The proposed algorithm predicts the lowest energy structure for each value of activation energy. A priori knowledge or ad hoc assumptions about the peripheral atom locations are not needed.
When the peripheral atoms are moved, the interior atoms must also move to the new optimal saddle point and reactant minimum configurations.
The SQP algorithm uses ab initio 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.
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.
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 .
The site energy vs. activation energy (ΔE site vs. ΔE ‡) curve corresponding to Figure 4 (in arbitrary units). From analysis of ΔE site vs. ΔE ‡ curves, specific structural changes that affect ΔE ‡ could be identified.
A six-membered ring Mo/SiO2 cluster model, terminated with basis set deficient fluorine atoms, was used to study an off-pathway kinetic trap in ethene metathesis.
The ΔE site vs. ΔE ‡ curve for metallacycle rotation using a six-membered ring Mo/SiO2 cluster model. The sites that contribute the most to the rate assuming a Boltzmann distribution are where dΔE site /dΔE ‡ = −1.
A minimal Mo/SiO2 cluster model, terminated with basis set deficient fluorine atoms, was used to study an off-pathway kinetic trap in ethene metathesis.
The ΔE site vs. ΔE ‡ curve for metallacycle rotation using a minimal Mo/SiO2 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 ∖ Δg red . The sites that contribute the most to the rate assuming a Boltzmann distribution are where dΔE site /dΔE ‡ = −1.
The reaction energy (ΔE rxn ) vs. ΔE ‡ for metallacycle rotation using a minimal Mo/SiO2 cluster model. Toward decreasing activation energy, the product state is beginning to lose metastability toward conversion back to the reactants.
The distance between the two Si atoms (r Si–Si) vs. ΔE ‡ for metallacycle rotation using a minimal Mo/SiO2 cluster model.
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.
A schematic depicting a type-4 termination caused by a bifurcation.
The structures of both silsesquioxane and HOSiF3 along with the corresponding structures after a single deprotonation. The objective is to match the HOSiF3 deprotonation energy, ΔE deprotonation, to the silsesquioxane deprotonation energy, ΔE target.
The deprotonation energy of HOSiF3 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. ΔE deprotonation was matched to ΔE target by systematically tuning the basis set size on the fluorine atoms of HOSiF3. The fluorine basis set found to best match ΔE deprotonation to ΔE target was 6-31G.
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