Challenges in the Use of Quantum Computing Hardware-Efficient Ansätze in Electronic Structure Theory.

Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls connected with the use of hardware-efficient Ansätze in variational quantum simulations of electronic structure. We illustrate that hardware-efficient Ansätze may break Hamiltonian symmetries and yield nondifferentiable potential energy curves, in addition to the well-known difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansätze versus unitary coupled cluster and full configuration interaction, and of second- and first-quantization strategies to encode Fermionic degrees of freedom to qubits. Our analysis should be useful in understanding potential limitations and in identifying possible areas of improvement in hardware-efficient Ansätze.

Quantum chemistry simulation of ground- and excited-state properties of the sulfonium cation on a superconducting quantum processor.

The computational description of correlated electronic structure, and particularly of excited states of many-electron systems, is an anticipated application for quantum devices. An important ramification is to determine the dominant molecular fragmentation pathways in photo-dissociation experiments of light-sensitive compounds, like sulfonium-based photo-acid generators used in photolithography. Here we simulate the static and dynamical electronic structure of the H3S+ molecule, taken as a minimal model of a triply-bonded sulfur cation, on a superconducting quantum processor of the IBM Falcon architecture. To this end, we generalize a qubit reduction technique termed entanglement forging or EF [A. Eddins et al., Phys. Rev. X Quantum, 2022, 3, 010309], currently restricted to the evaluation of ground-state energies, to the treatment of molecular properties. While in a conventional quantum simulation a qubit represents a spin-orbital, within EF a qubit represents a spatial orbital, reducing the number of required qubits by half. We combine the generalized EF with quantum subspace expansion [W. Colless et al., Phys. Rev. X, 2018, 8, 011021], a technique used to project the time-independent Schrodinger equation for ground- and excited-states in a subspace. To enable experimental demonstration of this algorithmic workflow, we deploy a sequence of error-mitigation techniques. We compute dipole structure factors and partial atomic charges along ground- and excited-state potential energy curves, revealing the occurrence of homo- and heterolytic fragmentation. This study is an important step towards the computational description of photo-dissociation on near-term quantum devices, as it can be generalized to other photodissociation processes and naturally extended in different ways to achieve more realistic simulations.

N-Electron Valence Perturbation Theory with Reference Wave Functions from Quantum Computing: Application to the Relative Stability of Hydroxide Anion and Hydroxyl Radical.

Quantum simulations of the hydroxide anion and hydroxyl radical are reported, employing variational quantum algorithms for near-term quantum devices. The energy of each species is calculated along the dissociation curve, to obtain information about the stability of the molecular species being investigated. It is shown that simulations restricted to valence spaces incorrectly predict the hydroxyl radical to be more stable than the hydroxide anion. Inclusion of dynamical electron correlation from nonvalence orbitals is demonstrated, through the integration of the variational quantum eigensolver and quantum subspace expansion methods in the workflow of N-electron valence perturbation theory, and shown to correctly predict the hydroxide anion to be more stable than the hydroxyl radical, provided that basis sets with diffuse orbitals are also employed. Finally, we calculate the electron affinity of the hydroxyl radical using an aug-cc-pVQZ basis on IBM's quantum devices.

Quantum computation of dominant products in lithium-sulfur batteries.

Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.

Computational Investigations of the Lithium Superoxide Dimer Rearrangement on Noisy Quantum Devices.

Quantum chemistry studies of biradical systems are challenging due to the required multiconfigurational nature of the wavefunction. In this work, Variational Quantum Eigensolver (VQE) is used to compute the energy profile for the lithium superoxide dimer rearrangement, involving biradical species, on quantum simulators and devices. Considering that current quantum devices can only handle limited number of qubits, we present guidelines for selecting an appropriate active space to perform computations on chemical systems that require many qubits. We show that with VQE performed with a quantum simulator reproduces results obtained with full-configuration interaction (Full CI) for the chosen active space. However, results deviate from exact values by about 39 mHa for calculations on a quantum device. This deviation can be improved to about 4 mHa using the readout mitigation approach and can be further improved to 2 mHa, approaching chemical accuracy, using the state tomography technique to purify the calculated quantum state.

Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer.

Quantum simulations of electronic structure with a transformed Hamiltonian that includes some electron correlation effects are demonstrated. The transcorrelated Hamiltonian used in this work is efficiently constructed classically, at polynomial cost, by an approximate similarity transformation with an explicitly correlated two-body unitary operator. This Hamiltonian is Hermitian, includes no more than two-particle interactions, and is free of electron-electron singularities. We investigate the effect of such a transformed Hamiltonian on the accuracy and computational cost of quantum simulations by focusing on a widely used solver for the Schrödinger equation, namely the variational quantum eigensolver method, based on the unitary coupled cluster with singles and doubles (q-UCCSD) Ansatz. Nevertheless, the formalism presented here translates straightforwardly to other quantum algorithms for chemistry. Our results demonstrate that a transcorrelated Hamiltonian, paired with extremely compact bases, produces explicitly correlated energies comparable to those from much larger bases. For the chemical species studied here, explicitly correlated energies based on an underlying 6-31G basis had cc-pVTZ quality. The use of the very compact transcorrelated Hamiltonian reduces the number of CNOT gates required to achieve cc-pVTZ quality by up to two orders of magnitude, and the number of qubits by a factor of three.

Reducing Qubit Requirements for Quantum Simulations Using Molecular Point Group Symmetries.

Simulating molecules is believed to be one of the early stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence; therefore, optimizing resources to execute quantum algorithms is crucial. In this work, we develop the second quantization representation of spatial symmetries, which are then transformed to their qubit operator representation. These qubit operator representations are used to reduce the number of qubits required for simulating molecules. We present our results for various molecules and elucidate a formal connection of this work with a previous technique that analyzed generic Z2 Pauli symmetries.

Influence of Solvent on the Drug-Loading Process of Amphiphilic Nanogel Star Polymers.

We present an all-atom molecular dynamics study of the effect of a range of organic solvents (dichloromethane, diethyl ether, toluene, methanol, dimethyl sulfoxide, and tetrahydrofuran) on the conformations of a nanogel star polymeric nanoparticle with solvophobic and solvophilic structural elements. These nanoparticles are of particular interest for drug delivery applications. As drug loading generally takes place in an organic solvent, this work serves to provide insight into the factors controlling the early steps of that process. Our work suggests that nanoparticle conformational structure is highly sensitive to the choice of solvent, providing avenues for further study as well as predictions for both computational and experimental explorations of the drug-loading process. Our findings suggest that when used in the drug-loading process, dichloromethane, tetrahydrofuran, and toluene allow for a more extensive and increased drug-loading into the interior of nanogel star polymers of the composition studied here. In contrast, methanol is more likely to support shallow or surface loading and, consequently, faster drug release rates. Finally, diethyl ether should not work in a formulation process since none of the regions of the nanogel star polymer appear to be sufficiently solvated by it.

Identifying Molecular Structural Aromaticity for Hydrocarbon Classification.

Determination of aromaticity in hydrocarbons may be as simple as determining the average bond length for the molecule of interest. This would greatly assist in classifying the nature of hydrocarbon chemistry, especially for large molecules such as polycyclic aromatic hydrocarbons (PAHs) where today's aromatic classification methods are prohibitively expensive. The average C-C bond lengths for a test set of known aromatic, antiaromatic, and aliphatic cyclic hydrocarbons are computed here, and they show strong delineating patterns for the structural discernment of these aromaticity classifications. Aromatic molecules have average C-C bond lengths of 1.41 Å or less with the largest molecules, PAHs, having the longest average C-C bond lengths; aliphatic species have such lengths of 1.50 Å or more; and antiaromatic species fall between the two. Consequently, a first-order guess as to the aromaticity of a system may simply arise from its geometry. Although this prediction will likely have exceptions, such simple screening can easily classify most cases, and more advanced techniques can be brought to bear on the cases that lie in the boundaries. Benchmarks for hydrocarbons are provided here, but other classes of molecular structural aromaticity likely will have to be defined on an ad hoc basis.

