arXiv subjects

Ramón Alain Miranda-Quintana

Publications and source records attributed to Ramón Alain Miranda-Quintana.

10 recordsLinked to original sources

arXiv2026

Second-Derivative-Corrected FANPT for Robust Continuation of Nonlinear Wavefunction Equations

We present a second-derivative-corrected extension of the Flexible Ansatz for N-body Perturbation Theory (FANPT) for solving nonlinear Flexible Ansatz for N-body Configuration Interaction (FANCI) wavefunction equations. The original quasilinear FANPT approximation neglects second- and higher-order derivatives of the determinant overlap with respect to wavefunction parameters. In this work, we retain the overlap Hessian and neglect only third- and higher-order parameter derivatives, thereby including the leading nonlinear response of the wavefunction ansatz while preserving the same response-matrix structure used in the original FANPT formulation. The resulting additional terms enter only through the constant vector of the response equations and are implemented for coupled-cluster wavefunctions in the FanPy/FANCI framework. The new approximation is tested on the Lithium Hydride molecule and the insertion of Beryllium into H$_2$ using seniority-restricted coupled-cluster wavefunctions in the STO-6G basis. The main advantage of the second-derivative correction is that it provides a better initial guess for solving the projected FANCI equations at the next point along the adiabatic connection. This improvement is diagnosed by comparing the FANPT-propagated parameters with the independently optimized FANCI parameters at the same value of $λ$. For nonlinear coupled-cluster ansatzes, especially when larger $λ$-steps are used, the corrected approximation reduces the same-$λ$ parameter deviations and suppresses large parameter-space excursions. These results show that the leading nonlinear overlap correction improves the reliability of FANPT as a continuation strategy for nonlinear wavefunction equations.

physics.chem-ph↗

arXiv2026

Fanpy 2.0: Wavefunction Implementation and Analysis Tools for Flexible Ansatz Design

Fanpy is a Python library for developing new wavefunction methods. It enables users to quickly convert mathematical expressions into working code through a modular design based on the Flexible Ansatz for N-electron Configuration Interaction (FANCI) theory. This architecture facilitates a straightforward extension of the codebase. Here we present version 2.0 of the Fanpy package. This release includes several new wavefunction implementations, including coupled- cluster-inspired geminal approaches. A new analysis module enables a more detailed inspection of computational results and lays the groundwork for future features. In addition, the PySCF interface has been redesigned, and an interface to the PyCI package has been introduced to offload computationally expensive components. Finally, we introduce an improved software development environment, including automated testing and issue tracking.

physics.chem-ph↗

arXiv2025

Baker-Campbell-Hausdorff expansion in creation-only coupled cluster

We study the properties of the exponential ansatz formed by strings of creation operators. We discuss the conditions under which we can recover a structure similar to traditional coupled cluster methods. We pay particular attention to the Baker-Campbell-Hausdorff expansion of these operators.

physics.chem-ph↗

arXiv2025

Exploring new construction schemes for extended-hierarchy CI (ehCI) wavefunctions

Following the work of Loos et al. on hierarchy CI (hCI) we propose an extended way of partitioning the Hilbert space by combining the excitation and the seniority sectors in a more general way. We define the hierarchy parameter, h, involving two "weights" (alphas), measuring the importance of excitation (e) and seniority (s) contributions to the wavefunction according to: h = α1.e + α2.s. We test these new CI methods on the dissociation of chemical systems and analyze them based on the importance of these contributions.

physics.chem-ph↗

arXiv2025

A new family of seniority-restricted coupled cluster methods

We introduce a novel class of coupled cluster (CC) methods that leverage the seniority concept to enhance efficiency and accuracy in electronic structure calculations. While existing approaches, such as the pair coupled cluster doubles (pCCD) method, are limited to seniority-zero (Ω = 0) wavefunctions,1 we propose a more flexible framework: seniority-restricted coupled cluster (sr-CC). This new methodology selectively constrains the seniority sectors accessible through excitation operators in the cluster expansion, enabling a more systematic exploration of electron correlation effects. By balancing computational cost and accuracy, sr-CC provides a promising pathway for advancing electronic structure theory, particularly in strongly correlated systems.

physics.chem-ph↗

arXiv2023

Coupled Cluster-Inspired Geminal Wavefunctions

Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes, to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals), have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly-correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally-tractable, and do not demand significant input from the user (particularly, via cumbersome and often ill-behaved orbital optimization steps). Here we propose new families of geminal wavefunctions, inspired by the pair Coupled Cluster (pCCD) ansatz. We present a new hierarchy of two-electron wavefunctions that extend the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework, without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions, and benchmark these new methods on model strongly-correlated systems.

physics.chem-ph↗

arXiv2023

Flexible Ansatz for N-body Perturbation Theory

We propose a new Perturbation Theory framework that can be used to help with the projective solution of the Schrödinger equation for arbitrary wavefunctions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly non-linear wavefunctions.

physics.chem-ph↗

arXiv2023

Inductive Proof of Borchardt's Theorem

We provide an inductive proof of Borchardt's theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and suggests that the restriction of the APIG coefficients to Cauchy form (typically called APr2G) is special in its tractability.

physics.chem-ph↗

arXiv2021

Flexible ansatz for N-body Configuration Interaction

We present a Flexible Ansatz for N-body Configuration Interaction (FANCI) that includes any multideterminant wavefunction. This ansatz is a generalization of the Configuration Interaction (CI) wavefunction, where the coefficients are replaced by a specified function of certain parameters. By making an appropriate choice for this function, we can reproduce popular wavefunction structures like CI, Coupled-Cluster, Tensor Network States, and geminal-product wavefunctions. The universality of this framework suggests a programming structure that allows for the easy construction and optimization of arbitrary wavefunctions. Here, we will discuss the structures of the FANCI framework and its implications for wavefunction properties, particularly accuracy, cost, and size-consistency. We demonstrate the flexibility of this framework by reconstructing popular wavefunction ansätze and modifying them to construct novel wavefunction forms. FANCI provides a powerful framework for exploring, developing, and testing new wavefunction forms.

physics.chem-ph↗

arXiv2021

Fanpy: A Python Library for Prototyping Multideterminant Methods in Ab Initio Quantum Chemistry

Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to transfer the mathematical conception of a new wavefunction ansätze to a working implementation. Fanpy uses the framework of our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI), where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system's Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly try new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for most operating systems; it adheres to principles of modern software development, including comprehensive documentation, extensive testing, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library.

physics.chem-ph↗