Theoretical Study of the PyridineâHelium van der Waals Complexes

Article pubs.acs.org/JPCA

Theoretical Study of the Pyridine−Helium van der Waals Complexes Published as part of The Journal of Physical Chemistry A virtual special issue “Spectroscopy and Dynamics of Medium-Sized Molecules and Clusters: Theory, Experiment, and Applications”. Hubert Cybulski* Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland

Christian Henriksen* Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lynbgy, Denmark

Berta Fernández* Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials (CIQUS), University of Santiago de Compostela, 15782 Santiago de Compostela, Spain ABSTRACT: In this study we evaluate a high-level ab initio ground-state intermolecular potential-energy surface for the pyridine−He van der Waals complex, using the CCSD(T) method and Dunning’s augmented correlation consistent polarized valence double-ζ basis set extended with a set of 3s3p2d1f1g midbond functions. The potential is characterized by two symmetric global minima of −93.2 cm−1 that correspond to geometries where the distance between the helium atom and the pyridine center of mass is 3.105 Å and the angle with respect to the pyridine c rotational axis is 3.9°. Six local minima can be observed for geometries with the helium atom in the plane cotaining the pyridine molecule. To further analyze the nature of the intermolecular interactions in the complex, we use symmetryadapted perturbation theory (SAPT). Additional consideration of the pyridine−He2 complex provides a better insight into many-body nonadditive contributions to intermolecular interactions in systems with more helium atoms.

I. INTRODUCTION Interest in complexes of helium atoms with aromatic molecules is mainly stimulated by spectroscopic investigations of aromatic systems embedded in helium droplets. For such microdroplets of helium with a guest molecule dissolved in it, evidence for microscopic superfluid behavior has been found.1 However, the most intriguing question of what is the minimal number of He atoms for the appearance of macroscopic properties like superfluidity remains open. Additionally, an analysis of simple complexes formed by an aromatic molecule and helium atoms opens possibilities for detailed studies of prototypical sp2-hybridized systems related to graphite surfaces or stacking interactions responsible, e.g., for the structure stabilization in DNA or RNA strands. In such systems, the aromatic electrons provide a significant driving force for weak intermolecular bonds with the main contribution coming from the dispersion interaction. Nitrogen heteroatoms are present in nucleic acid bases and presumably they influence the stacking interactions between the bases and hence the structure of DNA and RNA. Weakly bound complexes consisting of an aromatic molecule and a rare-gas atom have been investigated by means of both © 2015 American Chemical Society

experimental and theoretical methods. The experimental studies revealed that the rare-gas atom usually binds perpendicularly (at an R distance) to the center of mass of the aromatic molecule. In the case of complexes with pyridine, the rare-gas atom is slightly displaced (by a θ angle) away from the c principal inertia axis of the C6H5N monomer toward the nitrogen atom. High-resolution rotational spectra of the pyridine−He complex2 showed that the He atom lies at R0 = 3.529 Å from the pyridine center of mass and θ0 = 7.0°. Additionally, ab initio counterpoise corrected3 structure optimizations were carried out by means of second-order Møller−Plesset perturbation theory (MP2) and Dunning’s augmented correlation consistent polarized valence double-ζ basis set (aug-cc-pVDZ).4,5 The results yielded an equilibrium geometry (Re = 3.14 Å, θe = 4°) consistent with the experimental findings and a well depth of 86.7 cm−1.2 The discrepancies in the observed and calculated geometric parameters were attributed to the neglect of zeroReceived: August 31, 2015 Revised: October 17, 2015 Published: October 19, 2015 10999

