(HNg+)(OH2) complexes (Ng = He–Xe): An ab initio and DFT theoretical investigation

Computational and Theoretical Chemistry 1017 (2013) 117–125

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ðHNgþ ÞðOH2 Þ complexes (Ng = He–Xe): An ab initio and DFT theoretical investigation Paola Antoniotti a, Paola Benzi a, Elena Bottizzo a, Lorenza Operti a, Roberto Rabezzana a, Stefano Borocci b, Maria Giordani b, Felice Grandinetti b,⇑ a b

Dipartimento di Chimica, Università degli Studi di Torino, Via P. Giuria, 7, 10125 Torino, Italy Dipartimento per la Innovazione nei sistemi Biologici, Agroalimentari e Forestali (DIBAF), Università della Tuscia, L.go dell’Università, s.n.c., 01100 Viterbo, Italy

a r t i c l e

i n f o

Article history: Received 4 March 2013 Received in revised form 13 May 2013 Accepted 14 May 2013 Available online 22 May 2013 Keywords: Ab initio calculations AIM analysis DFT calculations ETS-NOCV analysis Noble gas cations Structure and stability

a b s t r a c t The HNgOH2+ cations (Ng = He–Xe), formally arising from the insertion of a Ng atom into the O–H bond of H3O+, were characterized by MP2, CCSD(T), B3LYP, and BP86 calculations as ion–dipole complexes, best described by the resonance form (HNg+)(OH2). While the MP2, CCSD(T), and B3LYP methods predict planar structures of C2v symmetry, the BP86 predicts non-planar structures of Cs symmetry. The structural differences are however only minor, and do not affect the bonding situation, as described by the atomic charges, and the AIM bond topologies. The energy decomposition analysis performed by the ETS method at the BP86 level of theory revealed that the interaction between NgH+ and H2O is prevailingly electrostatic for Ng = Ne, Ar, Kr, and Xe, while the electrostatic and the orbital contributions become comparable for Ng = He. The NOCV analysis unraveled also that, for any Ng, the dominant orbital contribution is the donor–acceptor interaction between the r(O–H) orbital of H2O (3 A1) and the empty r orbital of NgH+. All the (HNg+)(OH2) are however largely unstable with respect to dissociation into H3O+ and Ng, and only the heaviest (HAr+)(OH2), (HKr+)(OH2), and (HXe+)(OH2) are predicted to be metastable, and conceivably observable at low temperature. The structure and stability of the Ng-H3O+ intermediates involved in the decomposition of the (HNg+)(OH2) were also briefly examined. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The noble-gas hydrides HNgY (Ng = noble gas atom; Y = electronegative fragment) constitute a relevant part of modern noble gas chemistry [1–5]. The family includes HArF, the only known neutral argon compound [6], more than twenty HKrY and HXeY, and dinuclear species such as HXeCCXeH and HXeOXeH. The HNgY are prepared by photodissociation of HY in a cold Ng matrix, and are investigated by infrared spectroscopy and theoretical calculations. These molecules are in general best described by the resonance form (HNg+)Y, with a covalent Ng–H bond and a strong ionic interaction between NgH+ and Y [1–3]. Cationic noble-gas hydrides of general formula HNgY+ and HNgYNgH+ are still experimentally unknown, but species such as HNgCO+ [7], HNgN2+ [8], HNgFNgH+ [9], and HNgHNgH+ (Ng = He–Xe) [10–12] were investigated by theoretical calculations. Interestingly, the bonding situation of the dinuclear HNgFNgH+ and HNgHNgH+ closely resembles that of the neutral HNgY. These cations are in fact best described by the resonance form (HNg+)2Y (Y = H, F) [9–12], with large average interaction energies of ca. 90–100 kcal mol1 be⇑ Corresponding author. Tel.: +39 0761 357126; fax: +39 0761 357111. E-mail address: [email protected] (F. Grandinetti). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.05.015

tween NgH+ and Y (likewise the HNgY, the HNgYNgH+ possess however also exothermic dissociation channels, and only HArFArH+, HKrFKrH+, and HXeYXeH+ (Y = F, H) were predicted to be metastable [9,12]). The mononuclear HNgCO+ and HNgN2+ are also described by the resonance form (HNg+)Y (Y = CO, N2), but, at variance with the neutral (HNg+)Y and the cationic (HNg+)2Y (Y = H, F), the interactions between NgH+ and Y are as weak as nearly 4– 7 kcal mol1 [8,9]. This is in keeping with the neutral character, and the zero or very low polarity of CO or N2 (both HNgCO+ and HNgN2+ are in any case metastable with respect to dissociation into Ng and HCO+ or HN2+ [8,9]). The bonding situation of the (HNg+)CO and (HNg+)N2 suggests that the stability of any (HNg+)Y should in principle increase with Y groups of high polarity. As exemplary species in this regard, we explored the structure, stability, and bonding properties of the (HNg+)(OH2) (Ng = He–Xe). Further interest for these ions comes from the fact that they are isomeric with the Ng-H3O+. While the gaseous complexes between H+(H2O)n (n P 2) clusters and Ng atom(s) (especially argon) were already investigated by spectroscopic and computational methods [13], the simplest Ng-H3O+ are still experimentally unreported, and only Ar-H3O+ was so far theoretically investigated [14]. The results obtained in the present study allow a comparison between the (HNg+)(OH2) and the Ng-H3O+ (Ng = He–Xe).

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2. Computational details The geometries were first optimized at the ab initio and DFT levels of theory using the second-order Møller–Plesset (MP2) [15], the coupled cluster method [16], including the contribution from single and double substitutions and an estimate of connected triples, CCSD(T), and the hybrid exchange–correlation functional B3LYP, which combines the three-terms exchange functional by Becke (B3) [17] with the correlation functional by Lee, Yang and Parr (LYP) [18]. In these calculations, the Xe atom was treated by the small-core (28 electrons), scalar-relativistic effective core potential (ECP-28) developed by the Stuttgart/Cologne group [19]. The employed basis sets were the def2-TZVPP designed by Weigend and Ahlrichs [20], which are available for all the group 18 elements, and the aug-cc-pVTZ-PP, obtained combining the Dunning’s correlation consistent triple-zeta basis set for H, He, O, Ne, Ar, and Kr, augmented with diffuse functions (aug-cc-pVTZ) [21], with the (13s12p10d2f)/[6s5p4d2f] basis set designed for Xe in conjunction with the ECP-28 [19]. Both the MP2 and the CCSD(T) were employed within the frozen-core approximation (for the Xe atom, the frozen-core orbitals were 4s4p4d with the aug-cc-pVTZ-PP, and 4s4p with the def2-TZVPP [20]). The critical points located at the MP2, CCSD(T), and B3LYP levels of theory were characterized as energy minima or transition structures (TSs) by calculating their harmonic frequencies, used also to evaluate the zero-point vibrational energies (ZPE). Any TS was also unambiguously related to its interconnected energy minima by intrinsic reaction coordinate (IRC) calculations [22]. At any computational level, the dissociation energies were corrected for the basis set superposition error (BSSE) using the counterpoise method of Boys and Bernardi [23]. The atomic charges were computed by Natural Bond Orbital (NBO) analysis [24] of the MP2/def2-TZVPP and B3LYP/def2-TZVPP wave functions. The MP2, CCSD(T), and B3LYP calculations were performed with the Gaussian03 set of programs [25]. The Atoms-in-Molecules (AIM) [26] calculations were performed with the AIMAll program [27], using the MP2/def2-TZVPP electron density. We calculated in particular, at the MP2/def2TZVPP optimized geometries, the charge density q, the Laplacian of the charge density r2q, and the energy density H at the bond critical points (bcp), intended as the points on the attractor interaction lines where rq = 0. For the xenon-containing species, the missing core electron density on the Xe atom was modeled by a single s-type Gaussian function, with exponent a = 4p and coefficient c = 8  Nc (Nc = number of core electrons = 28). As recently discussed [28], for small-core pseudopotentials, the inclusion of a single function is in general sufficient to avoid the interference of the spurious electron density critical points which arise from the absence of the core electron density. The ETS-NOCV analysis [29], which is a merge of the extended transition state (ETS) decomposition scheme [30–32] with the theory of natural orbitals for chemical valence (NOCV) [33–37], was performed with the Amsterdam Density Functional (ADF) code [38–40]. The geometries were optimized by analytical-gradient techniques [41] at the BP86 level of the generalized gradient approximation (GGA): the exchange is described by the LDA function [42] with self-consistent addition of Becke non-local corrections [17a,43], and the correlation is treated by the Vosko–Wilk–Nusair (VWN) parametrization [44], with Perdew non-local corrections [45] added self-consistently. The MOs were expanded in a large uncontracted set of Slater-type orbitals (STOs) [46] containing diffuse functions. The employed basis set, denoted as TZ2P, is of triple-f quality for all atoms and is augmented with two sets of polarization functions, namely, 2p and 3d on H and He, 3d and 4f on O, Ne, Ar, 4d and 4f for Kr, and 5d and 4f for Xe. An auxiliary set of s, p, d, f, and g STOs, centered on all nuclei,

