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Isolated catalyst sites on amorphous supports: A systematic algorithm for understanding heterogeneities in structure and reactivity
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10.1063/1.4807384
/content/aip/journal/jcp/138/20/10.1063/1.4807384
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/20/10.1063/1.4807384
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The proposed algorithm predicts the lowest energy structure for each value of activation energy. knowledge or assumptions about the peripheral atom locations are not needed.

Image of FIG. 2.
FIG. 2.

When the peripheral atoms are moved, the interior atoms must also move to the new optimal saddle point and reactant minimum configurations.

Image of FIG. 3.
FIG. 3.

The SQP algorithm uses gradients and second derivatives of the energy to systematically generate low energy active sites with successively lower or higher activation energies. At each activation energy, the peripheral atoms are properly constrained to mimic the solid environment around an active site.

Image of FIG. 4.
FIG. 4.

An empirical valence bond model energy landscape displaying the locus of reactant states (black) and the locus of transition states (red) at different values of the fixed peripheral coordinate.

Image of FIG. 5.
FIG. 5.

The smallest eigenvalue of the interior block Hessian of the reactant state, , and the negative eigenvalue of the interior block Hessian of the transition state, , are shown as a function of the peripheral coordinate corresponding to Figure 4 .

Image of FIG. 6.
FIG. 6.

The site energy vs. activation energy (Δ vs. Δ ) curve corresponding to Figure 4 (in arbitrary units). From analysis of Δ vs. Δ curves, specific structural changes that affect Δ could be identified.

Image of FIG. 7.
FIG. 7.

A six-membered ring Mo/SiO cluster model, terminated with basis set deficient fluorine atoms, was used to study an off-pathway kinetic trap in ethene metathesis.

Image of FIG. 8.
FIG. 8.

The Δ vs. Δ curve for metallacycle rotation using a six-membered ring Mo/SiO cluster model. The sites that contribute the most to the rate assuming a Boltzmann distribution are where dΔ /dΔ = −1.

Image of FIG. 9.
FIG. 9.

A minimal Mo/SiO cluster model, terminated with basis set deficient fluorine atoms, was used to study an off-pathway kinetic trap in ethene metathesis.

Image of FIG. 10.
FIG. 10.

The Δ vs. Δ curve for metallacycle rotation using a minimal Mo/SiO cluster model. Two minima were generated for this system, and the two corresponding SQP curves are differentiated graphically by the data point type. Points to the left of the tick mark had a negative eigenvalue present in ∖ Δ . The sites that contribute the most to the rate assuming a Boltzmann distribution are where dΔ /dΔ = −1.

Image of FIG. 11.
FIG. 11.

The reaction energy (Δ ) vs. Δ for metallacycle rotation using a minimal Mo/SiO cluster model. Toward decreasing activation energy, the product state is beginning to lose metastability toward conversion back to the reactants.

Image of FIG. 12.
FIG. 12.

The distance between the two Si atoms ( ) vs. Δ for metallacycle rotation using a minimal Mo/SiO cluster model.

Image of FIG. 13.
FIG. 13.

A model energy landscape showing the locus of reactant states (black) and the locus of transition states (red) at different fixed peripheral atom positions. Type-1 termination occurs from a loss of metastability in the product or reactant state, type-2 termination occurs when the transition state jumps discontinuously along the interior coordinate, and type-3 termination occurs when vanishes.

Image of FIG. 14.
FIG. 14.

A schematic depicting a type-4 termination caused by a bifurcation.

Image of FIG. 15.
FIG. 15.

The structures of both silsesquioxane and HOSiF along with the corresponding structures after a single deprotonation. The objective is to match the HOSiF deprotonation energy, Δ , to the silsesquioxane deprotonation energy, Δ .

Image of FIG. 16.
FIG. 16.

The deprotonation energy of HOSiF was matched to the deprotonation energy of silsesquioxane with non-fluorine atoms modeled at B3LYP/LANL2DZ and fluorine atoms modeled at B3LYP/X, where X is any basis set. Δ was matched to Δ by systematically tuning the basis set size on the fluorine atoms of HOSiF. The fluorine basis set found to best match Δ to Δ was 6-31G.

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/content/aip/journal/jcp/138/20/10.1063/1.4807384
2013-05-29
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Isolated catalyst sites on amorphous supports: A systematic algorithm for understanding heterogeneities in structure and reactivity
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/20/10.1063/1.4807384
10.1063/1.4807384
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