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DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2025

Enhanced Collisional Losses from a Magnetic Mirror Using the Lenard-Bernstein Collision Operator

Collisions are crucial in governing particle and energy transport in plasmas confined in a magnetic mirror trap. Modern gyrokinetic codes model transport in magnetic mirrors, but some utilize approximate model collision operators. This study focuses on a Pastukhov-style method of images calculation of particle and energy confinement times using a Lenard-Bernstein model collision operator. Prior work on parallel particle and energy balances used a different Fokker-Planck plasma collision operator. The method must be extended in non-trivial ways to study the Lenard-Bernstein operator. To assess the effectiveness of our approach, we compare our results with a modern finite element solver. Our findings reveal that the particle confinement time scales like a exp( a 2 ) using the Lenard-Bernstein operator, in contrast to the more accurate scaling that the Coulomb collision operator would yield a 2 exp( a 2 ), where a 2 is approximately proportional to the ambipolar potential. We propose that codes solving for collisional losses in magnetic mirrors utilizing the Lenard-Bernstein or Dougherty collision operator scale their collision frequency of any electrostatically confined species. This study illuminates the collision operator’s intricate role in the Pastukhov-style method of images calculation of collisional confinement.

fusion plasma↗
DOE OSTI2020

Emerging Potassium Metal Anodes: Perspectives on Control of the Electrochemical Interfaces

Potassium metal acts as the anode in emerging potassium metal batteries (KMBs). It further serves as the counter-electrode for potassium ion battery (KIB) half-cells, with its reliable performance being critical for assessing the working electrode material. This first-of-its-kind critical review focuses on the dual challenge of controlling the potassium metal-substrate and the potassium metal-electrolyte interface so as to prevent dendrites. The discussion begins with a comparison of the physical and chemical properties of K metal anodes versus the much oft studied Li and Na metal anodes. Based on established descriptions for root causes of dendrites, the problem should be less severe for K than for Li or Na, while in fact the opposite is observed. The key reason that the K metal surface rapidly becomes dendritic in common electrolytes is its unstable solid electrolyte interphase (SEI). An unstable SEI layer is defined as being non self-passivating. No SEI is perfectly stable during cycling, and all SEI structures are heterogenous both vertically and horizontally relative to the electrolyte interface. The difference between a "stable" and an "unstable" SEI may be viewed as the relative degree to which during cycling it thickens and becomes further heterogeneous. The unstable SEI on K metal leads to a number of interrelated problems, such as low cycling Coulombic efficiency (CE), a severe impedance rise, large overpotentials, and possibly electrical shorting; all of which have been reported to occur as early as in the first ten plating/stripping cycles. Many of the traditional "interface fixes" employed for Li and Na metal anodes, such as various artificial SEIs, surface membranes, barrier layers, the secondary separators, etc. have not been attempted or optimized for the case of K. This is an important area for further exploration, with an understanding that success may come harder than with Li due to K-based SEI reactivity with both ether and ester solvents. The second critical problem with K metal anodes is that they do not thermally or electrochemically wet a standard (untreated) Cu foil current collector. Published experimental and modeling research directly highlights the weak bonding between the K atoms and a Cu surface. Existing surface treatment approaches that achieve improved K wetting are discussed, along with the general design rules for future studies. Also discussed are geometry-based methods to tune nucleation, as well dual approaches where nucleation and SEI structure are tuned through complementary schemes to achieve extended half-cell and full battery stability. We hypothesize that K metal never achieves a planar wetting morphology even at cycle one making the dendrites "baked-in". We propose that classical thin films growth models, Frank van der Merwe (F-M), Volmer Weber (V-W), and Stranski-Krastanov (S-K) can be employed to describe early stage plating behavior. It is demonstrated that island-like V-W growth is the applicable description for the natural plating behavior of K on pristine Cu. Moving forward, there are three inter-related thrusts to be pursued: First, K salt - based electrolyte formulations have to mature and become further tailored to handle the increased reactivity of a metal rather than an ion anode. Second, the K-based SEI structure needs to be further understood and ultimately tuned to be less reactive. Third, the energetics of the K metal - current collector interface must be controlled to promote planar wetting/dewetting throughout cycling.

