperfine components included in the fit.

^cStandard deviation of the fit, in kHz.

Structural parameters describing the arrangement of Ne with respect Pyr were obtained using different approaches. Substitution coordinates of the ²⁰Ne atom were first determined using the Kraitchman’s substitution method⁴² and compared with those predicted by quantum chemical calculations (see Table 5). The derived polar coordinates R and θ (referred to the center of mass of pyrrole) are shown in Table 6. Alternatively, the molecular structure was calculated using Kisiel’s program RGDFIT,⁴³ which calculates the coordinates of a rare gas atom in a dimer from the moments of inertia of the molecule and the dimer. This method was first explained by Suenram et al.⁴⁴ The resulting polar coordinates are R = 3.454 Å and θ = 80.2º.

Table 5.

Substitution coordinates (in Å) of the ²⁰Ne atom in the Pyr-Ne and Pyr-Ne₂ complexes.

	Experiment			Theorya
	|a|	|b|	|c|	a	b	c
Pyr-20Ne(parent)/Pyr-22Ne
20Ne	2.62182(57)b	[0]c	0.148(10)	−2.6216	0.0078	−0.2170
Pyr-20Ne20Ne (parent)/Pyr-20Ne22Ne
20Ne	3.38952(46)	0.2588(61)	[0]c	3.4725	−0.3077	0.0009

^aB97D/def2-TZVPP and B97D-D3BJ/def2-TZVPP coordinates of the Ne atom in the Pyr-Ne and Pyr-Ne₂ complexes, respectively.

^bDerived errors in parentheses in units of the last digit. These were calculated according to Constain’s formula: σ(x)=K/1 x | ; σ(x) is the error in the coordinate x and K=0.0012 Å.

^cValue is constrained to zero.

Table 6.

r_s structural van der Waals parameters.

	Pyr-Ne	Pyr-Ne2
Ra	3.397	3.418
θ	79.5	82.2

^a R in Å an θ in degrees.

The stretching force constant between Ne atom and pyrrole can be estimated from the centrifugal distortion constant, DJ, using the pseudodiatomic model. Then assuming a Lennard-Jones 6/12 potential the binding energy can be derived from the force constant. Using the Kisiel’s program DJ,⁴³ we obtained a value around 1.11 kJ/mol for the binding energy of Pyr-Ne complex.

Pyrrole-Ne₂

After removing all the lines of Pyr-²⁰Ne and Pyr-²²Ne from the spectrum, careful analysis led to the assignment of R- and Q-branch b-type transitions to the three isotopologues Pyr-²⁰Ne²⁰Ne, Pyr-²⁰Ne²²Ne and Pyr-²²Ne²²Ne. The rotational spectrum for Pyr-²⁰Ne²⁰Ne species was found to be around 8 times weaker to that for Pyr-²⁰Ne. It should be noted that the only non zero dipole moment component lies along the b axis because the order of the principal axes systems is permuted when passing from dimer to trimer, see Fig.1. Comparison of the isotopic rotational constant changes based on the ab initio structure was useful in order to predict the systematic shifts and to facilitate the identification of the isotopologues. All assigned transitions display well resolved ¹⁴N nuclear quadrupole hyperfine structure. A total of 35, 38 and 18 hyperfine components were observed (Table S10-S12 of ESI) for Pyr-²⁰Ne²⁰Ne, Pyr-²⁰Ne²²Ne and Pyr-²²Ne²²Ne, respectively. The experimental rotational and ¹⁴N nuclear quadrupole coupling constants for the three isotopic species, summarized in Table 4, were determined by the least-squares fit of the transition frequencies using the same Watson’s S-reduced Hamiltonian described above. As for Pyr-Ne complex, the intensity ratios between the Pyr-Ne₂ isotopic species are in sharp contrast with those expected when natural abundances are taking into account. We found an intensity trend Pyr-²⁰Ne²⁰Ne:Pyr-²⁰Ne²²Ne:Pyr-²²Ne²²Ne to be 1: 0.68: 0.26 while the expected one should be 1: 0.21: 0.01. This will be discussed in the next section.

