Electronic Structure Theory Research Articles

Relativistic resolution-of-the-identity with Cholesky integral decomposition.

In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. We compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.

Chromophore Planarity, -BH Bridge Effect, and Two-Photon Activity: Bi- and Ter-Phenyl Derivatives as a Case Study.

In this work, we have employed electronic structure theories to explore the effect of the planarity of the chromophore on the two-photon absorption properties of bi- and ter-phenyl systems. To that end, we have considered 11 bi- and 7 ter-phenyl-based chromophores presenting a donor-π-acceptor architecture. In some cases, the planarity has been enforced by bridging the rings at ortho-positions by -CH2 and/or -BH, -O, -S, and -NH moieties. The results presented herein demonstrate that in bi- and ter-phenyl systems, the planarity achieved via a -CH2 bridge increases the 2PA activity. However, the introduction of a bridge with the -BH moiety perturbs the electronic structure to a large extent, thus diminishing the two-photon transition strength to the lowest electronic excited state. As far as two-photon absorption activity is concerned, this work hints toward avoiding -BH bridge(s) to enforce planarity in bi- and ter-phenyl systems; however, one may use -CH2 bridge(s) to achieve the enhancement of the property in question. All of these conclusions have been supported by in-depth analyses based on generalized few-state models.

Analysis of the single reference coupled cluster method for electronic structure calculations: the full-coupled cluster equations

The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian—a semi-unbounded, self-adjoint operator acting on an L^2-type Hilbert space of antisymmetric functions. Coupled cluster (CC) methods, which are based on a non-linear parameterisation of the sought-after eigenfunction and result in non-linear systems of equations, are the method of choice for high-accuracy quantum chemical simulations. The existing numerical analysis of coupled cluster methods relies on a local, strong monotonicity property of the CC function that is valid only in a perturbative regime, i.e., when the sought-after ground state CC solution is sufficiently close to zero. In this article, we introduce a new well-posedness analysis for the single reference coupled cluster method based on the invertibility of the CC derivative. Under the minimal assumption that the sought-after eigenfunction is intermediately normalisable and the associated eigenvalue is isolated and non-degenerate, we prove that the continuous (infinite-dimensional) CC equations are always locally well-posed. Under the same minimal assumptions and provided that the discretisation is fine enough, we prove that the discrete Full-CC equations are locally well-posed, and we derive residual-based error estimates with guaranteed positive constants. Preliminary numerical experiments indicate that the constants that appear in our estimates are a significant improvement over those obtained from the local monotonicity approach.

Ab initio electronic structure calculations based on numerical atomic orbitals: Basic fomalisms and recent progresses

AbstractThe numerical atomic orbital (NAO) basis sets offer a computationally efficient option for electronic structure calculations, as they require fewer basis functions compared with other types of basis sets. Moreover, their strict localization allows for easy combination with current linear scaling methods, enabling efficient calculation of large physical systems. In recent years, NAO bases have become increasingly popular in modern electronic structure codes. This article provides a review of the ab initio electronic structure calculations using NAO bases. We begin by introducing basic formalisms of the NAO‐based electronic structure method, including NAO base set generation, self‐consistent calculations, force, and stress calculations. We will then discuss some recent advances in the methods based on the NAO bases, such as real‐time dependent density functional theory (rt‐TDDFT), efficient implementation of hybrid functionals, and other advanced electronic structure methods. Finally, we introduce the ab initio tight‐binding model, which can be generated directly after the self‐consistent calculations. The model allows for efficient calculation of electronic structures, and the associated topological, and optical properties of the systems.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory Structure and Mechanism > Computational Materials Science

Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals.

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Toward first-principles approaches for mechanistic study of self-trapped exciton luminescence

In recent years, broadband photo-luminescence phenomena arising from self-trapped exciton (STE) in metal halides, including perovskites and various low-dimensional derivatives and variants, have attracted increasing attention for their potential diverse optoelectronic applications like lighting, display, radiation detection, and sensing. Despite great success in experimental discovery of many efficient STE emitters, the current understanding of the STE emission mechanism in metal halides is still immature, and often controversial, which calls for help urgently from predictive first-principles theoretical calculation. Although density-functional theory (DFT) based calculations are routinely used to provide electronic band structure of materials and have contributed greatly to qualitative analysis of luminescence mechanism, more in-depth and quantitative information is highly needed to provide guidelines for rational design of new luminescent materials with desirable features. However, due to the complicated nature of STE emission, involving in particular electron–phonon coupling in both ground and excited states, the usage of DFT is no longer a routine job as for ground state properties. While more sophisticated methods formulated in the framework of many-body perturbation theory like GW-Bethe–Salpeter equation are available and provide theoretically rigorous and accurate description of electronic transitions in extended systems, their application to real STE systems is still severely limited due to highly demanding computational cost. In practice, approximated DFT methods are employed, which have their own strengths and limitations. In this review, we focus on the theoretical approaches that have been heavily used in interpreting STE luminescence mechanism, with a particular emphasis on theoretical methods for exciton self-trapping structural optimization. It is hoped that this review, by summarizing the current status and limitations of theoretical research in the STE emission, will motivate more methodological development efforts in this important field, and push forward the frontiers of excited state electronic structure theory of materials in general.

