arXiv subjects

Katarzyna Pernal

Publications and source records attributed to Katarzyna Pernal.

18 recordsLinked to original sources

arXiv2026

Dynamic electron correlation energy for multireference wavefunction methods from one- and two-electron reduced density matrices

Efficiently recovering dynamic correlation in strongly correlated systems without incurring prohibitive computational costs remains a central challenge in quantum chemistry. In this Perspective, we review and benchmark methods capable of recovering dynamic correlation for multireference wave functions exclusively from low-order reduced density matrices and densities. These approaches require at most the two-electron reduced density matrix of the reference wave function and fall into two categories: density functional theory (DFT)-based methods and purely ab initio multireference adiabatic connection (AC) methods. The former include MC-srDFT, which recovers dynamic correlation through a short-range exchange-correlation functional depending on the charge and spin densities, as well as MC-PDFT and MC-srPDFT, which employ translated functionals that additionally depend on the on-top pair density. Within the post-CASSCF framework, we perform a direct, head-to-head benchmark of these approaches under identical computational settings (including active spaces and basis sets) against challenging multireference problems, including singlet-triplet gaps in organic biradicals, excitation energies, and spin-state splittings in iron complexes. Among the DFT-based methods, MC-srPDFT emerges as the most accurate, underscoring the benefit of incorporating the on-top pair density. However, all considered DFT-based methods fail to provide reliable spin-state energetics for transition-metal complexes. Conversely, linearized AC0 rivals or outperforms more computationally expensive second-order perturbation theory approaches across all benchmark sets. We discuss these findings in the context of alternative formulations and existing literature, highlighting critical limitations and identifying promising directions for the future development of scalable multireference methods.

physics.chem-ph↗

arXiv2026

Machine learning the two-electron reduced density matrix in molecules and condensed phases

Machine learning is rapidly accelerating materials and chemical discovery, but most current models target energies, forces, or selected molecular properties rather than the underlying many-body electronic structure. Learning electronic-structure proxies, such as reduced density matrices, offers a path to surrogates that can predict a broad range of observables from a single ML model. Short of learning the full wavefunction, the two-electron reduced density matrix (2-RDM) is among the most information-rich, minimally lossy targets, providing direct access to expectation values of arbitrary one- and two-electron operators regardless of the strength of the underlying electron correlation. Here we show that learning the 2-RDM is a feasible goal, yielding exceptionally accurate models. We develop surrogates for correlated wavefunction methods (including configuration interaction and coupled cluster) that yield 2-RDMs with sufficient fidelity to provide direct, training-free access to energies and forces for driving energy-conserving molecular dynamics. To tackle realistic molecular condensed phases, we leverage a many-body expansion of the 2-RDM, using our ML models to supply the expansion terms and enabling ML-powered, coupled-cluster-quality electronic structure and energetics for large solvated systems. As a demonstration, we showcase a coupled-cluster-level electronic-structure calculation of glucose solvated by 500 water molecules achieved at Hartree-Fock cost. This work establishes a general framework for learning correlated electronic structure with high fidelity and deploying it to systems beyond the reach of conventional ab initio methods.

physics.chem-ph↗

arXiv2026

Why Projection-Based DMRG-in-DFT Cannot Be Exact, Even with the Exact Exchange-Correlation Functional

We establish the theoretical foundations for embedding a correlated wave function in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation which equates two, in principle distinct, kinetic-energy functionals yields an embedding functional identical to the projection-based wavefunction-in-DFT formulation of Miller and co-workers. We demonstrate that this functional is inherently nonvariational: its minimum is not guaranteed to coincide with the exact ground-state energy and remains bounded from above by it. Building on this formal framework, we analyze the dominant sources of error in projection-based DMRG-in-DFT embedding with approximate exchange-correlation (xc) functionals. Using molecules with dissociating covalent bonds as a diagnostic example, we demonstrate that the primary source of error is the nonadditive exchange-correlation energy describing the nonclassical coupling between the active subsystem and its environment. Eliminating the fractional-spin error by employing a pair-density xc functional (PDFT) instead of a semilocal GGA does not remedy this deficiency, because the inaccuracy stems from self-interaction effects at the subsystem-environment interface.

physics.chem-ph↗

arXiv2026

Optimally Tuned Multiconfigurational Short-Range DFT for Linear Response Properties

