The cost of calculating nuclear hessians, either analytically or by finite difference methods, during the course of quantum chemical analyses can be prohibitive for systems containing hundreds of atoms. In many applications, though, only a few eigenvalues and eigenvectors, and not the full hessian, are required. For instance, the lowest one or two eigenvalues of the full hessian are sufficient to characterize a stationary point as a minimum or a transition state (TS), respectively. We describe here a method that can eliminate the need for hessian calculations for both the characterization of stationary points as well as searches for saddle points. A finite differences implementation of the Davidson method that uses only first derivatives of the energy to calculate the lowest eigenvalues and eigenvectors of the hessian is discussed. This method can be implemented in conjunction with geometry optimization methods such as partitioned-rational function optimization (P-RFO) to characterize stationary points on the potential energy surface. With equal ease, it can be combined with interpolation methods that determine TS guess structures, such as the freezing string method, to generate approximate hessian matrices in lieu of full hessians as input to P-RFO for TS optimization. This approach is shown to achieve significant cost savings relative to exact hessian calculation when applied to both stationary point characterization as well as TS optimization. The basic reason is that the present approach scales one power of system size lower since the rate of convergence is approximately independent of the size of the system. Therefore, the finite-difference Davidson method is a viable alternative to full hessian calculation for stationary point characterization and TS search particularly when analytical hessians are not available or require substantial computational effort.

Increased demand for light alkenes has motivated research on the catalytic dehydrogenation of the light alkanes and on understanding the role of catalyst composition on the activity, selectivity, and stability of Pt-based catalysts used for this purpose. The present study examines the structure and performance of Pt-Ir catalysts for ethane and propane dehydrogenation, and compares them with the performance of Pt and Pt-Sn catalysts. Nanoparticles of Pt, PtSn, and PtIr were prepared in a colloidal suspension and then dispersed onto calcined hydrotalcite (Mg(Al)O). After characterization to confirm formation of a bimetallic alloy, it was observed that at high conversions, Pt3Ir/Mg(Al)O exhibited lower initial activity than Pt3Sn/Mg(Al)O but greater stability to coke deposition. Intrinsic rate measurements at low feed residence time revealed the following trend in activity: Pt3Sn > Pt3Ir > Pt. DFT calculations carried out on tetrahedral clusters (Pt4, Pt3Ir, Pt3Sn) reveals that this trend in activity can be replicated and Ir is capable of alkane activation, a trait unique to this bimetallic system.

Wavefunction stability analysis is commonly applied to converged self-consistent field (SCF) solutions to verify whether the electronic energy is a local minimum with respect to second-order variations in the orbitals. By iterative diagonalisation, the procedure calculates the lowest eigenvalue of the stability matrix or electronic Hessian. However, analytical expressions for the electronic Hessian are unavailable for most advanced post-Hartree-Fock (HF) wave function methods and even some Kohn-Sham (KS) density functionals. To address such cases, we formulate the Hessian-vector product within the iterative diagonalisation procedure as a finite difference of the electronic gradient with respect to orbital perturbations in the direction of the vector. As a model application, following the lowest eigenvalue of the orbital-optimised second-order Møller-Plesset perturbation theory (OOMP2) Hessian during H2 dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a second independent unrestricted solution. We show that a single stable solution can be recovered by using the regularised OOMP2 method (δ-OOMP2), which contains a level shift. Internal and external stability analyses are also performed for SCF solutions of a recently developed range-separated hybrid density functional, ωB97X-V, for which the analytical Hessian is not yet available due to the complexity of its long-range non-local VV10 correlation functional.

To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to molecular CO₂ reduction catalysis. For [FeTPP(CO₂-κC)]^2- (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO₂ binding, -N(CH₃)₃ ⁺ (TMA) and -OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The coulombic interaction between the positively charged TMA group and activated CO₂ is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO₂ via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible "pockets" in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the p-terphenyl radical anion to CO₂, we demonstrate that the double terminal substitution of p-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.

Experimental measurements of the rate coefficient (kapp) and apparent enthalpies and entropies of activation (ΔHapp and ΔSapp) for alkane cracking catalyzed by acidic zeolites can be used to characterize the effects of zeolite structure and alkane size on the intrinsic enthalpy and entropy of activation, (Formula presented.) and (Formula presented.). To determine (Formula presented.) and (Formula presented.), enthalpies and entropies of adsorption, ΔHads-H⁺ and ΔSads-H⁺, must be determined for alkane molecules moving from the gas phase to Brønsted acid sites at reaction temperatures (>673 K). Experimental values of ΔHapp and ΔSapp must also be properly defined in terms of ΔHads-H⁺ and ΔSads-H⁺. We report here a method for determining ΔHads-H⁺ and ΔSads-H⁺ in which the adsorption site is represented by a fixed volume that includes the proton. Values of ΔHads-H⁺ and ΔSads-H⁺ obtained from Monte Carlo simulations are in good agreement with values obtained from experimental data measured at 300-400 K. An important feature of the simulations, however, is their ability to account for the redistribution of alkane adsorbed at protons in different locations with increasing temperature. Values of (Formula presented.) and (Formula presented.) for the cracking of propane through n-hexane, determined from measured values of kapp and ΔHapp and simulated values of ΔHads-H⁺ and ΔSads-H⁺, agree well with values obtained independently from quantum mechanics/molecular mechanics calculations. Application of our method of analysis reveals that the observed increase in kapp with increasing n-alkane size is due primarily to a decrease in (Formula presented.) with increasing chain length and that (Formula presented.) is independent of chain length.

Recent experimental work has shown that variations in the confinement of n-butane at Brønsted acid sites due to changes in zeolite framework structure strongly affect the apparent and intrinsic enthalpy and entropy of activation for cracking and dehydrogenation. Quantum chemical calculations have provided good estimates of the intrinsic enthalpies and entropies of activation extracted from experimental rate data for MFI, but extending these calculations to less confining zeolites has proven challenging, particularly for activation entropies. Herein, we report our efforts to develop a theoretical model for the cracking and dehydrogenation of n-butane occurring in a series of zeolites containing 10-ring channels and differing in cavity size (TON, FER, -SVR, MFI, MEL, STF, and MWW). We combine a QM/MM approach to calculate intrinsic and apparent activation parameters, with thermal corrections to the apparent barriers obtained from configurational-bias Monte Carlo simulations, to account for configurational contributions due to global motions of the transition state. We obtain good agreement between theory and experiment for all activation parameters for central cracking in all zeolites. For terminal cracking and dehydrogenation, good agreement between theory and experiment is found only at the highest confinements. Experimental activation parameters, especially those for dehydrogenation, tend to increase with decreasing confinement. This trend is not captured by the theoretical calculations, such that deviations between theory and experiment increase as confinement decreases. We propose that, because transition states for dehydrogenation are later than those for cracking, relative movements between the fragments produced in the reaction become increasingly important in the less confining zeolites. (Chemical Equation Presented).