DOI: 10.1021/acs.jpca.5b08492 J. Phys. Chem. A 2015, 119, 10999−11006

Article

The Journal of Physical Chemistry A point vibrational effects and the methodology used in the theoretical calculations. The equilibrium configuration of the pyridine−Ne complex was deduced by Maris et al.6 using free jet millimeter-wave spectroscopy. A dissociation energy of ca. 90 cm−1, an equilibrium distance Re = 3.316 Å, and θe = 4.2° were obtained. After a dynamics analysis, three van der Waals motions with approximated fundamentals in the range of 19− 31 cm−1 were reported. The structure of the pyridine−Ar complex was determined through pulsed-nozzle Fourier transform microwave spectroscopy.7 A structure with the Ar atom above the ring plane was found: R0 = 3.545(1) Å from the center of mass of the C6H5N molecule and θ0 = 3.2(4)°. In 2005 the MP2 method was used to obtain the structure and energetics of complexes of Ar with several azabenzenes.8 Inter- and intramolecular frequencies were also evaluated. For all complexes, changes in the intramolecular structure due to interaction with the Ar atom were found negligible in the evaluation of the interaction energies, but these changes became significant when the intramolecular frequencies were considered. For the pyridine−Ar dimer a binding energy De of 397 cm−1 and an equilibrium distance ze of 3.506 Å (z axis passing through the pyridine center of mass and perpendicular to the molecule) were obtained using the aug-cc-pVDZ basis set. Good agreement (differences of less than 1.5 cm−1) with the experimental intermolecular frequencies was achieved after further scaling of the calculated values by a factor of 0.85. Microwave spectra of noble gas−pyridine dimers: pyridine− Ar and pyridine−Kr, demonstrated that the noble gas atoms are located above the plane of the aromatic ring (R0= 3.545 (3.648) Å and θ0 = 3.5 (3.4)°, for pyridine−Ar(Kr)).9 Using a very simple pseudopotential model for the interaction potentials, equilibrium distances Re of 3.509 and 3.621 Å were obtained for the Ar- and the Kr-complex, respectively. In the same work, the authors compared the results for pyridine−Ar with those for the furan−Ar dimer. They found similar Ar−aromatic ring distances and well depths (232 and 236 cm−1, respectively),9 despite a large difference in the dipole moments of the molecules (2.19 D vs 0.66 D for pyridine and furan, respectively). The rotational spectrum and molecular properties of the pyridine−Xe complex were studied by Tang et al. by pulsed-jet Fourier transform microwave spectroscopy,10 yielding an equilibrium structure of R0 = 3.809(1) Å and θ0 = 5.50(4)°. Additionally, the authors considered the dynamics of the Xe van der Waals motions obtained from centrifugal distortion and from changes in the moments of inertia in the pyridine plane due to the complex formation. Apart from the structures containing only one atom of noble gas, the existence of several species with two noble-gas atoms was also reported. Successive additions of one rare-gas atom should finally yield a microdroplet with a molecule embedded within. For instance, in the case of helium, a recognized nonclassical behavior of molecular properties as a function of the number of rare-gas atoms was interpreted as a manifestation of an onset of microscopic superfluidity.1,11,12 In microwave studies on the pyridine−Ne2 system the [1,1] species with the neon atoms located symmetrically one on each side of the ring plane (R0 = 3.391(1) Å and θ0 = 2.7(6)°) was detected. No lines for the [2,0] conformer with the two atoms on the same side were identified.13

The structure of the pyridine−Ar2 complex, with the two argon atoms in symmetrically equivalent positions above and below the ring, at distances R0 of 3.544 Å and angles θ0 of 3.9°, was determined using pulsed-nozzle Fourier transform microwave spectroscopy.7 Only slight changes in these values in comparison with those in the pyridine−Ar complex indicated that three-body effects were negligible. The [1,1] conformer of the van der Waals hetero triad pyridine−Ar−Ne was detected through pulsed-jet microwave spectroscopy.14 An R0 distance of 3.540 (3.396) Å and a θ0 angle of 2.2 (4.6)° were found for Ar (Ne). The [2,0] species with the rare-gas atoms on the same side of the ring was not observed. Ab initio MP2/6-311++G** calculations performed by the authors suggested a flat potential with several almost equivalent minima separated by low barriers. The aim of the present study is to obtain a high-level ab initio ground-state intermolecular potential-energy surface (IPES) for the pyridine−He van der Waals complex that can be used in subsequent accurate studies of the complex (e.g., molecular dynamics). To shed more light on the nature of the intermolecular interactions, we apply symmetry-adapted perturbation theory (SAPT).15 Additionally, we investigate the global and several local minima of the pyridine−He2 trimer. Considerations of complexes containing more helium atoms provide a better insight into many-body nonadditive contributions to the intermolecular interactions in more complex molecular arrangements. The manuscript is organized as follows: In section II we briefly describe the employed computational methodology, in section III the characteristics of the obtained IPES are presented, the results of the SAPT calculations are discussed and the found optimal geometries for the pyridine−He2 trimer are described. In section IV we summarize and present our final conclusions.