Table 4.

Experimental rotational and nuclear quadrupole coupling constants, all in MHz, for the pyrrole-Ne₂ complex.

	Pyrrole-20Ne20Ne	Pyrrole-20Ne22Ne	Pyrrole-22Ne22Ne
A	4408.6361(36)a	4403.9374(59)	4398.9474(57)
B	965.0390(26)	925.3609(45)	887.2532(79)
C	954.7953(13)	915.7295(23)	878.3792(28)
DJ	0.004548(76)	0.00427(13)	-
DJK	0.01978(60)	0.0190(10)	-
χaa	−2.6302(97)	−2.629(15)	−2.684(18)
χbb	1.3667(83)	1.382(13)	1.400(16)
N b	35	38	18
σ c	10.4	18.1	15.2

^aValues in parentheses denote 1σ errors, applied to the last digit.

^bNumber of hyperfine components included in the fit.

^cStandard deviation of the fit, in kHz.

Once all the isotopic species of Pyr-Ne and Pyr-Ne₂ were identified, no lines remained unassigned in the spectrum and no other species which can be attributed to the [2,0] isomer was found in the spectrum. The non-observation of this isomer can be attributed to a conformational relaxation in the supersonic jet.¹⁶

Kraitchman’s equations were used to determine the substituted coordinates of the Ne atoms, using the three possible combinations of parent/substituted species. In Table 5 the r_s coordinates of the ²⁰Ne derived from the pair Pyr-²⁰Ne²⁰Ne(parent)/Pyr-²⁰Ne²²Ne are shown while the resulting polar coordinates are depicted in Table 6. Similar results were obtained from the pairs Pyr-²⁰Ne²²Ne(parent)/Pyr-²²Ne²²Ne and Pyr-²²Ne²²Ne(parent)/ Pyr-²⁰Ne²²Ne.

Discussion

Unconventional high spectral intensities in isotopic species with ²²Ne

As mentioned before, an unusual intensity profile is shown for isotopic species containing ²²Ne in both complexes Pyr-Ne and Pyr-Ne₂ with a significant enrichment of the heavier isotopologues in the supersonic expansion (see Figure 2). A supersonic expansion is usually described as a non-equilibrium method for the formation of van der Waals complexes, depending upon kinetic factors to produce high concentrations of the species in the jet. This effect can be explained in terms of a quasi-thermal equilibrium caused by the dissociation and subsequent re-formation of dimers and trimers in the molecular expansion, which favors the isotopic exchange ²⁰Ne←²²Ne in the jet region where collisions are still going on. This thermodynamic selection is then frozen into the jet at the point of free molecular flow, where no further collisions occur. A relatively large increase in mass can lower the zero-point energy level resulting in an increment of the dissociation energy of the heavier species which enhances its abundance. A similar behavior has been previously reported in the pyridine-Ne₂ complex¹⁶ and in other complexes such as Ne₂Ar⁴⁵ or Ne-SiH₄.⁴⁶

Statistical Weight

Pyr-²⁰Ne²⁰Ne and Pyr-²²Ne²²Ne complexes have a C_2v symmetry and thus the intensity of their rotational transitions are subjected to spin statistics. This is due to the geometry of the molecule, which allows an interchange of identical particles by the rotation about one of the principal axes. The C_2b operation of the C_2v symmetry point group, which corresponds to the rotation about the b axis by radians, simultaneously exchanges the positions of two non-equivalent pairs of hydrogen (fermions with I = 1/2). The total wavefunction, expressed as ψ _tot = ψ _ele ψ _vi ψ _rot ψ _ns, must be symmetric, Bose-Einstein statistics, with respect to the C_2b operation, considering the two pairs of fermions. The corresponding wavefunctions, ψ _ele and ψ _vib, for the ground electronic and vibrational states, respectively, are symmetric. The parity of the rotational wavefunction, ψ _rot, depends on the K_a and K_c values and it is symmetric for the levels with K_a + K_c = even, while for the levels with K_a + K_c = odd it is antisymmetric. Hence, to satisfy Bose-Einstein statistics symmetric and antisymmetric nuclear spin functions must be combined with symmetric and antisymmetric rotational wavefunctions, respectively. As shown in Bunker & Jensen (1998),⁴⁷ the nuclear statistical weight for the rotational levels with K_a + K_c = even and odd is 10 and 6, respectively. Hence, nuclear spin function has a ratio 5/3 between symmetric and antisymmetric components and the rotational transitions with a K_a + K_c = even will have a favorable intensity ratio of 5/3 with respect to those with K_a + K_c = odd. However, no b-type K doublets can be observed for Pyr-Ne₂ complex in the 2-8 GHz region and no lines can be shown to illustrate the influence of nuclear spin statistics on the transition intensities.

