arXiv subjects

Szymon Śmiga

Publications and source records attributed to Szymon Śmiga.

11 recordsLinked to original sources

arXiv2026

MERCE: Method-Space Correlation Energy Extrapolation toward High-Rank Coupled Cluster Accuracy

Energy extrapolation is a well-established strategy for approaching quantum-chemical limits without performing prohibitively expensive calculations. Complete basis set extrapolation is widely used, whereas extrapolation across electronic structure methods remains much less developed. Method-Space Effective-Rank Correlation Energy Extrapolation (MERCE) is introduced as an adaptive effective-rank framework for estimating high-rank finite-basis correlation energies from second-order Moller-Plesset perturbation theory (MP2), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triples [CCSD(T)]. The method assigns adaptive effective ranks to MP2 and CCSD(T) from the local MP2-CCSD-CCSD(T) correlation energy pattern and fits a compact three-point extrapolation form for each system. A hierarchical model-selection protocol balances cross-dataset transferability, maximum dataset-level mean absolute error (MAE) ratios, robustness on developmental sets referenced to full configuration interaction (FCI), size-consistency defects, and performance for A24 noncovalent interaction energies. Across the chemically diverse benchmarks used during model development, the selected MERCE model substantially reduces CCSD(T) errors and frequently improves upon the tested higher-rank coupled cluster baselines. Transferability is further assessed using calculations performed only after the functional form and parameters were frozen. Formal nonadditivity is quantified using artificial noninteracting pairs and the actual A24 and selected S66 component calculations.

physics.chem-ph↗

arXiv2026

Accurate starting points for one-shot $G_0W_0$ and Bethe-Salpeter Equation calculations via effective tuning of range-separated hybrid functionals

The accuracy of one-shot $G_0W_0$ and Bethe-Salpeter equation (BSE) calculations depends strongly on the underlying starting-point eigensystem, which is commonly obtained from a mean-field density-functional approximation. Range-separated hybrid (RSH) functionals provide a particularly effective starting point, however, conventional optimally tuned RSH procedures often require costly, system-specific, multi-step optimizations of the range-separation parameter $ω$. In this work, we show that a recently proposed effective tuning protocol [Singh \textit{et. al.}, Journal of Physical Chemistry Letters, 16, 32, 8198-8208, (2025)] for RSH functionals can serve as an efficient alternative for determining $ω$ used in $G_0W_0$ and BSE calculations. This simplified tuning scheme yields range-separation parameters that are effectively equivalent to those obtained from more elaborate tuning strategies, while avoiding their substantial computational overhead. The resulting tuned RSH eigensystems provide reliable starting points for many-body perturbation theory. In particular, one-shot $G_0W_0$ calculations based on effectively tuned RSH orbitals reproduce reference ionization potentials with high accuracy, while subsequent BSE calculations yield quantitatively reliable neutral excitation energies, optical absorption spectra, and excitonic properties for a diverse set of molecular systems and clusters. These results demonstrate that effective RSH tuning offers a practical and broadly applicable route to accurate quasiparticle and excited-state calculations, combining the accuracy of optimally tuned starting points with the low computational cost required for routine applications of $G_0W_0$ and BSE.

physics.chem-ph↗

arXiv2026

Adaptive Expansions of the Optimized Effective Potential in Physically Motivated Response Spaces