II. COMPUTATIONAL DETAILS A. Interaction Energies. Pyridine−He interaction energies are calculated on a set of grid points for various positions of the He atom relative to the rigid pyridine molecule described by the Cartesian coordinates (x, y, z) of the He position vector r ⃗ with origin in the pyridine center of mass. The z axis is perpendicular to the pyridine plane, and the y axis lies in the molecular plane and passes through the nitrogen atom and the C−H bond, with the N atom in the negative part of the axis. The x axis is perpendicular to the y and z axes and cuts two C− C bonds. The interaction energy calculations are performed using the coupled-cluster singles and doubles model including connected triples corrections (CCSD(T)) correlation method and the aug-cc-pVDZ basis set4,5 extended with a set of 3s3p2d1f1g midbond functions (denoted as 33211)16,17 centered in the middle of the r ⃗ vector. The dependence of the interaction energy on the position of the midbond functions along the van der Waals bond is small and, in the case of asymmetric complexes, the errors due to their emplacement in the middle of the bond are negligible. The exponents for the 33211 midbond set are 0.90, 0.30, and 0.10 for the s and p, 0.60 and 0.20 for d, and 0.30 for f and g functions. The above combination of correlation method and basis set is selected because it has provided very good agreement with accurate experimental results for similar complexes we studied (see ref 18 and references cited therein). In the case of the pyridine− He2 trimer we use the aug-cc-pVDZ basis and three sets of 11000


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The Journal of Physical Chemistry A Table 1. IPES Parameters (c, in cm−1) dil 1.7651 Å s 0.5037 c0 0 0 0 0 0 2 c5 0 0 0 0 0 0 c1 0 0 0 0 0 2 c0 0 0 0 2 0 2 c0 0 0 2 0 0 3 c0 0 0 0 1 0 5 c0 0 1 0 1 0 1 c2 0 0 0 1 0 1 c0 0 0 1 0 2 2 c0 0 0 0 2 2 2 c0 0 0 1 0 3 2 c2 0 0 1 0 0 3

−39.5743 27.3082 22.3323 −835.1477 −2043.3821 −697.1958 −54.8705 56.9055 −1356.7295 −785.8535 2492.0376 −140.2928

−6.8193 191.0373 −273.8024 291.8828 −46.5659 310.5337 929.5461 −359.5367 2535.9146 3603.6343 −681.8654

c3 0 0 0 0 0 0 c0 0 0 0 0 0 6 c0 0 0 0 0 1 3 c0 0 0 0 1 0 4 c4 0 0 0 0 0 1 c0 0 0 0 3 0 3 c0 0 0 1 0 2 1 c0 0 0 0 1 2 2 c0 0 0 2 0 1 2 c0 0 0 1 0 1 4 c0 0 0 1 3 0 2

t

midbond funtions placed in the midway between two constituents of each pair of the monomers in the complex. The exception to this is at the global minimum geometry, where we use only two midbond function sets, located between the pyridine molecule and each of two He atoms (which are on the opposite sides of C5H5N). The supermolecular model corrected for basis-set superposition error (BSSE) employing the counterpoise method of Boys and Bernardi3 is used to evaluate the interaction energies. The counterpoise correction is essential when a double-ζ quality basis set is used.19 In all the calculations the geometry of the pyridine molecule is kept rigid at the experimental one reported by Innes et al.20 Small changes in intramolecular geometries usually have a negligible effect on van der Waals complex interaction energies (see, for instance, ref 8). All interaction energy calculations are performed with the DALTON program.21 The zero-point energy is calculated using the BOUND program.22 B. Symmetry-Adapted Perturbation Theory. In this work we employ the following SAPT approximation to the intermolecular interaction energy, roughly equivalent to a supermolecular second-order many-body perturbation-theory (MBPT2) calculation, namely ESAPT2 :23,24 int t

sum (10) (20) (1) (22) Eexch = Eexch + Eexch − ind,r + ϵexch (2) + Eexch−ind (20) + Eexch − disp

t

sum (20) (22) E ind = E ind,r + E ind

(1)

with the interaction energy calculated at the Hartree−Fock level defined as

E(10) elst

(2)

