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Quantum Computing for Energy-Related Applications

Growing interest in quantum computing and simulations have created opportunities for its deployment to improve processes pertaining to energy production, distribution, and consumption. While quantum computing is considered as a paradigm shift in our basic understanding of physical computation, effective implementation of quantum computing in energy applications also depends on progress and development in the dimensions of both quantum computing hardware and quantum computing algorithms. To fully address the status and future challenges of quantum information science (QIS) applied within the energy sector, in this presentation, we firstly summarize recent advancements on the applications of quantum computing to energy infrastructure and materials, complex energy system processes, advanced manufacturing, and energy system security. Then, we will demonstrate the results of quantum computing both on a simulator and a quantum device accessing from OLCF. Our first example is to use the variational quantum eigensolver (VQE) with a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LixHyq molecules (q=-1, 0, +1). The obtained results showed that the quantum computing VQE-UCCSD is comparable to classical CCSD for small systems like LiH with respect to full configuration interaction (FCI). Targeting on CO2 capture application, our second example is to use VQE to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3 to form H2NCOOH. This research showcases quantum computing applications in the study of CO2 capture reactions.

Duan, Yuhua↗

Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)

A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simulating Effective QED on Quantum Computers

In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T -gates needed to perform such simulations on a 3 D lattice of n s sites scales at worst as O ( n s 3 / ϵ ) 1 + o ( 1 ) in the thermodynamic limit for position basis simulations and O ( n s 4 + 2 / 3 / ϵ ) 1 + o ( 1 ) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O ~ ( n s 2 + 2 / 3 / ϵ ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O ~ ( n s 5 + 2 / 3 / ϵ ) . We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 10 13 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

CI-MBPT and Intensity-Based Lifetime Calculations for Th II

Lifetime calculations of Th II J = 1.5 and 2.5 odd states are performed with configuration–interaction many-body perturbation theory (CI-MBPT). For many J = 2.5 states, lifetimes are quite accurate, but two pairs of J = 2.5 odd states and many groups of J = 1.5 states are strongly mixed, making theoretical predictions unreliable. To solve this problem, a method based on intensities is used. To relate experimental intensities to lifetimes, two parameters, one an overall coefficient of proportionality for transition rates and one temperature of the Boltzmann distribution of populations, are introduced and fitted to minimize the deviation between theoretical and intensity-derived lifetimes. For strongly mixed groups of states, the averaged lifetimes obtained from averaged transition rates were used instead of individual lifetimes in the fit. Close agreement is obtained. Then intensity branching ratios are used to extract individual lifetimes for the strongly mixed states. The resulting lifetimes are compared to available directly measured lifetimes and reasonable agreement is found, considering limited accuracy of intensity measurements. The method of intensity-based lifetime calculations with fit to theoretical lifetimes is quite general and can be applied to many complex atoms where strong mixing between multiple states exists.

74 ATOMIC AND MOLECULAR PHYSICS↗

Photodissociation of CS from Excited Rovibrational Levels

Accurate photodissociation cross sections have been computed for transitions from the X 1 Σ+ ground electronic state of CS to six low-lying excited electronic states. New $ab$ initio potential curves and transition dipole moment functions have been obtained for these computations using the multi-reference configuration interaction approach with the Davidson correction (MRCI+Q) and aug-cc-pV6Z basis sets. State-resolved cross sections have been computed for transitions from nearly the full range of rovibrational levels of the X 1 Σ+ state and for photon wavelengths ranging from 500 Å to threshold. Destruction of CS via predissociation in highly excited electronic states originating from the rovibrational ground state is found to be unimportant. Photodissociation cross sections are presented for temperatures in the range between 1000 and 10,000 K, where a Boltzmann distribution of initial rovibrational levels is assumed. Applications of the current computations to various astrophysical environments are briefly discussed focusing on photodissociation rates due to the standard interstellar and blackbody radiation fields.

79 ASTRONOMY AND ASTROPHYSICS↗

Dicarbon Formation in Collisions of Two Carbon Atoms

Abstract Radiative association cross sections and rates are computed, using a quantum approach, for the formation of C 2 molecules (dicarbon) during the collision of two ground-state C( 3 P ) atoms. We find that transitions originating in the C 1 Π g , d 3 Π g , and 1 5 Π u states are the main contributors to the process. The results are compared and contrasted with previous results obtained from a semiclassical approximation. New ab initio potential curves and transition dipole moment functions have been obtained for the present work using the multi-reference configuration interaction approach with the Davidson correction (MRCI+Q) and aug-cc-pCV5Z basis sets, substantially increasing the available molecular data on dicarbon. Applications of the current computations to various astrophysical environments and laboratory studies are briefly discussed, focusing on these rates.

79 ASTRONOMY AND ASTROPHYSICS↗

Microscopic Derivation of Transition-state Theory for Complex Quantum Systems

The decay of quantum complex systems through a potential barrier is often described with transition-state theory, also known as RRKM theory in chemistry. Here we derive the basic formula for transition-state theory based on a generic Hamiltonian as might be constructed in a configuration-interaction basis. Two reservoirs of random Hamiltonians from Gaussian orthogonal ensembles are coupled to intermediate states representing the transition states at a barrier. Under the condition that the decay of the reservoirs to open channels is large, an analytic formula for reaction rates is derived. Here, the transition states act as independent Breit–Wigner resonances which contribute additively to the total transition probability, as is well known for electronic conductance through resonant tunneling states. It is also found that the transition probability is independent of the decay properties of the states in the second reservoir over a wide range of decay widths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electronic wave functions for atoms. I.

Atomic wave functions determination by configuration interaction method, constructing Slater type orbitals into orthogonal set of smaller dimensions

Bunge, C. F.↗

Zeeman effect of As II.

Spectrograms of As electrodeless-discharge tubes operated in a field of 24,025 G have given Zeeman patterns for 232 As II spectral lines from 2361 to 10,556 A and yielded 80 Lande g factors, of which more than half are new. There is agreement between these and the g values calculated by least-squares fitting for single configurations or for multiconfigurations, where configuration interaction is noticeable. All of the measured g values as well as the energy levels are used in the fitting process.

Li, H.↗

Electron impact excitation and assignment of the low-lying electronic states of CO2

Electron scattering spectra of CO2 are reported in the 7 to 10 eV energy-loss range, at energies of 0.2, 0.35, 0.6, 0.7, and 7.0 eV above threshold, and at a scattering angle of 90 deg. Several new distinct overlapping continua with weak, diffuse bands superimposed are observed to lie in this energy-loss range. The experimental spectra are discussed in the light of recent ab initio configuration-interaction calculations of the vertical transition energies of CO2. The experimental spectra are shown to be consistent with the excitation states of CO2.

Hall, R. I.↗

Spin contamination in unrestricted Hartree-Fock calculations.

Several pi-electron doublets are treated by both the unrestricted Hartree-Fock method and the restricted approximation of Longuet-Higgins and Pople. For two of the molecules, which contain oxygen heteroatoms, serious spin contamination occurs in the UHF wavefunctions, and this negates the usefulness of the single annihilation procedure that is often used for spin-density calculations. The restricted approximation provides a convenient alternative, especially because configuration interaction is easily taken into account.

Schug, J. C.↗

Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/

The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.

Phillips, D. H.↗