NgMCp+: Noble Gas Bound Half-Sandwich Complexes (Ng = HeâRn

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NgMCp+: Noble Gas Bound Half-Sandwich Complexes (Ng = He-Rn, M = Be-Ba, Cp = #5-C5H5) Ranajit Saha, Sudip Pan, and Pratim Kumar Chattaraj J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 19 Apr 2017 Downloaded from http://pubs.acs.org on April 19, 2017

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The Journal of Physical Chemistry

NgMCp+: Noble Gas Bound Half-Sandwich Complexes (Ng = He-Rn, M = Be-Ba, Cp = η5-C5H5) Ranajit Saha,1 Sudip Pan,*,2 and Pratim K. Chattaraj*,1 1

Department of Chemistry and Centre for Theoretical Studies Indian Institute of Technology Kharagpur, 721302, India

2

Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados

Unidad Mérida. km 6 Antigua carretera a Progreso. Apdo. Postal 73, Cordemex, 97310, Mérida, Yuc., México

*Authors to whom correspondence should be addressed; E-Mails: [email protected]; [email protected]

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Abstract Structures, bonding and stability half-sandwich complexes with general formula, NgMCp+ (Ng = He-Rn, M = Be-Ba, Cp = η5-C5H5) are analyzed through ab initio computation. MCp+ complexes possess remarkable Ng binding ability, particularly for M = Be and Mg. While for Ar-Rn bound analogues the bond dissociation energy in the former complex ranges within 17.5-28.0 kcal mol-1, it becomes 10.4-18.7 kcal mol-1 in the latter complex. In fact, BeCp+ is able to form strong bond with the two most inert elements, He and Ne. Although, the Ng binding ability of MCp+ gradually diminishes in moving from Be to Ba, the corresponding free energy change values show that Kr-Rn bound complexes involving the heavier congeners of Mg would remain in bound state avoiding dissociation into Ng and MCp+. The nature of the Ng-M bond is characterized by natural bond orbital, electron density and energy decomposition analyses in conjunction with the natural orbital for chemical valence (EDA-NOCV) analysis. While the electron density analysis reveals that Ng-Be (Ng = Kr, Xe, Rn) and Ng-Mg (Ng = Xe, Rn) bonds are partly covalent in nature, the orbital interaction (∆Eorb) is found to be the most important term in Ng-M attractive energy as revealed by the EDA-NOCV. For all Ngs, the major contribution towards the ∆Eorb energy term originates from Ng→MCp+ σ-donation. Additionally, CpBeNgF (Ng = Xe, Rn) and CpNgF (Ng = Kr-Rn) are found to be viable systems with kinetic protection for the exergonic dissociation channels, CpBeNgF → Ng + CpBeF and CpNgF → Ng + CpF, respectively, where the activation free energy barrier in the latter systems (24.1-34.7 kcal mol-1) is significantly larger than that in the former ones (6.6-8.9 kcal mol-1). CpNgF (Ng = Kr-Rn) complexes are predicted to be stable even above 300 K, whereas CpBeNgF (Ng = Xe, Rn) would be viable up to ~100 K. While the F-Ng bonds are ionic in nature, the Ng-Be and Ng-C bonds in these complexes have significant covalent character. `


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Introduction Different in silico studies showed that metal centers with high positive charge can effectively polarize the electron density of noble gas (Ng) atoms to form a chemical bond predominantly through a donor-acceptor interaction.1 -3 Be atom attached to electronegative 2

atoms or groups in neutral cases and/or be a part of an overall positively charged system could serve as an excellent Ng binding center as it would have high polarizing power because of its small radius to deform the valence electron cloud of Ng facilitating a bond formation. However, when the size of the metal (M) center becomes larger as found in heavier members of group 2, the polarizing ability diminishes thereby lowering their Ng binding ability. It might be noted that with an increase in the size of M, it would become more polarizable, improving a dipole-induced dipole or ion-induced dipole interaction, but at the same time it prevents Ng to come closer, and hence reduces other attractive terms. In general, the combined effect of these factors reduces the Ng binding ability with an increase in the size of M, which is also valid for group 2 elements. The first molecule with Ng-Be bond was reported by Frenking and co-workers with the theoretical prediction of stable NgBeO (Ng = He-Xe) complexes.1,4 - 7 Fascinatingly, the 5

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interaction in heavier Ng cases turns out to be strong enough as detected by Andrews et al. through matrix infrared spectroscopy.8 Later on, Pyykkö suggested by ab initio computation that Lewis acid of the type, SX (X = Be, B+, C2+, N3+, O4+) can form strong bond with Ne.9 Particularly, he noted a short Ne-Be bond distance in NeBeS which was recently characterized spectroscopically.10 Then, different groups reported a series of NgBeY (Y = S, Se, Te, NH and its different derivatives, NCN, NBO, CO3, SO4, SO2, CrO4, HPO4) complexes.11 - 18 Remarkably, 121314

151617

BeNCN and BeNBO were shown to bind Ng atoms more efficiently than that of BeNH and BeO. Grandinetti et al.19 tried to verify the enhancement of the Ng binding ability of BeO through the attachment of a Lewis acid, BH3, at the O-end of BeO. The energy required to detach He from HeBeO-BH3 was double than that required for HeBeO. However, BeO-BH3 does not correspond to the global minimum rather the global minimum is HBeO-BH2. Nevertheless, for the conversion of HBeO-BH2 to BeO-BH3, an activation energy barrier of around 3 kcal mol-1 has to be overcome. The stability of multiple Ng bound mono- and dicationic BeO and CN3Be3+ clusters was explored recently.20 Furthermore, Ng bound various beryllium nitrides, viz., Be2N2, Be3N2 and BeSiN2 were also reported as viable candidates.21 3 ACS Paragon Plus Environment


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There are another XNgY (X and Y = H, F, Cl, Br, CN, BN-, BO, BS, CCH, CO+, CS+, OSi+ etc.)22 - 26 type of Ng compounds in which the Ng atom is inserted in the X-Y bond, known 2324

25

as insertion Ng-compounds. Long back in 1979, first experimentally Xe was inserted in B-F bond in FXeBF2 compound by Goetschel and Loos.27 In recent days, many theoretical and experimental studies are performed to enrich this type of compounds. Few developments in this area are HArF,28 HKrF,29 HXeF,30 HXeCCH,31 HXeNC, HKrCN,32 HNgC2Cl (Ng = Kr, Xe),33 HNgC3N (Ng = Kr, Xe),34 FNgBNR (Ng = Ar, Kr, Xe; R = H, CH3, CCH, CHCH2, F, OH)35, H3SiNgNSi (Ng = Xe, Rn)36 etc. Although a good number of donor-acceptor Ng-complexes having Ng-Be bonds were reported in the literature, there are only a few systems known to have Ng-Mg bonds. In 1973, Hayes et al.37 first reported a strong interaction between Ng and MgF2 which in fact distorts the structure of MgF2 from its linear arrangement. In a couple of studies, Ghanty and co-workers explored the possibility of viable Ng-insertion compounds with Ng-M (M = Be, Mg) bonds.38,39 The possible bonding of M+ and M2+ (M = Be, Mg) with Ng atoms was also studied theoretically by Breckenridge and co-workers.40,41 Recently, Ng binding ability of TpM+ (M = Be, Mg; Tp = 1-tris(pyrazolyl)borate)complexes and the bonding therein were analyzed.42 The species with bonds involving Ng and the heavier congeners of Mg are very rare in literature. While in 1996, Pullins et al. detected weakly bound complexes of Ca+-Ng (Ng = Ar, Kr, Xe) by means of laser spectroscopic technique,43 in 2001, Massaouti et al. reported Sr+-Xe using photofragmentation spectroscopy.44 Further, in a couple of theoretical studies, Wright and co-workers predicted the stability of HM+-Ng species (M = Be-Ra).45,46 Wright group has also predicted several other Ng compounds where the group 2 metals have a significant role in the stabilization of these compounds.47 - 50 Therefore, all these studies are limited to transient simple cations. More realistic 48

