Cryokinetics and spin quenching in the N₂ adsorption onto rhodium cluster cations

Figures & data

Figure 1. Temporal evolution of the FT-ICR mass spectra of Rh₆⁺ and Rh₉⁺ exposed to 3.0 · 10⁻⁷ mbar and 3.1 · 10⁻⁷mbar N₂ at a temperature of 26 K at various storage times in the cryogenic hexapole ion trap. Note that the N₂ adsorption stops after the uptake of 12 and 9 N₂, respectively. m/z on the abscissa represents the ‘mass-to charge number ratio’ where the symbol m stands for a dimensionless mass with this symbol m = mass/u.

Figure 2. The recorded adsorption limits m_max (purple circles) and the intermittent adsorption limits m_x (purple stars) of N₂ adsorbates to Rh_i⁺-clusters (in colour only in electronic format). The grey lines indicate adsorbate to cluster size ratios of m: i = (1: 1), (2: 1), namely a monolayer and a double occupation of all rhodium atoms, respectively [47]. Note that in correction to the previous publication ([47], Figure S1 therein), we assign an intermittent adsorption limit (5,7) at m = 7 to the [Rh₅(N₂)_m]⁺ cluster that is clearly supported by the present kinetic investigations.

Figure 3. Isothermal kinetics of the stepwise N₂ adsorption at 26 K (a) by isolated Rh₅⁺ clusters and (b) by isolated Rh₆⁺ clusters (solid symbols, in colour only in electronic format). The fits (solid lines) assume pseudo-first-order kinetics in an adsorption chain of up to 10 consecutive steps for Rh₅⁺ and up to 12 for Rh₆⁺ clusters. Fitted values of relative rate constants (c) of Rh₅⁺ and (d) of Rh₆⁺ for the adsorption (k_(i,m), black filled circles) and the desorption (k_-(i,m+1), green open circles) as a function of the stepwise N₂ adsorption (level m). The grey shaded areas indicate the approximate background noise level. Values of 0.001 s⁻¹ represent an upper limit. Rate constants k_(5,10) and k_(6,12) are at the noise level and indicate an adsorption limit.

Figure 4. Isothermal kinetics of the stepwise N₂ adsorption at 26 K (a) by isolated Rh₇⁺ clusters and (b) by isolated Rh₉⁺ clusters (solid symbols, in colour only in electronic format). The fits (solid lines) assume pseudo-first-order kinetics in an adsorption chain of up to 13 consecutive steps for Rh₇⁺ and up to 9 for Rh₉⁺ clusters. Fitted values of relative rate constants (c) of Rh₇⁺ and (d) of Rh₉⁺ for the adsorption (k_(i,m), black filled circles) and the desorption (k_-(i,m+1), green open circles) as a function of the stepwise N₂ adsorption level m. Values of 0.001 s⁻¹ represent an upper limit. The grey shaded areas indicate the approximate background noise level. Rate constants k_(7,13) and k_(9,9) are at the noise level and indicate an adsorption limit.

Figure 5. A selection of conceivable Rh_i⁺, i = 5,6,7, and 9, cluster core structures. The number of next neighbours and average coordination numbers for Rh atoms in the clusters are given in Table S16.

Figure 6. Experimental absolute rate constants for the first adsorption step of Rh_i⁺ with N₂ (filled squares) compared to classical Langevin collision rates k_coll (solid line), the ‘Surface Charge Capture model’ k_SCC (dashed line), and the ‘Hard Sphere Average dipole orientation model’ k_HSA (open circles) [67].

Table 1. Relative pseudo-first-order rate constants, absolute rate constants, collision rates and sticking probabilities for the N₂ adsorption on [Rh₅(N₂)_m]⁺ clusters. The γ_(5,m) values are calculated by Equation (3). The relative errors are 20% for k_(5,m) and 40% for k_abs and γ_(5,m). The k_coll values are theoretically determined.

m	k(5,m) / s^−1	kabs / 10^−10 cm^3 s^−1	kcoll / 10^−10 cm^3 s^−1	γ(5,m)
0	0.97	0.74	6.05	0.12
1	3.0	2.3	6.04	0.38
2	5.3	4.0	6.03	0.67
3	5.5	4.2	6.03	0.70
4	4.8	3.7	6.02	0.61
5	5.0	3.8	6.01	0.64
6	6.2	4.7	6.01	0.79
7	1.5	1.1	6.00	0.19
8	2.3	1.8	6.00	0.29
9	2.9	2.2	6.00	0.37

Table 2. Relative pseudo-first-order rate constants, absolute rate constants, collision rates and sticking probabilities for the N₂ adsorption on [Rh₆(N₂)_m]⁺ clusters. The γ_(6,m) values are calculated by Equation (3). The relative errors are 20% for k_(6,m) and 40% for k_abs and γ_(6,m). The k_coll values are theoretically determined.