was used to fit the electron density and to obtain accurate Coulomb potentials in each SCF cycle [47,48]. For the xenon species, relativistic effects were included by the zero-order regular approximation (ZORA) [49]. Contours of deformation densities were plotted by the ADF–GUI interface [50].

3. Results and discussion 3.1. Structure of the (HNg+)(OH2) (Ng = He–Xe) The connectivities of the (HNg+)(OH2) cations (Ng = He–Xe) are shown in Fig. 1, and their geometric parameters are listed in Table 1. The theoretical and experimental [51,52] bond distances of the diatomic NgH+ are also included. At the MP2, CCSD(T), and B3LYP levels of theory, irrespective of the employed basis set (def2-TZVPP or aug-cc-pVTZ/aug-cc-pVTZPP), the (HNg+)(OH2) (Ng = He–Xe) resulted to be planar structures of C2v symmetry. The only exception is HHeOH2+, which resulted non planar at the B3LYP level of theory. At the CCSD level of theory, the T1 diagnostics [53] resulted well below the threshold of 0.02, thus suggesting the validity of a single-determinant description of the wave functions. In general, at the B3LYP level of theory, the experimental distances of the NgH+ are overestimated by 0.010–0.015 Å. The MP2 and the CCSD(T) estimates are much closer to the experimental values, even though the average accuracy decreases from ca. 0.001 Å to ca. 0.006 Å passing from HeH+ to XeH+. Passing from the diatomic NgH+ to the (HNg+)(OH2), the Ng–H distance (Ng– H1 in Fig. 1 and Table 1) tends to decrease for Ng = He, Ne, Ar, and tends to increase for Ng = Kr and Xe. The predicted differences amount however to only ca. 0.02 Å for HHeOH2+, and are even smaller for the other species. The O–H distance and the H–O–H angle of any (HNg+)(OH2) are also invariably strictly similar to those computed for the free H2O (e.g. 0.962 Å and 104.2° at the CCSD(T)/ aug-cc-pVTZ level of theory). In addition, for any (HNg+)(OH2) (Ng = He–Xe), the Ng–O distance results definitely longer than the sum of the single-bond covalent radium [54] of Ng (ranging from 0.46 Å for He to 1.31 Å for Xe) and O (0.63 Å). The MP2 and B3LYP NBO atomic charges, listed in Table 2, indicate that the (HNg) moiety of any (HNg+)(OH2) carries a net charge of nearly +1e (the predicted values of q(Ng) + q(H1) range from 0.925 to 0.999e), while the H2O moiety is essentially neutral. It is however possible to appreciate that the formation of the (HNg+)(OH2) reduces the degree of charge separation in the diatomic NgH+ (by a flux of charge from Ng to H), and enhances the polarity of the O– H bonds of H2O (by a flux of charge from H to O). Overall, the optimized geometries and NBO charges of the (HNg+)(OH2) point to non-covalent complexes between NgH+ and H2O. This is also supported by the AIM analysis, whose results are given in Table 3 and Fig. 2.

Fig. 1. Connectivities of the (HNg+)(OH2) energy minima and TS (Ng = He–Xe).

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Table 1 Optimized geometries (Å and °) of NgH+ and of the (HNg+)(H2O) minima and transition structures (TS) (Fig. 1) (B1 = def2-TZVPP, B2 = aug-cc-pVTZ or aug-cc-pVTZ-PP, B3 = TZ2P). NgH+

Ng = He MP2/B1 MP2/B2 CCSD(T)/B1 CCSD(T)/B2 B3LYP/B1 B3LYP/B2 BP86/B3 Ng = Ne MP2/B1 MP2/B2 CCSD(T)/B1 CCSD(T)/B2 B3LYP/B1 B3LYP/B2 BP86/B3 Ng = Ar MP2/B1 MP2/B2 CCSD(T)/B1 CCSD(T)/B2 B3LYP/B1 B3LYP/B2 BP86/B3 Ng = Kr MP2/B1 MP2/B2 CCSD(T)/B1 CCSD(T)/B2 B3LYP/B1 B3LYP/B2 BP86/B3 Ng = Xe MP2/B1 MP2/B2 CCSD(T)/B1 CCSD(T)/B2 B3LYP/B1 B3LYP/B2 BP86/B3 a b c

Minima (C2v or Cs)