49

prediction of the complexes with Ng-M bonds (M = Ca-Ba) is still missing. Metallocenes and various half sandwich complexes of group 2 metals are well known in literature for a long time.51 - 55 Be shows a huge range of sandwich complexes having Cp (Cp = 52

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η5-C5H5) and substituted Cp as its slice of bread.56 - 58 Be also has a variety of half sandwich 57

complexes of type CpBeX (X = H, Cl, Br, BH4, C≡CH, SiMe3)59 - 63 and type Cp*BeX (Cp* = 6061

62

C5Me5; X = P(t-Bu)2, As(t-Bu)2).64,65 Quite recently, Cp*BeX (X = Cl, Br, I) (Cp* = C5Me5) complexes were synthesized and theoretical calculations were carried out to reveal their bonding 4 ACS Paragon Plus Environment

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nature.66 BeCp+ can be generated by the dissociation of the Be-X bond in CpBeX (X = H, Cl, Br, BH4, C≡CH, SiMe3). On a similar note, experimentally available homoleptic Mg(Cp)2 or heteroleptic CpMgX (X = Cl, Br)67,68 complexes can also be used for the formation of MgCp+. Similar types of complexes of Ca, Sr and Ba are also available in literature with slight modification in the crystal structure. For example, two tetrahydrofuran (THF) molecules are needed to stabilize the sandwich complex of Cp2Ca.69 In the present work, we have studied the Ng binding ability of MCp+ (M = Be-Ba) complexes by evaluating the dissociation energy and the thermochemical parameters like change in enthalpy (∆H) and free energy (∆G) via ab initio computations. Further, the possibility of Nginsertion within Be-F and C-F bonds of CpBeF and CpF70 (5-fluorocyclopentadiene) complexes, respectively, are also evaluated. The nature of the Ng-M bond is characterized by natural bond orbital (NBO), electron density, and energy decomposition in conjunction with the natural orbital for chemical valence (EDA-NOCV) analyses. MCp+ complexes are found to have quite high Ng binding ability with the bond dissociation energy mainly originating from a donor-acceptor type of interaction. The Ng→MCp+ σ-donation of electron density is a key factor for the stability of these complexes. On the other hand, CpBeNgF and CpNgF are metastable systems with kinetic protection along a spontaneous dissociation channel.

Computational details Geometries of all the studied NgMCp+ complexes are optimized at the MP2 level71,72 of theory in conjunction with correlation consistent triple zeta quality basis sets. For He-Ar, and Be and Mg, aug-cc-pVTZ73 - 76 basis set is used. For Kr-Rn and Ca-Ba aug-cc-pVTZ-PP basis set is 74

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used along with relativistic effective core potentials (RECPs), and ECP10MDF for Kr and Ca, ECP28MDF for Xe and Sr, ECP60MDF for Rn, and ECP46MDF for Ba are used .77 For brevity, the aug-cc-pVTZ/aug-cc-pVTZ-PP basis set is only mentioned as aug-cc-pVTZ. We believe that the basis set is adequate enough for the present systems to provide reliable results. Nevertheless, in order to compare the results obtained with the aug-cc-pVTZ basis set with another basis set, we have computed the dissociation energy and thermochemical parameters for NgBeCp+ at the MP2/def2-TZVPD level also (see Table S1 in supporting information). In general, MP2/def25 ACS Paragon Plus Environment


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TZVPD level yields slightly smaller dissociation energies, ∆H and ∆G values along with longer Ng-Be bonds than those obtained at the MP2/aug-cc-pVTZ level. Harmonic frequency calculations are also performed at the same level to find out whether the stationary point is a minimum or a saddle point on the potential energy surface (PES). As all the frequencies are real it ensures that the present complexes exhibit minimum energy structures. The zero point energy (ZPE) and the thermochemical parameters are also evaluated from the frequency calculations. The basis set superposition error (BSSE) corrected dissociation energy is also computed by the counterpoise method proposed by Boys and Bernardi.78 In these calculations, we have considered the Ng as one fragment and MCp+ as another in their optimized geometries. Dissociation energy (De) is also calculated at the CCSD(T)79 - 81/aug-cc-pVTZ level by single point energy calculation 80

using the optimized geometries taken from the MP2 calculation. Natural population analysis (NPA)82 and Wiberg bond index (WBI)83 calculations are performed at the MP2/aug-cc-pVTZ level to compute the charge (q) at each atomic center and to compute the bond order, respectively, using the NBO84 scheme. On the other hand, the analysis of the Ng-insertion complexes, CpBeNgF and CpNgF are studied at the MP2/def2-TZVPD level. All of these above calculations are carried out using Gaussian 09 program package.85 The topological analysis of the electron density86 is carried out at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVTZ/WTBS level by using Multiwfn software.87 For Kr-Rn and Ca-Ba all electron WBTS basis set has been used. The

EDA88

is

carried

out

in

conjunction

with

NOCV89,90

at

the

PBE-

D3(BJ)91/TZ2P//MP2/aug-cc-pVTZ or PBE-D3(BJ)92/TZ2P//MP2/def2-TZVPD level using the ADF(2013.01) program package.93,94 Zeroth order regular approximation (ZORA)95 is adopted to implement scalar relativistic effects for the heavier atoms. The EDA scheme decomposes the interaction energy (∆Eint) between the fragments into four contributing energy terms as, ∆Eint = ∆EPauli + ∆Eelstat + ∆Eorb + ∆Edisp

(1)

The repulsion between the electrons in the occupied orbitals at the interacting fragments generates the repulsive Pauli interaction energy (∆EPauli). The ∆Eelstat term stands for the quasiclassical electrostatic interaction energy between those fragments which is found to be attractive in most cases. The next attractive contribution in energy comes from the orbital interaction energy, ∆Eorb, which arises due to the charge transfer and mixing of the occupied and unoccupied orbitals between the fragments and polarization effect. The ∆Edisp represents the dispersion 6 ACS Paragon Plus Environment

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energy correction towards the total attraction energy. The sum of the three attractive energy factors predominates over the ∆EPauli and stabilizes the overall system. Further, EDA-NOCV calculations provide the information about the direction of the charge flow in between those fragments. In EDA-NOCV, the differential density (∆ρ(r)) is decomposed into deformation densities (∆ρi(r)), which can be expressed over the pairs of NOCV. Thus, ∆ρ(r) = ∑ ∆ρi(r)

(2)

On a similar ground, the total ∆Eorb is also decomposed into ∆Eiorb corresponding to each charge transfer channel as ∆Eorb = ∑ ∆Eiorb

(3)

Results and Discussions Structures and dissociation energies The optimized geometries of NgMCp+ (M = group 2 elements) complexes are displayed in Figure 1. The bare MCp+ complexes correspond to the C5v point group with 1A1 electronic state. The M center possesses a large positive charge ranging from 1.13-1.77 |e| which gradually increases in moving down the group (except for the case of Ba) due to the increasing metallic character. A slight decrease in positive charge on Ba center compared to Sr is noted presumably due to the inert pair effect. The dissociation energy, corrected from both the BSSE and ZPE (D0BSSE) for the process, MCp+ → M2+ + Cp− is found to be within the range of 243.2-506.8 kcal mol-1 and the corresponding D0BSSE values gradually decrease on going from Be to Ba (see Table 1). We have also characterized the nature of interaction between M2+ and Cp− and the factors responsible for the decreased stability along Be to Ba. The complexes are mainly stabilized by the electrostatic interaction where the contribution from ∆Eelstat term (ca. 52-73% of the total attraction). ∆Eorb term contributes around 27-48% of the total attraction. On the other hand, the dispersion contribution is not at all significant. The interaction between M2+ and Cp− gradually becomes even more ionic in nature along Be to Ba. The increase in size of M along Be to Ba



