arXiv:1709.03460 · Physical review. B./Physical review. B

Accurate correlation energies in one-dimensional systems from small system-adapted basis functions

Thomas E. Baker, Kieron Burke, Steven R. White

Published Feb 21, 2018• 8 citations

Abstract

We propose a general method for constructing system-dependent basis functions for correlated quantum calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2--3 basis functions per electron to achieve high accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many one-dimensional atoms. We discuss the promise and challenges for realistic quantum chemical calculations.

DOI: 10.1103/physrevb.97.085139

Related papers

Correlation-Converged Virtual Orbitals for Accurate and Efficient Quantum Molecular Simulations

Qian Wang, Calvin Ku, Jyh-Pin Chou +3 more

Density functional theory with plane-wave basis sets is widely employed in computational materials science, including applications to isolated molecular systems. However, the inadequate description of electron correlation remains a fundamental limitation. Accurate correlation treatments based on many-body Hamiltonians require reliable representations of both occupied and virtual orbitals, yet virtual orbitals are often poorly described in conventional computational schemes, resulting in reduced accuracy. In this work, we introduce localized correlation-converged virtual orbitals (LCCVOs) as an efficient basis for constructing accurate many-body Hamiltonians in molecular systems. Using a substantially reduced number of orbitals, the LCCVO framework yields dissociation energies for singlet, doublet, and triplet molecules that are comparable to, and in many cases exceed, those obtained with high-level correlation-consistent basis sets such as cc-pVXZ (X = D, T, Q, 5). These results demonstrate the efficiency, scalability, and robustness of the LCCVO approach for high-accuracy quantum chemical calculations.

physics.chem-phCross-listedarXiv:2604.16928Apr 21, 2026

Quantum simulations of molecular systems with intrinsic atomic orbitals

Stefano Barison, Davide Emilio Galli, Mário Motta

Quantum simulations of molecular systems on quantum computers often employ minimal basis sets of Gaussian orbitals. In comparison with more realistic basis sets, quantum simulations employing minimal basis sets require fewer qubits and quantum gates but yield results of lower accuracy. A natural strategy to achieve more accurate results is to increase the basis set size, which, in turn, requires increasing the number of qubits and quantum gates. Here we explore the use of intrinsic atomic orbitals in quantum simulations of molecules to improve the accuracy of energies and properties at the same computational cost required by a minimal basis. We investigate ground-state energies and one- and two-body density operators in the framework of the variational quantum eigensolver employing and comparing different Ans\"atze. We also demonstrate the use of this approach in the calculation of ground- and excited-state energies of small molecules by a combination of quantum algorithms using IBM quantum computers.

arXiv:2011.08137Physical Review AAug 9, 202218 citations

Quantum Chemistry in Solid-State Simulations: Gaussian Basis Sets Development and ab-initio Green's Function Based Realistic System Applications

Yanbing Zhou

Understanding emergent many-body phenomena in correlated materials remains one of the grandest challenges in solid-state quantum chemistry calculations. The individuality of electrons diminishes as correlation increases, which leads to the emergence of new features in the system. Seeking to address such problems accurately requires the aid of non-perturbative many-body techniques as well as the corresponding high-quality basis sets. In periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, and an elemental basis set independent of the physical properties of materials may lead to significant simulation inaccuracies. In fact, with the rapid progress of quantum chemistry methods in condensed-phase simulations, the need for a library of reliable Gaussian basis sets explicitly designed for periodic calculations has become urgent. In the meantime, the development of parameter-free, systematic and reliable quantum chemistry methods for simultaneously treating weak and strong correlations in periodic systems has never stopped. Their ability to treat realistic solid materials needs to be tested, and the obtained results can serve as benchmarks for empirical parameter-guided solid-state calculations. In this thesis, we present numerical studies of various solid-state systems, emphasizing the design and optimization of Gaussian basis sets and assessing the band structure properties of the periodic solid systems. The work begins by introducing the theoretical framework of the electronic structure theory and presenting the fundamentals of a fully self-consistent GW approximation and the self-energy embedding theory (SEET) in Chapters 2 and 3. It continues with a description of the Gaussian basis set optimization scheme we devised for solid-state quantum chemistry calculations. The scheme we present is designed to avoid a lack of material specificity within a given basis set by simultaneously minimizing the total energy of the system and optimizing the band energies when compared to the reference plane wave calculation while accounting for the overlap matrix condition number. We compare the quality of the Gaussian basis sets generated via our method against the existing basis sets. And the optimization scheme is tested to yield improved results. We finally present a quantitative study of electronic properties of realistic materials with the treatment of Green's function based weakly correlated self-consistent GW approximation and the strongly correlated self-energy embedding theory. In the transition metal oxide BiVO3, we found the inaccurate illustration of orbitals including t_{2g} in transition metal Vanadium by DFT. Our calculation shows a systematic trend of DFT failure in illustrating both insulating and metallic solutions, demonstrating the dangers of using DFT when the experimental data is scarce.

Jan 1, 20220 citations

A well-scaling natural orbital theory

Ralph Gebauer, Morrel H. Cohen, Roberto Car

We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.

arXiv:1611.08692Proceedings of the National Academy of SciencesNov 1, 201617 citations

Multisliced gausslet basis sets for electronic structure

Steven R. White, Edwin Miles Stoudenmire

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced waveletlike smooth orthogonal functions. We adapt the gausslets to particular systems using one-dimensional (1D) coordinate transformations, putting more basis functions near the nuclei, while maintaining orthogonality. Three-dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate these bases with both Hartree-Fock and density matrix renormalization group calculations on hydrogen chain systems. With both methods, we can go to higher accuracy in the complete basis set limit than is practical for conventional Gaussian basis sets, with errors near 0.1 mH per atom.

arXiv:1809.10258Physical review. B./Physical review. BFeb 11, 201929 citations

Accurate and gate-efficient quantum Ansätze for electronic states without adaptive optimization

Hugh G. A. Burton

The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but current approximations struggle to combine chemical accuracy and gate efficiency while preserving physical symmetries, and rely on measurement-intensive adaptive methods that tailor the wave function to each molecule. In this contribution, we present a symmetry-preserving and gate-efficient that provides chemically accurate molecular energies with a well-defined circuit structure. Our approach exploits local qubit connectivity, orbital optimization, and connections with generalized valence bond theory to maximize the accuracy that is obtained with shallow quantum circuits. Numerical simulations for molecules with weak and strong electron correlation, including benzene, water, and the singlet-triplet gap in tetramethyleneethane, demonstrate that chemically accurate energies are achieved with as much as 84% fewer two-qubit gates compared to state-of-the-art adaptive techniques. Published by the American Physical Society 2024

Physical Review ResearchJun 20, 202427 citations