E(10) exch

is the classical (Coulombic) electrostatic energy, is the exchange term that results from the antisymmetrization (symmetry adaptation) of the wave function, E(20) ind,r denotes the induction (with response) energy, E(20) exch−ind,r is the second-order exchange−induction (with response) energy term, E(20) disp is the (20) dispersion energy, and Eexch−disp denotes the exchange− dispersion contribution. δEHF int collects all third- and higherorder induction and exchange-induction terms. For more details, see refs.23,24 To simplify the analysis of the SAPT decomposition, we introduce terms denoting the electrostatic, exchange, and induction contributions to the total energy. sum (10) (12) Eelst = Eelst + Eelst,r

(5)

The interaction energy components are calculated using the SAPT2008 program.15 C. Fit of the Interaction Potential. The 613 ab initio computed are fitted to an analytical function V(r)⃗ with 36 adjustable parameters. The analytic function V(r)⃗ used is a many body expansion with exponential terms and it has been already used in our previous studies.25 It is constructed as follows. The non-hydrogen atoms of the pyridine molecule form the vertices of an almost regular hexagon. We exploit this almost symmetry, and in some terms treat the nitrogen atom as the carbon atoms. However, the molecule is not truly so symmetric, so in other terms, we treat the nitrogen atom differently. To implement this practically, we give the nitrogen atom two labels, 1 and 2, whereas we number the carbon atoms 3, 4, ..., 7. The numbering is chosen in a way that going from 2 to 7, we traverse consecutive atoms in the ring. We denote the position of the atom with label i by C⃗ i, and that of the hydrogen atom bonded to the ith non-hydrogen atom by H⃗ i, i = 3, 4, ..., 7. We let H⃗ 1 = H⃗ 2 = C⃗ 1. Given the adjustable unitless parameters s, we introduce virtual points at the positions A⃗ i = A⃗ i(s) by the formula A⃗ i = (1 − s) C⃗ i + sH⃗ i. Thus, when s ∈ (0, 1), A⃗ i lies somewhere on the C−H bond, i = 3, ..., 7. We think of A⃗ i as the effective position of the corresponding carbon atom that takes the bonded hydrogen atom into account. Constructing V as a function of the Ai’s eliminates the need to deal any further with anisotropy.

t

HF (10) (20) (20) HF (10) E int = Eelst + Eexch + E ind,r + Eexch − ind,r + δE int

(4)

and

SAPT2 HF (22) (22) (12) E int = E int + Eelst,r + ϵ(1) exch (2) + E ind + Eexch−ind (20) (20) + Edisp + Eexch − disp

−117.2721 3.3113 264.3077 375.2618 −278.8862 −1043.8731 −42.6860 530.2771 942.2433 −4036.0939 213.5864

c0 0 0 0 0 0 5 c6 0 0 0 0 0 0 c0 0 0 0 0 2 2 c0 0 0 1 0 0 4 c0 0 0 0 0 1 5 c0 0 0 1 0 0 5 c2 0 0 0 0 1 1 c0 0 0 0 1 3 1 c0 0 0 0 1 1 4 c0 0 0 1 0 2 3 c1 0 0 0 2 0 3

∥ r ⃗ − A⃗ ∥

i , where dil is an adjustable parameter. Also Let di = dil let Di = 10 exp(−di) . The function V(r)⃗ is a polynomial in Di. Before writing up the expression, we account for symmetry. Let G ⊂ S7 be the permutation group generated by, in cycle notation, σ1 = (2 3 4 5 6 7) and σ2 = (3 7 4 6). Then G has order 12 and is isomorphic to the symmetries of the hexagon (the dihedral group D6), σ1 corresponding to a rotation by onesixth of a turn, whereas σ2 corresponds to a reflection. We chose a set K ⊂ 7 of exponents, and let

(3) 11001


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The Journal of Physical Chemistry A V=

