Implementation of the Projective Quantum Eigensolver on a Quantum Computer.

We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

Intruder-free cumulant-truncated driven similarity renormalization group second-order multireference perturbation theory.

Accurate multireference electronic structure calculations are important for constructing potential energy surfaces. Still, even in the case of low-scaling methods, their routine use is limited by the steep growth of the computational and storage costs as the active space grows. This is primarily due to the occurrence of three- and higher-body density matrices or, equivalently, their cumulants. This work examines the effect of various cumulant truncation schemes on the accuracy of the driven similarity renormalization group second-order multireference perturbation theory. We test four different levels of three-body reduced density cumulant truncations that set different classes of cumulant elements to zero. Our test cases include the singlet-triplet gap of CH2, the potential energy curves of the XΣg+1 and AΣu+3 states of N2, and the singlet-triplet splittings of oligoacenes. Our results show that both relative and absolute errors introduced by these cumulant truncations can be as small as 0.5 kcal mol-1 or less. At the same time, the amount of memory required is reduced from O(NA6) to O(NA5), where NA is the number of active orbitals. No additional regularization is needed to prevent the intruder state problem in the cumulant-truncated second-order driven similarity renormalization group multireference perturbation theory methods.

Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs.

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

Cumulants as the variables of density cumulant theory: A path to Hermitian triples.

We study the combination of orbital-optimized density cumulant theory and a new parameterization of reduced density matrices in which the variables are the particle-hole cumulant elements. We call this combination OλDCT. We find that this new Ansatz solves problems identified in the previous unitary coupled cluster Ansatz for density cumulant theory: the theory is now free of near-zero denominators between occupied and virtual blocks, can correctly describe the dissociation of H2, and is rigorously size-extensive. In addition, the new Ansatz has fewer terms than the previous unitary Ansatz, and the optimal orbitals delivered by the exact theory are the natural orbitals. Numerical studies on systems amenable to full configuration interaction show that the amplitudes from the previous ODC-12 method approximate the exact amplitudes predicted by this Ansatz. Studies on equilibrium properties of diatomic molecules show that even with the new Ansatz, it is necessary to include triples to improve the accuracy of the method compared to orbital-optimized linearized coupled cluster doubles. With a simple iterative triples correction, OλDCT outperforms other orbital-optimized methods truncated at comparable levels in the amplitudes, as well as coupled cluster single and doubles with perturbative triples [CCSD(T)]. By adding four more terms to the cumulant parameterization, OλDCT outperforms CCSDT while having the same O(V5O3) scaling.

Assessing the orbital-optimized unitary Ansatz for density cumulant theory.

The previously proposed Ansatz for density cumulant theory that combines orbital-optimization and a parameterization of the 2-electron reduced density matrix cumulant in terms of unitary coupled cluster amplitudes (OUDCT) is carefully examined. Formally, we elucidate the relationship between OUDCT and orbital-optimized unitary coupled cluster theory and show the existence of near-zero denominators in the stationarity conditions for both the exact and some approximate OUDCT methods. We implement methods of the OUDCT Ansatz restricted to double excitations for numerical study, up to the fifth commutator in the Baker-Campbell-Hausdorff expansion. We find that methods derived from the Ansatz beyond the previously known ODC-12 method tend to be less accurate for equilibrium properties and less reliable when attempting to describe H2 dissociation. New developments are needed to formulate more accurate density cumulant theory variants.

Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering.

Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical with equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and the reduced density matrices are entirely combinatorial constructions, where the differences can be associated with changes in the notion of "multiplicative separability" for expectation values of random variables compared to reduced density matrices. We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present a simple proof of the generalized normal ordering formalism to explore the role of reduced density matrix cumulants therein. While the formalism can be used without cumulants, the combinatorial structure of expressing RDMs in terms of cumulants is the same combinatorial structure on cumulants that allows for a simple extended generalized Wick's theorem.

Psi4 1.4: Open-source software for high-throughput quantum chemistry.