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hinders Cp and M to be closer distance, and consequently both the electrostatic and orbital interactions between M2+ and Cp− diminish, making the total interaction gradually decreased along the down the group. Most importantly, in these MCp+ complexes one side of M center is open to bind with another ligand. The large positive charge on M could behave like an efficient electrophilic center facilitating the polarization of electron cloud of the incoming ligands towards itself making it possible to form a chemical bond. In fact, the polarizing power of M is found to be so high that it could even deform the electron density of Ng atoms. All MCp+ complexes are found to bind ArRn atoms quite effectively. The Ng bound complexes preserve the point group and electronic state of their mother moieties. For a given Ng, the BeCp+ forms the strongest bond with Ng which gradually weakens in going towards its heavier homologues. In cases of Ar-Rn bound analogues, the D0BSSE values are within the range of 17.5-28.0 kcal mol-1 for Be, 10.4-18.7 kcal mol-1 for Mg, 3.8-9.0 kcal mol-1 for Ca, 3.9-7.1 kcal mol-1 for Sr, and 2.7-6.2 kcal mol-1 for Ba at the MP2 level with gradual increase along He to Rn (see Table 2). Particularly, BeCp+ shows so much efficiency to bind Ng atoms that it even forms reasonably strong bond with He and Ne atoms, two most inert elements in this series. The dissociation energy values (DeC) at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level are also very close to those (De) obtained at the MP2/aug-cc-pVTZ level. For a given Ng, DeC follows the same trend as the De values with the variation of M. DeC values are found to be slightly smaller than those of De values for NgMCp+ complexes (Ng = Ar-Rn; M= Be–Ca), whereas slightly larger or equal value is noted in other complexes. We have compared the Ng-M bond strength and stability in NgMCp+ with different systems like NgMX+ (M=Be-Ba; X = F, Cl, Br, OH), NgMY (M=Be-Ba; Y = O, S) (see Table S2) and NgM+ (M=H, Be-Ba) (see Table S3). The result shows that the Ng-M bond in NgMCp+ is significantly stronger when it is compared with the NgMY (M=Be-Ba; Y = O, S) and NgM+ (M= Be-Ba). But the Ng-H bonding is much stronger in NgH+ than the Ng-M bond in all of the cases. The Ng-M bond strength NgMX+ is not straight-forward as the former discussed systems. The Ng-M bond in these complexes are found to be stronger than that in NgMCp+ for the Be and Mg analouges. But for the heavier metal analogues (Ca-Ba), the D0 values become more or less comparable. The thermochemical parameters show that for all Ng atoms the formation of 8 ACS Paragon Plus Environment

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NgBeX+ is a favorable process as the ∆G298K are exergonic at 298K. Here it can be noted that the formation of HeBeCp+ complex is non spontaneous at this temperature. But, for the heavier M atoms the formation of He and Ne analogues of NgMX+ are endergonic and thus nonspontaneous at this temperature. Therefore, the present results regarding NgMX+ (X = F, Cl, Br, OH) indicate that they are also excellent systems for experimental realization, which were not considered before. The enthalpy change (∆H298K) and the free energy change (∆G298K) for the NgMCp+ complex formation process from Ng and MCp+ are calculated at 298 K (see Table 2). All the complex formation processes are exothermic in nature. On the other hand, in cases of NgBeCp+, the association processes are also exergonic in nature at room temperature, except for HeBeCp+. The formation of the Ar-Rn bound Mg and Ca complexes, and Kr-Rn bound Sr and Ba complexes are found to be spontaneous at room temperature, the rest of the complexes are not stable at room temperature with respect to the dissociation. However, they would be stable at a lower temperature. We have calculated the corresponding ∆G values at lower temperatures (200, 100 and 4 K) to check the viability of these complexes (see Table S4 in supporting information). For the Be and Mg analogues, 100 K is enough to make the complex formation spontaneous, whereas much lower temperature (4 K) is needed for the Ca-Ba complexes to be stable. Thus, they might be detected at low temperature matrix-isolation experiments. Note that despite larger positive charge, the Ng binding ability gradually diminishes along Be to Ba. This can be explained by the fact that the ionic potential of M center decreases along the same due to their larger radii. All the dissociation processes are endothermic in nature and the endothermicity gradually increases along He to Rn. Despite favorable entropy term the dissociations of NgMCp+ into Ng and MCp+ become endergonic except for He bound Be complex, He and Ne bound Mg and Ca complexes, and He-Ar bound Sr and Ba complexes. The Ng-M stretching frequencies are also provided in Table 2 (lying within the range of 50-479 cm-1) which would help experimentalists to detect the experimental signatures of these Ng bound complexes. Natural bond orbital analysis Positive NPA charges on Ng centers of NgMCp+ imply that the electron transfer is taking place from Ng to M center. The charge transfer is small for He and Ne, and the least for Nebound complex. For Ar-Rn analogues, charge transfer is of considerable magnitude and it 9 ACS Paragon Plus Environment


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increases as we move from Ar to Rn. Similar to D0BSSE values the degree of electron transfer from Ng to M gradually diminishes along Be to Ba. We have further computed the valence orbital populations of M center as well as Ng center in NgMCp+ complexes to understand that which of the orbitals are responsible for the electron transfer (see Tables 3 and S5). A comparison between the valence orbital populations of M and Ng centers in MCp+ and its Ng bound analogues shows that the Ng→M electron transfer mostly happens from the filled valence orbitals of Ng atoms to the empty valence orbitals of M. For Be and Mg analogues, the population in s and p orbitals of Ng (only s orbital for He) gets decreased, and the same in the valence s and p orbitals of M increases. The pz orbital is affected the most among all the valence orbitals at both Ng and M centers. The symmetry of the complex is responsible for this. The NgM bonds in NgMCp+ complexes lie in the z direction making the interaction between filled pz orbital of Ng atom and the co-aligned vacant pz orbitals of M center effective. It may be noted that not only the symmetry but also the energetic proximity of the relevant orbitals are important for the effective interaction. For the Ca-Ba complexes also, the above discussion is valid, except for the fact that the d orbitals (mainly d z2 orbital) of M are also involved in the bonding to a little extent. Obviously, the increase in the population in pz orbitals of M centers is much higher than those in s and d z2 orbitals. Low WBI values of Ng-M bond for He and Ne indicate the noncovalent character of the bond. However, the WBI values are quite significant for Ar-Rn cases indicating significant covalent character of the bond. For a given Ng, WBI value gradually diminishes in moving from Be to Ba which implies that the degree of covalent character also decreases along the same. For the Ng-Be bonds, more than half a bond order is noted for Ar-Rn bound analogues. However, the WBI values are quite low in Ca, Sr and Ba complexes even for the bonds involving heavier Ng atoms like Xe and Rn.

Electron density analysis Further, several electron density based descriptors are calculated at the bond critical points (BCP) of Ng-M bonds to characterize the nature of bonding (see Tables 4 and S6). Negative and positive values of Laplacian of the electron density (∇2ρ(rc)) at the BCP imply accumulation and depletion of electron density, respectively. Therefore, ∇2ρ(rc) < 0 represents a covalent or shared bond by the two atoms, whereas ∇2ρ(rc) > 0 implies non-covalent interaction.