Building a More Predictive Protein Force Field: A Systematic and Reproducible Route to AMBER-FB15.

The increasing availability of high-quality experimental data and first-principles calculations creates opportunities for developing more accurate empirical force fields for simulation of proteins. We developed the AMBER-FB15 protein force field by building a high-quality quantum chemical data set consisting of comprehensive potential energy scans and employing the ForceBalance software package for parameter optimization. The optimized potential surface allows for more significant thermodynamic fluctuations away from local minima. In validation studies where simulation results are compared to experimental measurements, AMBER-FB15 in combination with the updated TIP3P-FB water model predicts equilibrium properties with equivalent accuracy, and temperature dependent properties with significantly improved accuracy, in comparison with published models. We also discuss the effect of changing the protein force field and water model on the simulation results.

Effect of Hydrophobic Core Topology and Composition on the Structure and Kinetics of Star Polymers: A Molecular Dynamics Study.

We present a molecular dynamics study of the effect of core chemistry on star polymer structural and kinetic properties. This work serves to validate the choice of a model adamantane core used in previous simulations to represent larger star polymeric systems in an aqueous environment, as well as to explore how the choice of size and core chemistry using a dendrimer or nanogel core may affect these polymeric nanoparticle systems, particularly with respect to thermosensitivity and solvation properties that are relevant for applications in drug loading and delivery.

Simulation and Experiments To Identify Factors Allowing Synthetic Control of Structural Features of Polymeric Nanoparticles.

To develop a detailed picture of the microscopic structure of gelcore star polymers and to elucidate parameters of the synthetic process that might be exploited to control this structure, simulations of their synthesis were performed that were based on a particular synthetic approach. A range of results was observed from gelation at high reactant concentrations to the formation of various sizes and compositions of star polymers. Contrary to the prevailing experimental viewpoint, the simulations always suggest the production of a broad distribution of star polymer sizes. However, the GPC traces computed from simulation results are in good qualitative agreement with experiment. Topologically, the gelcore star polymers produced by simulation are not compact but, rather, sparse blobs loosely connected by filaments of linker when modeled in a good solvent. This is reflected in scaling relationships that relate polymer size (e.g., radius of gyration) and degree of polymerization. The arm-core composition is observed to be stoichiometric, strongly reflecting relative reactant concentrations during the synthesis. Reactions within star polymers that result in greater intramolecular cross-linking compete with those between star polymers that result in the production of larger star polymers from the joining of smaller ones. The balance in this competition can be controlled through the overall reactant concentration to limit and control resulting star polymer size. Therefore, the mean size, as well as the mean number of arms, can be controlled during synthesis by careful tuning of the overall ratio of the arm and linker reactant concentrations and the total reactant concentration.

Dominant Decomposition Pathways for Ethereal Solvents in Li-O2 Batteries.

The promise of high specific energies for Li-O2 batteries has driven research toward the development of new compatible materials for this emerging technology. Obtained energies, however, fall short of the theoretical values partly due to parasitic chemistries arising from organic solvent decomposition during battery cycling. Electrolyte solvent and salt decomposition have also been identified as limiting factors for rechargeability of the battery. Although lithium trifluorosulfonamide (LiTFSI) dissolved in 1,2-dimethoxyethane (DME) has been shown to be a promising solvent/electrolyte candidate for Li-O2 batteries, significant challenges remain, namely minimizing decomposition of both the solvent and electrolyte salt during battery cycling. Herein, we provide spectroscopic labeling studies to identify the source of H2 at high potentials during charge and propose a decomposition pathway for DME to lithium formate and acetate products at low potentials. NMR studies were preformed to show that DME decomposes to lithium formate and acetate in aqueous Li2O2, products which are also observed after D2O workups on cathodes after discharge. Finally, we use density functional theory (DFT) to elucidate a mechanistic pathway for DME decomposition that is based on known organic oxidation processes.

N-Heterocyclic Carbene-Catalyzed Ring Opening Polymerization of ε-Caprolactone with and without Alcohol Initiators: Insights from Theory and Experiment.

