# A. Eugene DePrince III

## Florida State University

H-index: 28

North America-United States

## About A. Eugene DePrince III

A. Eugene DePrince III, With an exceptional h-index of 28 and a recent h-index of 24 (since 2020), a distinguished researcher at Florida State University,

His recent articles reflect a diverse array of research interests and contributions to the field:

Variational determination of the two‐electron reduced density matrix: A tutorial review

Dirac–Coulomb–Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory

Relativistic coupled cluster with completely renormalized and perturbative triples corrections

Correction to “Enhanced Diastereocontrol via Strong Light–Matter Interactions in an Optical Cavity”

N-representability violations in truncated equation-of-motion coupled-cluster methods

Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials

Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian

Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory

### A. Eugene DePrince III Information

University | Florida State University |
---|---|

Position | ___ |

Citations(all) | 4757 |

Citations(since 2020) | 3704 |

Cited By | 2288 |

hIndex(all) | 28 |

hIndex(since 2020) | 24 |

i10Index(all) | 50 |

i10Index(since 2020) | 38 |

University Profile Page | Florida State University |

## Top articles of A. Eugene DePrince III

### Variational determination of the two‐electron reduced density matrix: A tutorial review

Authors

A Eugene DePrince III

Published Date

2024/1

The two‐electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many‐electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave function, by minimizing this energy with respect to variations in the elements of the 2RDM, while also enforcing known N‐representability conditions. In this tutorial review, we provide an overview of the theoretical underpinnings of the v2RDM approach and the N‐representability constraints that are typically applied to the 2RDM. We also discuss the semidefinite programming (SDP) techniques used in v2RDM computations and provide enough Python code to develop a working v2RDM code that interfaces to the libSDP library of SDP solvers. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum …

### Dirac–Coulomb–Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory

Authors

Tianyuan Zhang,Samragni Banerjee,Lauren N Koulias,Edward F Valeev,A Eugene DePrince III,Xiaosong Li

Journal

The Journal of Physical Chemistry A

Published Date

2024/4/23

We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin–orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac–Coulomb, and Dirac–Coulomb–Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin–orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin–orbit-driven processes, such as the spontaneous phosphorescence lifetime.

### Relativistic coupled cluster with completely renormalized and perturbative triples corrections

Authors

Stephen H Yuwono,Run R Li,Tianyuan Zhang,Edward F Valeev,Xiaosong Li,A Eugene DePrince III

Journal

arXiv preprint arXiv:2404.13231

Published Date

2024/4/20

We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems changes the dissociation energies by about 0.1--0.2 eV or about 4--7\%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au than in Ag or Cu.

### Correction to “Enhanced Diastereocontrol via Strong Light–Matter Interactions in an Optical Cavity”

Authors

Nam Vu,Grace M McLeod,Kenneth Hanson,A Eugene DePrince III

Journal

The Journal of Physical Chemistry A

Published Date

2023/1/30

Appendix B presented equations for a cavity quantum electrodynamics (QED) generalization of the random phase approximation (RPA). The QED-RPA equations contained errors which we correct here.• For both unrelaxed and relaxed QED-RPA (and QED time-dependent density functional theory [TDDFT]), the reference wave function 0 0e p| appearing in eqs 27− 30 and 36− 45 should be 0 0 e||, which is a product between a determinant of Kohn− Sham orbitals, 0 e|, and the photon vacuum state, 0|.

### N-representability violations in truncated equation-of-motion coupled-cluster methods

Authors

Stephen H Yuwono,A Eugene DePrince

Journal

The Journal of Chemical Physics

Published Date

2023/8/7

One-electron reduced density matrices (1RDMs) from equation-of-motion (EOM) coupled-cluster with single and double excitations (CCSD) calculations are analyzed to assess their N-representability (ie, whether they are derivable from a physical N-electron state). We identify EOM-CCSD stationary states whose 1RDMs violate either ensemble-state N-representability conditions or pure-state conditions known as generalized Pauli constraints. As such, these 1RDMs do not correspond to any physical N-electron state. Unphysical states are also encountered in the course of time-dependent EOM-CC simulations; when an external field drives transitions between a pair of stationary states with pure-state N-representable 1RDMs, the 1RDM of the time-dependent state can violate ensemble-state conditions. These observations point to potential challenges in interpreting the results of time-dependent EOM-CCSD …

### Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials

Authors

Dominic W Berry,Nicholas C Rubin,Ahmed O Elnabawy,Gabriele Ahlers,A Eugene DePrince III,Joonho Lee,Christian Gogolin,Ryan Babbush