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This criterion is adequate to describe bonding in many instances but it particularly fails for the bonds involving heavier atoms.96 - 100 Even it fails to describe the bonds in simple molecules like 97

9899

CO and F2.86; (pp. 312-314) Then, Cremer et al.101 put forward the criterion that despite ∇2ρ(rc) > 0 if the local total energy density (H(rc)) is less than zero then the bond may be considered to be partly covalent in nature. This argument is particularly valid when ρ(rc) is quite low. H(rc) is the sum of local kinetic energy density (G(rc)) and local potential energy density (V(rc)). Here,

∇2ρ(rc) is larger than zero for all cases but H(rc) values are negative for Ng-Be (Ng = Kr, Xe, Rn) and Ng-Mg (Ng = Xe, Rn) bonds. Therefore, based on the electron density criteria these bonds are of covalent type, whereas the rest of the bonds are of non-covalent type. Figures 2 and S1 display the contour plots of ρ(r) and ∇2ρ(r) for these NgMCp+ complexes where the black solid lines represents the ρ(r); the solid blue lines show the region having ∇2ρ(r) > 0 and the pink dotted lines represent the region with ∇2ρ(r) < 0. These plots of ρ(r) clearly show that for a particular M atom the electron densities of Ng atoms get polarized towards the metal centers and in moving towards the heavier Ng atoms the degree of deformation in electron density gradually increases. The plots ∇2ρ(r) also support the above statement and in cases of the Kr, Xe and Rn bound BeCp+ and Xe and Rn bound MgCp+ complexes, the electron density gets accumulated in between Ng and M centers, similar to a covalent bond formation.

Energy decomposition analysis Additional insights into the nature of bonding can be perceived from the results of EDA, performed taking Ng as one fragment and MCp+ as another. The associated results are provided in Tables 5 and S6. It is noted that irrespective of M and Ng in all the complexes, the Ng-M bonds are exclusively supported by the orbital interaction where the contribution from ∆Eorb term ranges within 71-93% of the total attraction. For a given Ng, both the magnitude and percentage contribution of ∆Eorb term reduce along Be to Ba, indicating diminished covalent character in Ng-M bond along the same. Further, for a given M the associated orbital interaction gradually increases in moving from He to Rn. The ∆Eelstat and ∆Edisp terms account for only 3-17% and 322% of the total attraction respectively. By changing either Ng or M, the obtained variation in

∆∆Eint can be explained solely in terms of the corresponding ∆∆Eorb values.



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Now, the decomposition of ∆Eorb term into its σ- and π-components and the plots of deformation density associated with those orbital terms provide important information regarding the origin of the orbital interaction. The plots of deformation density taking NgBeCp+ as an example are given in Figure 3. Similar plots for the other systems are necessarily same and only associated ∆Eorb values change (see Figure S2). In these plots, the red color implies the region with ∆ρ(r) < 0 and blue one is for ∆ρ(r) > 0 which means that the electron density gets shifted from red to blue region. For all Ngs, the major contribution towards the ∆Eorb energy term comes from Ng→BeCp+ σ-donation (∆ρσ(r)). Apart from this σ-donation, two equal π-donations (∆ρπ(r)) of electron density from Ng→BeCp+ are also noticed. The energy corresponding to this Ng→BeCp+ σ-donation is abbreviated as ∆Eσ, which ranges from 54-94% (for all NgMCp+) of

∆Eorb and the energy corresponding to the two Ng→BeCp+ π-donation is denoted as ∆E π 1 and

∆E π 2 . Further, a comparison of the deformation density plots and the related MOs of each fragment and overall complex taking XeMCp+ (M = Be, Ba) complexes as examples clearly shows the orbitals which are participating in the interaction (see Figure 4 for XeBeCp+ and Figure S3 for XeBaCp+). In Xe, there are three filled 5p-orbitals acting as HOMO and 5s orbital as HOMO-1, which mainly contribute in the M-Ng bonding by donating their electron density to the vacant orbitals on MCp+. The σ-donation is the strongest in Xe→BeCp+, where the electron density gets shifted from 5pz and 5s -orbital of Ng to the vacant LUMO and LUMO+1 of BeCp+. The next electron density contribution comes from the electron density transfer from other two porbitals (5px and 5py) of Xe to the vacant degenerate LUMO+2 of BeCp+, representing Xe→BeCp+ π-donation. In case of XeBaCp+ complex (see Figure S3), the Xe→BaCp+ σdonation comprises electron transfer from the 5pz and 5s-orbitals on Xe to the LUMO and LUMO+2 on BaCp+. Particularly, LUMO+2 possesses some d orbital coefficient from Ba center. The Xe→BaCp+ π-donation follows the same fashion as in XeBeCp+.

Ng insertion complexes The Ng inserted analogues of CpBeF and CpF (in the latter case Cp means only C5H5) along with the key geometrical parameters are depicted in Figure 5, where Ng is inserted into the Be-F bond of former and into the C-F bond of the latter system. While CpBeNgF corresponds to


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C5v point group, CpNgF possesses a Cs symmetry. We have computed the stability of these complexes with respect to the possible dissociation channels as provided in Tables 6 and 7. In cases of CpBeNgF, there are ten various dissociation channels among which five are two body (2-B) dissociation channels, three are 3-B dissociation channels, and two are 4-B dissociation channels. However, except one 2-B channel, CpBeNgF → CpBeF + Ng, other channels are thermochemically endergonic in nature. The process, CpBeNgF → CpBeF + Ng, is found to be exergonic at 298 K by -97.1 to -127.5 kcal mol-1 with gradual increase in moving from Rn to Ar (see Table 6). We have computed the associated TS for such dissociation. The corresponding free energy barrier (∆G‡) is negative for Ar, whereas it is only 2.2 for Kr, 6.6 for Xe, and 8.9 kcal mol-1 for Rn. Hu and coworkers argued that for the 2-B dissociation channel like XNgY → XY + Ng (X, Y are not hydrogen), XNgY would have ~102 second half-life in gas phase at 100, 200 and 300 K if they possess a barrier height of 6, 13 and 21 kcal mol-1, respectively.102 Therefore, Xe and Rn analogues might be stable in the gas phase up to ~ 100 K. On the other hand, in cases of CpNgF there are six possible dissociation processes, two of which are 3-B dissociation channels and the rest are 2-B dissociation channels. While CpNgF → CpF + Ng process is highly exergonic in nature at room temperature for Ar-Rn (-58.5 for Rn to 117.2 kcal mol-1 for Ar), CpArF also tends to dissociate spontaneously as CpArF → Cp + ArF and CpArF → Cp + Ar + F with a ∆G298K value of -15.1 and -17.9 kcal mol-1, respectively. The corresponding TS computation reveals that the dissociation, CpNgF → CpF + Ng is kinetically protected by 15.2 (Ar), 24.1 (Kr), 32.3 (Xe), and 34.7 (Rn) kcal mol-1, implying the viability of CpNgF (Ng = Kr-Rn) complexes even at ambient temperature. In fact, following the arguments of Hu and coworkers, Kr-Rn analogues would be stable even above 300 K. In both cases, the mode of the imaginary frequency in TS involves either the bending mode of Be-Ng-F (for CpBeNgF) or C-Ng-F (for CpNgF). While the Be-Ng bond is slightly larger than the typical Be-Ng covalent bond103 for Ar (by 0.250 Å) and Kr (0.176 Å), in cases of Be-Xe and Be-Rn bonds, the corresponding distances become slightly shorter than those of ideal covalent distances (2.36 Å for Be-Xe and 2.46 Å for Be-Rn). It indicates that significant covalent character exists in Be-Ng bond of these complexes. In cases of CpNgF, similar situation as that in CpBeNgF is noted, i.e., C-Xe and C-Rn bonds in the complexes are slightly shorter than the corresponding covalent bond distances, whereas C-Ar 13 ACS Paragon Plus Environment