25 ENERGY STORAGE↗
DOE OSTI2021

Control of Peptide Amphiphile Supramolecular Nanostructures by Isosteric Replacements

Supramolecular nanostructures with tunable properties can have applications in medicine, pharmacy, and biotechnology. In this work, we show that the self-assembly behavior of peptide amphiphiles (PAs) can be effectively tuned by replacing the carboxylic acids exposed to the aqueous media with isosteres, functionalities that share key physical or chemical properties with another chemical group. Transmission electron microscopy, atomic force microscopy, and small-angle X-ray scattering studies indicated that the nanostructure’s morphologies are responsive to the ionization states of the side chains, which are related to their pK a values. Circular dichroism studies revealed the effect of the isosteres on the internal arrangement of the nanostructures. The interactions between diverse surfaces and the nanostructures and the effect of salt concentration and temperature were assessed to further understand the properties of these self-assembled systems. These results indicate that isosteric replacements allow the pH control of supramolecular morphology by manipulating the pK a of the charged groups located on the nanostructure’s surface. Theoretical studies were performed to understand the morphological transitions that the nanostructures underwent in response to pH changes, suggesting that the transitions result from alterations in the Coulomb forces between PA molecules. Furthermore, this work provides a strategy for designing biomaterials that can maintain or change behaviors based on the pH differences found within cells and tissues.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Material Design Strategy for Halide Solid Electrolytes Li 3 MX 6 (X = Cl, Br, and I) for All-Solid-State High-Voltage Li-Ion Batteries

Although several solid electrolyte (SE) candidates have been explored, achieving the necessary combination of performance, stability, and processability has been challenging. Recently, several lithium ternary halides have attracted increasing attention for SEs because of their favorable combination of high ionic conductivity and wide electrochemical window. This study aims to provide a material design strategy for lithium halides Li 3 MX 6 (X = Cl, Br, and I) for high-voltage all-solid-state Li-ion batteries, achieved by the systematic investigation of crystal structures, phase and electrochemical stabilities, electronic and mechanical properties, and ionic conductivities. Calculation results reveal that the electronegativity difference between M and X affects structural properties and stabilities. Weak Coulomb interactions in Li 3 MX 6 result in the preference of the monoclinic phase, and the oxidation potential and chemical stability against the cathode materials of Li 3 MX 6 increase for relatively small X. Chlorides exhibit the highest oxidation potential (~4.3 V) among Li 3 MX 6 , suggesting that chlorides are appropriate SEs for high-voltage cathodes. The band gap and elastic moduli increase for relatively small X, suggesting the relatively low electronic conductivity and elastic deformability of chlorides. Chlorides with transition metals typically exhibit trigonal phases, a wider electrochemical stability window, a larger band gap, and higher elastic moduli compared to other types of halides. Additionally, chloride Li 3 MCl 6 is expected to have relatively high ionic conductivities with the aliovalent substitution of M 3+ to Zr 4+ and the anion mixing of Cl with Br. The findings of this study will provide fundamental guidelines for the development of lithium halide SEs for high-voltage all-solid-state Li-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2021

Li + Diffusion in Amorphous and Crystalline Al 2 O 3 for Battery Electrode Coatings

Al 2 O 3 is often applied protectively to lithium-ion battery anode and cathode materials to inhibit surface degradation, suppress dendrite formation, and relieve mechanical stresses. Given the very high intrinsic band gap and diffusion barrier of the material, the mechanism that allows Li diffusion through these coatings is not well understood, and widely varying laboratory results indicate that there may be dependencies on morphology and stoichiometry. Using nudged elastic band calculations and ab initio molecular dynamics, we perform a systematic investigation across Al 2 O 3 structures, both crystalline and amorphous, and at various concentrations of Li + to uncover the optimal parameters for maximally diffusive coatings. We find a correlation between the low proximity of Li + to Al 3+ and the low Li + migration barrier. Although barriers are the lowest in the highly diffusive one-dimensional channels of crystalline θ-Al 2 O 3 , the system is structurally delicate and subject to detrimental distortion as the Li + content is increased. The α-Al 2 O 3 lattice is, conversely, highly stable against distortion at all Li + concentrations but disadvantageous for Li + migration. In amorphous systems, unscreened Li + –Li + Coulomb repulsion and pre-emptive occupation of “trapping sites” combine to lower the energy barriers as a function of increasing concentration. One of our most important findings is that Al-deficient materials can sharply increase Li + movement, and we predict that an amorphous material with a combination of high Li + concentration and Al deficiency would enable highly Li + -conductive protective coatings for electrodes.

