Multiconfigurational Approach Research Articles

Erratum: Revealing quantum effects in bosonic Josephson junctions: a multi-configuration atomic coherent state approach

Erratum: Revealing quantum effects in bosonic Josephson junctions: a multi-configuration atomic coherent state approach

Multireference Correlated Oscillator Strengths from Adiabatic Connection Approaches Based on Extended Random Phase Approximation.

We show that accurate oscillator strengths can be obtained from adiabatic connection (AC) approaches based on the extended random phase approximation (ERPA) combined with multireference (complete active space, CAS) wave functions. The oscillator strengths calculated using the perturbation-corrected ERPA transition density matrices, proposed in this work, and the excitation energies calculated with recently introduced AC correlation energy methods, AC0 and AC0D, compete with accuracy in the perturbational CASPT2 approach and require less computational effort. AC0 and AC0D methods scale more favorably with the number of active orbitals than multiconfigurational perturbation approaches like CASPT2 and NEVPT2 thanks to their dependence on reduced density matrices up to the order of 2. Importantly, the newly developed approach for computing correlated transition dipole moments does not entail any additional costs, as all intermediate quantities become available when AC0 energies are being computed. We also test the performance of the recently proposed AC method corrected for the negative-transition contributions to the correlation energy, AC0D, for triplet excitation energies. Similarly, as for the singlet excitations, the correction improves the performance of the AC0 method, particularly for the low-lying excited states.

Organic Reactivity Made Easy and Accurate with Automated Multireference Calculations.

In organic reactivity studies, quantum chemical calculations play a pivotal role as the foundation of understanding and machine learning model development. While prevalent black-box methods like density functional theory (DFT) and coupled-cluster theory (e.g., CCSD(T)) have significantly advanced our understanding of chemical reactivity, they frequently fall short in describing multiconfigurational transition states and intermediates. Achieving a more accurate description necessitates the use of multireference methods. However, these methods have not been used at scale due to their often-faulty predictions without expert input. Here, we overcome this deficiency with automated multiconfigurational pair-density functional theory (MC-PDFT) calculations. We apply this method to 908 automatically generated organic reactions. We find 68% of these reactions present significant multiconfigurational character in which the automated multiconfigurational approach often provides a more accurate and/or efficient description than DFT and CCSD(T). This work presents the first high-throughput application of automated multiconfigurational methods to reactivity, enabled by automated active space selection algorithms and the computation of electronic correlation with MC-PDFT on-top functionals. This approach can be used in a black-box fashion, avoiding significant active space inconsistency error in both single- and multireference cases and providing accurate multiconfigurational descriptions when needed.

Unveiling the electronic and molecular structure of a trinuclear ruthenium cluster containing one nitrosyl ligand

The understanding of the Ru-NO bond in Ru nitrosyl systems is of great interest due to the non-innocent nature of the NO ligand, and because of the ability of such compounds to release nitric oxide, an essential physiological regulator. The Ru-NO bond description can be even more complicated when it comes to polynuclear systems such as the μ-oxo clusters of general formula [Ru3O(CH3COO)6(L)3]n, which can be electronically localized or delocalized themselves depending on the nature of the L ligands, or present unpaired electrons depending on the Ru ions oxidation state. Herein, we present a detailed electronic- and molecular-structure description of the [Ru3O(CH3COO)6(py)2NO]PF6 (py = pyridine) cluster using multiconfigurational approaches and X-ray diffraction analysis. The X-ray data unveil a linear Ru–NO moiety with a Ru-NO angle of 180°. Although most linear {RuNO}6 complexes have been largely described as RuII–NO+, our valence bond-type analysis based on a CASSCF ground state wavefunction, with an active space comprised of 18 electrons and 16 orbitals, showed a predominance of the RuIII–NO° configuration, with minor contributions from RuIV–NO– and RuII–NO+. These findings provide a more precise framework to rationalize the electronic properties of trinuclear ruthenium nitrosyls, aiding the planning of new NO releasers based on those clusters.