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and C-Kr bonds are somewhat longer than then a typical covalent bond. Since the Ar analogues in both cases are not stable, we have only discussed the bonding discussion for Kr-Rn cases. The computed WBI values range from 0.75-0.91 in Be-Ng and C-Ng bonds, implying a single covalent bond formation therein (see Table 8). On the other hand, the corresponding WBI values for Ng-F bonds are very small, presumably due to the ionic nature of the bond. Note that the WBI values (0.17-0.21) in Ng-F bonds of CpNgF is somewhat larger than those in CpBeNgF (0.05-0.08), which implies the presence of a small degree of covalent character in former bonds. A negative charge of -0.82 to -0.96 |e| on F supports the ionic interaction between Ng and F . The electron density analysis further corroborates with the covalent interaction in Be-Ng and C-Ng bonds. While in Be-Xe and Be-Rn bonds ∇2ρ(rc) becomes negative, for Be-Ng and CNg (Ng = Kr-Rn) bonds the corresponding H(rc) values are highly negative, reflecting their covalent nature (see Table 9). Note that despite negative H(rc) values, the Ng-F should be categorized as an ionic bond, rather than a covalent one. The contour plots of ρ(r) and ∇2ρ(r) are provided in Figure 6. While the contour plots of ρ(r) reveals that the electron density of Ng gets polarized towards Be and C centers and the degree of deformation is larger in moving towards the heavier Ng, the plots of ∇2ρ(r) show the electron accumulation in between Be and Ng = Xe, Rn. Further, EDA sheds light into the bonding situation of these systems. However, use of the proper fragmentation scheme is important. Because of the large negative charge on F atoms, the EDA is computed taking F- as one fragment and [CpBeNg]+ or [CpNg]+ as another. On the other hand, neutral fragmentation schemes are considered to know the nature of interaction in CpBeNgF and Cp-NgF bonds. As obvious, in F-Ng bonds, ∆Eelstat is responsible for the 63-75% of the total attraction with smaller percentage in CpNgF than that in CpBeNgF (see Table 10). On the other hand, in Be-Ng or C-Ng bond the contribution from ∆Eorb ranges from 59-69% of the total attraction, corroborating the inference drawn based on the WBI values.


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Conclusions Ab initio calculations are performed to explore the structures, bonding and stability of half-sandwich complexes of Ng having the general formula, NgMCp+ (Ng = He-Rn, M = Be-Ba, Cp = η5-C5H5). The Ng binding ability of MCp+ complexes is analysed by computing bond dissociation energy (D0BSSE), and changes in enthalpy and free energy. Although all MCp+ complexes are found to bind Ar-Rn atoms quite effectively, for a given Ng, the BeCp+ forms the strongest bond with Ng which gradually weakens in going towards its heavier analogues. Nevertheless, the dissociations of NgMCp+ into Ng and MCp+ are endergonic in nature at 298 K for most of the Ar-Rn bound analogues. Remarkably, BeCp+ can even form strong bonds with He (5.5 kcal mol-1) and Ne (6.4 kcal mol-1) atoms. Ng→M electron transfer is noticed in natural population analysis and for a given M, it gradually increases along Ar to Rn, whereas it gradually diminishes along Be to Ba. Even though the Laplacian of electron density (∇2ρ(rc)) at the bond critical point of Ng-M bond is positive in all cases, the local total energy density (H(rc)) is negative for Ng-Be (Ng = Kr, Xe, Rn) and Ng-Mg (Ng = Xe, Rn) bonds, implying partly covalent nature of these bonds. The contour plots of ∇2ρ(r) for these NgMCp+ complexes further support the above statement. The attractive interaction between Ng and M centers originates exclusively from the orbital interaction and for a given Ng, the orbital contribution gradually reduces along Be to Ba, indicating a diminished covalent character in Ng-M bond along the same. Ng→MCp+ σ-donation along with two degenerate Ng→BeCp+ π-donation are responsible for the orbital interaction. An analysis of the stability of CpBeNgF and CpNgF (Ng = Kr-Rn) reveals that these systems are stable with respect to the dissociation processes considered here, but for one exergonic dissociation channel: CpBeNgF → Ng + CpBeF and CpNgF → Ng + CpF, respectively. However, the calculated activation free energy barrier in the latter systems (24.134.7 kcal mol-1) is significantly larger than that in the former ones (2.2-8.9 kcal mol-1). This free energy barrier for the above mentioned complexes reveals that the CpNgF (Ng = Kr-Rn) complexes are kinetically stable even above 300 K, whereas CpBeNgF (Ng = Xe, Rn) might be viable up to ~100 K. The F-Ng bonds are found to be ionic in nature, whereas, the Ng-Be and Ng-C bonds in these complexes exhibit significant covalent character.



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Supporting information Supporting Information Available: A comparison of results between the MP2/aug-cc-pVTZ level and MP2/def2-TZVPD level, Ng-binding results of MX (M = Be-Ba; X = H+, F+, Cl+, Br+, OH+, O, S), M+ (M = Be-Ba) and H+, ∆G values at lower temperatures, valence orbital populations of the M and Ng atoms in NgMCp+ (Ng = He-Rn; M = Ca-Ba) complexes, electron density descriptors (au) at the bond critical points (BCP) of Ng-M bond in NgMCp+ (Ng = He-Rn; M = Ca-Ba), contour plots of the electron dnesity and the Laplacian of electron density of NgMCp+ (Ng = He-Rn; M = Ca-Ba) complexes and plots of deformation densities of the pair-wise orbital interactions for NgMCp+ (Ng = He-Rn; M = Mg-Ba) complexes. This material is available free of charge via the Internet at http://pubs.acs.org.

Notes The authors declare no competing financial interest.

Acknowledgements PKC would like to thank DST, New Delhi for the J. C. Bose National Fellowship. RS thanks UGC, New Delhi for his fellowships.

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Dunning, Jr. T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007-1023.

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Page 26 of 43

Tables

Table 1. The ZPE-uncorrected dissociation energy (De), ZPE-corrected dissociation energy (D0), ZPE- and BSSE-corrected dissociation energy (D0BSSE) for the dissociation process: MCp+ ⟶ M2+ + Cp-, (M = Be - Ba) at MP2/aug-cc-PVTZ level. EDA results of the MCp+ complexes studied at the PBE-D3(BJ)/TZ2P//MP2/ aug-cc-pVTZ taking M2+ as one fragment and Cp- as another. All the energy values are in kcal/mol. MCp+

De

D0

D0BSSE

∆EPauli

∆Eelstat a

∆Eorb a

∆Edisp a

∆Eint

BeCp+

514.1

508.7

506.8

54.3

-303.6 (52.1)

-278.4 (47.8)

-0.9 (0.1)

-528.6

MgCp+

368.0

364.6

363.5

45.7

-250.5 (65.6)

-130.1 (34.1)

-1.3 (0.3)

-381.9

CaCp+

304.5

301.5

300.9

54.4

-273.6 (70.6)

-112.2 (29.0)

-1.4 (0.4)

-333.1

SrCp+

267.5

264.1

263.7

59.3

-265.6 (72.9)

-97.4 (26.7)

-1.4 (0.4)

-305.1

BaCp+

248.4

243.7

243.2

67.4

-259.7 (72.6)

-96.7 (27.0)

-1.5 (0.4)

-290.4

a

The values within the parentheses are in percentage and show the contribution towards the total attractive interaction ∆Eelstat + ∆Eorb + ∆Edisp.