TS (Cs) Ng–H1

Ng–O

O–H

H1–Ng–O

H–O–H

Ôa

360.0 360.0 360.0 360.0 356.4 356.2 343.5

0.752 0.761 0.755 0.755 0.776 0.775

1.925 1.953 1.922 1.923 1.902 1.908

0.962 0.969 0.962 0.965 0.966 0.967

129.4 124.7 129.0 127.8 118.1 117.9

104.2 104.1 104.3 104.5 105.1 105.1

358.2 357.8 358.1 358.0 356.7 356.0

103.7 103.8 103.9 104.0 105.1 105.1 104.4

360.0 360.0 360.0 360.0 360.0 360.0 347.9

0.983 0.985 0.980

2.373 2.366 2.376

0.961 0.964 0.961

170.3 162.5 160.8

103.6 103.8 103.7

359.9 359.8 359.2

0.998 0.999

2.355 2.360

0.963 0.964

151.1 152.1

104.9 105.0

359.3 359.6

180.0 180.0 180.0 180.0 180.0 180.0 176.3

104.2 104.3 104.4 104.5 105.9 105.8 105.4

360.0 360.0 360.0 360.0 360.0 360.0 350.6

1.270 1.275 1.271 1.276 1.284 1.288

2.763 2.755 2.772 2.760 2.763 2.779

0.961 0.964 0.961 0.964 0.963 0.964

107.7 107.9 107.9 108.1 105.7 106.6

103.3 103.5 103.4 103.4 104.4 104.4

359.7 359.6 359.6 359.6 359.6 359.8

0.962 0.965 0.962 0.964 0.964 0.965 0.974

180.0 180.0 180.0 180.0 180.0 180.0 177.2

104.4 104.5 104.8 104.8 106.1 105.9 105.7

360.0 360.0 360.0 360.0 360.0 360.0 353.5

1.411 1.407 1.414 1.411 1.428 1.428

2.909 2.886 2.923 2.893 2.923 2.935

0.961 0.964 0.961 0.964 0.963 0.964

102.0 101.9 102.1 102.1 100.0 100.5

103.3 103.4 103.4 103.6 104.4 104.4

359.8 359.8 359.9 359.7 359.7 359.9

0.962 0.965 0.962 0.964 0.964 0.965 0.975

180.0 180.0 180.0 180.0 180.0 180.0 177.8

104.6 104.8 104.7 105.0 106.2 106.2 105.7

360.0 360.0 360.0 360.0 360.0 360.0 353.7

1.581 1.596 1.590 1.603 1.607 1.610

3.077 3.082 3.099 3.090 3.109 3.122

0.962 0.964 0.961 0.964 0.963 0.964

97.1 97.8 97.5 97.9 96.3 96.7

103.3 103.4 103.4 103.6 104.4 104.4

359.9 359.9 359.9 359.9 359.9 359.9

Ng–H1

Ng–O

O–H

H1–Ng–O

H–O–H

Ô

0.774 0.774 0.776 0.776 0.789 0.789 0.791 0.7743b

0.751 0.751 0.754 0.754 0.778 0.776 0.803

1.845 1.845 1.842 1.842 1.782 1.786 1.775

0.963 0.965 0.962 0.965 0.965 0.967 0.977

180.0 180.0 180.0 180.0 172.5 172.6 170.0

104.9 105.1 105.1 105.0 106.8 106.8 105.9

0.993 0.995 0.990 0.992 1.006 1.007 1.021 0.9912b

0.983 0.985 0.980 0.983 0.999 1.000 1.051

2.372 2.361 2.371 2.356 2.337 2.343 2.345

0.961 0.963 0.961 0.963 0.963 0.964 0.975

180.0 180.0 180.0 180.0 180.0 180.0 167.8

1.276 1.281 1.277 1.282 1.291 1.295 1.303 1.2804b

1.270 1.276 1.272 1.277 1.290 1.293 1.311

2.512 2.515 2.523 2.524 2.478 2.500 2.436

0.962 0.964 0.961 0.964 0.964 0.965 0.974

1.416 1.413 1.420 1.416 1.433 1.434 1.447 1.4212b

1.414 1.411 1.417 1.415 1.436 1.436 1.457

2.585 2.564 2.597 2.576 2.562 2.569 2.524

1.586 1.600 1.593 1.607 1.611 1.614 1.623 1.6028c

1.589 1.602 1.596 1.609 1.617 1.619 1.637

2.691 2.679 2.701 2.688 2.670 2.670 2.637

a

Sum of the bond angles at the O atom. Gas-phase experimental value taken from Ref. [51]. Gas-phase experimental value taken from Ref. [52].

Thus, for any Ng, the values of q, r2q, and H computed at the bcp of the Ng–H1 and O–H bonds are strictly similar to those predicted for the free NgH+ and H2O and point to covalent bonds (high charge density, negative Laplacian, and negative energy density [26]). On the other hand, at the bcp of any Ng–O bond, the charge density is low, the Laplacian is positive, and the energy density is vanishingly small. These findings are typical of closed-shell interactions, such as ionic, hydrogen, and van der Waals bonds [26]. The non-covalent character of the bond between NgH+ and H2O is also graphically appreciated in Fig. 2, which shows the contour lines diagrams of the r2q(r) of the (HNg+)(OH2) (Ng = He–Xe). As typical for closed-shell interactions, the lines separating the Ng and O basins lie in regions of charge depletion, and one only notes at most the polarization of the density of Ng toward H2O. At the BP86/TZ2P level of theory, the (HNg+)(OH2) (Ng = He–Xe) were characterized as non-planar structures of Cs symmetry (Fig. 1). As shown in Table 1, the deviations from planarity are however only minor (the H1–Ng–O bond angles range between

170.0 and 177.8°, and the sum of the bond angles at the O atom range between 343.5 and 353.7°), and the bond distances are in general quite similar to those predicted in particular at the B3LYP level of theory. Consistently, single-point calculations performed at the BP86/def2-TZVPP level of theory furnished NBO atomic charges (see Table 2) and AIM properties (see Table 3) which are strictly similar to those predicted for the planar isomers. This suggests that the bonding situation of the planar and non-planar structures is strictly similar, and that the ETS-NOCV analysis performed at the BP86/TZ2P level of theory for the non-planar isomers (vide infra) is also informative on the corresponding planar structures. 3.2. Harmonic vibrational frequencies The structural description of the (HNg+)(H2O) complexes is also consistent with their vibrational pattern, which includes four motions associated with the NgH+ and H2O moieties (using the

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Table 2 MP2, B3LYP, and BP86 NBO atomic charges (e) of NgH+, H2O, and of the (HNg+)(OH2) minima and transition structures (TS) (Fig. 1) calculated with the def2-TZVPP basis set (the PB86 values are computed at the BP86/TZ2P optimized geometries). NgH+

H2O

Minima (C2v or Cs)

TS (Cs)

q(Ng)

q(H)

q(O)

q(H)

q(Ng)

q(H1)

q(O)

q(H)

q(Ng)

q(H1)

q(O)

q(H)

Ng = He MP2 B3LYP BP86

0.260 0.260 0.268

0.740 0.740 0.732

0.914 0.910 0.907

0.457 0.455 0.453

0.296 0.292 0.288

0.674 0.633 0.589

0.986 0.951 0.897

0.508 0.513 0.589

0.287 0.278

0.696 0.679

0.995 0.975

0.506 0.509

Ng = Ne MP2 B3LYP BP86

0.226 0.217 0.223

0.774 0.783 0.777

0.241 0.231 0.221

0.758 0.758 0.698

0.979 0.971 0.879

0.490 0.491 0.480

0.241 0.230

0.758 0.761

0.979 0.973

0.490 0.491

Ng = Ar MP2 B3LYP BP86

0.507 0.505 0.504

0.493 0.495 0.496

0.531 0.526 0.510

0.454 0.443 0.427

0.979 0.969 0.938

0.497 0.500 0.501

0.519 0.518

0.481 0.481

0.976 0.975

0.488 0.488

Ng = Kr MP2 B3LYP BP86

0.603 0.596 0.590

0.397 0.404 0.410

0.632 0.621 0.601

0.348 0.344 0.336

0.980 0.969 0.944

0.500 0.502 0.503

0.614 0.605

0.386 0.394

0.972 0.973

0.486 0.487

Ng = Xe MP2 B3LYP BP86

0.724 0.716 0.707

0.276 0.284 0.293

0.755 0.745 0.721

0.220 0.216 0.216

0.979 0.969 0.949

0.502 0.504 0.506

0.735 0.726

0.266 0.272

0.971 0.968

0.485 0.485

Table 3 MP2/def2-TZVPP AIM analysisa of NgH+, H2O, and of the (HNg+)(OH2) minima and transition structures (TS) (Fig. 1). The values in parenthese are the BP86/def2-TZVPP//BP86/ TZ2P data of the Cs minima (Fig. 1). NgH+

H2O

Minima (C2v or Cs)

Ng–H

O–H

Ng–H1

Ng–O

O–H

Ng–H1

Ng–O

O–H

0.206 3.351 0.840

0.370 2.761 0.775

0.244 (0.232) 3.293 (1.897) 0.831 (0.494)