Rotational, centrifugal and nuclear quadrupole coupling constants

The experimental rotational constants of Pyr-Ne are consistent with a nearly symmetric prolate top with the Ne atom located above the plane of pyrrole. The trimer presents C _2v symmetry with each Ne atom on different sides of pyrrole. In both complexes, the Ne atoms are very close to the a axis. Further confirmation comes from the experimental A rotational constants of both the dimer and the trimer which are very similar to the experimental C rotational constant of the pyrrole monomer when the switching of the inertial axes is taken into account (Figure 1).

The centrifugal distortion constants of Pyr-Ne are about one order of magnitude larger than those of its heavier congener Pyr-Ar (Table 7), indicative of a reasonably floppy system. The same behavior has been also observed in complexes of pyridine with a series of rare gases. When moving from Py-Kr to Py-He,^10–12,48 the centrifugal distortion constants increase considerably due to the flatter potential energy surfaces and the smaller reduced masses of the van der Waals vibrations. In fact, the values for the centrifugal distortion constants of Pyr-Ne are of the same order than those found for Py-Ne complex.⁴⁸ In the same manner, for Pyr-Ne₂ complex, the values of the distortion constants are similar to those obtained for Py-Ne₂ (D_J = 3.617 (2) kHz and D_JK = 18.09 (2) kHz).¹⁶

Table 7.

Comparison of the spectroscopic constants (in MHz) of the series pyrrole-Rg and pyrrole monomer.

	Pyrrole-20Ne	Pyrrole-20Ne20Ne	Pyrroleb	Pyrrole-Arc
A	4654.5380(60)a	4408.6361(36)a	9130.637(10)	4601.423(4)
B	2101.6705(51)	965.0390(26)	9001.360(10)	1355.701(1)
C	2099.3956(54)	954.7953(13)	4532.120(10)	1355.070(1)
DJ	0.03272(80)	0.004548(76)	−	0.00475(2)
DJK	0.13554(31)	0.01978(60)	−	0.02503(1)
DK	−0.1429(12)	−	−	−0.02612(8)
d1	-	-	-	−0.00021(1)
χaa	−2.498(12)	−2.6302(97)	−2.704(4)	−2.581(3)
χbb	1.231(14)	1.3667(83)	1.412(3)	1.315(2)
χcc	1.267a	1.2635a	1.292(4)	1.266(4)

^aDerived value using χ_aa and χ_bb which have been obtained from the fit.

^bReference [37]

^cReference [20]

As mentioned before, using the D_J centrifugal distortion constant value we estimated the stretching force constant (k_s) between Ne atom and pyrrole and then the dissociation energy of the complex. We found a value of 0.8769 Nꞏm-¹ for the stretching force constant and a dissociation energy of 1.11 kJ/mol for Pyr-Ne complex. This energy value is almost the same than that found for the Py-Ne complex⁴⁸ but smaller than that estimated for the Pyr-Ar complex, 2.77 kJ/mol.¹¹ This is in agreement with one of the findings in the study of Py-Ne complex,⁴⁸ where the authors stated that Ne has a binding energy to aromatic molecules which is about 1/3 of that of Ar, and about two or three orders of magnitude smaller than that for normal chemical bonds. The predicted value for the dissociation energy of Pyr-Ne complex calculated at MP2/6-311G++(d,p) including the zero-point corrections was found to be 1.105 kJ/mol, in very good agreement with the experimental derived value. On the other hand, the energy associated to the addition of a second Ne atom to the Pyr-Ne complex was calculated to be 1.796 kJ/mol.