Journal

arXiv preprint arXiv:2312.07654

Published Date

2023/12/12

This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first quantized simulation that accurately includes pseudopotentials. We focus on the Goedecker-Tetter-Hutter (GTH) pseudopotential, which is among the most accurate and widely used norm-conserving pseudopotentials enabling the removal of core electrons from the simulation. The resultant screened nuclear potential regularizes cusps in the electronic wavefunction so that orders of magnitude fewer plane waves are required for a chemically accurate basis. Despite the complicated form of the GTH pseudopotential, we are able to block encode the associated operator without significantly increasing the overall cost of quantum simulation. This is surprising since simulating the nuclear potential is much simpler without pseudopotentials, yet is still the bottleneck. We also generalize prior methods to enable the simulation of materials with non-cubic unit cells, which requires nontrivial modifications. Finally, we combine these techniques to estimate the block-encoding costs for commercially relevant instances of heterogeneous catalysis (e.g. carbon monoxide adsorption on transition metals) and compare to the quantum resources needed to simulate materials in second quantization. We conclude that for computational cells with many particles, first quantization often requires meaningfully less spacetime volume.

### Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian

Authors

Stephen H Yuwono,Brandon C Cooper,Tianyuan Zhang,Xiaosong Li,A Eugene DePrince

Journal

The Journal of Chemical Physics

Published Date

2023/7/28

Simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent …

### Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory

Authors

David B Williams-Young,Stephen H Yuwono,A Eugene DePrince III,Chao Yang

Journal

Journal of Chemical Theory and Computation

Published Date

2023/12/12

With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438–5447], the fourth-order Runge–Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.

### Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory

Authors

Grier M Jones,Run R Li,A Eugene DePrince III,Konstantinos D Vogiatzis

Journal

The Journal of Physical Chemistry Letters

Published Date

2023/7/7

The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced-density matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can enable large-scale calculations on such systems, the quality of the solution is limited by the fact that only a subset of known necessary N-representability constraints can be applied to the 2RDM in practical calculations. Here, we demonstrate that violations of partial three-particle (T1 and T2) N-representability conditions, which can be evaluated with knowledge of only the 2RDM, can serve as physics-based features in a machine-learning (ML) protocol for improving energies from v2RDM calculations that consider only two-particle (PQG) conditions. Proof-of-principle calculations demonstrate that the model yields substantially improved energies relative to reference values …

### Ab initio methods for polariton chemistry

Authors

Jonathan J Foley,Jonathan F McTague,A Eugene DePrince

Published Date

2023/12/1

Polariton chemistry exploits the strong interaction between quantized excitations in molecules and quantized photon states in optical cavities to affect chemical reactivity. Molecular polaritons have been experimentally realized by the coupling of electronic, vibrational, and rovibrational transitions to photon modes, which has spurred a tremendous theoretical effort to model and explain how polariton formation can influence chemistry. This tutorial review focuses on computational approaches for the electronic strong coupling problem through the combination of familiar techniques from ab initio electronic structure theory and cavity quantum electrodynamics, toward the goal of supplying predictive theories for polariton chemistry. Our aim is to emphasize the relevant theoretical details with enough clarity for newcomers to the field to follow, and to present simple and practical code examples to catalyze further …

### Assessing the effects of orbital relaxation and the coherent-state transformation in quantum electrodynamics density functional and coupled-cluster theories

Authors

Marcus D Liebenthal,Nam Vu,A Eugene DePrince III

Journal

The Journal of Physical Chemistry A

Published Date

2023/6/8

Cavity quantum electrodynamics (QED) generalizations of time-dependent (TD) density functional theory (DFT) and equation-of-motion (EOM) coupled-cluster (CC) theory are used to model small molecules strongly coupled to optical cavity modes. We consider two types of calculations. In the first approach (termed “relaxed”), we use a coherent-state-transformed Hamiltonian within the ground- and excited-state portions of the calculations, and cavity-induced orbital relaxation effects are included at the mean-field level. This procedure guarantees that the energy is origin-invariant in post-self-consistent-field calculations. In the second approach (termed “unrelaxed”), we ignore the coherent-state transformation and the associated orbital relaxation effects. In this case, ground-state unrelaxed QED-CC calculations pick up a modest origin dependence but otherwise reproduce relaxed QED-CC results within the coherent …

### Single Reference Treatment of Strongly Correlated H4 and H10 Isomers with Richardson–Gaudin States

Authors

Paul Andrew Johnson,A Eugene DePrince III

Journal

Journal of Chemical Theory and Computation

Published Date

2023/11/13

Richardson–Gaudin (RG) states are employed as a variational wave function ansatz for strongly correlated isomers of H4 and H10. In each case, a single RG state describes the seniority-zero sector quite well. Simple natural orbital functionals offer a cheap and reasonable approximation of the outstanding weak correlation in the seniority-zero sector, while systematic improvement is achieved by performing a configuration interaction in terms of RG states.