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

Sulfurous and sulfonic acids: Predicting the infrared spectrum and setting the surface straight.

Sulfurous acid (H2SO3) is an infamously elusive molecule. Although some theoretical papers have supposed possible roles for it in more complicated systems, it has yet to be experimentally observed. To aid experiment in detecting this molecule, we have examined the H2O + SO2 potential energy surface at the CCSDT(Q)/CBS//CCSD(T)-F12b/cc-pVTZ-F12b level of theory to resolve standing discrepancies in previous reports and predict the gas-phase vibrational spectrum for H2SO3. We find that sulfurous acid has two potentially detectable rotamers, separated by 1.1 kcal mol-1 ΔH0K with a torsional barrier of 1.6 kcal mol-1. The sulfonic acid isomer is only 6.9 kcal mol-1 above the lowest enthalpy sulfurous acid rotamer, but the barrier to form it is 57.2 kcal mol-1. Error in previous reports can be attributed to misidentified stationary points, the use of density functionals that perform poorly for this system, and, most importantly, the basis set sensitivity of sulfur. Using VPT2+K, we determine that the intense S=O stretch fundamental of each species is separated from other intense peaks by at least 25 cm-1, providing a target for identification by infrared spectroscopy.

The non-covalently bound SOH2O system, including an interpretation of the differences between SOH2O and O2H2O.

Despite the interest in sulfur monoxide (SO) among astrochemists, spectroscopists, inorganic chemists, and organic chemists, its interaction with water remains largely unexplored. We report the first high level theoretical geometries for the two minimum energy complexes formed by sulfur monoxide and water, and we report energies using basis sets as large as aug-cc-pV(Q+d)Z and correlation effects through perturbative quadruple excitations. One structure of SOH2O is hydrogen bonded and the other chalcogen bonded. The hydrogen bonded complex has an electronic energy of -2.71 kcal mol-1 and a zero kelvin enthalpy of -1.67 kcal mol-1, while the chalcogen bonded complex has an electronic energy of -2.64 kcal mol-1 and a zero kelvin enthalpy of -2.00 kcal mol-1. We also report the transition state between the two structures, which lies below the SOH2O dissociation limit, with an electronic energy of -1.26 kcal mol-1 and an enthalpy of -0.81 kcal mol-1. These features are much sharper than for the isovalent complex of O2 and H2O, which only possesses one weakly bound minimum, so we further analyze the structures with open-shell SAPT0. We find that the interactions between O2 and H2O are uniformly weak, but the SOH2O complex surface is governed by the superior polarity and polarizability of SO, as well as the diffuse electron density provided by sulfur's extra valence shell.

Re-examining ammonia addition to the Criegee intermediate: converging to chemical accuracy.

Stabilized Criegee intermediates (SCI) are formed during the ozonolysis of unsaturated hydrocarbons and have been implicated in the formation of hydroxyl radicals and aerosols. Previous theoretical research [S. Jørgenson and A. Gross, J. Phys. Chem. A, 2009, 113, 10284-10290] computed the rate constants for addition of ammonia to simple SCIs, but reported a wide distribution of quantum chemical energies, depending on the basis set used. We report optimized geometries for these reactions at the CCSD(T)/ANO2 and CCSD(T)/ANO1 levels, and CCSD(T)/CBS energies with perturbative quadruples corrections. We find the inclusion of perturbative quadruples corrections elevates the energy of the transition state by 0.76-0.88 kcal mol-1 relative to the reactants, which qualitatively changes the reaction surface. We calculate rate constants and find that Jørgenson and Gross previously overestimated the rate constants for ammonia addition to SCIs, but were within an order of magnitude. This supports the previous conclusion of Vereecken et al. [L. Vereecken, H. Harder and A. Novelli, Phys. Chem. Chem. Phys., 2012, 14, 14682-14695] that ammonia addition to SCIs is a negligible sink of Criegee intermediates.