Probing relativistic effects in the gas-phase CS2 ligation of late transition metal cations (groups 9–11) with rate measurements and quantum chemical calculations of ligation energies

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Highlights

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    Strong relativistic effect in CS2 ligation rate of Group 9–11 atomic cations.

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    First observation of relativistic effect in ligation rate for a second ligation.

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    Computations for relativistic ligation energies.

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    Relativistic effect very strong for third-row atomic ions.

Abstract

Striking relativistic effects are demonstrated for the ligation of carbon disulphide to late atomic transition metal cations (Groups 9–11) with both measurements of rate coefficients for ligation in helium buffer gas at 0.35 ± 0.01 Torr and 295 ± 2 K and quantum chemical calculations of ligation energies. The rates of ligation with one CS2 molecule were observed to be enhanced by a factor of about 10 going from second row to third-row atomic transition metal cations (Groups 9–11). The addition of a second CS2 ligand, although intrinsically much faster due to effects of degrees of freedom on the lifetime of the intermediate, also exhibits enhancement of the ligation rate for the third-row atomic cations for Groups 10 and 11. The trends in the computed M+-CS2 bond dissociation energies down Groups 9-11 clearly follow the trends in the measured rate coefficients for the first addition of CS2 and, to a degree, the second addition. A novel isodesmic reaction method was used to estimate the percent relativistic contribution to the M+-CS2 bond energy down the periodic table which exceeds 25% for third-row atomic ions. The computations also provided optimized structures for the ligated ions M+(CS2) and M+(CS2)2. A correlation between the measured ligation efficiency and the computed ligation energy provided a measure of the number of vibrational modes active in the stabilization of these ligated ions.

Introduction

Relativistic effects in chemistry now have a firm basis in theory and, increasingly so, in experiments as well [[1], [2], [3], [4], [5], [6], [7], [8]]. They are associated with inner electrons orbiting highly charged nuclei at higher speeds (with higher mass) and, “at the orbital level, the relativistic effect is apparent in the radial contraction of penetrating s and p shells, expansion of nonpenetrating d and f shells, and the spin-orbit splitting of p-, d-, and f-shells,” according to Yatsimirskii [8]. Chemical relativistic effects are manifested in a number of different ways [[1], [2], [3], [4], [5], [6], [7], [8]], including in stronger orbital bonding of heavy atomic transition metal cations with molecular ligands and, as a consequence, in higher rates of ligation that can be measured going down the periodic table, as we have recently demonstrated in our laboratory [[9], [10], [11]]. For example, our measurements of ammonia ligation with Group 10 [9] and 11 [10] atomic transition metal cations showed a strong rate enhancement with the third-row cations Pt+ and Au+ that could be attributed to relativistic effects in ammonia bonding with supporting quantum chemical calculations. Also, more recently, we reported rate enhancements for the ligation of Hg+ (third Row, Group 12) with OCS and CH3Cl that also could be attributed to relativistic effects that enhance the stability of these ligated cations [11].

Here we revisit our previous experimental results with CS2 as a ligand [12], as we continue to explore the relativistic effect in ligation reactions with late transition metal cations. We found that at least two molecules of CS2 can attach to Group 9–11 atomic transition metal cations sequentially and this provides an opportunity to follow the relativistic effect in the addition of a second ligand, for the first time. We have excluded Groups 7, 8 and 12 for which 3rd row reactions are dominated by S atom transfer, as with Re+ (Group 7) and Os+ (Group 8), or by electron transfer, as with Hg+ (Group 12). Also, we have excluded a previous analogous study with the related CO2 molecule for which we found that the ligation reactions, although observed, were all too slow to measure [13], and with the related OCS molecule that we reported earlier [11].

We have also scrutinized the nature and extent of relativistic effects with quantum chemical calculations of ligand binding energies for the first and second addition of CS2 to Group 9–11 atomic transition metal cations.

Section snippets

Experimental

All experiments were performed using the Inductively Coupled Plasma - Selected Ion Flow Tube (ICP-SIFT) tandem mass spectrometer at York University as described previously [12].

Computational methods

All density functional calculations (DFT) were run using ORCA [14] on the Graham server through Compute Canada acting in regional partnership with Compute Ontario. Full geometry optimizations were performed using the all-electron jorge-TZP-DKH basis set [15] with the B3PW91 functional [16] and a second-order Douglas-Kroll-Hess relativistic Hamiltonian [17]. Vibrational analyses were run in all cases to assure geometry convergence. All calculations utilized the atom-pairwise dispersion

Measured rate coefficients for ligation at room temperature

Our previous ICP-SIFT measurements of the kinetics of CS2 ligation with Group 9 to 11 atomic transition-metal cations, M+, were taken in helium buffer gas at 0.35 ± 0.01 Torr and 295 ± 2 K [11]. The ligation occurs sequentially by termolecular association as indicated in reactions (1) and (2).M+ + CS2 + He → M+(CS2) + HeM+(CS2) + CS2 + He → M+(CS2)2 + He

The experiments provide the effective bimolecular rate coefficients k(2); the termolecular rate coefficient, k(3), can be deduced from

Calculated ligation energies

DFT calculations provided the values for the dissociation energies, ΔE298, for the first and second adducts of M+ with CS2 presented in Table 3. The third-row dissociation energies are seen to be always the highest and the second-row dissociation energies the lowest (except for Rh+(CS2)2). The Group 11 M+(CS2)2 cations show the lowest binding energies, likely due to increased electron-electron repulsion between the metal cation and the second ligand due to increased orbital occupancy compared

Stabilization of the intermediate ligated transition metal ions

With the availability of the computed ligation energies of the Group 9–11 metal cations, the opportunity arises to assess the magnitude of s, the number of coupled harmonic oscillators, that participate in the stabilization of the ligated intermediate (M+-L)∗, and so influence its classical RRKM lifetime, τ0 ((D + rRT)/rRT)s−1.

By taking the natural logarithm, ln, of equation (5), we can derive a simplified expression, ln(k) = (s-1) ln(D+2RT) + c, so that plotting the dependence of k on D allows

Conclusions

Chemical relativistic effects have been strikingly exposed with measurements of the kinetics of ligation reactions of CS2 with Group 9–11 atomic transition metal cations going down three rows on the periodic table. A strong relativistic effect was seen for the first CS2 addition to Group 9–11 atomic transition metal cations. For the faster second CS2 addition, the relativistic effect was clearly apparent for the Group 10 and 11 ions but was obfuscated for the Group 9 cations, all of which were

Credit author statement

Voislav Blabojevic: Conceptialization, Formal analysis, Investigation, Data curation, Visualization; Gregory K Koyanagi: Formal analysis, Investigation; Pirouz Kiani: Software, Validation Formal analysis, Visualization; William J Pietro: Methodology, Software, Validation, Formal analysis, Resources, Data curation, Writing, Review &Editing, Visualization, Supervision, Funding acquisition; Diethard K. Bohme: Conceptialization, Investigation, Resources, Writing, Review & Editing, Supervision,

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Financial support from the Natural Sciences and Engineering Research Council of Canada is greatly appreciated. W. J. P. is funded by an NSERC Collaborative Research and Development grant (CRDPJ 445703-12). As former holder of a Canada Research Chair in Physical Chemistry, D.K.B. (now retired) thanks the contributions of the Canada Research Chair Program to this research. Compute Canada is funded through the Canadian Foundation for Innovation (CFI), matched through ACENET, Calcul Quebec, Compute

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Cited by (3)

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In memory of William L. Hase for his many insightful contributions to our understanding of ion chemistry.

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