Multiconfigurational short-range density functional theory (MC-srDFT) rigorously combines ground state wavefunction theory with DFT. Unlike single-reference range-separated hybrid functionals, MC-srDFT has lacked theoretically grounded protocols for choosing the system-specific range-separation parameter. To address this problem, we introduce an optimal-tuning scheme based on enforcing the correct exponential decay of the electron density. We show that the range-separation parameter can be determined from the ionization potential given by the smallest-magnitude eigenvalue of the Extended Koopmans' Theorem matrix constructed for the model Hamiltonian. We validate this approach for static and dynamic dipole polarizabilities of ground-state molecular systems using MC-srDFT within both full linear response and its extended random phase approximation (ERPA) variant. Optimal tuning substantially improves polarizabilities relative to the commonly used universal $\mu = 0.4\,\mathrm{bohr}^{-1}$ parameter.

physics.chem-ph↗

arXiv2025

Projection-based DMRG-in-DFT embedding corrected by non-additive exchange-correlation

The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. et al. J. Phys. Chem. Lett. 2023, 14, 3, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

physics.chem-ph↗

arXiv2025

Correcting basis set incompleteness in wave function correlation energy by dressing electronic Hamiltonian with an effective short-range interaction

We propose a general approach to reducing basis set incompleteness error in electron correlation energy calculations. The correction is computed alongside the correlation energy in a single calculation by modifying the electron interaction operator with an effective short-range electron-electron interaction. Our approach is based on a local mapping between the Coulomb operator projected onto a finite basis and a long-range interaction represented by the error function with a local range-separated parameter, originally introduced by Giner et al. [J. Chem. Phys. 149, 194301 (2018)]. The complementary short-range interaction, included in the Hamiltonian, effectively accounts for the Coulomb interaction missing in a given basis. As a numerical demonstration, we apply the method with complete active space wavefunctions. Correlation energies are computed using two distinct approaches: the linearized adiabatic connection (AC0) method and n-electron valence state second-order perturbation theory (NEVPT2). We obtain encouraging results for the dissociation energies of test molecules, with accuracy in a triple-$ζ$ basis set comparable to or exceeding that of uncorrected AC0 or NEVPT2 energies in a quintuple-$ζ$ basis set.

physics.chem-ph↗

arXiv2024

Duality of particle-hole and particle-particle theories for strongly correlated electronic systems

We propose a novel approach to electron correlation for multireference systems. It is based on particle-hole (ph) and particle-particle (pp) theories in the second-order, developed in the random phase approximation (RPA) framework for multireference wavefunctions. We show a formal correspondence (duality), between contributions to the correlation energy in the ph and pp pictures. It allows us to describe correlation energy by rigorously combining pp and ph terms, avoiding correlation double counting. The multireference ph, pp, and the combined correlation methods are applied to ground and excited states of systems in the intermediate and strong correlation regimes and compared with the multireference second-order perturbation method (MRPT2). It is shown that the pp approximation fails to describe dissociation of multiple bonds. The ph-pp combined method is overall superior to both ph and pp alone. It parallels good accuracy of the second-order perturbation theory for ground states and singlet excitation energies. For the singlet-triplet gaps of biradicals its accuracy is significantly better. This is impressive, taking into account that it relies only on one- and two-body density matrices, while MRPT2 methods typically require density matrices up to the four-body.

physics.chem-ph↗

arXiv2023

Variational quantum eigensolver boosted by adiabatic connection

In this work we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital optimized VQE methods are employed to capture the strong correlation within an active space and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely the dissociation of N$_2$ and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can literally boost the VQE algorithms. Our work paves the way towards quantum simulations of real-life problems on near-term quantum computers.

quant-ph↗

arXiv2023

The role of spin polarization and dynamic correlation in singlet-triplet gap inversion of heptazine derivatives

The new generation of proposed light-emitting molecules for OLEDs has raised a considerable research interest due to its exceptional feature-a negative singlet-triplet (ST) gap violating the Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wavefunction expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization is approximately inverse-proportional to the HOMO-LUMO exchange integral. Comparison of single- and multireference coupled- cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

physics.chem-ph↗

arXiv2023

Efficient calculation of dispersion energy for multireference systems with Cholesky decomposition. Application to excited-state interactions

