Matrix Approximation with Side Information: When Column Sampling is Enough

A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein full matrix computation is expensive, and partial computations only lead to column information. The proposed algorithm successfully estimates the column and row-space of a true matrix given a priori structural knowledge of the true matrix. A theoretical spectral error bound is provided, which captures the possible inaccuracies of the side information. The error bound proves it scales in its signal-to-noise (SNR) ratio. The proposed algorithm is validated via simulations which enable the characterization of the amount of information provided by the quasi-polynomial side information

Penilaian Karya Ilmiah C-11

Recent experimental work has shown that variations in the confinement of <i>n</i>-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 <i>n</i>-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

Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube

Software for the frontiers of quantum chemistry:An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design

Development of a Hessian-Free Algorithm for Transition State Searches, Application to Reactions of Light Alkanes in Zeolite Catalysts, and Extension to Wavefunction Stability Analysis in the Absence of Analytical Hessians

The cost of calculating second derivatives of the energy, or nuclear hessians, in the course of quantum chemical analyses can be prohibitive for systems containing hundreds of atoms. In particular, when searching for reaction transition states (TSs), only a few eigenvalues and eigenvectors, and not the full hessian, are required. Here, a method is described that can eliminate the need for hessian calculations for both TS searches as well as characterization of stationary 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. When implemented in conjunction with a double-ended interpolation method for generating TS guesses, such as the freezing string method (FSM), an approximate hessian can be constructed in lieu of the full hessian as input to any quasi-Newton TS optimization routine. With equal ease, the finite differences Davidson approach can be implemented at the end of geometry optimization for verifying stationary points on a potential energy surface. The approach scales one power of system size lower than exact hessian calculation since the rate of convergence is approximately independent of the size of the system. Therefore, it achieves significant cost savings relative to exact hessian calculation when applied to both stationary point characterization as well as TS search, particularly when analytical hessians are not available or require substantial computational effort.The TS search approach is a useful tool for reaction kinetics and catalysis studies. Zeolite catalysts are employed extensively in industry owing to their high Brønsted acidity and shape selective properties, which are probed typically using monomolecular cracking and dehydrogenation reactions of alkanes. The TS search method is combined with hybrid quantum mechanics/molecular mechanics (QM/MM), and a modified harmonic oscillator approximation in order to calculate intrinsic activation parameters for monomolecular reactions of n-butane. The first study calculates TSs for all cracking and dehydrogenation pathways in MFI. Based on an examination of adsorption enthalpies and intrinsic activation energies for these reactions at active sites located at the channel intersection as well as the sinusoidal channel in MFI, the analysis concludes that reaction energetics are highly sensitive to the active site location due to varying acidities and non-bonding framework-substrate interactions.The second investigation extends the QM/MM approach to examine the sensitivity of intrinsic reaction kinetics to zeolite pore topology. Monomolecular cracking and dehydrogenation reactions of n-butane are examined in six zeolite frameworks - TON, SVR, MFI, MEL, STF and MWW, with active sites located within channels, channel intersections and cage geometries. By analyzing calculated intrinsic enthalpies and entropies of activation together with experimental values, the sensitivity of cracking and dehydrogenation pathways to active site location is examined for all site types. Dehydrogenation exhibits a surprising preference for the methyl pathway in cages in spite of the higher barrier relative to methylene, which points towards significant entropy compensation occurring at these active sites. However, although computed enthalpies of activation are in good agreement with experiment, thermochemical approximations that better account for anharmonic contributions are required to accurately determine entropy differences between these pathways.The hessian-free finite differences Davidson approach can also be extended to the space of molecular orbital coefficients. 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 variation in the orbitals, by calculating the lowest eigenvalue of the electronic hessian. Analytical expressions for the electronic hessian are unavailable for some advanced post-Hartree–Fock (HF) wave function methods and even certain Kohn–Sham (KS) density functionals. Calculating full finite difference hessians for even small molecules can prove intractable in such cases. To address this issue, the hessian-vector product within the Davidson scheme is formulated as a finite difference of the electronic gradient with respect to orbital perturbations. As a model application, following the lowest eigenvalue of the orbital-optimized 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. A single stable solution can be recovered by using the regularized 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

Analysis of Preferred Mechanisms of CO Oxidation with Atomically Dispersed Pt1/TiO2 Using the Energetic Span Model

This work examines the mechanisms of low-temperature CO oxidation with atomically dispersed Pt on rutile TiO2 (110) using density functional theory and the energetic span model (ESM). Of the 13 distinct pathways spanning Eley-Rideal (ER), termolecular ER (TER), Langmuir-Hinshelwood(LH), Mars-Van Krevelen (MvK) mechanisms as well as their combinations, TER with CO-assisted CO2 desorption yields the highest turnover frequency (TOF). However, this pathway is ruled out because Pt is dynamically unstable in an intermediate state in the TER cycle, determined in a prior ab initio molecular dynamics study by our group. We instead find that a previously neglected pathway – the ER mechanism – is the most plausible CO oxidation route based on agreement with experimental TOFs and turnover-determining states. The preferred mechanism is sensitive to temperature, with LH becoming more favorable than ER and TER above 750 K. By comparing TOFs for Pt1/TiO2 with prior mechanistic studies of various oxide-supported atomically dispersed catalysts in the literature, we also attempt to identify the most viable metal and support materials for CO oxidation

Linear Free Energy Relationships for Transition Metal Complex Chemistry: Opportunity or Pipe Dream?

We propose a computational framework for developing Taft-like linear free energy relationships to characterize steric effects on the catalytic activity of transition metal complexes. The framework uses the activation strain model and energy decomposition analysis to isolate electronic and geometric effects, and identifies structural descriptors to construct the linear relationship. We demonstrate proof-of-principle for CH activation with enzyme-inspired [Cu2O2]2+ complexes, each coordinated to two identical bidentate diamine N-donors. Electronic effects are largely similar across the chosen systems and geometric effects – quantified by strain energies – are accurately captured by a linear combination of two structural descriptors. A powerful linear free energy relationship emerges that is both transferable to asymmetrically substituted complexes and independent of choice of theory. We outline steps for expanding this approach to create a generalizable Taft framework for inorganic catalyst design

Computational Strategies to Probe CH Activation in Dioxo-Dicopper Complexes

Our work addresses the long-standing question of the preferred mechanism of CH activation in dioxodicopper complexes, with implications for [Cu2O2]2+ -containing enzymes as well as homogeneous and heterogeneous catalysts, which are capable of performing selective oxidation. Using density functional theory (DFT), we show that the two proposed mechanisms, one-step oxo-insertion and two-step radical recombination, have very distinct and measurable responses to changes in the electrophilicity of N-donors in the catalyst. Using energy decomposition analysis, we calculate the electronic interactions that contribute to transition state stabilization, and the effect of N-donors on these interactions. The analysis shows that oxo-insertion, by virtue of possessing a late and charged transition state, is highly sensitive to N-donor electrophilicity and barriers decrease with more electron-withdrawing N-donors. On the other hand, the radical pathway possesses an early transition state and is therefore relatively insensitive to N-donor variations. One possible strategy, going forward, is the design and execution of complementary experiments to deduce the mechanism based on the presence or absence of N-donor dependence. We adopt an alternative approach where DFT results are contrasted with prior experiments via Hammett relationships. The remarkable agreement between experimental and calculated trends for oxo-insertion with imidazole N-donor catalysts presents compelling evidence in favor of the one-step pathway for CH activation