Page 27 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. BSSE uncorrected dissociation energy (DeC, kcal mol-1) at CCSD(T)/ aug-cc-pVTZ level, BSSE and ZPE uncorrected dissociation energy (De, kcal mol-1) and BSSE and ZPE corrected dissociation energy (D0BSSE, kcal mol-1) for Ng-M bonds for the dissociation process: NgMCp+→ MCp+ + Ng; the enthalpy change (∆H298K, kcal mol-1), and the free energy change (∆G298K, kcal mol-1) for the complex formation process: Ng + MCp+ → NgMCp+ at 298 K; vibrational frequency of Ng-M bond (νM-Ng, cm-1), NPA charge at M and Ng centers (q, au), Wiberg bond indices of Ng-M bond (WBI), Ng-M bond distances (r, Å) in NgMCp+ at the MP2/aug-cc-pVTZ level.(Ng = He-Rn; M = Be-Rn) DeC

De

D0BSSE ∆H298K ∆G298K

νM-Ng

BeCp+

qM

qNg

WBI

r

1.13

HeBeCp+

7.6

7.5

5.5

-6.7

0.6

479

0.84 0.17 0.300 1.502

NeBeCp+

8.8

8.7

6.4

-8.2

-1.0

240

0.94 0.13 0.234 1.758

ArBeCp+

19.3 20.0

17.5

-19.5

-12.2

228

0.71 0.31 0.528 2.033

KrBeCp+

25.1 26.2

21.3

-25.7

-18.4

190

0.64 0.38 0.625 2.151

XeBeCp+

30.3 31.5

26.1

-31.1

-23.9

173

0.56 0.47 0.733 2.326

RnBeCp+

34.7 36.3

28.0

-36.0

-28.8

159

0.54 0.50 0.763 2.392

MgCp+

1.63

HeMgCp+

3.1

3.0

2.2

-2.6

2.8

283

1.53 0.06 0.116 2.030

NeMgCp+

4.7

4.6

3.7

-4.3

1.2

158

1.56 0.05 0.093 2.206

ArMgCp+

11.4 11.5

10.4

-11.1

-5.3

159

1.44 0.14 0.261 2.485

KrMgCp+

15.2 15.3

13.1

-15.0

-8.9

201

1.39 0.18 0.334 2.615

XeMgCp+

19.3 19.5

16.8

-19.2

-13.3

123

1.32 0.25 0.444 2.778

RnMgCp+

22.9 23.2

18.7

-22.9

-17.0

115

1.29 0.28 0.486 2.840

CaCp+

1.72

HeCaCp+

1.1

1.0

0.7

-0.7

2.4

146

1.69 0.03 0.052 2.644

NeCaCp+

1.9

1.9

1.5

-1.6

0.6

90

1.69 0.02 0.044 2.770



ArCaCp+

4.1

4.3

3.8

-4.0

-1.8

121

1.67 0.05 0.105 3.257

KrCaCp+

6.9

7.0

5.9

-6.7

-2.4

85

1.62 0.10 0.184 3.143

XeCaCp+

9.3

9.4

7.9

-9.1

-4.8

80

1.58 0.14 0.268 3.295

RnCaCp+

11.3 11.5

9.0

-11.2

-6.9

76

1.56 0.16 0.302 3.347

SrCp+

1.77

HeSrCp+

0.7

0.7

0.4

-0.4

2.4

124

1.75 0.02 0.033 3.047

NeSrCp+

1.0

1.0

0.5

-0.7

3.6

145

1.75 0.02 0.033 3.020

ArSrCp+

4.5

4.4

3.9

-4.1

0.0

84

1.70 0.05 0.106 3.254

KrSrCp+

6.4

6.2

5.3

-6.0

-1.7

72

1.68 0.08 0.149 3.344

XeSrCp+

7.9

7.9

6.8

-7.7

-4.5

76

1.66 0.10 0.192 3.607

RnSrCp+

9.6

9.5

7.1

-9.3

-2.3

68

1.63 0.13 0.243 3.548

BaCp+ a

a

Page 28 of 43

1.72

HeBaCp+

0.3

0.3

-0.9

0.0

0.5

57

1.72 0.01 0.014 3.592

ArBaCp+

3.1

3.0

2.7

-2.8

1.2

65

1.69 0.04 0.072 3.576

KrBaCp+

4.6

4.5

3.9

-4.3

-0.5

55

1.67 0.05 0.104 3.640

XeBaCp+

6.3

6.1

5.3

-6.0

-2.3

53

1.65 0.08 0.150 3.792

RnBaCp+

7.9

7.7

6.2

-7.6

-3.8

50

1.64 0.09 0.176 3.814

The minimum energy structure of NeBaCp+ cannot be located.


Page 29 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Valence orbital populations of the M and Ng centers in NgMCp+ (Ng = He-Rn; M = Be, Mg) complexes at the MP2/aug-cc-pVTZ level. Valence orbital population Complexes M center

Ng center

BeCp+

2s0.152px0.322py0.322pz0.07

HeBeCp+

2s0.192px0.362py0.362pz0.23

1s1.83

NeBeCp+

2s0.172px0.352py0.352pz0.18

2s1.942px1.992py1.992pz1.95

ArBeCp+

2s0.222px0.372py0.372pz0.31

3s1.903px1.983py1.983pz1.82

KrBeCp+

2s0.242px0.372py0.372pz0.36

4s1.904px1.974py1.974pz1.76

XeBeCp+

2s0.272px0.372py0.372pz0.41

5s1.905px1.975py1.975pz1.69

RnBeCp+

2s0.282px0.372py0.372pz0.42

6s1.916px1.976py1.976pz1.65

MgCp+

5s0.085px0.135py0.135pz0.02

HeMgCp+

5s0.105px0.145py0.145pz0.07

1s1.94

NeMgCp+

5s0.105px0.145py0.145pz0.06

2s1.972px2.002py2.002pz1.98

ArMgCp+

5s0.125px0.155py0.155pz0.12

3s1.953px1.993py1.993pz1.92

KrMgCp+

5s0.145px0.165py0.165pz0.14

4s1.954px1.994py1.994pz1.89

XeMgCp+

5s0.165px0.165py0.165pz0.18

5s1.945px1.985py1.985pz1.83

RnMgCp+

5s0.175px0.165py0.165pz0.20

6s1.956px1.986py1.986pz1.80



Page 30 of 43

Table 4. Electron density descriptors (au) at the bond critical points (BCP) of Ng-M bonds in NgMCp+ (Ng = He-Rn; M = Be, Mg) obtained from the wave functions generated at the MP2/aug-cc-pVTZ/WTBS level. Complex

ρ(rc)

ρ(rc)

G(rc)

V(rc)

H(rc)

HeBeCp+

0.032

0.349

0.073

-0.059

0.014

NeBeCp+

0.028

0.312

0.065

-0.052

0.013

ArBeCp+

0.039

0.264

0.064

-0.062

0.002

KrBeCp+

0.044

0.219

0.062

-0.070

-0.008

XeBeCp+

0.044

0.174

0.054

-0.064

-0.011

RnBeCp+

0.047

0.161

0.053

-0.067

-0.013

HeMgCp+ 0.014

0.114

0.022

-0.015

0.007

NeMgCp+ 0.016

0.130

0.026

-0.019

0.007

ArMgCp+ 0.021

0.126

0.027

-0.023

0.004

KrMgCp+ 0.024

0.095

0.024

-0.024

0.000

XeMgCp+ 0.025

0.082

0.022

-0.024

-0.002

RnMgCp+ 0.027

0.080

0.023

-0.025

-0.003


Page 31 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 5. EDA results of the NgMCp+ (Ng = He-Rn; M = Be-Ba) complexes studied at the PBED3(BJ)/TZ2P//MP2/aug-cc-pVTZ taking Ng as one fragment and MCp+ as another. All the energy values are in kcal mol-1. Complex

∆EPauli

∆Eelstat a

∆Eorb a

∆Edisp a

∆Eint

∆Eσ b

HeBeCp+

6.1

-0.6 (4.4)

-13.1 (92.7)

-0.4 (2.9)

-8.0

-12.3 (94.0)

NeBeCp+

8.1

-1.5 (9.0)

-14.3 (87.4)

-0.6 (3.6)

-8.3

-10.2 (71.4)

-1.8 (12.3)

-1.8 (12.3)

ArBeCp+

14.1

-1.9 (5.8)

-30.1 (89.9)

-1.4 (4.3)

-19.3

-21.7 (72.1)

-3.5 (11.7)

-3.5 (11.7)

KrBeCp+

16.3

-1.8 (4.5)

-37.0 (91.3)

-1.7 (4.3)

-24.2

-26.5 (71.6)

-4.0 (10.7)

-4.0 (10.7)

XeBeCp+

17.4

-1.6 (3.5)

-42.3 (91.9)

-2.1 (4.4)

-28.7

-32.2 (76.0)

-4.2 (9.9)

-4.2 (9.9)

RnBeCp+

18.9

-1.4 (2.9)