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of Lyness [Math. Comp. 30 (1976), pp. 1–23] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations (see X. Xing, X. Li, and L. Lin [J. Chem. Theory Comput. 17 (2021), pp. 4733–4745]). Our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

Designing mechanosensitive molecules from molecular building blocks: A genetic algorithm-based approach.

Single molecules can be used as miniaturized functional electronic components, when contacted by macroscopic electrodes. Mechanosensitivity describes a change in conductance for a certain change in electrode separation and is a desirable feature for applications such as ultrasensitive stress sensors. We combine methods of artificial intelligence with high-level simulations based on electronic structure theory to construct optimized mechanosensitive molecules from predefined, modular molecular building blocks. In this way, we overcome time-consuming, inefficient trial-and-error cycles in molecular design. We unveil the black box machinery usually connected to methods of artificial intelligence by presenting all-important evolutionary processes. We identify the general features that characterize well-performing molecules and point out the crucial role of spacer groups for increased mechanosensitivity. Our genetic algorithm provides a powerful way to search chemical space and to identify the most promising molecular candidates.

TAMM: Tensor algebra for many-body methods.

Tensor algebra operations such as contractions in computational chemistry consume a significant fraction of the computing time on large-scale computing platforms. The widespread use of tensor contractions between large multi-dimensional tensors in describing electronic structure theory has motivated the development of multiple tensor algebra frameworks targeting heterogeneous computing platforms. In this paper, we present Tensor Algebra for Many-body Methods (TAMM), a framework for productive and performance-portable development of scalable computational chemistry methods. TAMM decouples the specification of the computation from the execution of these operations on available high-performance computing systems. With this design choice, the scientific application developers (domain scientists) can focus on the algorithmic requirements using the tensor algebra interface provided by TAMM, whereas high-performance computing developers can direct their attention to various optimizations on the underlying constructs, such as efficient data distribution, optimized scheduling algorithms, and efficient use of intra-node resources (e.g., graphics processing units). The modular structure of TAMM allows it to support different hardware architectures and incorporate new algorithmic advances. We describe the TAMM framework and our approach to the sustainable development of scalable ground- and excited-state electronic structure methods. We present case studies highlighting the ease of use, including the performance and productivity gains compared to other frameworks.

Photophysical oxidation of HCHO produces HO2 radicals.

Formaldehyde, HCHO, is the highest-volume carbonyl in the atmosphere. It absorbs sunlight at wavelengths shorter than 330 nm and photolyses to form H and HCO radicals, which then react with O2 to form HO2. Here we show HCHO has an additional HO2 formation pathway. At photolysis energies below the energetic threshold for radical formation we directly detect HO2 at low pressures by cavity ring-down spectroscopy and indirectly detect HO2 at 1 bar by Fourier-transform infrared spectroscopy end-product analysis. Supported by electronic structure theory and master equation simulations, we attribute this HO2 to photophysical oxidation (PPO): photoexcited HCHO relaxes non-radiatively to the ground electronic state where the far-from-equilibrium, vibrationally activated HCHO molecules react with thermal O2. PPO is likely to be a general mechanism in tropospheric chemistry and, unlike photolysis, PPO will increase with increasing O2 pressure.

Investigating Molecular Exciton Polaritons Using Ab Initio Cavity Quantum Electrodynamics.

Coupling molecules to the quantized radiation field inside an optical cavity creates a set of new photon-matter hybrid states called polariton states. We combine electronic structure theory with quantum electrodynamics (QED) to investigate molecular polaritons using ab initio simulations. This framework joins unperturbed electronic adiabatic states with the Fock state basis to compute the eigenstates of the QED Hamiltonian. The key feature of this "parametrized QED" approach is that it provides the exact molecule-cavity interactions, limited by only approximations made in the electronic structure. Using time-dependent density functional theory, we demonstrated comparable accuracy with QED coupled cluster benchmark results for predicting potential energy surfaces in the ground and excited states and showed selected applications to light-harvesting and light-emitting materials. We anticipate that this framework will provide a set of general and powerful tools that enable direct ab initio simulation of exciton polaritons in molecule-cavity hybrid systems.