Computational investigations with density functional theory (DFT) have been performed on the N-heterocyclic carbene (NHC) catalyzed ring-opening polymerization of ε-caprolactone in the presence and in the absence of a methanol initiator. Much like the zwitterionic ring opening (ZROP) of δ-valerolactone which was previously reported, calculations predict that the mechanism of the ZROP of caprolactone that occurs without an alcohol present involves a high-barrier step involving ring opening of the zwitterionic tetrahedral intermediate formed after the initial nucleophilic attack of NHC on caprolactone. However, the operative mechanism by which caprolactone is polymerized in the presence of an alcohol initiator does not involve the analogous mechanism involving initial nucleophilic attack by the organocatalytic NHC. Instead, the NHC activates the alcohol through hydrogen bonding and promotes nucleophilic attack and the subsequent ring-opening steps that occur during polymerization. The largest free energy barrier for the hydrogen-bonding mechanism in alcohol involves nucleophilic attack, while that for both ZROP processes involves ring opening of the initially formed zwitterionic tetrahedral intermediate. The DFT calculations predict that the rate of polymerization in the presence of alcohol is faster than the reaction performed without an alcohol initiator; this prediction has been validated by experimental kinetic studies.

Role of hydrophilicity and length of diblock arms for determining star polymer physical properties.

We present a molecular simulation study of star polymers consisting of 16 diblock copolymer arms bound to a small adamantane core by varying both arm length and the outer hydrophilic block when attached to the same hydrophobic block of poly-δ-valerolactone. Here we consider two biocompatible star polymers in which the hydrophilic block is composed of polyethylene glycol (PEG) or polymethyloxazoline (POXA) in addition to a polycarbonate-based polymer with a pendant hydrophilic group (PC1). We find that the different hydrophilic blocks of the star polymers show qualitatively different trends in their interactions with aqueous solvent, orientational time correlation functions, and orientational correlation between pairs of monomers of their polymeric arms in solution, in which we find that the PEG polymers are more thermosensitive compared with the POXA and PC1 star polymers over the physiological temperature range we have investigated.

ff14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins.

We present the ff14ipq force field, implementing the previously published IPolQ charge set for simulations of complete proteins. Minor modifications to the charge derivation scheme and van der Waals interactions between polar atoms are introduced. Torsion parameters are developed through a generational learning approach, based on gas-phase MP2/cc-pVTZ single-point energies computed of structures optimized by the force field itself rather than the quantum benchmark. In this manner, we sacrifice information about the true quantum minima in order to ensure that the force field maintains optimal agreement with the MP2/cc-pVTZ benchmark for the ensembles it will actually produce in simulations. A means of making the gas-phase torsion parameters compatible with solution-phase IPolQ charges is presented. The ff14ipq model is an alternative to ff99SB and other Amber force fields for protein simulations in programs that accommodate pair-specific Lennard-Jones combining rules. The force field gives strong performance on α-helical and ß-sheet oligopeptides as well as globular proteins over microsecond time scale simulations, although it has not yet been tested in conjunction with lipid and nucleic acid models. We show how our choices in parameter development influence the resulting force field and how other choices that may have appeared reasonable would actually have led to poorer results. The tools we developed may also aid in the development of future fixed-charge and even polarizable biomolecular force fields.

Experimental and computational studies on the mechanism of zwitterionic ring-opening polymerization of δ-valerolactone with N-heterocyclic carbenes.

