A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

Bac, Selin; Quiton, Stephen Jon; Kron, Kareesa J.; Chae, Jeongmin; Mitra, Urbashi; Sharada, Shaama Mallikarjun

doi:10.1063/5.0091155

Cited by 10 publications

(18 citation statements)

References 78 publications

(71 reference statements)

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“…The ground truth matrices for all reactions have 24 columns, chosen such that the eigenvalue spectra and resulting observables vary smoothly along the MEP. 29 Along similar lines to our previous HVMC study, we calculate zero-point energies (ZPEs), vibrational free energies at high temperature (G vib , 1000K), and the position and value of adiabatic ground state potential barrier (V AG ) and free energy barrier (ΔG CVT ). Furthermore, tunneling can significantly accelerate reaction rates especially at low temperatures and when the reaction step involves displacement of a low-weight atom, such as hydrogen (reaction classes 2, 3, and 4 above).…”

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 88%

“…The reactions chosen for benchmarking PVMC performance are largely identical to those employed in our prior HVMC studies. 26,29 The reactions span gas phase, enzymatic, and catalytic chemistry and are selected based on availability of prior VTST studies, the importance of quantum and variational effects in kinetics, and the need to assess algorithm scaling and robustness. 48 This is by far the most complex reaction we could identify with the most number of internal degrees of freedom changing significantly over the course of the reaction step.…”

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 99%

“…10 However, neglecting curvature eliminates the necessity of Hessian eigenvector information which makes ZCT more appropriate for this work, which focuses exclusively on recovery of eigenvalues. Similar to previous work, 29 we adapt the procedure described in the Pilgrim software to calculate κ ZCT . 12 Therefore, we calculate quantities that constitute the rate coefficient expression but not the variational rate coefficient itself.…”

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 99%

“…As black-box approaches to determine variational contributions from these modes are few and far between (e.g., MSTor for torsional anharmonicity), 61,62 we simplify our analysis of PVMC performance by replacing any frequency ≤100 cm −1 with 100 cm −1 and treating it as a vibrational mode for calculating free energies. 29 While there are multiple ways to measure "complexity" of the X true matrices constituting the reactions examined in this work, we calculate rank, R, based on singular values (σ). Although one can count the number of singular values that are nonzero, a more practical strategy is to establish a threshold below which a singular value does not contribute to the rank.…”

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 99%

“…26 We demonstrate that both quantum (zero-curvature tunneling at 300 K, zero-point energy) and variational (vibrational free energy) effects are accurately predicted for a wide range of reaction types with very low sampling required for S N 2 reactions (4.5−20% of all elements), low to moderate sampling needs for hydrogen atom transfer reactions (10−35%), and sampling in excess of 50% for only the most complex reaction step with an Ir catalyst that involves simultaneous transfer of one hydride and two protons (60%). 29 Therefore, MC methods offer promising means to accelerate rate coefficient calculations using variational theories. However, our HVMC approach has one critical shortcoming.…”

Section: Introductionmentioning

confidence: 99%

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Toward Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

Quiton

Chae

Bac

et al. 2022

J. Chem. Theory Comput.

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This paper describes the development and testing of a polynomial variety-based matrix completion (PVMC) algorithm. Our goal is to reduce computational effort associated with reaction rate coefficient calculations using variational transition state theory with multidimensional tunneling (VTST-MT). The algorithm recovers eigenvalues of quantum mechanical Hessians constituting the minimum energy path (MEP) of a reaction using only a small sample of the information, by leveraging underlying properties of these eigenvalues. In addition to the low-rank property that constitutes the basis for most matrix completion (MC) algorithms, this work introduces a polynomial constraint in the objective function. This enables us to sample matrix columns unlike most conventional MC methods that can only sample elements, which makes PVMC readily compatible with quantum chemistry calculations as sampling a single column requires one Hessian calculation. For various types of reactionsS N 2, hydrogen atom transfer, metal–ligand cooperative catalysis, and enzyme chemistrywe demonstrate that PVMC on average requires only six to seven Hessian calculations to accurately predict both quantum and variational effects.

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Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 88%

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 99%

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 99%

Section: Polynomial Variety-based Matrix Completionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Toward Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

Quiton

Chae

Bac

et al. 2022

J. Chem. Theory Comput.

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Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

et al. 2022

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In this paper, we provide an overview of state-of-the-art techniques that are being developed for efficient calculation of second and higher nuclear derivatives of quantum mechanical (QM) energy. Calculations of nuclear Hessians and anharmonic terms incur high costs and memory and scale poorly with system size. Three emerging classes of methodsmachine learning (ML), automatic differentiation (AD), and matrix completion (MC)have demonstrated promise in overcoming these challenges. We illustrate studies that employ unsupervised ML methods to reduce the need for multiple Hessian calculations in dynamics simulations and those that utilize supervised ML to construct approximate potential energy surfaces and estimate Hessians and anharmonic terms at reduced cost. By extension, if electronic structure operations could be written in a manner similar to functions underlying ML methods, rapid differentiation or AD routines can be employed to inexpensively calculate higher arbitrary-order derivatives. While ML approaches are typically black-box, we describe methods such as compressed sensing (CS) and MC, which explicitly leverage problem-specific mathematical properties of higher derivatives such as sparsity and low-rank, to complete higher derivative information using only a small, incomplete sample. The three classes of methods facilitate reliable predictions of observables ranging from infrared spectra to thermal conductivity and constitute a promising way forward in accurately capturing otherwise intractable higher-order responses of QM energy to nuclear perturbations.

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A Simple Evaluation of Adiabatic Proton Tunneling across the Electrified Double Layer

Askari,

Huckabee,

Gauthier

2024

J. Phys. Chem. C

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Coupled proton−electron transfer (CPET) reactions are likely to play a pivotal role in the global transition to a sustainable energy future. However, our atomic scale understanding of this class of reactions remains limited, despite recent advances in density functional theory (DFT) simulations. The ultimate goal of such simulations is to intelligently predict rates of CPET reactions at the electrified double layer, leading to the design of new catalysts. These studies often utilize harmonic transition state theory (HTST), which assumes that quantum tunneling through energy barriers is negligible. In this study, we present a simple evaluation of the contribution of quantum tunneling in the adiabatic limit of CPET reactions. We investigate the effect of different potential profiles on tunneling probabilities and compare these profiles with calculated CPET minimum energy paths (MEPs). We find that the calculated CPET MEPs can be significantly stiffer than the commonly used Eckart profile, and study the effect of changing barrier height and width on overall zero curvature tunneling correction factors. Depending on the reaction of interest and the bulk pH, proton tunneling can be a non-negligible phenomenon for CPET reactions at the electrified double layer. In particular, reactions involving large barriers are predicted to have significant contributions from nonclassical tunneling, possibly explaining observed kinetic isotope effects for the hydrogen evolution reaction (HER) in alkaline media. Our model choices are significantly simplified−for example, neglecting the effects of reaction coordinate curvature and vibronic coupling−suggesting that our predicted tunneling contributions may be underestimated. However, our findings provide a simple way to evaluate whether tunneling is relevant for a particular CPET reaction of interest.

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A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

Cited by 10 publications

References 78 publications

Toward Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

Toward Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

A Simple Evaluation of Adiabatic Proton Tunneling across the Electrified Double Layer

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