The electron density: a fidelity witness for quantum computation.

There is currently no combination of quantum hardware and algorithms that can provide an advantage over conventional calculations of molecules or materials. However, if or when such a point is reached, new strategies will be needed to verify predictions made using quantum devices. We propose that the electron density, obtained through experimental or computational means, can serve as a robust benchmark for validating the accuracy of quantum computation of chemistry. An initial exploration into topological features of electron densities, facilitated by quantum computation, is presented here as a proof of concept. Additionally, we examine the effects of constraining and symmetrizing measured one-particle reduced density matrices on noise-driven errors in the electron density distribution. We emphasize the potential benefits and future need for high-quality electron densities derived from diffraction experiments for validating classically intractable quantum computations of materials.

Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry.

Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on current and near-term devices. REM can be applied alongside existing mitigation procedures, while requiring minimal postprocessing and only one or no additional measurements. The approach is agnostic to the underlying quantum mechanical ansatz and is designed for the variational quantum eigensolver. Up to two orders-of-magnitude improvement in the computational accuracy of ground state energies of small molecules (H2, HeH+, and LiH) is demonstrated on superconducting quantum hardware. Simulations of noisy circuits with a depth exceeding 1000 two-qubit gates are used to demonstrate the scalability of the method.

A Density Functional Theory for the Average Electron Energy.

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn-Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations.

Towards a global model of spin-orbit coupling in the halocarbenes.

We report a global analysis of spin-orbit coupling in the mono-halocarbenes, CH(D)X, where X = Cl, Br, and I. These are model systems for examining carbene singlet-triplet energy gaps and spin-orbit coupling. Over the past decade, rich data sets collected using single vibronic level emission spectroscopy and stimulated emission pumping spectroscopy have yielded much information on the ground vibrational level structure and clearly demonstrated the presence of perturbations involving the low-lying triplet state. To model these interactions globally, we compare two approaches. First, we employ a diabatic treatment of the spin-orbit coupling, where the coupling matrix elements are written in terms of a purely electronic spin-orbit matrix element which is independent of nuclear coordinates, and an integral representing the overlap of the singlet and triplet vibrational wavefunctions. In this way, the structures, harmonic frequencies, and normal mode displacements from ab initio calculations were used to calculate the vibrational overlaps of the singlet and triplet state levels, including the full effects of Duschinsky mixing. These calculations have allowed many new assignments to be made, particularly for CHI, and provided spin-orbit coupling parameters and values for the singlet-triplet gaps. In a second approach, we have computed and fit full geometry dependent spin-orbit coupling surfaces and used them to compute matrix elements without the product form approximation. Those matrix elements were used in similar fits varying the anharmonic constants and singlet-triplet gap to reproduce the experimental levels. The derived spin-orbit parameters for carbenes CHX (X = Cl, Br, and I) show an excellent linear correlation with the atomic spin-orbit constant of the corresponding halogen, indicating that the spin-orbit coupling in the carbenes is consistently around 14% of the atomic value.

Communication: An accurate global potential energy surface for the ground electronic state of ozone.

We report a new full-dimensional and global potential energy surface (PES) for the O + O2 → O3 ozone forming reaction based on explicitly correlated multireference configuration interaction (MRCI-F12) data. It extends our previous [R. Dawes, P. Lolur, J. Ma, and H. Guo, J. Chem. Phys. 135, 081102 (2011)] dynamically weighted multistate MRCI calculations of the asymptotic region which showed the widely found submerged reef along the minimum energy path to be the spurious result of an avoided crossing with an excited state. A spin-orbit correction was added and the PES tends asymptotically to the recently developed long-range electrostatic model of Lepers et al. [J. Chem. Phys. 137, 234305 (2012)]. This PES features: (1) excellent equilibrium structural parameters, (2) good agreement with experimental vibrational levels, (3) accurate dissociation energy, and (4) most-notably, a transition region without a spurious reef. The new PES is expected to allow insight into the still unresolved issues surrounding the kinetics, dynamics, and isotope signature of ozone.

Spectroscopy and dynamics of the predissociated, quasi-linear S2 state of chlorocarbene.

In this work, we report on the spectroscopy and dynamics of the quasi-linear S(2) state of chlorocarbene, CHCl, and its deuterated isotopologue using optical-optical double resonance (OODR) spectroscopy through selected rovibronic levels of the S(1) state. This study, which represents the first observation of the S(2) state in CHCl, builds upon our recent examination of the corresponding state in CHF, where pronounced mode specificity was observed in the dynamics, with predissociation rates larger for levels containing bending excitation. In the present work, a total of 14 S(2) state vibrational levels with angular momentum l = 1 were observed for CHCl, and 34 levels for CDCl. The range of l in this case was restricted by the pronounced Renner-Teller effect in the low-lying S(1) levels, which severely reduces the fluorescence lifetime for levels with K(a) > 0. Nonetheless, by exploiting different intermediate S(1) levels, we observed progressions involving all three fundamental vibrations. For levels with long predissociation lifetimes, rotational constants were determined by measuring spectra through different intermediate J levels of the S(1) state. Plots of the predissociation linewidth (lifetime) vs. energy for various S(2) levels show an abrupt onset, which lies near the calculated threshold for elimination to form C((3)P) + HCl on the triplet surface. Our experimental results are compared with a series of high level ab initio calculations, which included the use of a dynamically weighted full-valence CASSCF procedure, focusing maximum weight on the state of interest (the singlet and triplet states were computed separately). This was used as the reference for subsequent Davidson-corrected MRCI(+Q) calculations. These calculations reveal the presence of multiple conical intersections in the singlet manifold.

Communication: highly accurate ozone formation potential and implications for kinetics.

Atmospheric ozone is formed by the O + O(2) exchange reaction followed by collisional stabilization of the O(3)(∗) intermediate. The dynamics of the O + O(2) reaction and to a lesser extent the O(3) stabilization depend sensitively on the underlying potential energy surface, particularly in the asymptotic region. Highly accurate Davidson corrected multi-state multi-reference configuration interaction calculations reported here reveal that the minimal energy path for the formation of O(3) from O + O(2) is a monotonically decaying function of the atom-diatom distance and contains no "reef" feature found in previous ab initio calculations. The absence of a submerged barrier leads to an exchange rate constant with the correct temperature dependence and is in better agreement with experiment, as shown by quantum scattering calculations.