0.041 (0.056) 0.210 (0.213) 0.003 (0.001)

0.360 (0.352) 2.756 (2.613) 0.765 (0.718)

0.237 3.445 0.867

0.034 0.182 0.004

0.361 2.758 0.766

0.212 2.755 0.727

0.226 (0.200) 2.821 (1.513) 0.748 (0.427)

0.019 (0.022) 0.126 (0.125) 0.006 (0.005)

0.365 (0.358) 2.762 (2.573) 0.770 (0.718)

0.226 2.282 0.748

0.019 0.126 0.006

0.365 2.760 0.769

0.235 1.279 0.360

0.244 (0.224) 1.228 (0.823) 0.352 (0.248)

0.026 (0.035) 0.125 (0.134) 0.003 (0.002)

0.363 (0.356) 2.754 (2.618) 0.766 (0.722)

0.240 1.283 0.363

0.016 0.080 0.003

0.364 2.752 0.768

0.208 0.698 0.215

0.212 (0.193) 0.675 (0.506) 0.214 (0.166)

0.028 (0.034) 0.115 (0.118) 0.002 (0.001)

0.362 (0.356) 2.754 (2.623) 0.766 (0.723)

0.211 0.700 0.217

0.015 0.066 0.002

0.364 2.752 0.768

0.174 0.397 0.151

0.174 (0.158) 0.365 (0.288) 0.149 (0.118)

0.028 (0.033) 0.105 (0.105) 0.001 (0.001)

0.361 (0.355) 2.750 (2.621) 0.765 (0.723)

0.175 0.392 0.152

0.014 0.055 0.002

0.364 2.749 0.768

TS (Cs)

Ng = He

q r2q H Ng = Ne

q r2q H Ng = Ar

q r2q H Ng = Kr

q r2q H Ng = Xe

q r2q H a

The charge density q (e a0-3), the Laplacian of the charge density r2q (e a0-5), and the energy density H (hartree a0-3) are calculated at the bond critical point on the specified bond.

labeling of Fig. 1, the Ng–H1 stretch, two O–H stretchs, and the H– O–H bend), and five motions arising from their interaction (the Ng–O stretch, two H1–Ng–O bends, and the H–O–H wagging and rocking). We discuss here in particular the MP2/def2-TZVPP wave numbers (m) and IR intensities of the planar isomers listed in Table 4. The theoretical and experimental [51,52,55] values of the gaseous NgH+ and H2O are also shown for comparison. The experimental vibrations of the diatomic NgH+ and H2O are in general overestimated, with largest differences of nearly 200– 250 cm1 for HeH+ and the O–H stretchs of H2O. However, the calculations correctly reproduce both the periodic decrease of the wave number of the strecth of the diatomic NgH+ passing from

HeH+ to XeH+, and the difference of nearly 100 cm1 between the symmetric and antisymmetric stretch of H2O. Compared with the diatomic NgH+, the Ng–H1 stretch of any (HNg+)(H2O) is blue-shifted, with Dm ranging between + 346 cm1 for Ng = He–+8 cm1 for Ng = Xe. This absorption is predicted to be relatively intense (up to 824 km mol1 for (NeH+)(H2O)), but in general less intense than in the diatomic NgH+. On the other hand, compared with the free H2O, the O–H stretchs are slightly red-shifted (Dm = 20/50 cm1) and comparatively more intense, with wave numbers falling between 3811 and 3836 cm1 (a1 component) and between 3912 and 3936 cm1 (b2 component). The H– O–H bend is instead slightly blue-shifted (Dm = +20/+30 cm1), and

P. Antoniotti et al. / Computational and Theoretical Chemistry 1017 (2013) 117–125

Fig. 2. Left: contour line diagrams of the Laplacian of the electronic charge density r2q(r) of the (HNg+)(OH2) (MP2/def2-TZVPP, C2v). Full and dashed lines are in regions of charge depletion (r2q(r) < 0) and charge concentration (r2q(r) > 0), respectively. Solid lines which connect the atomic nuclei are the bond paths, and solid lines which cross the bond paths indicate the zero-flux surfaces in the molecular plane. Right: contours of the contributions to the deformation densities of the (HNg+)(OH2) (BP86/TZ2P, Cs) arising from the r interaction between NgH+ and H2O (DE is in kcal mol1). The quoted Dq (a.u.) are the numerically smallest contour values (blue is positive and red is negative). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

comparatively more intense. The wave number of the Ng–O stretch strongly decreases from (HHe+)(H2O) (482 cm1) to (HNe+)(H2O) (231 cm1), and further slightly decreases up to 198 cm1 for (HXe+)(H2O). The corresponding IR intensity is also relatively high for (HHe+)(H2O) (267 km mol1), but remarkably weaker for the other congeners (16–29 km mol1). The H1–Ng–O bends (b1 and b2) are predicted to fall between 300 and 400 cm1 for Ng = He, Ar, Kr, Xe, and at significantly lower values of 28 and 137 cm1 for (NeH+)(H2O). The H–O–H wagging (b1) and rocking (b2) are instead less dependent on Ng and fall around 300 and 400 cm1, respectively. 3.3. Dissociation energies and stabilities The stability of the (HNg+)(H2O) depends on the energetics and the activation barriers of their dissociation channels. The conceivable reactions of lowest energy are listed below:

ðHNgþ ÞðH2 OÞ ! NgHþ þ H2 O

ð1Þ

121

ðHNgþ ÞðH2 OÞ ! Hþ þ Ng þ H2 O

ð2Þ

ðHNgþ ÞðH2 OÞ ! H þ Ngþ þ H2 O

ð3Þ

ðHNgþ ÞðH2 OÞ ! H3 Oþ þ Ng

ð4Þ

The energy changes at 0 K (DE) calculated for the planar structures at the MP2, CCSD(T), and B3LYP levels of theory with the def2-TZVPP basis set are listed in Table 5. The values quoted for reactions (1)–(3) are all corrected for the BSSE. As shown in Table 5, at the B3LYP level of theory, these corrections are invariably less than 1 kcal mol1, and range from less than 1 (Ng = He) to less than 4 kcal mol1 (Ng = Xe) at the MP2 and CCSD(T) levels of theory. We computed also the activation barriers E– of reaction (4). In general, the values of DE and E– predicted by B3LYP are slightly more positive than those obtained by the two ab initio methods, which furnish in turn comparable estimates. Unless stated otherwise, the forthcoming discussion is based on the in principle most accurate CCSD(T) values. The dissociation of (HNg+)(H2O) into NgH+ and H2O results endothermic for any Ng. Interestingly, the highest DE predicted for Ng = He (20.4 kcal mol1) appreciably decreases passing to Ng = Ne (13.2 kcal mol1), and slightly increases up to 15.7 kcal mol1 for Ng = Xe. To investigate this irregular periodic trend we performed the ETS-NOCV analysis of the interaction between NgH+ and H2O in the non-planar structures. The obtained results are listed in Table 6 and shown in Fig. 2. While the BP86/TZ2P level of theory tends to overestimate the absolute DEs of reaction (1), it correctly reproduces the trend predicted by all the other theoretical methods. More interestingly, it is now possible to appreciate that the largest stability of (HHe+)(H2O) arises from a largest contribution to DEint of the orbital term DEorb. The predicted value of 23.5 kcal mol1 is significantly larger than that of the other congeners, which range from 6.5 kcal mol1 for (HNe+)(H2O) to 14.4 kcal mol1 for (HXe+)(H2O). The term DEelstat is instead comparable for Ng = He, Ar, Kr, and Xe (between ca. 22 and 25 kcal mol1), and only slightly lower for Ng = Ne (16.2 kcal mol1). Thus, the contributions of the electrostatic and orbital terms to the attractive part of the interaction between NgH+ and H2O are comparable for (HHe+)(H2O), but prevailing (63– 70%) for the other congeners. The DEorb terms were further analyzed by the NOCV decomposition scheme. It was thus possible to unravel that, for any Ng, the orbital term is by far dominated by the donor–acceptor interaction between the r(O–H) bonding orbital of H2O (3 A1), and the empty r orbital of NgH+. The latter arises from s-type atomic orbitals for HeH+, but includes contributions from p and d orbitals on Ng for the other NgH+. This reasonably explains the weaker character of the NgH+/H2O interaction passing from HeH+ to the heaviest congeners. As expected, this interaction is accompanied by a flow of charge from H2O to NgH+, which is clearly appreciated by inspecting the corresponding contribution to the total deformation densities (see Fig. 2). We also note from Table 6 that DEorb includes minor contributions from the interaction between the r(O–H) bonding (1B2) and the non-bonding orbital (1B1) of H2O, and the empty p orbitals of NgH+. Interestingly, these contributions are absent for (HNe+)(H2O), which shows also the smallest values for the various terms which contribute to DEint. Overall, as already noted for other groups of noble-gas neutrals and ions [56–61], the neon-congener is the less stable among the various (HNg+)(H2O). As shown in Table 5, reactions (2) and (3) are definitely endothermic for any Ng, with predicted DEs which range between 63 and 134 kcal mol1, and 103 and 314 kcal mol1, respectively. On the other hand, any (HNg+)(H2O) is unstable with respect to the decomposition into H3O+ + Ng. Therefore, the overall metastability of the (HNg+)(H2O) depends on the activation barrier of reaction

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P. Antoniotti et al. / Computational and Theoretical Chemistry 1017 (2013) 117–125

Table 4 MP2/def2-TZVPP harmonic vibrational frequencies (cm1) and IR intensities (km mol1, in parentheses) of the (HNg+)(OH2) minima (C2v, Fig. 1). The experimental and theoretical values of NgH+ and H2O are also included. Ng–H1 stretch

Ng–O stretch

H1–Ng–O bend

O–H stretch

H–O–H bend

H–O–H wagg

H–O–H rock

HeH+

Ng–H stretch 3228 (811) 2973a

HHeOH2+

3574 (469) (a1)

483 (267) (a1)

376 (503) (b1) 414 (285) (b2)

3813 (100) (a1) 3912 (180) (b2)

1674 (75) (a1)

239 (52) (b1)

475 (55) (b2)

NeH+

2941 (875) 2904b

HNeOH2+

3071 (824) (a1)

231 (29) (a1)

28 (250) (b1) 137 (303) (b2)

3836 (45) (a1) 3936 (130) (b2)

1677 (78) (a1)

323 (382) (b1)

358 (133) (b2)

ArH+

2764 (590) 2711b

HArOH2+

2820 (398) (a1)

219 (24) (a1)

349 (270) (b1) 336 (194) (b2)

3821 (71) (a1) 3923 (146) (b2)

1672 (65) (a1)

290 (131) (b1)

412 (1) (b2)

KrH+

2570 (421) 2495b

HKrOH2+

2601 (230) (a1)

206 (16) (a1)

354 (162) (b1) 331 (144) (b2)

3817 (85) (a1) 3920 (151) (b2)

1667 (58) (a1)

275 (190) (b1)

424 (2) (b2)

XeH+

2375 (249) 2270b

HXeOH2+

2383 (97) (a1)

198 (16) (a1)

339 (90) (b1) 318 (82) (b2)

3811 (96) (a1) 3915 (154) (b2)

1666 (55) (a1)

270 (213) (b1)

429 (15) (b2)

3854 (7) (a1) 3657c 3976 (63) (b2) 3756c

1647 (64) (a1) 1595c

H2O

a b c

Gas-phase experimental value taken from Ref. [51]. Gas-phase experimental value taken from Ref. [52]. Gas-phase experimental value taken from Ref. [55].

Table 5 Dissociation energies at 0 K (kcal mol1) of the (HNg+)(OH2) minima (C2v, Fig. 1) calculated with the def2-TZVPP basis set (the values in parenthesis are the BSSE corrections).

a

NgH+ + H2O

H+ + Ng + H2O

H + Ng+ + H2O

H3O+ + Ng

E–a

Ng = He MP2 CCSD(T) B3LYP

20.4 (0.3) 20.4 (0.3) 23.9 (0.2)

61.9 (0.6) 62.6 (0.6) 65.6 (0.5)

310.1 (0.4) 314.4 (0.4) 325.5 (0.3)

102.3 102.9 98.4

0.1 0.1 1.0

Ng = Ne MP2 CCSD(T) B3LYP

13.4 (0.3) 13.2 (0.3) 14.3 (0.1)

61.7 (1.8) 62.2 (2.0) 63.1 (0.4)

245.3 (1.2) 241.0 (1.2) 248.2 (0.2)

102.5 103.2 101.1

0.1 0.1 0.1

Ng = Ar MP2 CCSD(T) B3LYP

13.0 (0.4) 14.7 (0.4) 16.2 (0.2)

103.8 (2.1) 105.3 (2.3) 106.5 (0.4)

152.3 (1.7) 150.6 (1.8) 155.4 (0.3)

60.5 60.2 57.8

2.9 2.8 4.1

Ng = Kr MP2 CCSD(T) B3LYP

15.7 (0.7) 14.3 (0.7) 16.7 (0.3)

113.8 (3.1) 117.2 (3.2) 119.0 (0.5)

126.9 (2.8) 126.2 (2.8) 130.5 (0.5)

48.9 48.3 45.4

4.6 4.5 5.7

Ng = Xe MP2 CCSD(T) B3LYP

16.2 (0.9) 15.7 (0.9) 17.0 (0.4)

130.9 (3.5) 133.6 (3.6) 135.6 (0.4)

103.5 (3.1) 103.2 (3.2) 107.1 (0.4)

33.3 31.8 28.9

6.1 6.1 7.2

Energy barrier of the reaction (HNg+)(OH2) ? H3O+ + Ng.

(4). We ascertained in particular that this process passes through the transition structures TSs shown in Fig. 1. These TSs were located at the MP2, CCSD(T), and B3LYP level of theory with both the def2-TZVPP and aug-cc-pVTZ or aug-cc-pVTZ-PP basis set, and their geometric parameters, NBO charges, and AIM data are reported in Tables 1–3, respectively. In general, the obtained data revealed only a minor influence of the theoretical level. In addition, likewise the (HNg+)(H2O) energy minima, the CCSD T1 diagnostic resulted below the recommended threshold of 0.02 [53]. As shown in Fig. 1 and detailed in Table 1, the most important structural difference between any (HNg+)(H2O) energy minimum and the corresponding TS is the value of the H1–Ng–O bond angle, which reduces to ca. 120–130° for Ng = He, to ca. 160–170° for Ng = Ne, and to ca. 100–110° for Ng = Ar, Kr, and Xe. Consistently, the eigenvector corresponding to the single negative eigenvalue of the Hessian matrix is invariably dominated by this geometric parameter. For any (HNg+)(H2O) the closing of the H1–Ng–O angle is accompa-