Experimental and computational investigations of the zwitterionic ring-opening polymerization (ZROP) of δ-valerolactone (VL) catalyzed by the N-heterocyclic carbenes (NHC) 1,3-diisopropyl-4,5-dimethyl-imidazol-2-ylidene (1) and 1,3,4,5-tetramethyl-imidazol-2-ylidene (2) were carried out. The ZROP of δ-valerolactone generates cyclic poly(valerolactone)s whose molecular weights are higher than predicted from [VL]0/[NHC]0. Kinetic studies reveal the rate of polymerization is first order in [VL] and first order in [NHC]. Density functional theory (DFT) calculations were carried out to elucidate the key steps involved in the ring-opening of δ-valerolactone and its subsequent oligomerization. These studies have established that the initial steps of the mechanism involve nucleophilic attack of the NHC on δ-valerolactone to form a zwitterionic tetrahedral intermediate. DFT calculations indicate that the highest activation barrier of the entire mechanism is associated with the ring-opening of the tetrahedral intermediate formed from the NHC and δ-valerolactone, a result consistent with inefficient initiation to generate reactive zwitterions. The large barrier in this step is due to the fact that ring-opening requires a partial positive charge to develop next to the directly attached NHC moiety which already bears a delocalized positive charge.

Organic acid-catalyzed polyurethane formation via a dual-activated mechanism: unexpected preference of N-activation over O-activation of isocyanates.

A systematic study of acid organocatalysts for the polyaddition of poly(ethylene glycol) to hexamethylene diisocyanate in solution has been performed. Among organic acids evaluated, sulfonic acids were found the most effective for urethane formations even when compared with conventional tin-based catalysts (dibutyltin dilaurate) or 1,8-diazabicyclo[5.4.0]undec-7-ene. In comparison, phosphonic and carboxylic acids showed considerably lower catalytic activities. Furthermore, sulfonic acids gave polyurethanes with higher molecular weights than was observed using traditional catalyst systems. Molecular modeling was conducted to provide mechanistic insight and supported a dual activation mechanism, whereby ternary adducts form in the presence of acid and engender both electrophilic isocyanate activation and nucleophilic alcohol activation through hydrogen bonding. Such a mechanism suggests catalytic activity is a function of not only acid strength but also inherent conjugate base electron density.

Computational investigations on base-catalyzed diaryl ether formation.

We report investigations with the dispersion-corrected B3LYP density functional method on mechanisms and energetics for reactions of group I metal phenoxides with halobenzenes as models for polyether formation. Calculated barriers for ether formation from para-substituted fluorobenzenes are well correlated with the electron-donating or -withdrawing properties of the substituent at the para position. These trends have also been explained with the distortion/interaction energy theory model which show that the major component of the activation energy is the energy required to distort the arylfluoride reactant into the geometry that it adopts at the transition state. Resonance-stabilized aryl anion intermediates (Meisenheimer complexes) are predicted to be energetically disfavored in reactions involving fluorobenzenes with a single electron-withdrawing group at the para position of the arene, but are formed when the fluorobenzenes are very electron-deficient, or when chelating substituents at the ortho position of the aryl ring are capable of binding with the metal cation, or both. Our results suggest that the presence of the metal cation does not increase the rate of reaction, but plays an important role in these reactions by binding the fluoride or nitrite leaving group and facilitating displacement. We have found that the barrier to reaction decreases as the size of the metal cation increases among a series of group I metal phenoxides due to the fact that the phenoxide becomes less distorted in the transition state as the size of the metal increases.

Derivation of fixed partial charges for amino acids accommodating a specific water model and implicit polarization.

We have developed the IPolQ method for fitting nonpolarizable point charges to implicitly represent the energy of polarization for systems in pure water. The method involves iterative cycles of molecular dynamics simulations to estimate the water charge density around the solute of interest, followed by quantum mechanical calculations at the MP2/cc-pV(T+d)Z level to determine updated solute charges. Lennard-Jones parameters are updated starting from the Amber FF99SB nonbonded parameter set to accommodate the new charge model, guided by the comparisons to experimental hydration free energies (HFEs) of neutral amino acid side chain analogs and assumptions about the computed HFEs for charged side chains. These Lennard-Jones parameter adjustments for side-chain analogs are assumed to be transferable to amino acids generally, and new charges for all standard amino acids are then derived in the presence of water modeled by TIP4P-Ew. Overall, the new charges depict substantially more polarized amino acids, particularly in the backbone moieties, than previous Amber charge sets. Efforts to complete a new force field with appropriate torsion parameters for this charge model are underway. The IPolQ method is general and applicable to arbitrary solutes.