-45.6 (92.5)

-2.3 (4.6)

-30.4

-35.7 (78.4)

-4.1 (9.0)

-4.1 (9.0)

HeMgCp+

2.0

-0.5 (8.3)

-5.0 (87.5)

-0.2 (4.2)

-3.7

-4.7 (94.5)

NeMgCp+

2.9

-0.8 (10.2)

-6.7 (85.4)

-0.4 (4.5)

-5.0

-4.4 (65.0)

-1.0 (14.5)

-1.0 (14.5)

ArMgCp+

6.0

-1.3 (7.2)

-16.0 (88.0)

-0.9 (4.8)

-12.2

-10.4 (65.1)

-2.3 (14.1)

-2.3 (14.1)

KrMgCp+

7.0

-1.4 (6.0)

-21.4 (89.7)

-1.0 (4.3)

-16.8

-13.5 (63.1)

-2.8 (13.0)

-2.8 (13.0)

XeMgCp+

8.5

-1.6 (5.4)

-26.1 (90.1)

-1.3 (4.4)

-20.4

-17.8 (68.2)

-3.4 (12.9)

-3.4 (12.9)

RnMgCp+

9.5

-1.6 (5.1)

-28.8 (90.6)

-1.4 (4.2)

-22.3

-20.5 (71.0)

-3.5 (12.0)

-3.5 (12.0)

HeCaCp+

0.4

-0.2 (8.4)

-1.6 (81.7)

-0.2 (9.9)

-1.5

-1.4 (93.3)

NeCaCp+

0.9

-0.3 (10.6)

-2.4 (80.2)

-0.3 (9.2)

-2.1

-1.7 (70.4)

-0.4 (16.5)

-0.4 (16.5)

ArCaCp+

0.9

-0.3 (5.3)

-4.6 (84.1)

-0.6 (10.7)

-4.7

-3.4 (72.9)

-0.7 (14.2)

-0.7 (14.2)

KrCaCp+

3.3

-1.0 (8.8)

-9.4 (84.5)

-0.8 (6.7)

-7.9

-5.9 (63.2)

-1.5 (15.4)

-1.5 (15.4)

XeCaCp+

4.4

-1.3 (9.1)

-12.0 (84.4)

-0.9 (6.5)

-9.7

-8.0 (67.3)

-1.9 (15.9)

-1.9 (15.9)

RnCaCp+

5.3

-1.5 (9.5)

-13.6 (84.5)

-1.0 (6.0)

-10.8

-8.4 (62.1)

-2.1 (15.1)

-2.1 (15.1)

HeSrCp+

0.1

-0.1 (7.2)

-0.9 (78.4)

-0.2 (14.4)

-1.0

-0.1 (94.3)

NeSrCp+

0.6

-0.3 (13.8)

-1.6 (75.2)

-0.2 (11.0)

-1.6

-1.1 (64.3)

-0.2 (14.4)

-0.2 (14.4)

∆Eπ1

b

∆Eπ 2


b


Page 32 of 43

ArSrCp+

2.0

-0.7 (12.1)

-4.8 (78.5)

-0.6 (9.4)

-4.0

-3.1 (64.6)

-0.6 (12.9)

-0.6 (12.9)

KrSrCp+

3.1

-1.1 (11.7)

-7.5 (81.2)

-0.7 (7.1)

-6.2

-4.4 (57.9)

-1.0 (13.7)

-1.0 (13.7)

XeSrCp+

2.7

-1.0 (9.6)

-8.5 (82.9)

-0.8 (7.5)

-7.5

-5.5 (64.1)

-1.2 (14.0)

-1.2 (14.0)

RnSrCp+

4.9

-1.7 (12.9)

-11.0 (81.1)

-0.8 (6.1)

-8.6

-7.2 (65.2)

-1.5 (14.0)

-1.5 (14.0)

HeBaCp+

0.03

0.04 (6.8)

-0.42 (71.2)

-0.13 (22.0)

-0.63

-0.37 (89.3)

ArBaCp+

1.3

-0.6 (14.5)

-3.1 (73.0)

-0.5 (12.6)

-2.9

-2.0 (63.3)

-0.4 (13.7)

-0.4 (13.7)

KrBaCp+

2.3

-1.0 (14.0)

-5.4 (77.5)

-0.6 (8.6)

-4.7

-3.0 (54.4)

-0.7 (13.1)

-0.7 (13.1)

XeBaCp+

3.2

-1.3 (14.9)

-6.8 (77.0)

-0.7 (8.1)

-5.7

-4.1 (60.7)

-1.0 (14.7)

-1.0 (14.7)

RnBaCp+

4.2

-1.8 (16.6)

-8.0 (76.4)

-0.7 (6.9)

-6.3

-5.1 (63.7)

-1.2 (14.6)

-1.2 (14.6)

a

The values within the parentheses are in percentage and show the contribution towards the total attractive interaction ∆Eelstat + ∆Eorb + ∆Edisp. b

The values within the parentheses are in percentage and show the contribution towards the ∆Eorb.


Page 33 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6. ZPE corrected dissociation energy (D0, kcal mol-1) for the dissociation process, the enthalpy change (∆H298K, kcal mol-1), and the free energy change (∆G298K, kcal mol-1) for the dissociation process of CpBeNgF at the MP2/def2-TZVPD level. Dissociation Process CpBeNgF → CpBeF + Ng

CpBeNgF → CpNgF + Be

CpBeNgF → CpBeNg+ + F-

CpBeNgF → CpBe + NgF

CpBeNgF → CpBe+ + NgF-

∆G‡ a

D0

∆H298K

∆G298K

Dissociation Process

Ar

-120.4

-120.4

-127.5

CpBeNgF → CpBe+ + Ng + F-

Kr

-111.4

-111.4

Xe

-98.2

Rn

D0

∆H298K

∆G298K

Ar

111.6

112.1

97.2

-118.8

Kr

120.7

121.2

105.9

-98.3

-105.8

Xe

133.8

134.3

118.9

-89.5

-89.6

-97.1

Rn

142.5

143.0

127.6

Ar

143.7

144.6

136.2

Ar

29.6

30.3

14.3

Kr

132.3

133.2

124.6

Kr

38.7

39.4

22.9

Xe

120.8

121.7

112.9

Xe

51.8

52.5

35.9

Rn

115.9

116.8

107.9

Rn

60.5

61.1

44.6

Ar

93.4

93.7

86.0

Ar

33.7

34.7

19.0

Kr

97.9

98.2

90.1

Kr

42.7

43.7

27.7

Xe

105.5

105.8

97.5

Xe

55.9

56.8

40.7

Rn

110.4

110.7

102.4

Rn

64.6

65.5

49.4

Ar

29.4

29.8

17.1

Ar

617.3

619.3

594.9

Kr

38.4

38.7

25.7

Kr

626.4

628.4

603.6

Xe

51.4

51.6

38.7

Xe

639.5

641.5

616.6

Rn

57.7

57.5

46.5

Rn

648.2

650.1

625.3

Ar

109.7

109.8

98.8

Ar

141.5

143.4

118.3

Kr

117.7

117.7

106.5

Kr

150.6

152.4

127.0

Xe

128.5

128.5

117.4

Xe

163.7

165.5

140.0

Rn

135.4

135.4

124.3

Rn

172.4

174.2

148.6

Ar

-0.3

Kr

2.2

Xe

6.6

Rn

8.9

a

CpBeNgF → CpBe + Ng + F

CpBeNgF → Be + Ng + FCp

CpBeNgF → Cp- + Be2+ + Ng + F-

CpBeNgF → Cp + Be + Ng+ F

The free energy barrier, ∆G‡ corresponds to CpBeNgF → CpBeF + Ng.



