Can GW handle multireference systems?

Due to the infinite summation of bubble diagrams, the GW approximation of Green's function perturbation theory has proven particularly effective in the weak correlation regime, where this family of Feynman diagrams is important. However, the performance of GW in multireference molecular systems, characterized by strong electron correlation, remains relatively unexplored. In the present study, we investigate the ability of GW to handle closed-shell multireference systems in their singlet ground state by examining four paradigmatic scenarios. First, we analyze a prototypical example of a chemical reaction involving strong correlation: the potential energy curve of BeH2 during the insertion of a beryllium atom into a hydrogen molecule. Second, we compute the electron detachment and attachment energies of a set of molecules that exhibit a variable degree of multireference character at their respective equilibrium geometries: LiF, BeO, BN, C2, B2, and O3. Third, we consider a H6 cluster with a triangular arrangement, which features a notable degree of spin frustration. Finally, the dissociation curve of the HF molecule is studied as an example of single bond breaking. These investigations highlight a nuanced perspective on the performance of GW for strong correlation depending on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking at the Hartree-Fock level.

Transcorrelated selected configuration interaction in a bi-orthonormal basis and with a cheap three-body correlation factor.

In this work, we develop a mathematical framework for a selected configuration interaction (SCI) algorithm within a bi-orthogonal basis for transcorrelated (TC) calculations. The bi-orthogonal basis used here serves as the equivalent of the standard Hartree-Fock (HF) orbitals. However, within the context of TC, it leads to distinct orbitals for the left and right vectors. Our findings indicate that the use of such a bi-orthogonal basis allows for a proper definition of the frozen core approximation. In contrast, the use of HF orbitals results in bad error cancellations for ionization potentials and atomization energies (AE). Compared to HF orbitals, the optimized bi-orthogonal basis significantly reduces the positive part of the second-order energy (PT2), thereby facilitating the use of standard extrapolation techniques of hermitian SCI. While we did not observe a significant improvement in the convergence of the SCI algorithm, this is largely due to the use in this work of a simple three-body correlation factor introduced in a recent study. This correlation factor, which depends only on atomic parameters, eliminates the need for re-optimization of the correlation factor for molecular systems, making its use straightforward and user-friendly. Despite the simplicity of this correlation factor, we were able to achieve accurate results on the AE of a series of 14 molecules on a triple-zeta basis. We also successfully broke a double bond until the full dissociation limit while maintaining the size consistency property. This work thus demonstrates the potential of the BiO-TC-SCI approach in handling complex molecular systems.

TREXIO: A file format and library for quantum chemistry.

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the hierarchical data format version 5 library, which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for Fortran, Python, and OCaml programming languages. In addition, a suite of tools have been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

Extension of selected configuration interaction for transcorrelated methods.

In this work, we present an extension of popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys. 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non-Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending on both left- and right-functions, we obtain a general framework, allowing for different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non-Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. In addition, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here, we find that the SCI expansion in the TC framework converges faster than the usual SCI in terms of both the basis set and the number of Slater determinants.

A complex Gaussian approach to molecular photoionization.

We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by nonlinear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH3 and H2 O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.

Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections.

We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex over real Gaussian expansions. We then consider the photoionization of atomic hydrogen, and ionization by electron impact in the first Born approximation, for which the closed form cross sections serve as a solid benchmark. Using the proposed complex Gaussian representation of the continuum combined with a real Gaussian expansion for the initial bound state, all necessary matrix elements within a partial wave approach become analytical. The successful numerical comparison illustrates that the proposed all-Gaussian approach works efficiently for ionization processes of one-center targets.

Biorthonormal Orbital Optimization with a Cheap Core-Electron-Free Three-Body Correlation Factor for Quantum Monte Carlo and Transcorrelation.

We introduce a novel three-body correlation factor that is designed to vanish in the core region around each nucleus and approach a universal two-body correlation factor for valence electrons. The transcorrelated Hamiltonian is used to optimize the orbitals of a single Slater determinant within a biorthonormal framework. The Slater-Jastrow wave function is optimized on a set of atomic and molecular systems containing both second-row elements and 3d transition metal elements. The optimization of the correlation factor and the orbitals, along with an increase in the basis set, results in a systematic lowering of the variational Monte Carlo energy for all systems tested. Importantly, the optimal parameters of the correlation factor obtained for atomic systems can be transferred to molecules. Additionally, the present correlation factor is computationally efficient and uses a mixed analytical-numerical integration scheme that reduces the costly numerical integration from R6 to R3.

Optimization of Large Determinant Expansions in Quantum Monte Carlo.

We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the nonorthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing 105-106 Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milli-Hartree convergence is reached within only two or three iterations of optimization.