Additional information on the structure can be obtained through the experimental ¹⁴N nuclear quadrupole coupling constants. The values of the constants obtained for the isotopologues of the Pyr-Ne and Pyr-Ne₂ complexes are very similar to those of isolated pyrrole (Table 7) when the aforementioned axes inversion is taken into account. This suggests that the electric field gradient around the N nuclei is similar in the complex than in the isolated pyrrole.³⁷ Similar values of the quadrupole constants have been also found for the Pyr-Ar complex²⁰ (Table 7). The quadrupole constants of Pyr-Ne present slightly larger deviations from the monomer values, probably due to the fact that the b (or c) axis does not lie in the ring plane.

Theoretical calculations assessment

Comparison between the experimental rotational constants (Tables 3 and 4) with the predicted ones (Tables 1 and 2 and S1 and S2 in ESI) has been done in order to establish which level of theory gives the best results. The best agreement is provided by B97D and wB97XD methods independently of the basis set employed. However, the best estimation of the rotational constants is reached with the CCSD/def2-TZVPP level of theory, with a discrepancy of 1.54%, taking into account the sum of the relative errors (100ꞏexperiemntal/theoretical) for A, B and C constants. The results for B97D and wB97XD methods are a bit less satisfactory but they reproduce the experimental constants with errors between 3-5%. Best results for each method are provided by B97D/def2-TZVPP and wB97XD/aug-cc-pVTZ levels of theory, with discrepancies of 2.62 and 3.23%. In general for these methods, the agreement for A rotational constant is very good while for B and C is a bit worse. Usually, A constant is underestimated and B and C values are overestimated.

With the exception of CCSD/def2-TZVPP level of theory, all the MP2 and CCSD calculations provide similar results with discrepancies between 4.20% or 8.77%, for CCSD/6-311++G(d,p) and MP2/6-311++G(2d,p) respectively, and 20.12% and 25.66% for the CCSD/ aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory, respectively. The results obtained with the DFT methods M06-2X and B3LYP indicate that these methodologies are not suitable to optimize this kind of molecular structures. The discrepancies between the experimental rotational constants and those predicted by these methods are at least 25% reaching 64% in some cases. However, when dispersion corrections (D3BJ) are taking into account in the B3LYP calculations the results are improved. For example for B3LYP /6-311++G(d,p) the error is 46.34% while it is reduced up to 17.05% for B3LYP-D3BJ/6-311++G(d,p) level of theory.

For Pyr-Ne₂ we used performed the same calculations than those for Pyr-Ne complex. Comparison of the experimental Pyr-Ne₂ values for the rotational constants with those predicted by the different levels of theory provide the almost the same results. It should be noted that all the levels of theory give worse results for Pyr-Ne₂ than for Pyr-Ne. B97D and wB97XD are in general terms the best methods, independently of the basis set used, and the best accordance between experimental and theoretical values is found when CCSD/def2-TZVPP level of theory is used, which provides an error of 3.52%. The discrepancies for B97D and wB97XD methods are around 8-12%, with the best results for B97D/aug-cc-pVTZ and wB97XD/aug-cc-pVTZ levels of theory with errors of 4.28 and 6.58%, respectively. As it was found for Pyr-Ne, MP2 and CCSD methods are in a second group with errors between 13-27%, except MP2/def2-TZVPP level of theory with 7.61%. DFT functional M06-2X and B3LYP provide poor results, as for Pyr-Ne, but the agreement for B3LYP calculations is better when the D3BJ dispersion corrected is considered.

As mentioned before we extended our calculations to other known analogue species such as Py-Ne and Pyr-Ar complexes to check the reliability of our calculations. Tables S3 and S4 show the results for Py-Ne and Pyr-Ar species using some of the methods employed for Pyr-Ne and Pyr-Ne₂ complexes. For Py-Ne the best results are achieved with CCSD/def2-TZVPP, CCSD/6-311++G(d,p) and B97D/aug-cc-pVTZ levels of theory with discrepancies of 0.76, 1.92 and 2.34 %, respectively. In the case of Pyr-Ar, CCSD/6-311++G(d,p), CCSD/def2-TZVPP and wB97XD/def2-TZVPP provide the best results, with associated errors 0.84, 3.33 and 4.56 %.