### Mean-Field Cavity Effects in Quantum Electrodynamics Density Functional and Coupled-Cluster Theories

Authors

Marcus D Liebenthal,Nam Vu,A Eugene DePrince III

Journal

arXiv preprint arXiv:2303.10821

Published Date

2023/3/20

Cavity quantum electrodynamics (QED) generalizations of time-dependent (TD) density functional theory (DFT) and equation-of-motion (EOM) coupled-cluster (CC) theory are used to model small molecules strongly coupled to optical cavity modes. We consider two types of calculations. In the first approach (termed ``relaxed''), cavity-induced orbital relaxation effects are included through a coherent-state transformation of the Hamiltonian; this procedure guarantees origin invariance of the energy in post-self-consistent-field calculations. In the second approach (termed ``unrelaxed''), we ignore the coherent-state transformation and the associated orbital relaxation effects. In this case, ground-state unrelaxed QED-CC calculations pick up a modest origin dependence but otherwise reproduces relaxed QED-CC results within the coherent-state basis. On the other hand, a severe origin dependence manifests in ground-state unrelaxed QED mean-field energies. For excitation energies computed at experimentally realizable coupling strengths, relaxed and unrelaxed QED-EOM-CC results are similar, while significant differences emerge for unrelaxed and relaxed QED-TDDFT. First, QED-EOM-CC and relaxed QED-TDDFT both predict that electronic states that are not resonant with the cavity mode are nonetheless perturbed by the cavity. Unrelaxed QED-TDDFT, on the other hand, fails to capture this effect. Second, in the limit of large coupling strengths, relaxed QED-TDDFT tends to overestimate Rabi splittings, while unrelaxed QED-TDDFT underestimates them, given splittings from relaxed QED-EOM-CC as a reference, and relaxed QED-TDDFT …

### Fault-tolerant quantum simulation of materials using Bloch orbitals

Authors

Nicholas C Rubin,Dominic W Berry,Fionn D Malone,Alec F White,Tanuj Khattar,A Eugene DePrince III,Sabrina Sicolo,Michael Küehn,Michael Kaicher,Joonho Lee,Ryan Babbush

Journal

PRX Quantum

Published Date

2023/10/6

The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block encoding, time evolving, and sampling in the eigenbasis of electronic structure Hamiltonians has either focused on modeling finite-sized systems, or has required a large number of plane-wave basis functions. In this work, we extend methods for quantum simulation with Bloch orbitals constructed from symmetry-adapted atom-centered orbitals so that one can model periodic ab initio Hamiltonians using only a modest number of basis functions. We focus on adapting existing algorithms based on combining qubitization with tensor factorizations of the Coulomb operator. Significant modifications of those algorithms are required to obtain an asymptotic speedup leveraging translational (or, more broadly, Abelian) symmetries. We implement block encodings using known …

### Equation-of-motion cavity quantum electrodynamics coupled-cluster theory for electron attachment

Authors

Marcus D Liebenthal,Nam Vu,A Eugene DePrince

Journal

The Journal of Chemical Physics

Published Date

2022/2/7

The electron attachment variant of equation-of-motion coupled-cluster theory (EOM-EA-CC) is generalized to the case of strong light–matter coupling within the framework of cavity quantum electrodynamics (QED). The resulting EOM-EA-QED-CC formalism provides an ab initio, correlated, and non-perturbative description of cavity-induced effects in many-electron systems that complements other recently proposed cavity-QED-based extensions of CC theory. Importantly, this work demonstrates that QED generalizations of EOM-CC theory are useful frameworks for exploring particle-non-conserving sectors of Fock space, thereby establishing a path forward for the simultaneous description of both strong electron–electron and electron–photon correlation effects.