Wavelength-Dependent Excitonic Properties of Covalent Organic Frameworks Explored by Theory and Experiments

Many aspects of the correlation between the physical structure, light harvesting, and excitonic properties of covalent organic frameworks (COFs) remain unclear despite being key properties determining their photocatalytic function. One area of COF research that could bring clarity is using both electronic structure theory and time-resolved spectroscopic analysis over a series of systematically varied COFs. Here, we show structure–property relationships between four imine COFs built from a combination of ditopic and tritopic monomers using transient absorption spectroscopy together with time-dependent density functional theory. We find that monomer selection only moderately affects the charge transfer (CT) behavior of the COFs. Instead, we infer that imine chemistry profoundly impacts CT by acting as a CT mediator. Moreover, we discover two distinct valence bands arising from varying degrees of locally excited/CT mixing, which is responsible for energy-dependent exciton dynamics. Finally, we use theory to hypothesize that interlayer interactions can modify excitonic properties that we correlate with tail states commonly observed but rarely investigated in COFs. These results reveal that imine chemistry should be recognized as a very important factor to consider in the development of COF photocatalysts and the correlation of their structural environment with light-harvesting and CT properties that should ultimately determine their photocatalytic function.

A Similarity Renormalization Group Approach to Green's Function Methods.

The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.

QM/AMOEBA description of properties and dynamics of embedded molecules

AbstractWe describe the development, implementation, and application of a polarizable QM/MM strategy, based on the AMOEBA polarizable force field, for calculating molecular properties and performing dynamics of molecular systems embedded in complex matrices. We show that polarizable QM/MM is a well‐understood, mature technology that can be deployed using a state‐of‐the‐art implementation that combines efficient numerical methods and linear scaling techniques. Thanks to these numerical advances and to the availability of parameters for a wide manifold of systems in the AMOEBA force field, polarizable QM/AMOEBA can be used for advanced production applications, that range from the prediction of spectroscopies to ground‐ and excited‐state multiscale ab initio molecular dynamics simulations.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Combined QM/MM Methods

Advances in modeling attosecond electron dynamics in molecular photoionization

AbstractThe dramatic progress of experimental attosecond science has called for the development of new theoretical and computational tools capable of accurately model the correlated electron dynamics triggered by attosecond molecular photoionization. We describe the nature and the main outcome of this development, with particular focus on the B‐spline ADC and RCS‐ADC ab initio methods.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Simulation Methods Theoretical and Physical Chemistry > Spectroscopy

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

The formation mechanism of modulation structures along three different crystallographic directions in pure hafnium

The microstructure of pure hafnium subjected to micro-hardness test was studied in detail by using transmission electron microscopy (TEM). Results indicated that the {101‾0}<112‾0> prismatic slip system was commonly activated and modulation structures along three modulation directions can be frequently observed. Based on the crystallographic characteristics of these modulation structures and the electronic structure theory, the formation mechanism of modulation structures in Hf was discussed. It was confirmed that the original Brillouin zone of α-Hf was shifted along three different directions, g1, g2 and g3, under the action of external load, which changed the relative locations of the Brillouin zone and the Fermi sphere of the α-Hf and stabilized the whole system, thereby causing the formation of the modulation structure along three different directions.

Excited Electronic States of Sr2: Ab Initio Predictions and Experimental Observation of the 21Σu+ State.

Despite its apparently simple nature with four valence electrons, the strontium dimer constitutes a challenge for modern electronic structure theory. Here we focus on excited electronic states of Sr2, which we investigate theoretically up to 25000 cm-1 above the ground state, to guide and explain new spectroscopic measurements. In particular, we focus on potential energy curves for the 11Σu+, 21Σu+, 11Πu, 21Πu, and 11Δu states computed using several variants of ab initio coupled-cluster and configuration-interaction methods to benchmark them. In addition, a new experimental study of the excited 21Σu+ state using polarization labeling spectroscopy is presented, which extends knowledge of this state to high vibrational levels, where perturbation by higher electronic states is observed. The available experimental observations are compared with the theoretical predictions and help to assess the accuracy and limitations of employed theoretical models. The present results pave the way for future more accurate theoretical and experimental spectroscopic studies.

A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems.

The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multiconfigurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference-coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper, we explore the potential of incorporating ideas from conventional MRCC-namely, the treatment of the strongly correlated space in a configuration interaction formalism-to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.

Semiclassical approximations of photoabsorption cross sections beyond the continuum threshold

We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state and semiclassical expansions only for the part of the cross section depending on the continuum states, thus avoiding the difficult explicit calculation of the continuum states. Even though the approach is general, we test it in electronic-structure theory for the photoionization cross sections of the hydrogen and helium atoms. The results suggest that these semiclassical approximations can be used to obtain good estimates of cross sections at high energy.