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An attractive way to model nuclear quantum effects is to describe select nuclei quantum mechanically at the same level as the electrons. This non-Born-Oppenheimer (non-BO) method is known by many names including the nuclear-electronic…

Chemical Physics · Physics 2026-04-20 Luukas Nikkanen , Susi Lehtola

We present an all-electron, periodic {\GnWn} implementation within the numerical atomic orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the…

Materials Science · Physics 2021-02-03 Xinguo Ren , Florian Merz , Hong Jiang , Yi Yao , Markus Rampp , Hermann Lederer , Volker Blum , Matthias Scheffler

We aim to develop novel reusable open source infrastructure [Lehtola, J. Chem. Phys. 159, 180901 (2023)] for numerical atomic orbitals (NAOs). Soft confinement potentials are typically used to force the NAO radial basis functions…

Computational Physics · Physics 2025-09-12 Hugo Åström , Susi Lehtola

Relativistic quintuple-zeta basis sets for the p elements are presented. The basis sets for the occupied spinors were optimized at the Dirac-Coulomb self-consistent field (SCF) level on the ground configurations. Valence and core…

As an extension to our previous work [1], a comprehensive theoretical study for Na-like Krypton and Xenon is carried out. Using MCDHF (Multiconfiguration Dirac-Hartee-Fock) along with RDW (Relativistic distorted wave) theory we calculate…

Atomic Physics · Physics 2025-08-05 Ashwini Malviya

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the…

Computational Physics · Physics 2022-06-29 Jianhang Xu , Ruiyi Zhou , Zhen Tao , Christopher Malbon , Volker Blum , Sharon Hammes-Schiffer , Yosuke Kanai

Ab initio calculations face the challenge of describing a complex multiscale quantum many-body system. The nuclear wave function has both strong short-range correlations and long-range contributions. Natural orbitals provide a means of…

Nuclear Theory · Physics 2017-04-11 Chrysovalantis Constantinou

We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold…

Materials Science · Physics 2015-09-04 Tuomas P. Rossi , Susi Lehtola , Arto Sakko , Martti J. Puska , Risto M. Nieminen

The cost of simulating quantum many-body systems - on classical or quantum hardware - scales with the number of variational parameters, so progress at fixed computational budget hinges on more parameter-efficient ans\"atze. Configuration…

Quantum Physics · Physics 2026-05-25 Hao Zhang , Matthew Otten

Density functional theory with plane-wave basis sets is widely employed in computational materials science, including applications to isolated molecular systems. However, the inadequate description of electron correlation remains a…

Chemical Physics · Physics 2026-04-21 Qian Wang , Calvin Ku , Jyh-Pin Chou , Peng-Jen Chen , Alice Hu , Min-Hsiu Hsieh

The random phase approximation (RPA) for the correlation energy functional of density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve some…

Other Condensed Matter · Physics 2009-11-13 Hong Jiang , Eberhard Engel

Atomic basis sets are widely employed within quantum mechanics based simulations of matter. We introduce a machine learning model that adapts the basis set to the local chemical environment of each atom, prior to the start of self…

Chemical Physics · Physics 2024-04-29 Danish Khan , Maximilian L. Ach , O. Anatole von Lilienfeld

We introduce a method for solving a self consistent electronic calculation within localized atomic orbitals, that allows us to converge to the complete basis set (CBS) limit in a stable, controlled, and systematic way. We compare our…

Strongly Correlated Electrons · Physics 2015-05-19 S. Azadi , C. Cavazzoni , S. Sorella

Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between…

In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic…

Materials Science · Physics 2016-01-28 Christopher E. Patrick , Kristian S. Thygesen

We present a formulation and implementation of the DFT+\textit{U} method within the framework of linear combination of numerical atomic orbitals (NAO). Our implementation not only enables single-point total energy and electronic-structure…

Materials Science · Physics 2022-06-29 Xin Qu , Peng Xu , Hong Jiang , Lixin He , Xinguo Ren

Reliable computational methodologies and basis sets for modeling x-ray spectra are essential for extracting and interpreting electronic and structural information from experimental x-ray spectra. In particular, the trade-off between…

Chemical Physics · Physics 2025-03-26 Alexis A. A. Delgado , Devin A. Matthews

Nuclear quantum effects such as zero-point energy and hydrogen tunnelling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei…

A new approach to approximate the kinetic-energy-functional dependent component ($v_t[\rho_A,\rho_B](\vec{r})$) of the effective potential in one-electron equations for orbitals embedded in a frozen density environment (Eqs. 20-21 in…

Chemical Physics · Physics 2008-04-04 Juan Maria Garcia Lastra , Jakub W. Kaminski , Tomasz A. Wesolowski

The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis…

Chemical Physics · Physics 2022-06-07 Hong-Zhou Ye , Timothy C. Berkelbach