25 ENERGY STORAGE↗
DOE OSTI2022

Excitonic Effects in X-ray Absorption Spectra of Fluoride Salts and Their Surfaces

Given their natural abundance and thermodynamic stability, fluoride salts may appear as evolving components of electrochemical interfaces in Li-ion batteries and emergent multivalent ion cells. This is due to the practice of employing electrolytes with fluorine-containing species (salt, solvent, or additives) that electrochemically decompose and deposit on the electrodes. Operando X-ray absorption spectroscopy (XAS) can probe the electrode–electrolyte interface with a single-digit nanometer depth resolution and offers a wealth of insights into the evolution and Coulombic efficiency or degradation of prototype cells, provided that the spectra can be reliably interpreted in terms of local oxidation state, atomic coordination, and electronic structure about the excited atoms. Here we explore fluorine K-edge XAS of mono- (Li, Na, and K) and di-valent (Mg, Ca, and Zn) fluoride salts from a theoretical standpoint and discover a surprising level of detailed electronic structure information about these materials despite the relatively predictable oxidation state and ionicity of the fluoride anion and the metal cation. Utilizing a recently developed many-body approach based on the ΔSCF method, we calculate the XAS using density functional theory and experimental spectral profiles are well reproduced despite some experimental discrepancies in energy alignment within the literature, which we can correct for in our simulations. We outline a general methodology to explain shifts in the main XAS peak energies in terms of a simple exciton model and explain line-shape differences resulting from the mixing of core-excited states with metal d character (for K and Ca specifically). Given ultimate applications to evolving interfaces, some understanding of the role of surfaces and their terminations in defining new spectral features is provided to indicate the sensitivity of such measurements to changes in interfacial chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Resonant X-ray Diffraction Reveals the Location of Counterions in Doped Organic Mixed Ionic Conductors

Organic mixed ionic–electronic conductors (OMIECs) have the potential to enable diverse new technologies, ranging from novel in situ biosensors to flexible energy storage devices and neuromorphic computing platforms. However, their complex behavior in functional films involving electrolyte-induced swelling, ion ingress, and electrochemical doping inhibits rational material design. Of critical importance is an understanding of the specific location of the ions in the volumetrically doped material, yet this information is not readily available. Here, in this report, we present the use of grazing- incidence resonant X-ray diffraction (RXRD, also known as anomalous diffraction) at S and Cl K-edges to determine the structure of a doped, prototypical, semicrystalline polymer OMIEC based on oligo(ethylene glycol) substitution of regioregular polythiophene. The RXRD measurement provides two key insights. Quantitative analysis of the RXRD allows the determination of the position of the ion relative to the polymer backbone in the crystalline regions. We find that the anion is relatively distant from the backbone, nearer to the lamella mid-plane naively in conflict with expected Coulombic attraction between the ion and the doped polymer polaron. Comparison of RXRD to Cl – fluorescence (total Cl – ) allows determination of the relative order of doping between the crystalline and amorphous regions. We find preferential doping of the crystalline regions. Both insights, the preferential doping of crystals at low potential and the specific location of the counterion with respect to the polymer backbone, are critical to developing a microscopic understanding of transport in OMIECs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Semiconducting Zn x Mo 3 S 13 -GO Chalcocarbogel: A High-Capacity and Stable Sulfur-Equivalent Conversion-Based Electrode for Lithium-Ion Batteries