nied by an elongation of the Ng–O bond, which is significant for Ng = He, Ar, Kr, Xe (between ca. 0.1 and 0.3–0.4 Å), but less pronounced for HNeOH2+. In any case, the NBO charges (Table 2) and the AIM data (Table 3) still describe any TS as a ‘‘complex’’ between the NgH+ and H2O. Therefore, reaction (4) occurs by a rotation of the NgH+ group of (HNg+)(H2O) around the H1–Ng–O angle, and by a concomitant elongation of the Ng–O bond. As shown in Table 5, the value of E– depends on Ng and results in particular negligibly small for both (HHe+)(H2O) and (HNe+)(H2O), which are therefore predicted to be overall unstable. On the other hand, for (HAr+)(H2O), and especially (HKr+)(H2O) and (HXe+)(H2O), the value of E– (2.8, 4.5, and 6.1 kcal mol1, respectively) is large enough to suggest their conceivable existence as metastable species, especially at low temperatures. 3.4. Structure, stability, and harmonic frequencies of the Ng-H3O+ (Ng = He–Xe) The IRC calculations revealed that the TSs shown in Fig. 1 do not connect directly the (HNg+)(H2O) with H3O+ and Ng. Rather, as shown in Fig. 3, reaction (4) passes through the Ng-H3O+ complexes shown in Fig. 4 (we searched also for conceivable (NgH+)OH2 complexes, but these structures invariably collapsed into the Ng-H3O+). As mentioned in the Introduction, while the gaseous complexes between H+(H2O)n (n P 2) clusters and Ng atom(s) (especially argon) were already investigated by spectroscopic and computational methods [13], the simplest Ng-H3O+ are still experimentally unreported, and only Ar-H3O+ was so far theoretically investigated [14]. We therefore decided to examine the Ng-H3O+ in further detail. The geometric parameters and NBO atomic charges computed at the MP2/def2-TZVPP level of theory are shown in Fig. 4, and the harmonic vibrational frequencies are listed in Table 7. Any Ng-H3O+ is characterized as co-linear H-bound complex between Ng and H3O+. The O–H1 distance ranges from 0.979 (Ng = He) to 1.007 Å (Ng = Xe), and is only slightly longer than the O–H distance of the free H3O+, 0.977 Å. The two equivalent O–H distances are also comparably short and range around 0.975 Å. The Ng–H1 distance is instead quite long and progressively increases from Ng = He (1.814 Å) to Ng = Xe (2.290 Å) (for Ar-H3O+, the value of 2.028 Å is nearly coincident with a previous estimate at the MP2/aug-cc-pVTZ# level of theory [14]). In addition, for any Ng-H3O+, the cationic moiety carries a charge of nearly

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P. Antoniotti et al. / Computational and Theoretical Chemistry 1017 (2013) 117–125 Table 6 Energy decomposition analysis of the interaction between NgH+ and H2O in the (HNg+)(OH2) complexes (Cs, Fig. 1) performed at the BP86/TZ2P level of theory.

a b

Ng

DEprep

DEelstata

DEPauli

DEorba

Contributions to DEorbb

DEint

DE

He

0.1

25.5 (52.0%)

21.8

23.5 (48.0%)

27.2

27.1

Ne

0.3

16.2 (71.4%)

7.5

6.5 (28.6%)

15.2

14.9

Ar

0.1

21.8 (64.1%)

17.0

12.2 (35.9%)

17.0

16.9

Kr

0.1

23.1 (62.9%)

18.7

13.6 (37.1%)

18.0

17.9

Xe

0.1

24.6 (63.1%)

20.6

14.4 (36.9%)

19.5 (r) 1.9 (p) 1.4 (p) 0.7 (rest) 4.7 (r) 1.8 (rest) 9.7 (r) 1.2 (p) 0.8 (p) 0.5 (rest) 10.4 (r) 1.4 (p) 0.9 (p) 0.9 (rest) 11.2 (r) 1.5 (p) 1.0 (p) 0.7 (rest)

18.4

18.3

The value in parenthesis is the percentage contribution to the attractive part of DEint (DEelstat + DEorb). The label r or p refers to the character of the empty orbital of NgH+ involved in the interaction.

+1e, with a minor degree of charge transfer from Ng, which progressively increases from He to Xe (this trend reflects the periodic increase of the polarizability of the Ng atoms). The structural description of the Ng-H3O+ essentially reflects the large difference between the proton affinities of the Ng atoms (ranging between 42.5 kcal mol1 for He to 119.4 kcal mol1 for Xe), and the proton affinity of H2O, 165.0 kcal mol1 [55]. At the CCSD(T)/aug-cc-pVTZ level of theory and 0 K, the DE of the reaction:

Ng-H3 Oþ ! H3 Oþ þ Ng

Fig. 3. Decomposition paths of the (HNg+)(OH2) (C2v, Ng = He–Xe) calculated at the CCSD(T)/def2-TZVPP level of theory and 0 K.

Fig. 4. MP2/def2-TZVPP optimized geometries (Å and °) and atomic charges (e, bold) of the Ng-H3O+ (Ng = He–Xe).

is computed (see Fig. 3) as 0.1 kcal mol1 for Ng = He (BSSE = 0.7 kcal mol1), 0.6 kcal mol1 for Ng = Ne (BSSE = 2.1 kcal mol1), 3.7 kcal mol1 for Ng = Ar (BSSE = 2.4 kcal mol1), 5.2 kcal mol1 for Ng = Kr (BSSE = 3.3 kcal mol1), and 7.1 kcal mol1 for Ng = Xe (BSSE = 3.8 kcal mol1). This suggests that, while He and Ne should leave H3O+ essentially unperturbed, the heaviest noble gases could appreciably affect its intrinsic properties. In particular, taking into account the current interest for the ‘‘Ng-messenger’’ technique as a tool for investigating the infrared spectra of gaseous cations [62], it is of interest to compare the harmonic frequencies of H3O+ with those of the Ng-H3O+. The obtained data (Table 7) suggest an indeed non-negligible influence of Ar, Kr and Xe on the intrinsic absorptions of H3O+. With respect to the free H3O+ (C3v), the complexation with Ng removes the degeneracy of the two O–H stretches and H–O–H bends of e symmetry, and produces three intermolecular modes, namely the Ng–H1 stretch (a0 ), and two H3O+ bends (a0 and a00 ) (for the labeling of the atoms, see Fig. 4). The Ng–H1 stretch is relatively weak and predicted at 144 cm1 for Ng = He, at 123 cm1 for Ng = Ne, and at around 170–180 cm1 for Ng = Ar, Kr, Xe. The two H3O+ bends are also predicted at quite similar wave numbers for Ng = Ar (266 and 360 cm1), Kr (281 and 375 cm1), and Xe (295 and 389 cm1), but at lower wave numbers for Ng = He and Ne (only the absorption of higher frequency is in any case predicted to have a non-negligible intensity). The H–O–H bends of H3O+ remain nearly degenerate in the Ng-H3O+, with largest red shifts of only 10–20 cm1 for Xe-H3O+. On the other hand, the complexation with the heaviest noble gases has a major effect on the O–H stretchs, especially the a1 component, which results redshifted by 280 (Ng = Ar), 386 (Ng = Kr), and 541 cm1 (Ng = Xe). This absorption is also predicted to be the by far most intense. The effect of Ng on the e component is instead significantly less

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P. Antoniotti et al. / Computational and Theoretical Chemistry 1017 (2013) 117–125

Table 7 MP2/def2-TZVPP harmonic vibrational frequencies (cm1) and IR intensities (km mol1, in parentheses) of Ng-H3O+ (Fig. 4) and H3O+. Ng–H1 stretch