The optimized effective potential (OEP) method provides an exact framework for incorporating orbital-dependent exchange within Kohn-Sham (KS) density-functional theory (DFT). Its practical implementation requires representing the exchange-response potential in a suitable auxiliary space, yet conventional choices are not necessarily adapted to the physical structure of the OEP response. Here, we introduce a general response-space strategy in which physically motivated response functions from existing model exchange potentials are repurposed as adaptive auxiliary directions for the OEP equation. Specifically, response functions associated with the Becke-Johnson (BJ), R"as"anen-Pittalis-Proetto (RPP), Gritsenko-van Leeuwen-van Lenthe-Baerends (GLLB), Krieger-Li-Iafrate (KLI), and localized Hartree-Fock (LHF) constructions are incorporated into compact auxiliary spaces, while their coefficients are determined directly from the projected OEP equation rather than fixed by the underlying model potentials. This establishes a systematic connection between model exchange potentials and finite-basis OEP: model potentials provide physically informed response directions, while OEP determines their system-dependent amplitudes. The framework encompasses one- and multidimensional response spaces, including occupied-orbital and occupied-pair representations, without modifying the underlying OEP condition. We show that these physically adapted spaces capture the dominant spatial structures of the OEP exchange response with substantially fewer degrees of freedom than conventional auxiliary expansions. The proposed approach therefore provides a general route to compact, adaptive representations of exchange-only OEP potentials and a systematic framework for developing low-dimensional OEP approximations from physically motivated model response functions.

physics.chem-ph↗

arXiv2026

Frontier Orbital Engineering in Heteroatom-Doped Prototypical Organic Dyes for Dye-Sensitized Solar Cells

The computational design of heteroatom-doped organic dyes for dye-sensitized solar cells (DSSCs) remains challenging, as predictive methods must accurately describe long-range charge-transfer (CT) excitations while remaining computationally efficient for systematic materials screening. In this work, we investigate the electronic structure and excited-state properties using the range-separated hybrid functional LC-$ω$PBE in conjunction with linear-response time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA). We employ a simplified, physically motivated, effective tuning protocol ($ω_{eff}$) to enable the rapid and reliable screening of electronic properties of organic dyes. Charge-transfer excitation energies and frontier orbital alignment the key factors governing light absorption and electron injection in DSSCs are analyzed through targeted heteroatom (N, O, and B) incorporation into donor-$π$-acceptor (D-$π$-A) organic dyes. A library of 27 mono-, di-, and tri-doped prototypical organic dyes is designed based on a carbazole donor and a cyanoacrylic acid acceptor through targeted doping at three positions of the $π$-bridge or linker. Distinct design trends emerge: electron-rich nitrogen and oxygen dopants increase the HOMO-LUMO gap and blue-shift CT excitations, with nitrogen exhibiting the strongest effect, whereas electron-deficient boron substitution narrows the gap and induces pronounced red shifts. Notably, the BBN-doped dye exhibits the smallest gap and lowest excitation energy, highlighting boron-rich motifs as promising candidates for enhanced solar light harvesting. Overall, this study establishes transferable heteroatom-doping guidelines and introduces an efficient, reliable, and cost-effective tuned DFT-TDDFT framework for high-throughput computational discovery and optimization of DSSC sensitizers.

physics.chem-ph↗

arXiv2025

Simplified, Physically Motivated, and Broadly Applicable Range-Separation Tuning

Range-separated hybrid functionals (RSH) with ``ionization energy'' and/or ``optimal tuning'' of the screening parameter have proven to be among the most practical and accurate approaches for describing excited-state properties across a wide range of systems, including condensed matter. However, this method typically requires multiple self-consistent calculations and can become computationally expensive and unstable, particularly for extended systems. In this work, we propose a very simple and efficient alternative approach to determine the screening parameter for RSH based solely on the total electron density of the system and the compressibility sum rule of density functional theory (DFT). This effective screening parameter achieves remarkable accuracy, particularly for charge-transfer excitations, surpassing the performance of previously suggested alternatives. Because it relies only on the electron density, the proposed approach is physically transparent and highly practical to automate DFT calculations in large and complex systems, including bulk solids, where ``tuning'' is not possible.

physics.chem-ph↗

arXiv2025

Advancing excited-state properties of two-dimensional materials using a dielectric-dependent hybrid functional

