Quantum Simulation of Molecular Response Properties in the NISQ Era.

Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.

Partitioning Quantum Chemistry Simulations with Clifford Circuits.

Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near term. In this work, we investigate the limits of their classical and near-classical treatment while staying within the framework of quantum circuits and the variational quantum eigensolver. To this end, we consider naive and physically motivated, classically efficient product ansatz for the parametrized wavefunction adapting the separable-pair ansatz form. We combine it with post-treatment to account for interactions between subsystems originating from this ansatz. The classical treatment is given by another quantum circuit that has support between the enforced subsystems and is folded into the Hamiltonian. To avoid an exponential increase in the number of Hamiltonian terms, the entangling operations are constructed from purely Clifford or near-Clifford circuits. While Clifford circuits can be simulated efficiently classically, they are not universal. In order to account for missing expressibility, near-Clifford circuits with only few, selected non-Clifford gates are employed. The exact circuit structure to achieve this objective is molecule-dependent and is constructed using simulated annealing and genetic algorithms. We demonstrate our approach on a set of molecules of interest and investigate the extent of our methodology's reach.

On the existence of CO32- microsolvated clusters: a theoretical study.

Microsolvated clusters of multiply charged anions play a crucial role in atmospheric chemistry and some of them were previously registered experimentally. At the same time, there are no experimental observations of [CO3·(H2O)n]2-. The reasons for this may be related to the thermodynamical or kinetical instability of microsolvated CO32- toward autoionization or autoprotonation processes. In this study we theoretically investigate the potential stability of the [CO3·(H2O)n]2- microsolvated clusters from both perspectives - thermodynamic and kinetic - and we claim they are stable toward autoionization and kinetically semi-stable toward autoprotonation. In addition, the behaviour of CO32- anions in bulk water solvent was analysed to highlight important precautions for synthetic purposes.

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer.

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.

Catalytic Stereoconvergent Synthesis of Homochiral ß-CF3, ß-SCF3, and ß-OCF3 Benzylic Alcohols.

We describe an efficient catalytic strategy for enantio- and diastereoselective synthesis of homochiral ß-CF3, ß-SCF3, and ß-OCF3 benzylic alcohols. The approach is based on dynamic kinetic resolution (DKR) with Noyori-Ikariya asymmetric transfer hydrogenation leading to simultaneous construction of two contiguous stereogenic centers with up to 99.9% ee, up to 99.9:0.1 dr, and up to 99% isolated yield. The origin of the stereoselectivity and racemization mechanism of DKR is rationalized by density functional theory calculations. Applicability of the previously inaccessible chiral fluorinated alcohols obtained by this method in two directions is further demonstrated: As building blocks for pharmaceuticals, illustrated by the synthesis of heat shock protein 90 inhibitor with in vitro anticancer activity, and in particular, needle-shaped crystals of representative stereopure products that exhibit either elastic or plastic flexibility, which opens the door to functional materials based on mechanically responsive chiral molecular crystals.

Molecular dynamics on quantum annealers.

In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.

Markovnikov alcohols via epoxide hydroboration by molecular alkali metal catalysts.

Synthesis of branched "Markovnikov" alcohols is crucial to various chemical industries. The catalytic reduction of substituted epoxides under mild conditions is a highly attractive method for preparing such alcohols. Classical methods based on heterogeneous or homogeneous transition metal-catalyzed hydrogenation, hydroboration, or hydrosilylation usually suffer from poor selectivity, reverse regioselectivity, limited functional group compatibility, high cost, and/or low availability of the catalysts. Here we report the discovery of highly regioselective hydroboration of nonsymmetrical epoxides catalyzed by ligated archetypal reductants in organic chemistry ‒ alkali metal triethylborohydrides. The chemoselectivity and turnover efficiencies of the present catalytic approach are excellent. Thus, terminal and internal epoxides with ene, yne, aryl, and halo groups were selectively and quantitatively reduced under a substrate-to-catalyst ratio (S/C) of up to 1000. Mechanistic investigations point to a mechanism reminiscent of frustrated Lewis pair action on substrates in which a nucleophile and Lewis acid act cooperatively on the substrate.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits.