O–H1 stretch

O–H stretch

H–O–H bend

H1–O–H bend

H3O+ bend

H3O+ umbrella

+

144 (10) (a )

3591 (75) (a )

3687 (580) (a )

1692 (94) (a )

1696 (92) (a )

176 (85) (a ) 127 (7) (a00 )

884 (430) (a0 )

Ne-H3O+

123 (34) (a0 )

3570 (227) (a0 )

3712 (481) (a00 ) 3671 (557) (a0 )

1691 (90) (a0 )

1696 (87) (a00 )

217 (87) (a0 ) 154 (8) (a00 )

883 (422) (a0 )

Ar-H3O+

179 (66) (a0 )

3317 (1255) (a0 )

1687 (69) (a0 )

1692 (57) (a00 )

Kr-H3O+

173 (78) (a0 )

3211 (1650) (a0 )

1683 (63) (a0 )

1685 (42) (a00 )

Xe-H3O+

175 (86) (a0 )

3056 (2291) (a0 )

1678 (55) (a0 )

1670 (28) (a00 )

360 266 375 281 389 295

He-H3O

0

H3O+

0

0

3716 3659 3733 3660 3737 3660

(475) (315) (438) (302) (420) (295)

(a00 ) (a0 ) (a00 ) (a0 ) (a00 ) (a0 )

3741 (397) (a00 ) 3597 (38) (a1) 3705 (488) (e)

pronounced. The ‘‘umbrella’’ motion of H3O+ is also essentially unaffected by He and Ne, and only slightly red-shifted by Ar, Kr, and Xe (Dm = 35, 43, and 58 cm1, respectively). 4. Concluding remarks The present study confirms that ionic species formally arising from the insertion of Ng atoms into protonated molecules MH+ must be actually viewed as (HNg+)M ion-neutral complexes. This description resembles that of the neutral (HNg+)Y; however, the anionic versus neutral character of the partner determines major differences between the neutrals and the cations. In the former species, the electrostatic interaction between NgH+ and Y is in general very high, and results in relatively compact structures. Since the recombination energy of any NgH+ is in general much higher than the electron affinity of Y, any (HNg+)Y is prone to dissociate into H + Ng + Y. All the (HNg+)Y observed to date are in fact stable with respect to this three-bodies (3B) channel. They are however unstable with respect to the two-bodies (2B) dissociation into Ng + HY, but the involved barriers are in general relatively high. Typical neutral molecules M have instead relatively high ionization potentials, and this prevents the 3B dissociation of the (HNg+)M into H + Ng + M+. Any (HNg+)M is also expected to be stable with respect to dissociation into NgH+ + M, especially for neutral molecules of high polarity and nucleophilicity. The kinetic stability of the (HNg+)M is instead determined by the 2B dissociation into Ng + MH+. For the poor Brønsted bases He and Ne, this process is fast. However, for Ar, and especially Kr and Xe, this process could be prevented by barriers high enough to allow the trapping of the (HNg+)M, especially at low temperatures. This could stimulate the experimental search of these hitherto unknown ionic species. Acknowledgements The authors thank the Università della Tuscia, the Università di Torino, and the Italian Ministero dell’Università e della Ricerca (MiUR) for financial support through the ‘‘Cofinanziamento di Programmi di Ricerca di Rilevante Interesse Nazionale’’. References [1] J. Lundell, L. Khriachtchev, M. Pettersson, M. Räsänen, Formation and characterization of neutral krypton and xenon hydrides in low-temperature matrices, Low Temp. Phys. 26 (2000) 680–690. [2] R.B. Gerber, Formation of novel rare-gas molecules in low-temperature matrices, Annu. Rev. Phys. Chem. 55 (2004) 55–78. [3] L. Khriachtchev, M. Räsänen, R.B. Gerber, Noble-gas hydrides: new chemistry at low temperatures, Acc. Chem. Res. 42 (2009) 183–191.

0

1691 (99) (e)

00

0

(102) (a0 ) (3) (a00 ) (110) (a0 ) (2) (a00 ) (119) (a0 ) (1) (a00 )

915 (343) (a0 ) 923 (305) (a0 ) 938 (262) (a0 )

880 (445) (a0 )

[4] W. Grochala, L. Khriachtchev, M. Räsänen, Noble-gas chemistry, in: L. Khriachtchev (Ed.), Physics and Chemistry at Low Temperatures, CRC Press, 2011, pp. 419–446. [5] R.B. Gerber, E. Tsivion, L. Khriachtchev, M. Räsänen, Intrinsic lifetimes and kinetic stability in media of noble-gas hydrides, Chem. Phys. Lett. 545 (2012) 1–8. [6] L. Khriachtchev, M. Pettersson, N. Runeberg, J. Lundell, M. Räsänen, A stable argon compound, Nature 406 (2000) 874–876. [7] T. Jayasekharan, T.K. Ghanty, Theoretical prediction of HRgCO+ ion (Rg = He, Ne, Ar, Kr, and Xe), J. Chem. Phys. 129 (2008) 184302. [8] T. Jayasekharan, T.K. Ghanty, Theoretical investigation of rare gas hydride cations: HRgN2+ (Rg = He, Ar, Kr, and Xe), J. Chem. Phys. 136 (2012) 164312. [9] S. Borocci, N. Bronzolino, M. Giordani, F. Grandinetti, Cationic noble gas hydrides: a theoretical investigation on the dinuclear HNgFNgH+ (Ng = He–Xe), J. Phys. Chem. A 114 (2010) 7382–7390. [10] J. Lundell, M. Pettersson, Molecular properties of Xe2H3+, J. Mol. Struct. 509 (1999) 49–54. [11] J. Lundell, S. Berski, Z. Latajka, Density functional study of the Xe2H3+ cation, Chem. Phys. 247 (1999) 215–224. [12] S. Borocci, N. Bronzolino, M. Giordani, F. Grandinetti, Cationic noble gas hydrides-2: a theoretical investigation on HNgHNgH+ (Ng = Ar, Kr, Xe), Comput. Theor. Chem. 964 (2011) 318–323. [13] F. Grandinetti, Gas-phase ion chemistry of the noble gases: recent advances and future perspectives, Eur. J. Mass Spectrom. 17 (2011) 423–463. and references therein. [14] O. Dopfer, Spectroscopic and theoretical studies of CH3+-Rg clusters (Rg = He, Ne, Ar): from weak intermolecular forces to chemical reaction mechanisms, Int. Rev. Phys. Chem. 22 (2003) 437–495. [15] C. Møller, M.S. Plesset, Note on the approximation treatment for manyelectrons systems, Phys. Rev. 46 (1934) 618–622. [16] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, A fifth-order perturbation comparison of electron correlation theories, Chem. Phys. Lett. 157 (1989) 479–483. [17] A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behaviour, Phys. Rev. A 38 (1988) 3098–3100; A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648. [18] C. Lee, W. Yang, R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785– 789. [19] K.A. Peterson, D. Figgen, E. Goll, H. Stoll, M. Dolg, Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements, J. Chem. Phys. 119 (2003) 11113–11123. [20] F. Weigend, R. Ahlrichs, Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy, Phys. Chem. Chem. Phys. 7 (2005) 3297–3305. [21] T.H. Dunning Jr., Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen, J. Chem. Phys. 90 (1989) 1007; D.E. Woon, T.H. Dunning Jr., Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties, J. Chem. Phys. 100 (1994) 2975; R.A. Kendall, T.H. Dunning Jr., R.J. Harrison, Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions, J. Chem. Phys. 96 (1992) 6796; D.E. Woon, T.H. Dunning Jr., Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon, J. Chem. Phys. 98 (1993) 1358. [22] C. Gonzalez, H.B. Schlegel, Reaction path following in mass-weighted internal coordinates, J. Phys. Chem. 94 (1990) 5523–5527. [23] S. Boys, F. Bernardi, The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors, Mol. Phys. 19 (1970) 553–566.