Predicting accurate band gaps and optical properties of lower-dimensional materials, including two-dimensional van der Waals (vdW) materials and their heterostructures, remains a challenge within density functional theory (DFT) due to their unique screening compared to their bulk counterparts. Additionally, accurate treatment of the dielectric response is crucial for developing and applying screened-exchange dielectric-dependent range-separated hybrid functionals (SE-DD-RSH) for vdW materials. In this work, we introduce a SE-DD-RSH functional to the 2D vdW materials like MoS2, WS2, hBN, black phosphorus (BP), and \b{eta}-InSe. By accounting for in-plane and out-of-plane dielectric responses, our method achieves accuracy comparable to advanced many-body techniques like G0 W0 and BSE@G0 W0 at a lower computational cost. We demonstrate improved band gap predictions and optical absorption spectra for both bulk and layered structures, including some heterostructures like MoS2/WS2 . This approach offers a practical and precise tool for exploring electronic and optical phenomena in 2D materials, paving the way for efficient computational studies of layered systems.

cond-mat.mtrl-sci↗

arXiv2025

Understanding the core limitations of second-order correlation-based functionals through: functional, orbital, and eigenvalue-driven analysis

Density Functional Theory has long struggled to obtain the exact exchange-correlational (XC) functional. Numerous approximations have been designed with the hope of achieving chemical accuracy. However, designing a functional involves numerous methodologies, which has a greater possibility for error accumulation if the functionals are poorly formulated. This study aims to investigate the performance and limitations of second-order correlation functionals within the framework of density functional theory. Specifically, we focus on three major classes of density functional approximations that incorporate second-order energy expressions: \textit{ab initio} (primarily Görling-Levy) functionals, adiabatic connection models, and double-hybrid functionals. The principal objectives of this research are to evaluate the accuracy of second-order correlation functionals, to understand how the choice of reference orbitals and eigenvalues affects the performance of these functionals, to identify the intrinsic limitations of second-order energy expressions, especially when using arbitrary orbitals or non-canonical configurations, and propose strategies for improving their accuracy. By addressing these questions, we aim to provide deeper insights into the factors governing the accuracy of second-order correlation functionals, thereby guiding future functional development.

physics.chem-ph↗

arXiv2024

Towards adiabatic-connection interpolation model with broader applicability

The Adiabatic Connection Integrand Interpolation (ACII) method represents a general path for calculating correlation energies in electronic systems within the Den sity Functional Theory. ACII functionals include both exact-exchange and the second-order correlation energy, as well as an interpolating function toward the strictly-correlated electron (SCE) regime. Several interpolating functions have been proposed in the last years targeting different properties, yet an accurate ACII approach with broad applicability is sti ll missing. Recently, we have proposed an ACII functional that was made accurate for the three-dimensional (3D) uniform electron gas as well as for model metal clusters. In this work we present an ACII functional (named genISI2) which is very accurate for both three-dimensional (3D) and two-dimensional (2D) uniform electron gases and for the q uasi-2D infinite barrier model, where most of the exchange-correlation functionals fail badly, as well as for strongly correlated two-electrons systems. Using the exact-exchange Kohn-Sham orbitals, we have also assessed the genISI2 for various molecular systems, showing a superior performance with respect to the o ther ACII methods for total energies, atomization energies, and ionization potentials. The genISI2 functional can thus find application in a broad range of systems and properties.

cond-mat.mtrl-sci↗

arXiv2023

Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas

The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being in principle exact in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct the genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z $\leq$ 912 and for the non-relativistic noble atoms with Z $\leq$ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.

physics.chem-ph↗

arXiv2021

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH$_4$(H$_2$O)$_{20}$, is a stringent test for approximate methods, including density-functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA). The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of MBE. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the MBE. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

physics.chem-ph↗

arXiv2020

Methods to generate the reference total and Pauli kinetic potentials

We have derived a new method which allows to compute the full and the Pauli reference kinetic potentials for atoms and molecules in a real space representation. This is done by applying the optimized effective potential (OEP) method to {the} Kohn-Sham non-interacting kinetic energy expression. Additionally, we have also derived a simplified OEP variant based on the common energy denominator approximation which has proven to give much more stable and robust results than the original OEP one. Moreover, we have also proved that at the solution point our approach is formally equivalent to the commonly used Bartolotti-Acharya formula.

physics.chem-ph↗