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Toward a QUBO-Based Density Matrix Electronic Structure Method.

Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate" the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree-Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave's new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. We also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

Performance Analysis of CP2K Code for Ab Initio Molecular Dynamics on CPUs and GPUs.

Using a realistic molecular catalyst system, we conduct scaling studies of ab initio molecular dynamics simulations using the popular CP2K code on both Intel Xeon CPU and NVIDIA V100 GPU architectures. Additional performance improvements were gained by finding more optimal process placement and affinity settings. Statistical methods were employed to understand performance changes in spite of the variability in runtime for each molecular dynamics timestep. Ideal conditions for CPU runs were found when running at least four MPI ranks per node, bound evenly across each socket. This study also showed that fully utilizing processing cores, with one OpenMP thread per core, performed better than when reserving cores for the system. The CPU-only simulations scaled at 70% or more of the ideal scaling up to 10 compute nodes, after which the returns began to diminish more quickly. Simulations on a single 40-core node with two NVIDIA V100 GPUs for acceleration achieved over 3.7× speedup compared to the fastest single 36-core node CPU-only version. These same GPU runs showed a 13% speedup over the fastest time achieved across five CPU-only nodes.

Sampling electronic structure quadratic unconstrained binary optimization problems (QUBOs) with Ocean and Mukai solvers.

The most advanced D-Wave Advantage quantum annealer has 5000+ qubits, however, every qubit is connected to a small number of neighbors. As such, implementation of a fully-connected graph results in an order of magnitude reduction in qubit count. To compensate for the reduced number of qubits, one has to rely on special heuristic software such as qbsolv, the purpose of which is to decompose a large quadratic unconstrained binary optimization (QUBO) problem into smaller pieces that fit onto a quantum annealer. In this work, we compare the performance of the open-source qbsolv which is a part of the D-Wave Ocean tools and a new Mukai QUBO solver from Quantum Computing Inc. (QCI). The comparison is done for solving the electronic structure problem and is implemented in a classical mode (Tabu search techniques). The Quantum Annealer Eigensolver is used to map the electronic structure eigenvalue-eigenvector equation to a QUBO problem, solvable on a D-Wave annealer. We find that the Mukai QUBO solver outperforms the Ocean qbsolv with one to two orders of magnitude more accurate energies for all calculations done in the present work, both the ground and excited state calculations. This work stimulates the further development of software to assist in the utilization of modern quantum annealers.

Pressurized Formic Acid Dehydrogenation: An Entropic Spring Replaces Hydrogen Compression Cost.

Formic acid is unique among liquid organic hydrogen carriers (LOHCs), because its dehydrogenation is highly entropically driven. This enables the evolution of high-pressure hydrogen at mild temperatures that is difficult to achieve with other LOHCs, conceptually by releasing the "spring" of energy stored entropically in the liquid carrier. Applications calling for hydrogen-on-demand, such as vehicle filling, require pressurized H2. Hydrogen compression dominates the cost for such applications, yet there are very few reports of selective, catalytic dehydrogenation of formic acid at elevated pressure. Herein, we show that homogenous catalysts with various ligand frameworks, including Noyori-type tridentate (PNP, SNS, SNP, SNPO), bidentate chelates (pyridyl)NHC, (pyridyl)phosphine, (pyridyl)sulfonamide, and their metallic precursors, are suitable catalysts for the dehydrogenation of neat formic acid under self-pressurizing conditions. Quite surprisingly, we discovered that their structural differences can be related to performance differences in their respective structural families, with some tolerant or intolerant of pressure and others that are significantly advantaged by pressurized conditions. We further find important roles for H2 and CO in catalyst activation and speciation. In fact, for certain systems, CO behaves as a healing reagent when trapped in a pressurizing reactor system, enabling extended life from systems that would be otherwise deactivated.