Lithium–sulfur batteries with a sulfur electrode offer a theoretical capacity of ∼1672 mAh g –1 , but rapid capacity loss mainly constrains their practical application. This work introduces a semiconducting and amorphous Zn x Mo 3 S 13 -GO (x = 0.5) chalcocarbogel sulfur-equivalent electrode with superior capacity and stability for lithium-ion batteries (LIBs). The Zn x Mo 3 S 13 -GO is synthesized in solution under ambient conditions, and its local structure contains S–S, M-Q (M = Mo, Zn; Q = S, O), C–S, and Mo–Mo bonding motifs with Mo coordination environment closely related to Mo 3 S 13 anions, as determined by X-ray photoelectron spectroscopy, synchrotron X-ray scattering, X-ray absorption spectroscopy, and ab initio molecular dynamics simulations. The Li/Zn x Mo 3 S 13 -GO cell offers an initial discharge capacity of 1019 mAh g –1 at a rate of C/3. After the activation cycles, the Li/Zn x Mo 3 S 13 -GO cell demonstrates good cycling stability, retaining a discharge capacity of 519.4 mAh g –1 after 250 cycles with ∼99.98% Coulombic efficiency and excellent rate capabilities. Moreover, it provides an initial discharge capacity of ∼574 mAh g –1 and maintains a retention capacity of 279 mAh g –1 at 1C after 625 cycles. The Lewis acidic Zn 2+ ion enhances the Lewis basic polysulfide anchoring ability and reduces the dissolution of polysulfides produced during the redox process through Zn–S covalent interaction, while the semiconducting and amorphous structure of the chalcocarbogel increases the electrical and ionic conductivity. Furthermore, this work highlights chalcocarbogels’ potential for developing high-capacity and stable electrodes for LIBs.

25 ENERGY STORAGE↗
DOE OSTI2025

On the Structural Origin of Fast Li-Ion Cycling in Tetragonal Bronze-Type Nb 8 W 9 O 47

Bronze and bronze-derived, mixed metal oxides are materials of growing interest for lithium-ion battery anodes due to their high-rate capabilities and the potential for high energy densities via multielectron redox. We report on the synthesis and electrochemical properties of the tetragonal tungsten bronzetype phase Nb 8 W 9 O 47 and our investigation into the structural evolution of this phase upon lithium (de)intercalation, with particular attention to how it relates to the fast-cycling capabilities. Electrochemical cycling shows Nb 8 W 9 O 47 can achieve greater than one Li + per transition metal at rates of C/2 or slower and maintains a capacity equivalent to 0.65 Li + per transition metal at a rate of 20C. Sequential Rietveld analysis of operando X-ray diffraction data reveals anisotropic changes to the unit cell parameters during discharge, accompanied by an off-centering of the transition metals within their octahedral environments. While higher capacities can be accessed below 1.2 V, cells discharged to 1.0 V exhibit a significant expansion of the unit cell volume and reduced Coulombic efficiencies. This report suggests that rigid crystal structures incapable of undergoing polyhedral rotational deformations can instead exploit displacive distortions of the transition metal redox center to enable fast Li-ion cycling with minimal atomic rearrangements.

25 ENERGY STORAGE↗
DOE OSTI2025

Low-Temperature Processing of Pyrolysis Bio-Oil for Sustainable Biographite Production

Catalytic graphitization of pyrolysis bio-oil with iron (Fe) can produce an anode material for lithium-ion batteries (LIBs) at a moderate temperature. The key challenge to scaling up the process is foaming, which occurs due to the oxidation of Fe by the organic acids present in bio-oil. This study explored five different pathways to control foaming in bio-oil upon Fe addition, including (i) defoamers use, (ii) use of iron oxide (Fe2O3) as graphitization catalyst, (iii) pH adjustment of bio-oil, (iv) bio-oil coking (300-500 degrees C), and (v) low-temperature pretreatment of bio-oil (150-200 degrees C). The low-temperature pretreatment successfully avoided foaming by removing the volatile acids in bio-oil. The bio-oil was solidified and powdered for even mixing with the Fe catalyst. The biographite catalytically prepared at 1500 degrees C following this pathway demonstrated nearly theoretical specific gravimetric capacity (~370 mAh/g), high initial Coulombic efficiency (90.03%), and minimal capacity fading after 50 cycles in LIB half-cells. The low-temperature pretreatment pathway also addressed the viscosity, swelling, and aging issues associated with bio-oil processing and will make scale-up endeavors more attainable.