Page 34 of 43

Table 7. ZPE corrected dissociation energy (D0, kcal mol-1) for the dissociation process, the enthalpy change (∆H298K, kcal mol-1), and the free energy change (∆G298K, kcal mol-1) for the dissociation processes of CpNgF at the MP2/def2-TZVPD level. Dissociation Process CpNgF → CpF + Ng

CpNgF → Cp- + NgF+

CpNgF → Cp + NgF

∆G‡ a

D0

∆H298K

∆G298K

Dissociation Process

Ar

-110.0

-109.9

-117.2

CpNgF → CpNg+ + F-

Kr

-89.6

-89.5

Xe

-64.9

Rn

D0

∆H298K

∆G298K

Ar

97.5

99.1

87.6

-96.9

Kr

116.4

117.3

107.9

-64.9

-72.3

Xe

136.2

136.9

128.3

-51.3

-51.3

-58.5

Rn

142.4

143.0

134.8

Ar

250.7

251.0

240.8

Ar

-2.2

-1.2

-17.9

Kr

235.0

235.3

224.9

Kr

18.2

19.2

2.4

Xe

217.1

217.3

206.8

Xe

42.9

43.8

27.0

Rn

213.1

213.3

202.9

Rn

56.5

57.4

40.7

Ar

-2.5

-1.8

-15.1

Ar

99.9

101.6

84.5

Kr

17.9

18.5

5.2

Kr

120.4

122.0

104.8

Xe

42.4

43.0

29.8

Xe

145.0

146.5

129.5

Rn

53.7

53.8

42.6

Rn

158.7

160.1

143.2

Ar

15.2

Kr

24.1

Xe

32.3

Rn

34.7 a

CpNgF → Cp + Ng + F

CpNgF → Cp+ + F- + Ng

The free energy barrier, ∆G‡ corresponds to CpNgF → CpF + Ng.


Page 35 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 8. The NPA charges (q, au), Wiberg bond indices (WBI) at the MP2/def2-TZVPD level. Systems

qNg

qF

WBIBe/C-Ng

WBINg-F

CpBeF

1.14

CpBeKrF

0.76

0.45

-0.96

0.748

0.052

CpBeXeF

0.63

0.59

-0.94

0.910

0.080

CpBeRnF

0.57

0.65

-0.94

0.818

0.045

CpF

a

qM/C

-0.71

0.21a

-0.39

CpKrF

-0.19a

0.73

-0.83

0.762

0.170

CpXeF

-0.35a

0.94

-0.82

0.783

0.206

CpRnF

-0.38a

1.02

-0.84

0.756

0.197

indicate the C-atom bonded to F or Ng.

Table 9. Electron density descriptors (au) at the bond critical points (BCP) of Ng-M/C and Ng-F bonds in CpBeNgF and CpNgF (Ng = Kr-Rn) obtained from the wave functions generated at the MP2/def2-TZVPD/WTBS level. Systems

BCP

ρ(rc)

∇2ρ(rc)

G(rc)

V(rc)

H(rc)

CpBeKrF

Be-Kr

0.056

0.176

0.059

-0.075

-0.016

Kr-F

0.055

0.202

0.053

-0.056

-0.003

Be-Xe

0.059

-0.005

0.031

-0.063

-0.032

Xe-F

0.058

0.232

0.064

-0.069

-0.006

Be-Rn

0.060

-0.048

0.022

-0.055

-0.034

Rn-F

0.059

0.227

0.064

-0.071

-0.007

CpBeXeF

CpBeRnF



CpKrF

CpXeF

CpRnF

Page 36 of 43

C-Kr

0.108

0.009

0.048

-0.094

-0.046

Kr-F

0.096

0.310

0.090

-0.102

-0.012

C-Xe

0.086

0.076

0.050

-0.082

-0.032

Xe-F

0.083

0.279

0.084

-0.098

-0.014

C-Rn

0.079

0.091

0.049

-0.075

-0.026

Rn-F

0.078

0.283

0.083

-0.095

-0.012

Table 10. EDA results of the CpBeNgF and CpNgF studied at the PBED3(BJ)/TZ2P//MP2/def2-TZVPD level at different dissociation channels. All the energy values are in kcal mol-1. Fragments

∆EPauli

∆Eelstat a

∆Eorb a

∆Edisp a

∆Eint

CpBe + KrF

320.7

-142.2 (35.9)

-250.1 (63.1)

-3.8 (1.0)

-77.4

CpBe + XeF

324.5

-149.7 (37.1)

-249.4 (61.8)

-4.4 (1.1)

-79.0

CpBe + RnF

319.8

-155.7 (39.1)

-237.4 (59.7)

-4.5 (1.1)

-78.1

CpBeKr+ + F-

50.1

-121.7 (74.9)

-40.1 (24.7)

-0.8 (0.5)

-112.4

CpBeXe+ + F-

71.8

-139.1 (72.1)

-52.8 (27.4)

-0.9 (0.5)

-121.1

CpBeRn+ + F-

76.1

-146.5 (73.0)

-53.4 (26.6)

-0.9 (0.4)

-124.7

Cp + KrF

190.3

-66.3 (28.7)

-160.7 (69.5)

-4.2 (1.8)

-40.9

Cp + XeF

198.9

-72.0 (29.2)

-169.6 (68.8)

-5.1 (2.1)

-47.8

Cp + RnF

189.0

-71.1 (30.0)

-160.7 (67.8)

-5.1 (2.2)

-47.9

CpKr+ + F-

119.8

-169.4 (63.7)

-95.8 (36.0)

-0.8 (0.3)

-146.2

CpXe+ + F-

133.3

-188.8 (65.2)

-100.0 (34.5)

-0.9 (0.3)

-156.4

CpRn+ + F-

127.6

-192.3 (67.1)

-93.5 (32.6)

-0.9 (0.3)

-159.1

a

The values within the parentheses are in percentage and show the contribution towards the total attractive interaction ∆Eelstat + ∆Eorb + ∆Edisp. 36 ACS Paragon Plus Environment

Page 37 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figures

Figure 1. The optimised geometries of MCp+ and NgMCp+ (Ng = He-Rn; M = Be-Ba). a HeBaCp+ is found at Cs point group of symmetry; bNeBaCp+ complex cannot be located as a minimum energy structure.



Page 38 of 43

Figure 2. Plots of (a) the electron densities and (b) the Laplacian of electron density (∇2ρ(r)) of NgMCp+ (Ng = He-Rn; M = Be, Mg) complexes. The black colored lines indicates the ρ(r), the blue and magenta colored lines indicate ∇2ρ(r) > 0 and ∇2ρ(r) < 0 region, respectively.


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Figure 3. Plots of deformation densities (∆ρi(r)) of the pair-wise orbital interactions for NgBeCp+ (Ng = He – Rn) complexes and the associated ∆Eorb energies obtained from the EDANOCV. The blue and red colored surfaces indicate regions with ∆ρ(r) > 0 and ∆ρ(r) < 0, respectively. The associated ∆Eorb values are given in kcal mol-1.



Page 40 of 43

Figure 4. Plots of deformation densities (∆ρi(r)) of the pair-wise orbital interactions and the related ∆Eorb energies obtained from the EDA-NOCV along with the molecular orbital of each associated fragments and the main moiety, XeBeCp+. The blue and red colored surfaces indicate regions where ∆ρ(r) > 0 and ∆ρ(r) < 0, respectively. Black arrows show the direction of electron flow.


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Figure 5. (a) The minimum energy structures, (b) the transition states of CpBeNgF, (c) the minimum energy structures and (d) the transition states of CpNgF at the MP2/def2-TZVPD level.



Page 42 of 43

Figure 6. Plots of (a) the electron densities and (b) the Laplacian of electron density (∇2ρ(r)) of CpNgF and CpBeNgF (Ng = Kr – Rn) complexes. The black colored lines indicates the ρ(r), the blue and magenta colored lines indicate ∇2ρ(r) > 0 and ∇2ρ(r) < 0 region, respectively


Page 43 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


NgMCp+: Noble Gas Bound Half-Sandwich Complexes (Ng = HeâRn

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