∑ k∈K

Ck 12

∑ Dgk(1)Dgk(2) ··· Dgk(7) 1

g∈G

2

7

(6)

where Ck are adjustable parameters. For example, if k = (1, 0, 0, 0, 0, 0, 0), the inner sum equals 12 D1. If k = (0, 1, 0, 0, 0, 0, 0), the inner sum equals 2D2 + 2D3 + 2D4 + 2D5 + 2D6 + 2D7. The values of the adjustable parameters are assigned as to minimize the square differences between the calculated interaction energies and V(r)⃗ . The set K is chosen so that V(r)⃗ seemed to behave reasonably close to the pyridine molecule. The fit exhibits a root-mean-square error of rms = 0.21 cm−1, considering all points, and a rms = 0.17 cm−1, including only points with negative interaction energy. The final parameters are shown in Table 1. The root-mean-square errors found are calculated at points that were also taken into consideration when the fit was constructed. Even if a ratio of 613 points to 36 adjustable parameters is good, one could worry about overfitting, that is, that the fit represents the interaction energies well at the geometries where the interaction energies have been calculated, but poorly in between. To dispel this doubt, we perform an exhaustive leave one out cross validation. In practice this amounts to, for each ab initio energy, a fit of the adjustable parameters leaving that data point out. The value of the resulting fit at the geometry we have left out is then compared to the ab initio value. Doing this for the 613 points, we obtain a root-meansquare derivation from the ab initio energies of 0.38 cm−1. If we only consider points where the energy is negative, the rms is 0.18 cm−1. So the fit seems to represent the interaction energy surface well, in particular, in the part where the energy is negative.

III. RESULTS AND DISCUSSION A. Intermolecular Potential-Energy Surface. The IPES global minima of −93.2 cm−1 correspond to the geometries given by (0, −0.2090, ±3.0984) Å. This is equivalent to a distance from the He atom to the pyridine center of mass of 3.105 Å and an angle of 3.9° with respect to the z axis (on both sides of the pyridine molecule). Several local minima can be observed with the helium atom in the xy-plane. More specifically there are minima at (±2.3750, 4.0551, 0) Å (with interaction energies of −46.57 cm−1), at (±2.1382, −4.0518, 0) Å (−46.21 cm−1), and at (±4.7136,−0.1280, 0) Å (−41.34 cm−1). The positions of the minima are shown in Figure 1. The obtained geometric parameters differ slightly from the MP2/aug-cc-pVDZ ones reported in ref 2: the θ angle is roughly the same, whereas the equilibrium intermolecular distance is shorter by ca. 0.03 Å. The MP2 dissociation energy is lower (in absolute value) by 6.5 cm−1 than the CCSD(T) one. The MP2 method is wellknown to overestimate interaction energies and we could expect the MP2/aug-cc-pVDZ-33211 disociation energy to be greater than the corresponding value calculated at the CCSD(T) level. The lower dissociation energy calculated in ref 2 may probably result from the use of the aug-cc-pVDZ basis set without any midbond functions. Surprisingly, if we compare our results with those for the pyridine−Ne complex,6 we obtain a slightly stronger interaction energy for the pyridine−He system. This can be attributed to the use of a Lennard-Jones potential in calculations for the complex with Ne.6

Figure 1. Energy level diagrams of the pyridine−He IPES in the xy, xz (y = −0.209 Å), and yz planes. Minima are marked with a circle, saddle points with a cross, and non-hydrogen atoms with a star.

In the case of He van der Waals complexes, comparison of ab initio intermolecular geometries to (R0, θ0) experimental results is not reliable without taking into account zero-point vibrations. For the pyridine−He complex a difference of 0.40 Å was obtained between Re and R0 in ref 2. For complexes with heavier rare-gas atoms, molecular vibrations do not play such a significant role in the intermolecular geometries. We can compare the pyridine−He IPES to the most accurate results for the isoelectronic benzene−He complex26 that yielded calculated observables that matched the experimental results very well. The IPES for the benzene−He dimer was evaluated using the CCSD(T) method and aug-cc-pVDZ basis set extended with a set of 3s3p2d1f1g midbond functions. Two symmetrically located global minima were characterized by a distance between the He atom and the benzene center of mass of 3.157 Å and a dissociation energy of −89.59 cm−1. The interaction in the pyridine−He complex is slightly stronger than that in the benzene−He dimer. This result could be expected considering the nonzero dipole moment of the pyridine molecule. A significant difference appears for calculated zero-point energies. The calculated value of −66.59 cm−1 for the pyridine−He complex is more than twice the value (−29.98 cm−1) for the benzene−He dimer.26 As previously shown, the zero-point energy value is sensitive not only to the depth26 but also to the overall shape of the IPES (see, for instance, ref 27). 11002