Computing molecular excited states on a D-Wave quantum annealer.

The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree-Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm-Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example [Formula: see text] molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for [Formula: see text] as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.

Mechanism of Potassium tert-Butoxide-Catalyzed Ketones Hydrogenation in the Solution Phase.

The mechanism of ketones homogeneous hydrogenation with t-BuOK in tert-butanol is currently portrayed as the one proceeding via a six-membered [2 + 2 + 2] cyclic transition state involving the H2 molecule, the base, and a ketone. However, the concerted nature of the reaction is inconsistent with a number of experimental observations. Here we reanalyze available experimental data and revise the mechanism of this paradigmatic reaction based on the static and dynamic density functional theory (DFT) calculations in solution phase. In contrast to the gas-phase profile where the overall reaction occurs in two elementary steps, there are three consecutive steps in solution: cleavage of the H-H bond in basic tert-butanol to afford potassium hydride, addition of potassium hydride across the C═O bond of a ketone through the rate-determining transition state, and rapid product formation through K/H exchange. Potassium hydride is therefore an important intermediate of the catalytic process. The free energy profile for the prophetic ester homogeneous hydrogenation with t-BuOK in tert-butanol is also computed herein. The reaction seems to be kinetically possible, but slightly harsher conditions need to be applied, consistent with rate-determining nature of the potassium hydride addition.

Reduction of the molecular hamiltonian matrix using quantum community detection.

Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree-Fock methods as future advances in quantum hardware become available.

Electronic structure with direct diagonalization on a D-wave quantum annealer.

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

Redox-Noninnocent Ligand-Supported Vanadium Catalysts for the Chemoselective Reduction of C═X (X = O, N) Functionalities.

Catalysis is the second largest application for V after its use as an additive to improve steel production. Molecular complexes of vanadium(V) are particularly useful and efficient catalysts for oxidation processes; however, their ability to catalyze reductive transformations has yet to be fully explored. Here we report the first examples of polar organic functionality reduction mediated by V. Open-shell VIII complexes that feature a π-radical monoanionic 2,2':6',2″-terpyridine ligand (Rtpy•)- functionalized at the 4'-position (R = (CH3)3SiCH2, C6H5) catalyze mild and chemoselective hydroboration and hydrosilylation of functionalized ketones, aldehydes, imines, esters, and carboxamides with turnover numbers (TONs) of up to ∼1000 and turnover frequencies (TOFs) of up to ∼500 h-1. Computational evaluation of the precatalyst synthesis and activation has revealed underappreciated complexity associated with the redox-active tpy chelate.

Cleavage of N-H Bond of Ammonia via Metal-Ligand Cooperation Enables Rational Design of a Conceptually New Noyori-Ikariya Catalyst.

The asymmetric transfer hydrogenation (ATH) of ketones/imines with Noyori-Ikariya catalyst represents an important reaction in both academia and fine chemical industry. The method allows for the preparation of chiral secondary alcohols/amines with very good to excellent optical purities. Remarkably, the same chiral Noyori-Ikariya complex is also a precatalyst for a wide range of other chemo- and stereoselective reductive and oxidative transformations. Among them are enantioselective sulfonamidation of acrylates (intramolecular aza-Michael reaction) and carboxylation of indoles with CO2. Development of these catalytic reactions has been inspired by the realized cleavage of the N-H bond of sulfonamides and indoles by the 16e- amido derivative of the 18e- precatalyst via metal-ligand cooperation (MLC). This paper summarizes our efforts to investigate N-H bond cleavage of gaseous ammonia in solution via MLC and reports the serendipitous discovery of a new class of chiral tridentate κ3[ N, N', N″] Ru and Ir metallacycles, derivatives of the famous M-FsDPEN catalysts (M = Ru, Ir). The protonation of these metallacycles by strong acids containing weakly coordinating (chiral) anions generates ionic complexes, which were identified as conceptually novel Noyori-Ikariya precatalysts. For example, the ATH of aromatic ketones with some of these complexes proceeds with up to 99% ee.