Flexible Ansatz for <i>N</i>-Body Perturbation Theory

Miranda-Quintana, Ramón Alain; Kim, Taewon D.; Lokhande, Rugwed A.; Richer, M.; Sánchez-Díaz, Gabriela; Gaikwad, Pratiksha B.; Ayers, Paul W.

doi:10.1021/acs.jpca.4c00855

J. Phys. Chem. A

2024

DOI: 10.1021/acs.jpca.4c00855

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Flexible Ansatz for N-Body Perturbation Theory

Ramón Alain Miranda-Quintana,

Taewon D. Kim,

Rugwed A. Lokhande

et al.

Abstract: We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrodinger equation for arbitrary wave functions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are wellbehaved across a wide range of conditions, including sta… Show more

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Cited by 3 publications

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Graphical Approach to Interpreting and Efficiently Evaluating Geminal Wavefunctions

Richer,

Kim,

Ayers

2024

Int J of Quantum Chemistry

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We consider wavefunctions built from antisymmetrized products of two‐electron wavefunctions (geminals), which is arguably the simplest extension of the antisymmetrized product of one‐electron wavefunctions (orbitals) (i.e., a Slater determinant). Extensive use of geminals in wavefunctions has been limited by their high cost stemming from the many combinations of the two‐electron basis functions (orbital pairs) used to build the geminals. When evaluating the overlap of the APG wavefunction with an orthogonal Slater determinant, this cost can be interpreted as the cost of evaluating the permanent, resulting from the symmetry with respect to the interchange of orbital pairs, and the cost of assigning the occupied orbitals to the orbital pairs of the wavefunction. Focusing on the latter, we present a graphical interpretation of the Slater determinant and utilize the maximum weighted matching algorithm to estimate the combination of orbital pairs with the largest contribution to the overlap. Then, the cost due to partitioning the occupied orbitals in the overlap is reduced from to . Computational results show that many of these combinations are not necessary to obtain an accurate solution to the wavefunction. Because the APG wavefunction is the most general of the geminal wavefunctions, this approach can be applied to any of the simpler geminal wavefunction ansätze. In fact, this approach may even be extended to generalized quasiparticle wavefunctions, opening the door to tractable wavefunctions built using components of arbitrary numbers of electrons, not just two electrons.

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Graphical Approach to Interpreting and Efficiently Evaluating Geminal Wavefunctions

Richer,

Kim,

Ayers

2024

Int J of Quantum Chemistry

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PyCI: A Python-scriptable library for arbitrary determinant CI

Richer,

Sánchez-Díaz,

Martínez-González

et al. 2024

The Journal of Chemical Physics

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PyCI is a free and open-source Python library for setting up and running arbitrary determinant-driven configuration interaction (CI) computations, as well as their generalizations to cases where the coefficients of the determinant are nonlinear functions of optimizable parameters. PyCI also includes functionality for computing the residual correlation energy, along with the ability to compute spin-polarized one- and two-electron (transition) reduced density matrices. PyCI was originally intended to replace the ab initio quantum chemistry functionality in the HORTON library but emerged as a standalone research tool, primarily intended to aid in method development, while maintaining high performance so that it is suitable for practical calculations. To this end, PyCI is written in Python, adopting principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. Computationally intensive steps, notably operations related to generating Slater determinants and computing their expectation values, are delegated to low-level C++ code. This article marks the official release of the PyCI library, showcasing its functionality and scope.

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ModelHamiltonian: A Python-scriptable library for generating 0-, 1-, and 2-electron integrals

Chuiko,

Richards,

Sánchez-Díaz

et al. 2024

The Journal of Chemical Physics

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ModelHamiltonian is a free, open source, and cross-platform Python library designed to express model Hamiltonians, including spin-based Hamiltonians (Heisenberg and Ising models) and occupation-based Hamiltonians (Pariser–Parr–Pople, Hubbard, and Hückel models) in terms of 1- and 2-electron integrals, so that these systems can be easily treated by traditional quantum chemistry software programs. ModelHamiltonian was originally intended to facilitate the testing of new electronic structure methods using HORTON but emerged as a stand-alone research tool that we recognize has wide utility, even in an educational context. ModelHamiltonian is written in Python and adheres to modern principles of software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. While we anticipate that most users will use ModelHamiltonian as a Python library, we include a graphical user interface so that models can be built without programming, based on connectivity/parameters inferred from, for example, a SMILES string. We also include an interface to ChatGPT so that users can specify a Hamiltonian in plain language (without learning ModelHamiltonian’s vocabulary and syntax). This article marks the official release of the ModelHamiltonian library, showcasing its functionality and scope.

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Flexible Ansatz for N-Body Perturbation Theory

Cited by 3 publications

References 94 publications

Graphical Approach to Interpreting and Efficiently Evaluating Geminal Wavefunctions

Graphical Approach to Interpreting and Efficiently Evaluating Geminal Wavefunctions

PyCI: A Python-scriptable library for arbitrary determinant CI

ModelHamiltonian: A Python-scriptable library for generating 0-, 1-, and 2-electron integrals

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