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The Journal of Physical Chemistry A B. SAPT Calculations. To get insight into the nature of the interaction in the pyridine−He complex, we perform SAPT calculations for three configurations of the system: (i) with the helium atom above the pyridine ring (interaction through the π-electrons), and with the helium atom placed along the pyridine C2 symmetry axis on the (ii) N, and (iii) H−C sides. The SAPT individual contributions for three points close to the minimal interaction energy for the three configurations are collected in Table 2. The distance dependencies are calculated Table 2. SAPT Individual Contributions (cm−1) for Three Orientations of the Pyridine−He Complexa Rred E(10) elst E(12) elst, r Esum elst E(10) exch E(20) ex−ind,r ϵ(1) exch(2) t (22) Eex−ind E(20) exch−disp Esum exch E(20) ind,r t (22) Eind Esum ind E(20) disp δHF int,r ESAPT2 int

He···π

He···N

He···H−C

3.10 −33.26 −4.72 −37.98 132.65 8.62 16.31 1.00 9.43 168.01 −10.02 −1.17 −11.19 −198.12 −14.23 −93.50

3.70 −5.45 −2.96 −8.40 17.87 1.64 7.23 0.20 0.83 27.76 −5.42 −0.65 −6.08 −31.28 −1.86 −19.85

3.00 −2.90 −1.60 −4.50 12.63 1.16 2.26 0.11 0.56 16.72 −2.47 −0.23 −2.70 −27.01 −0.80 −18.29

Figure 2. Total SAPT interaction energy for the pyridine−He complex. Rred is the distance between the He atom and the pyridine molecule (cf. text for definitions).

the interaction via the nitrogen atom: the system is bound stronger when it interacts through the π-electrons. The intermolecular interaction through the H−C part is generally much weaker, and the values of the corresponding terms are much lower (Figure 3). C. Pyridine−(He)2 Trimer. For the pyridine−(He)2 trimer to obtain a more precise location of the IPES minima, we employ a spherical coordinate system (r, θ, ϕ) with the origin in the pyridine molecule center of mass. The search for the minima are performed by probing the regions of the minima for the pyridine−He dimer, using a grid where r varies by 0.05 Å and each of the angles by 2°. Following this crude procedure, we locate 13 minima on the IPES. The results are depicted in Figure 4. In the global minimum structure for the pyridine−(He)2 trimer both helium atoms lie symmetrically above and below the pyridine ring. The geometric parameters are close to those in the pyridine−He dimer (R1 = R2 = 3.1 Å and θ = 4°): the influence of the second helium atom is practically negligible. The trimer interaction energy is approximately twice the interaction energy in the dimer. Several local minima located for the pyridine−(He)2 trimer relate to structures where the position of the first helium atom corresponds to that in the dimer global minimum geometry and the second helium atom occupies a position of one of the local minima found for the dimer. These interaction energies can be approximately expressed as the sum of the interaction energy of the dimer global minimum and that of the corresponding local minimum.

a Rred (Å) is the distance between He and the pyridine molecule (cf. text for definitions).

in such manner that the He atom is moved along the x, y, and z axes of the pyridine monomer (see definitions in section IIA). The Rred distance is defined as the distance between the helium atom and (i) the pyridine center of mass or (ii) N or (iii) H atoms. Such a definition of Rred as an intermolecular separation of the He atom and the closest part of C5H5N molecule allows us to compare directly the interaction-energy terms for different spacial orientations of the system. The results of the total SAPT interaction energy dependence on Rred are depicted in Figure 2, and the corresponding graphics for the individual contributions are shown in Figure 3. A short inspection of Table 2 reveals that for each of the three configurations the general patterns in the contributions to (10) the interaction energy are similar: the sum of the Eelst (10) electrostatic and Eexch exchange contributions is positive, and it is the substantial E(20) disp term that makes the total interaction energy negative. Therefore, we can conclude that this system is clearly bound by dispersion. More information comes from the dependencies of the individual contributions on the Rred separation drawn in Figure 3. For two configurations, the He atom above the aromatic ring and the He atom interacting via the nitrogen atom of the sum pyridine molecule, the behaviors of the Esum elst and Eexch terms are very similar and their values in the studied range of Rred are sum close to each other. A distance dependence of the Eind induction term apparently discriminates between these two orientations and its values are two times larger for the He···N sum interaction. An opposite tendency appears for the Edisp dispersion term. In the case of the helium atom above the aromatic ring this attractive contribution is about twice that of