m	k(6,m) / s^−1	kabs / 10^−10 cm^3 s^−1	kcoll / 10^−10 cm^3 s^−1	γ(6,m)
0	3.0	2.3	6.0	0.38
1	6.8	5.2	6.02	0.86
2	8.5	6.6	6.01	1.1
3	9.0	6.9	6.01	1.2
4	8.7	6.7	6.00	1.1
5	8.5	6.5	6.00	1.1
6	7.4	5.7	5.99	0.94
7	6.3	4.8	5.99	0.81
8	2.8	2.2	5.99	0.36
9	5.4	4.1	5.98	0.69
10	3.4	2.6	5.98	0.44
11	0.23	0.17	5.98	0.03

Table 3. Relative pseudo-first-order rate constants, absolute rate constants, collision rates and sticking probabilities for the N₂ adsorption on [Rh₇(N₂)_m]⁺ clusters. The γ_(7,m) values are calculated by Equation (3). The relative errors are 20% for k_(7,m) and 40% for k_abs and γ_(7,m). The k_coll values are theoretically determined.

m	k(7,m) / s^−1	kabs / 10^−10 cm^3 s^−1	kcoll / 10^−10 cm^3 s^−1	γ(7,m)
0	7.7	5.9	6.00	0.98
1	7.9	6.1	6.00	1.0
2	9.2	7.0	5.99	1.2
3	9.0	6.9	5.99	1.2
4	9.0	6.9	5.99	1.2
5	8.7	6.7	5.98	1.1
6	8.5	6.5	5.98	1.1
7	8.2	6.3	5.98	1.1
8	7.9	6.1	5.98	1.0
9	7.4	5.7	5.97	0.95
10	5.1	3.9	5.97	0.66
11	8.7	6.7	5.97	1.1
12	2.8	2.1	5.97	0.35

Table 4. Relative pseudo-first-order rate constants, absolute rate constants, collision rates and sticking probabilities for the N₂ adsorption on [Rh₉(N₂)_m]⁺ clusters. The γ_(9,m) values are calculated by Equation (3). The relative errors are 20% for k_(9,m) and 40% for k_abs and γ_(9,m). The k_coll values are theoretically determined.

m	k(9,m) / s^−1	kabs / 10^−10 cm^3 s^−1	kcoll / 10^−10 cm^3 s^−1	γ(9,m)
0	7.6	5.9	5.98	0.98
1	7.9	6.1	5.98	1.0
2	8.4	6.5	5.97	1.1
3	9.1	7.0	5.97	1.2
4	9.2	7.1	5.97	1.2
5	8.9	6.8	5.97	1.1
6	8.9	6.9	5.96	1.2
7	8.7	6.7	5.96	1.1
8	8.5	6.5	5.96	1.1

Figure 7. Plot of Gibbs energies ${\mathrm{\Delta }}_{\text{ads}}{\text{G}}_{(i,m)}^{26\text{ K}}$ for the equilibria of N₂ adsorption onto [Rh_i(N₂)_m]⁺ / desorption off [Rh_i(N₂)_m+1]⁺. Note that the ${\mathrm{\Delta }}_{\text{ads}}{\text{G}}_{(i,m)}^{26\text{ K}}$ values within the light blue plateau signify upper limits of otherwise unknown values (in colour only in electronic format). The last depicted step formally relates to the equilibrium of m_max with m_max+1. The positive Gibbs energies signify the last adsorption step towards m_max, with the only exception of Rh₅⁺. Its initial N₂ adsorption is hindered, and its subsequent steps become more spontaneous. [Rh_i(N₂)_m]⁺, i = 8, … , 10 possess all negative ${\mathrm{\Delta }}_{\text{ads}}{\text{G}}_{(i,m)}^{26\text{ K}}$ values but m_max. The grey area signifies non-occurring processes.

Figure 8. Total energies of most stable Rh₅⁺ cluster structures as a function of the spin multiplicity 2S + 1, normalised to the most stable trigonal bipyramid nonet, ⁹tbp. The second most stable isomer is a nonet square pyramid, ⁹sp, +9 kJ/mol. In the cases of high or low multiplicities, a single stable isomer is found (as indicated) while others relax into these. The fully relaxed path of successive spin isomers connects to an asymmetric spin valley (indicated in pink, in colour only in electronic format).

Figure 9. Total energies of computed [Rh₅(N₂)_m]⁺ cluster adsorbate complex structures (5,m) as a function of the spin multiplicity 2S + 1, normalised to the computed (5,0) spin isomer (trigonal bipyramid, ⁹tbp, nonet). The calculated minimum structures for (5,0), (5,7) and (5,10) are shown as insets. Spin contamination occurs in some low spin cases (red brackets). The horizontal grey dashed lines serve to interpolate singlet and nonet state energies where no computational data are available. Their offset against each other indicates the supposed average adsorption energy upon spin conservation. The red dashed lines connect the spin valley curves’ minima as indicated by the red circles.

M.P. Klein, A.A. Ehrhard, J. Mohrbach, S. Dillinger and G. Niedner-Schatteburg, Top. Catal. 61, 106–118 (2018). doi:https://doi.org/10.1007/s11244-017-0865-2.

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