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

Insights into the Kinetics of Cracking and Dehydrogenation Reactions of Light Alkanes in H‑MFI

Monomolecular reactions of alkanes in H-MFI were investigated by means of a dispersion-corrected density functional, ωB97X-D, combined with a hybrid quantum mechanics/molecular mechanics (QM/MM) method applied to a cluster model of the zeolite. The cluster contains 437 tetrahedral (T) atoms, within which a T5 region containing the acid site along with the representative alkane is treated quantum mechanically. The influence of active site location on reaction energetics was examined by studying cracking and dehydrogenation reactions of <i>n</i>-butane at two regions in H-MFI–T12, where the proton is at the intersection of straight and sinusoidal channels, and T10, where the proton is within the sinusoidal channel. Two transition states were observed for cracking: one where the proton attacks the C–C bond and another where it attacks a C atom. Dehydrogenation proceeds via a concerted mechanism, where the transition state indicates simultaneous H₂ formation and proton migration to the framework. Intrinsic activation energies can be determined accurately with this method, although heats of adsorption were found to be higher in magnitude relative to experiments, which is most likely mainly caused by the MM dispersion parameters for the zeolite framework atoms. Intrinsic activation energies calculated for reactions at the T10 site are higher than those at T12 owing to differences in interaction of the substrate with the acid site as well as with the zeolite framework, demonstrating that Brønsted acid sites in H-MFI are not equivalent for these reactions. Apparent activation energies, determined from calculated intrinsic activation energies and experimentally measured heats of adsorption taken from the literature, are in excellent agreement with experimental results

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