Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry.

The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.

Heteroatom-vacancy centres in molecular nanodiamonds: a computational study of organic molecules possessing triplet ground states through σ-overlap.

Small molecules possessing a triplet ground state are fundamentally intriguing but also in high demand for applications such as quantum sensing and quantum computing. Such molecules are rare, and most examples involve extended π-systems. Topology and shape of the spin density will be very different for molecules where the triplet state arises from σ-overlap. Drawing inspiration from NV- (anionic nitrogen-vacancy) centres in a diamond crystal, which possess triplet ground states that are robust due to the distortion-preventing crystal lattice, we investigate hetero-atom substituted diamondoids (molecular nanodiamonds) as molecular mimics for NV- centres. It is found that even in these small systems, distortions that stabilize singlet states are energetically costly, and the triplet states are more stable than the singlets. The stabilization of the triplet over the singlet is 13, 16, and 18 kcal mol-1, in anionic C3v-C33H36N- and in the charge-neutral molecules C3v-C33H36O and C3v-C33H36S, respectively, using CAM-B3LYP-D3(BJ)/Def2-QZVPP. Comparable numbers are obtained with other density functional theory (DFT) methods, including double-hybrids. Wavefunction-based approaches on the other hand disagree in their predictions: While the MP2 method applied with the DLPNO approximation predicts a preference for the singlet, density matrix renormalization group (DMRG) calculations qualitatively agree with DFT in their prediction of a triplet ground state, although by a small margin, for C3v-C33H36N- and C3v-C33H36O, but not for C3v-C33H36S. Weighing the evidence, we conclude, with reasonable confidence for C3v-C33H36N- and C3v-C33H36O and lesser confidence for C3v-C33H36S, that the ground state for the molecular nanodiamonds studied is a triplet state.

Hydrogen Atom Transfer (HAT) Processes Promoted by the Quinolinimide-N-oxyl Radical. A Kinetic and Theoretical Study.

A kinetic study of the hydrogen atom transfer (HAT) reactions from a series of organic compounds to the quinolinimide-N-oxyl radical (QINO) was performed in CH3CN. The HAT rate constants are significantly higher than those observed with the phthalimide-N-oxyl radical (PINO) as a result of enthalpic and polar effects due to the presence of the N-heteroaromatic ring in QINO. The relevance of polar effects is supported by theoretical calculations conducted for the reactions of the two N-oxyl radicals with toluene, which indicate that the HAT process is characterized by a significant degree of charge transfer permitted by the π-stacking that occurs between the toluene and the N-oxyl aromatic rings in the transition state structures. An increase in the HAT reactivity of QINO was observed in the presence of 0.15 M HClO4 and 0.15 M Mg(ClO4)2 due to the protonation or complexation with the Lewis acid of the pyridine nitrogen that leads to a further decrease in the electron density in the N-oxyl radical. These results fully support the use of N-hydroxyquinolinimide as a convenient substitute for N-hydroxyphthalimide in the catalytic aerobic oxidations of aliphatic hydrocarbons characterized by relatively high C-H bond dissociation energies.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials.

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials.

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

BH9, a New Comprehensive Benchmark Data Set for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials.

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. To assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as a benchmark for density functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness errors. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date and a useful tool for the development and assessment of computational methods.

BSE49, a diverse, high-quality benchmark dataset of separation energies of chemical bonds.

We present an extensive and diverse dataset of bond separation energies associated with the homolytic cleavage of covalently bonded molecules (A-B) into their corresponding radical fragments (A. and B.). Our dataset contains two different classifications of model structures referred to as "Existing" (molecules with associated experimental data) and "Hypothetical" (molecules with no associated experimental data). In total, the dataset consists of 4502 datapoints (1969 datapoints from the Existing and 2533 datapoints from the Hypothetical classes). The dataset covers 49 unique X-Y type single bonds (except H-H, H-F, and H-Cl), where X and Y are H, B, C, N, O, F, Si, P, S, and Cl atoms. All the reference data was calculated at the (RO)CBS-QB3 level of theory. The reference bond separation energies are non-relativistic ground-state energy differences and contain no zero-point energy corrections. This new dataset of bond separation energies (BSE49) is presented as a high-quality reference dataset for assessing and developing computational chemistry methods.

PEPCONF, a diverse data set of peptide conformational energies.

We present an extensive and diverse database of peptide conformational energies. Our database contains five different classes of model geometries: dipeptides, tripeptides, and disulfide-bridged, bioactive, and cyclic peptides. In total, the database consists of 3775 conformational energy data points and 4530 conformer geometries. All the reference energies have been calculated at the LC-ωPBE-XDM/aug-cc-pVTZ level of theory, which is shown to yield conformational energies with an accuracy in the order of tenths of a kcal/mol when compared to complete-basis-set coupled-cluster reference data. The peptide conformational data set (PEPCONF) is presented as a high-quality reference set for the development and benchmarking of molecular-mechanics and semi-empirical electronic structure methods, which are the most commonly used techniques in the modeling of medium to large proteins.

Atom-Centered Potentials with Dispersion-Corrected Minimal-Basis-Set Hartree-Fock: An Efficient and Accurate Computational Approach for Large Molecular Systems.

We present a computational methodology based on atom-centered potentials (ACPs) for the efficient and accurate structural modeling of large molecular systems. ACPs are atom-centered one-electron potentials that have the same functional form as effective-core potentials. In recent works, we showed that ACPs can be used to produce a correction to the ground-state wave function and electronic energy to alleviate shortcomings in the underlying model chemistry. In this work, we present ACPs for H, C, N, and O atoms that are specifically designed to predict accurate non-covalent binding energies and inter- and intramolecular geometries when combined with dispersion-corrected Hartree-Fock (HF-D3) and a minimal basis-set (scaled MINI or MINIs). For example, the combined HF-D3/MINIs-ACP method demonstrates excellent performance, with mean absolute errors of 0.36 and 0.28 kcal/mol for the S22x5 and S66x8 benchmark sets, respectively, relative to highly correlated complete-basis-set data. The application of ACPs results in a significant decrease in error compared to uncorrected HF-D3/MINIs for all benchmark sets examined. In addition, HF-D3/MINIs-ACP, has a cost only slightly higher than a minimal-basis-set HF calculation and can be used with any electronic structure program for molecular quantum chemistry that uses Gaussian basis sets and effective-core potentials.