### Enhanced Diastereocontrol via Strong Light–Matter Interactions in an Optical Cavity

Authors

Nam Vu,Grace M McLeod,Kenneth Hanson,A Eugene DePrince III

Journal

The Journal of Physical Chemistry A

Published Date

2022/12/6

The enantiopurification of racemic mixtures of chiral molecules is important for a range of applications. Recent work has shown that chiral group-directed photoisomerization is a promising approach to enantioenrich racemic mixtures of BINOL, but increased control of the diasteriomeric excess (de) is necessary for its broad utility. Here we develop a cavity quantum electrodynamics (QED) generalization of time-dependent density functional theory and demonstrate computationally that strong light–matter coupling can alter the de of the chiral group-directed photoisomerization of BINOL. The relative orientation of the cavity mode polarization and the molecules in the cavity dictates the nature of the cavity interactions, which either enhance the de of the (R)-BINOL diasteriomer (from 17% to ≈40%) or invert the favorability to the (S)-BINOL derivative (to ≈34% de). The latter outcome is particularly remarkable because it …

### Reduced-density-matrix-based ab initio cavity quantum electrodynamics

Authors

Joel D Mallory,A Eugene DePrince III

Journal

Physical Review A

Published Date

2022/11/14

An approach to ab initio cavity quantum electrodynamics (QED) based on the reduced density matrix (RDM) is developed. The expectation value of the Pauli-Fierz Hamiltonian is expressed in terms of one-and two-body electronic and photonic RDMs, and the elements of these RDMs are optimized directly in polynomial time by semidefinite programming techniques, without knowledge of the full wave function. QED generalizations of important ensemble N-representability conditions are derived and enforced in this procedure. The resulting approach is applied to the description of classic ground-state strong-electron-correlation problems, augmented by the presence of ultrastrong light-matter coupling. First, we assess cavity-induced changes to the singlet-triplet energy gap of the linear oligoacene series; for a heptacene molecule, this gap can change by as much as 1.9 kcal/mol (or 15%) when the molecule is …

### Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Authors

Cristian L Cortes,A Eugene DePrince III,Stephen K Gray

Journal

Physical Review A

Published Date

2022/10/6

Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of QSD algorithms have focused on solving the eigenpair problem for ground-state, excited-state, and thermal observable estimations, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on a quantum computer and a multireference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multireference methodology …

### Challenges for variational reduced-density-matrix theory: Total angular momentum constraints

Authors

Run R Li,Nicholas C Rubin,A Eugene DePrince III

Journal

Journal of Chemical Theory and Computation

Published Date

2022/9/23

The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum (J) and projection of total angular momentum (MJ) states in atomic systems described by nonrelativistic Hamiltonians, and it is shown that the approach exhibits serious deficiencies. Under ensemble N-representability constraints, v2RDM theory fails to retain the appropriate degeneracies among various J states for fixed spin (S) and orbital angular momentum (L), and for fixed L, S, and J, the manifold of MJ states is not necessarily degenerate. Moreover, a substantial energy error is observed for a system for which the two-electron reduced density matrix is exactly ensemble N-representable; in this case, the error stems from violations in pure-state N-representability conditions. Unfortunately, such violations do not appear to be good indicators of the reliability of energies from v2RDM …

### p†q: a tool for prototyping many-body methods for quantum chemistry

Authors

Nicholas C Rubin,A Eugene DePrince III

Journal

Molecular Physics

Published Date

2021/11/17

pq is a C++ accelerated Python library designed to generate equations for many-body quantum chemistry methods and to realise proof-of-concept implementations of these equations for rapid prototyping. Central to this library is a simple interface to define strings of second-quantised creation and annihilation operators and to bring these strings to normal order with respect to either the true vacuum state or the Fermi vacuum. Tensor contractions over fully-contracted strings can then be evaluated using standard Python functions (e.g. NumPy's einsum). Given one- and two-electron integrals, these features allow for the rapid implementation and assessment of a wide array of many-body quantum chemistry methods.

## A. Eugene DePrince III FAQs

### What is A. Eugene DePrince III's h-index at Florida State University?

The h-index of A. Eugene DePrince III has been 24 since 2020 and 28 in total.

### What are A. Eugene DePrince III's top articles?

The articles with the titles of

Variational determination of the two‐electron reduced density matrix: A tutorial review

Dirac–Coulomb–Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory

Relativistic coupled cluster with completely renormalized and perturbative triples corrections

Correction to “Enhanced Diastereocontrol via Strong Light–Matter Interactions in an Optical Cavity”

N-representability violations in truncated equation-of-motion coupled-cluster methods

Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials

Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian

Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory

...

are the top articles of A. Eugene DePrince III at Florida State University.

### What is A. Eugene DePrince III's total number of citations?

A. Eugene DePrince III has 4,757 citations in total.