IV. SUMMARY AND CONCLUSIONS In this work we evaluate a high-level ab initio CCSD(T) IPES for the ground state of the pyridine−He van der Waals complex. Taking into account our previous studies of similar complexes,18,28 we select the aug-cc-pVDZ Dunning’s basis set4,5 extended with a set of 3s3p2d1f1g midbond functions for the interaction energy calculations. The ab initio interaction energies lower than 1000 cm−1 are fitted to an analytical function, i.e., a many-body expansion with exponential terms and 36 adjustable parameters. The fit is characterized by a rootmean-square error of rms = 0.21 cm−1. The present potential improves previously available theoretical potentials for the 11003


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The Journal of Physical Chemistry A

Figure 3. Individual (a) electrostatic, (b) exchange, (c) induction, and (d) dispersion contributions to the total SAPT interaction energy for the pyridine−He complex. Rred is the distance between the He atom and the pyridine molecule (cf. text for definitions). See Figure 2 for line definitions.

Figure 4. Structures of the (a) global and the three (b)−(d) lowest local minima for the pyridine−(He)2 complex. Nine additionally found local minima are depicted below.

To further analyze the nature of the intermolecular interactions, we carry out SAPT calculations. We have found sum that the sum of the Esum elst electrostatic and Eexch exchange (20) contributions is positive and it is the large Edisp term that makes the total interaction energy negative. From this, we can conclude that the pyridine−He dimer is bound by dispersion. Considering the dependencies of the individual contributions on the Rred separation, one can notice that in spite of similar

complex and shall be useful in subsequent accurate spectroscopic or molecular dynamics studies. The IPES has two (equivalent by symmetry) global minima of −93.2 cm−1 at geometries where the distance from He to the pyridine center of mass is of 3.105 Å and the angle with respect to the pyridine c rotational axis of 3.9°, and six local minima in the plane of the pyridine molecule. The interaction is stronger than in the case of the benzene−He complex. 11004


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The Journal of Physical Chemistry A sum values of Esum elst and Eexch for the orientations where the system interacts through the pyridine π-electrons or via the N atom, the attractive dispersion contribution is 2 times larger in the former case. In the global minimum structure of the pyridine−(He)2 trimer both helium atoms lie symmetrically above and below the pyridine ring. The values of the geometric parameters are close to those in the pyridine−He dimer and the interaction energy is approximately twice that of the global minimum in the dimer. This proves that the presence of another helium atom on the opposite side of the pyridine ring does not influence the interaction. This is also valid for the local minima in the trimer, where the position of one of the helium atoms corresponds to that in the dimer global minimum geometry and the other He-atom has coordinates close to those of one of the local minima found for the dimer. These trimer interaction energies can be approximately obtained as the sum of the interaction energy of the dimer global minimum and that of the corresponding local minimum. From our preliminary studies on static pyridine−He2 clusters, it is difficult to predict any particular property concerning superfluidity. However, because the results suggest that many-body interactions are negligible, we could expect that formation of larger clusters would result in structures in which the helium atoms are weakly bound to each other and, thus, more susceptible to behave like a (super)liquid than an ordinary droplet. It is evident that further dynamic studies are indispensable.

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AUTHOR INFORMATION

Corresponding Authors

*H. Cybulski. Electronic mail: hubert@fizyka.umk.pl, [email protected]. *C. Henriksen. Electronic mail: [email protected]. dk. *B. Fernández. Electronic mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Spanish Ministerio de Ciencia e Innovación (CTQ2011-29311-C02-01 project). Centro de Supercomputación de Galicia (CESGA) is acknowledged for computational resources.

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Article

The Journal of Physical Chemistry A (27) Cybulski, H.; Baranowska-Ła̧czkowska, A.; Henriksen, C.; Fernández, B. Small and Efficient Basis Sets for the Evaluation of Accurate Interaction Energies: Aromatic Molecule-Argon GroundState Intermolecular Potentials and Rovibrational States. J. Phys. Chem. A 2014, 118, 10288−10297. (28) Koch, H.; Fernández, B.; Makarewicz, J. Ground State BenzeneArgon Intermolecular Potential Energy Surface. J. Chem. Phys. 1999, 111, 198.

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