In light of our results, it seems that CCSD/def2-TZVPP calculates very accurate values for the rotational constants for this kind of complexes. B97D/def2-TZVPP and wB97XD/def2-TZVPP are very close to the couple cluster method in terms of accuracy and with the advantage of lower computational resources, around 180 times faster. Similar results have been found before for other gas atom-aromatic molecule, i.e Rg-C₆H₆, where wB97XD provided the best results, similar to those found by CCSD methods.⁴⁹ Our results also shown the importance of accounting for dispersion in the quantum calculations for these molecular species. wB97XD and B97D provide much better results than other functional that do not consider dispersion, such as M06-2X or B3LYP. In this latter case, the results are improved when dispersion is taking into account.

Molecular structure

As in Pyr-Ar,²⁰ the structural parameters of the dimer (Tables 5 and 6) situate the Ne atom above the midpoint between the two ring C atoms adjacent to the N atom. The shorter distance R (3.39 vs 3.55 Å) in Pyr-Ne compared to Pyr-Ar is in accordance with the difference in the van der Waals radii for the two noble gases, as reported in previous studies.^11,12 A similar distance (3.400(2) Å) has been obtained in the Py-Ne complex.¹² The derived R and θ parameters match well with those predicted at B97D/def2-TZVPP and CCSD/def2-TZVPP levels of theory (Table 1) with maximum deviations of 0.8% and 2.2%, respectively. The configuration of the Pyr-Ne₂ complex (Tables 5 and 6) is in accordance with the one derived for the Pyr-Ne complex, and the Py-Ne₂ complex,¹⁶ with the Ne atoms shifted toward the N atom. In this case, CCSD/def2-TZVPP and B97D/aug-cc-pVTZ levels of theory (Table 2) provide the best agreement with the polar coordinates with maximum deviations of 0.7 and 1.2%, respectively.

Conclusions

The van der Waals complexes Pyr-Ne and Pyr-Ne₂ have been generated for the first time in a supersonic jet and characterized by chirped pulse Fourier transform microwave spectroscopy in the 2-8 GHz frequency region. Five isotopic species, Pyr-²⁰Ne, Pyr-²²Ne, Pyr-²⁰Ne²⁰Ne, Pyr-²⁰Ne²²Ne and Pyr-²²Ne²²Ne, have been detected in natural abundance. Our results indicate that the formation of [1,1] isomer is preferred over the [2,0] for Pyr-Ne₂, as it has been found for other complexes between and aromatic molecule and a rare gas.

The rotational, centrifugal distortion and ¹⁴N nuclear quadrupole coupling constants have been determined for all the species. The centrifugal distortion constants of the dimer are about one order of magnitude larger than those of its heavier congener Pyr-Ar, consistent with a floppy molecular system. The dissociation energy for Pyr-Ne has been estimated to be 1.11 kJ mol^-1. ¹⁴N nuclear quadrupole coupling constants of the Pyr-Ne and Pyr-Ne₂ complexes are very similar to those of isolated pyrrole, which suggests that the electric field gradient around the N nuclei is similar in the complex than in the isolated pyrrole.

CCSD/def2-TZVPP level of theory provides the best agreement with the experimental rotational constants for both Pyr-Ne and Pyr-Ne₂ complexes. DFT methods like wB97XD and B97D also provide very satisfactory results for these complexes and due to their low computational cost they are a good alternative to high level theoretical methods when large molecular systems are investigated. The importance of accounting for dispersion for these complexes is demonstrated since wB97XD and B97D methods provide much better results than other functional that do not consider dispersion, such as M06-2X or B3LYP. Overall, our results constitute an advancement in our understanding of weakly bound complexes which are considered to bridge the gap between the properties of isolated molecules and those of condensed phases.