P. Antoniotti et al. / Computational and Theoretical Chemistry 1017 (2013) 117–125 [24] E.D. Glendening, A.E. Reed, J.E. Carpenter, F. Weinhold, NBO version 3.1, Theoretical Chemistry Institute, University of Wisconsin, Madison. [25] M.J. Frish, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzevski, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Hishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratman, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004. [26] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, 1990. [27] AIMAll (version 12.11.09), T.A. Keith, TK Gristmill Software, Overland Park KS, USA, 2012 (aim.tkgristmill.com). [28] T.A. Keith, M.J. Frisch, Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions, J. Phys. Chem. A 115 (2011) 12879–12894. [29] M. Mitoraj, A. Michalak, T. Ziegler, A combined charge and energy decomposition scheme for bond analysis, J. Chem. Theory Comput. 5 (2009) 962–975. [30] T. Ziegler, A. Rauk, On the calculation of bonding energies by the Hartree Fock Slater method. I. The transition state method, Theor. Chim. Acta 46 (1977) 1– 10. [31] T. Ziegler, A. Rauk, A theoretical study of the ethylene-metal bond in complexes between Cu+, Ag+, Au+, Pt0 or Pt2+ and ethylene, based on the Hartree–Fock–Slater transition-state method, Inorg. Chem. 18 (1979) 1558– 1565. [32] T. Ziegler, A. Rauk, CO, CS, N2, PF3, and CNCH3 as r donors and p acceptors. A theoretical study by the Hartree–Fock–Slater transition-state method, Inorg. Chem. 18 (1979) 1755–1758. [33] M. Mitoraj, A. Michalak, Natural orbitals for chemical valence as descriptors of chemical bonding in transition metal complexes, J. Mol. Model. 13 (2007) 347– 355. [34] M. Mitoraj, A. Michalak, Donor–acceptor properties of ligands from the natural orbitals for chemical valence, Organometallics 26 (2007) 6576–6580. [35] M. Mitoraj, A. Michalak, Applications of natural orbitals for chemical valence in a description of bonding in conjugated molecules, J. Mol. Model. 14 (2008) 681–687. [36] A. Michalak, M. Mitoraj, T. Ziegler, Bond orbitals from chemical valence theory, J. Phys. Chem. A 112 (2008) 1933–1939. [37] M.P. Mitoraj, H. Zhu, A. Michalak, T. Ziegler, On the origin of the transinfluence in square planar d8-complexes: a theoretical study, Int. J. Quantum Chem. 109 (2009) 3379–3386. [38] ADF2012, SCM, Theoretical chemistry, Vrije Universiteit, Amsterdam, The Netherlands, . [39] G. te Velde, F.M. Bickelhaupt, S.J.A. van Gisbergen, C. Fonseca Guerra, E.J. Baerends, J.G. Snijders, T. Ziegler, Chemistry with ADF, J. Comput. Chem. 22 (2001) 931–967. [40] C. Fonseca Guerra, J.G. Snijders, G. te Velde, E.J. Baerends, Towards an order-N DFT method, Theor. Chem. Acc. 99 (1998) 391–403.

125

[41] L. Versluis, T. Ziegler, The determination of molecular structure by density functional theory. The evaluation of analytical energy gradients by numerical integration, J. Chem. Phys. 88 (1988) 322–328. [42] J.C. Slater, Quantum Theory of Molecules and Solids, vol. 4, McGraw-Hill, New York, 1974. [43] A.D. Becke, Density functional calculations of molecular bond energies, J. Chem. Phys. 84 (1986) 4524–4529. [44] S.H. Vosko, L. Wilk, M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Can. J. Phys. 58 (1980) 1200–1211. [45] J.P. Perdew, Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B 33 (1986) 8822–8824 (Erratum: J.P. Perdew, Phys. Rev. B 34 (1986) 7406)). [46] E. van Lenthe, E.J. Baerends, Optimized Slater-type basis sets for the elements 1–118, J. Comput. Chem. 24 (2003) 1142–1156. [47] E.J. Baerends, D.E. Ellis, P. Ros, Self-consistent molecular Hartree–Fock–Slater calculations. I. The computational procedure, Chem. Phys. 2 (1973) 41–51. [48] J. Krijn, E.J. Baerends, Fit-functions in the HFS method; internal report, Vrije Universiteit, Amsterdam, 1984. [49] E. van Lenthe, A.E. Ehlers, E.J. Baerends, Geometry optimization in the Zero Order Regular Approximation for relativistic effects, J. Chem. Phys. 110 (1999) 8943–8954. [50] O. Visser, P. Leyronnas, W.-J. van Zeist, M. Luppi, GUI 2012, SCM, Amsterdam, The Netherlands, . [51] J.A. Coxon, P.G. Hajigeorgiou, Experimental Born-Hoppenheimer potential for the X1R+ ground state of HeH+: comparison with the ab initio potential, J. Mol. Spectrosc. 193 (1999) 306–318. [52] S.A. Rogers, C.R. Brazier, P.F. Bernath, The infrared spectrum of XeH+, J. Chem. Phys. 87 (1987) 159. [53] T.J. Lee, P.R. Taylor, A diagnostic for determining the quality of single-reference electron correlation methods, Int. J. Quantum Chem. 36 (Suppl. S23) (1989) 199–207. [54] P. Pyykkö, M. Atsumi, Molecular single-bond covalent radii for elements 1– 118, Chem.-Eur. J. 15 (2009) 186–197. [55] NIST Chemistry WebBook, NIST Standard Reference Database Number 69 . [56] M.H. Wong, Prediction of a metastable helium compound: HHeF, J. Am. Chem. Soc. 122 (2000) 6289–6290. [57] T.-H. Li, C.-H. Mou, H.-R. Chen, W.-P. Hu, Theoretical prediction of noble gas containing anions FNgO (Ng = He, Ar, and Kr), J. Am. Chem. Soc. 127 (2005) 9241–9245. [58] P. Antoniotti, N. Bronzolino, F. Grandinetti, Stable compounds of the lightest noble gases: a computational investigation on RNBeNg (Ng = He, Ne, Ar), J. Phys. Chem. A 107 (2003) 2974–2980. [59] P. Antoniotti, N. Bronzolino, S. Borocci, P. Cecchi, F. Grandinetti, Noble gas anions: theoretical investigation of FNgBN (Ng = He–Xe), J. Phys. Chem. A 111 (2007) 10144–10151. [60] W. Zou, Y. Liu, J.E. Boggs, Theoretical study of RgMF (Rg = He, Ne; M = Cu, Ag, Au): bonded structures of helium, Chem. Phys. Lett. 482 (2009) 207–210. [61] W. Grochala, Metastable He–O bond inside ferroelectric molecular cavity: (HeO)(LiF)2, Phys. Chem. Chem. Phys. 14 (2012) 14860–14868. [62] M. Savoca, J. Langer, D.J. Harding, O. Dopfer, A. Fielicke, Incipient chemical bond formation of Xe to a cationic silicon cluster: vibrational spectroscopy and structure of the Si4Xe+ complex, Chem. Phys. Lett. 557 (2013) 49–52, and references therein.