09 BIOMASS FUELS↗
DOE OSTI2025

Interactions between Per- and Polyfluoroalkyl Substances (PFAS) at the Water–Air Interface

Per- and polyfluoroalkyl substances (PFAS)--so-called “forever chemicals”--contaminate the drinking water of about 100 million people in the U.S. alone and are inefficiently removed by standard treatment techniques. A key property of these compounds that underlies their fate and transport and the efficacy of several promising remediation approaches is that they accumulate at the water−air interface. This phenomenon remains incompletely understood, particularly under conditions relevant to natural and treatment systems where water−air interfaces often carry significant loads of other organic contaminants or natural organic matter. To understand the impact of organic loading on PFAS adsorption, we carried out molecular dynamics simulations of PFAS at varying interfacial densities. We find that adsorbed PFAS form strong mutual interactions (attraction between perfluoroalkyl chains and electrostatic interactions among charged head groups) that give rise to ordered interfacial coatings. Furthermore, these interactions often involve near-cancellation of hydrophobic attraction and Coulomb repulsion. Our findings explain an apparent paradox whereby PFAS adsorption isotherms often suggest minimal mutual interactions while simultaneously displaying a high sensitivity to the composition and density of interfacial coatings. Consideration of the compounds present with PFAS at the interface has the potential to allow for more accurate predictions of fate and transport and the design of more efficient remediation approaches.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Dicationic fac -Re(bpy)(CO) 3 Cl for CO 2 Electroreduction at a Reduced Overpotential

Here, a dicationic Re bipyridine-type complex, fac-Re(6,6'-(2-((trimethylammonio)-methyl)phenyl)-2,2'-bipyridine)(CO) 3 Cl hexafluorophosphate (1 2+ ), has been synthesized and its electrochemical behavior under Ar and CO 2 has been investigated. The presence of pendent tetra-alkylammonium cations induces an anodic shift in the electrocatalytic potential for CO 2 reduction relative to structurally similar model complexes. The electrochemical mechanisms in anhydrous CH 3 CN and in the presence of weak acids (water or trifluoroethanol) have been analyzed using cyclic voltammetry assisted by infrared spectroelectrochemistry and theoretical calculations. The dication enables catalysis at a diminished potential through coulombic stabilization of the doubly reduced pentacoordinate species, its CO 2 adduct, the hydroxide anion, and the conjugate base formed during acid-assisted C-OH bond cleavage of the metallocarboxylic acid to the metallocarbonyl and H 2 O. The major reduction product is CO, but in the presence of trifluoroethanol, formate is also produced with 14% Faradaic efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Quantum Embedding Theory for Strongly Correlated States in Materials

Quantum embedding theories are promising approaches to investigate strongly correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We present a detailed derivation of a quantum embedding theory recently introduced, which is based on the definition of effective Hamiltonians. The effect of the environment on a chosen active space is accounted for through screened Coulomb interactions evaluated using density functional theory. Importantly, the random phase approximation is not required, and the evaluation of virtual electronic orbitals is circumvented with algorithms previously developed in the context of calculations based on many-body perturbation theory. In addition, we generalize the quantum embedding theory to active spaces composed of orbitals that are not eigenstates of Kohn–Sham Hamiltonians. Finally, we report results for spin defects in semiconductors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem

For this work, we calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r 2 ) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee–Yang–Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee–Yang–Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Multinode Multi-GPU Two-Electron Integrals: Code Generation Using the Regent Language

The computation of two-electron repulsion integrals (ERIs) is often the most expensive step of integral-direct self-consistent field methods. Formally it scales as O(N 4 ), where N is the number of Gaussian basis functions used to represent the molecular wave function. In practice, this scaling can be reduced to O(N 2 ) or less by neglecting small integrals with screening methods. The contributions of the ERIs to the Fock matrix are of Coulomb (J) and exchange (K) type and require separate algorithms to compute matrix elements efficiently. We previously implemented highly efficient GPU-accelerated J-matrix and K-matrix algorithms in the electronic structure code TeraChem. Although these implementations supported the use of multiple GPUs on a node, they did not support the use of multiple nodes. This presents a key bottleneck to cutting-edge ab initio simulations of large systems, e.g., excited state dynamics of photoactive proteins. We present our implementation of multinode multi-GPU J- and K-matrix algorithms in TeraChem using the Regent programming language. Regent directly supports distributed computation in a task-based model and can generate code for a variety of architectures, including NVIDIA GPUs. We demonstrate multinode scaling up to 45 GPUs (3 nodes) and benchmark against hand-coded TeraChem integral code. Finally, we also outline our metaprogrammed Regent implementation, which enables flexible code generation for integrals of different angular momenta.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

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. In conclusion, 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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