We propose an algorithm, that scales with the fifth power of the system size, for computing the second-order dispersion energy for monomers described with multiconfigurational wave functions. This scaling can be achieved when the number of virtual (unoccupied) orbitals largely exceeds the number of active orbitals, which is the case in practical calculations. Our approach employs Cholesky decomposition of Coulomb integrals and a recently developed recursive formula for density response functions of the monomers, enabling dispersion energy computations for systems in nondegenerate ground or excited states with arbitrary spin. As a numerical illustration, we apply the new algorithm in the framework of multiconfigurational symmetry adapted perturbation theory, SAPT(MC), to study interactions in dimers with localized excitons. The SAPT(MC) analysis reveals that the dispersion energy may be the main force stabilizing excited-state dimers.

physics.chem-ph↗

arXiv2023

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 HDF5 library which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for the Fortran, Python, and OCaml programming languages. In addition, a suite of tools has 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.

physics.chem-ph↗

arXiv2022

Projection-based Density Matrix Renormalization Group in Density Functional Theory Embedding

The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favourable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On the two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.

physics.chem-ph↗

arXiv2022

Toward more accurate adiabatic connection approach for multireference wave functions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to computing dynamic correlation within CASSCF and DMRG models. Practical realizations of AC have been based on two approximations: i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and ii) extended random phase approximation (ERPA). This work investigates the the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall-Hamiltonians. Exact reference AC integrands are generated from the DMRG FCI solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving accuracy of the existing AC approximations.

physics.chem-ph↗

arXiv2022

Efficient adiabatic connection approach for strongly correlated systems. Application to singlet-triplet gaps of biradicals

Strong correlation can be essentially captured with multireference wavefunction methods such as complete active space self-consistent field (CASSCF) or density matrix renormalization group (DMRG). Still, an accurate description of the electronic structure of strongly correlated systems requires accounting for the dynamic electron correlation, which CASSCF and DMRG largely miss. In this work a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC$_{\rm n}$ method accounts for terms up to the desired order n in the coupling constant, is rigorously size-consistent, free from instabilities and intruder states. It employs the particle-hole multireference random phase approximation and the Cholesky decomposition technique, which leads to a computational cost growing with the fifth power of the system size. Thanks to AC$_{\rm n}$ depending solely on one- and two-electron CAS reduced density matrix, the method is much more efficient than existing ab initio dynamic correlation methods for strong correlation. AC$_{\rm n}$ affords excellent results for singlet-triplet gaps of challenging organic biradicals. Development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.

cond-mat.str-el↗

arXiv2021

Density matrix renormalization group with dynamical correlation via adiabatic connection

The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique, which requires only up to two-body active space reduced density matrices. We report encouraging results of this approach on typical candidates for DMRG computations, namely the $n$-acenes ($n = 2 \rightarrow 7$), Fe(II)-porphyrin, and Fe$_3$S$_4$ cluster.

physics.chem-ph↗

arXiv2021

Symmetry-adapted perturbation theory based on multiconfigurational wave function description of monomers

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA) equations. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H2-H2 dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. In both cases SAPT(MC) closely reproduces benchmark results. Using the C2H4-Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

physics.chem-ph↗

arXiv2017

Comment on "Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices"

Hubertus J. J. van Dam [Phys. Rev. A 93, 052512, 2016] claims that the one-particle reduced density matrix (1RDM) of an interacting system can be represented by means of a single-determinant wavefunction of fictitious non-interacting particles. van Dam introduced orbitals within a mean-field framework that produce energy levels similar to Hartree-Fock (HF) orbital energies, therefore he also claims that conventional analyses based on Koopmans theorem are possible in 1RDM functional theory (1RDMFT). In this comment, we demonstrate that both claims are unfounded.

physics.chem-ph↗

arXiv2010

Combining Density Functional Theory and Density Matrix Functional Theory

We combine density-functional theory with density-matrix functional theory to get the best of both worlds. This is achieved by range separation of the electronic interaction which permits to rigorously combine a short-range density functional with a long-range density-matrix functional. The short-range density functional is approximated by the short-range version of the Perdew-Burke-Ernzerhof functional (srPBE). The long-range density-matrix functional is approximated by the long-range version of the Buijse-Baerends functional (lrBB). The obtained srPBE+lrBB method accurately describes both static and dynamic electron correlation at a computational cost similar to that of standard density-functional approximations. This is shown for the dissociation curves of the H$_{2}$, LiH, BH and HF molecules.

physics.chem-ph↗