Understanding Interfaces at the Positive and Negative Electrodes on Sulfide-Based Solid-State Batteries.

Despite the high ionic conductivity and attractive mechanical properties of sulfide-based solid-state batteries, this chemistry still faces key challenges to encompass fast rate and long cycling performance, mainly arising from dynamic and complex solid-solid interfaces. This work provides a comprehensive assessment of the cell performance-determining factors ascribed to the multiple sources of impedance from the individual processes taking place at the composite cathode with high-voltage LiNi0.6Mn0.2Co0.2O2, the sulfide argyrodite Li6PS5Cl separator, and the Li metal anode. From a multiconfigurational approach and an advanced deconvolution of electrochemical impedance signals into distribution of relaxation times, we disentangle intricate underlying interfacial processes taking place at the battery components that play a major role on the overall performance. For the Li metal solid-state batteries, the cycling performance is highly sensitive to the chemomechanical properties of the cathode active material, formation of the SEI, and processes ascribed to Li diffusion in the cathode composite and in the space-charge layer. The outcomes of this work aim to facilitate the design of sulfide solid-state batteries and provide methodological inputs for battery aging assessment.

The versatility of the Cholesky decomposition in electronic structure theory

AbstractThe resolution‐of‐the‐identity (RI) or density fitting (DF) approximation for the electron repulsion integrals (ERIs) has become a standard component of accelerated and reduced‐scaling implementations of first‐principles Gaussian‐type orbital electronic‐structure methods. The Cholesky decomposition (CD) of the ERIs has also become increasingly deployed across quantum chemistry packages in the last decade, even though its early applications were mostly limited to high‐accuracy methods such as coupled‐cluster theory and multiconfigurational approaches. Starting with a summary of the basic theory underpinning both the CD and RI/DF approximations, thus underlining the extremely close relation of the CD and RI/DF techniques, we provide a brief and largely chronological review of the evolution of the CD approach from its birth in 1977 to its current state. In addition to being a purely numerical procedure for handling ERIs, thus providing robust and computationally efficient approximations to the exact ERIs that have been found increasingly useful on modern computer platforms, CD also offers highly accurate approaches for generating auxiliary basis sets for the RI/DF approximation on the fly due to the deep mathematical connection between the two approaches. In this review, we aim to provide a concise reference of the main techniques employed in various CD approaches in electronic structure theory, to exemplify the connection between the CD and RI/DF approaches, and to clarify the state of the art to guide new implementations of CD approaches across electronic structure programs.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry Quantum Computing > Theory Development

Revealing quantum effects in bosonic Josephson junctions: a multi-configuration atomic coherent state approach

The mean-field approach to two-site Bose–Hubbard systems is well-established and leads to non-linear classical equations of motion for population imbalance and phase difference. It can, for example, be based on the representation of the solution of the time-dependent Schrödinger equation either by a single Glauber state or by a single atomic (SU(2)) coherent state [S. Wimberger et al., Phys. Rev. A 103, 023326 (2021)]. We demonstrate that quantum effects beyond the mean-field approximation are easily uncovered if, instead, a multiconfiguration ansatz with a few time-dependent SU(2) basis functions is used in the variational principle. For the case of plasma oscillations, the use of just two basis states, whose time-dependent parameters are determined variationally, already gives a good qualitative agreement of the phase space dynamics with numerically exact quantum solutions. In order to correctly account for more non-trivial effects, like macroscopic quantum self-trapping, moderately more basis states are needed. For the onset of spontaneous symmetry breaking, however, a multiplicity of 2 gives a significant improvement already. In any case, the number of variational trajectories needed for good agreement with the full quantum results is orders of magnitude smaller than that in the semi-classical case, which is based on multiple mean-field trajectories.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art abinitio methods.

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Exploring disordered quantum spin models with a multilayer multiconfigurational approach

Numerical simulations of quantum spin models are crucial for a profound understanding of many-body phenomena in a variety of research areas in physics. An outstanding problem is the availability of methods to tackle systems that violate area-laws of entanglement entropy. Such scenarios cover a wide range of compelling physical situations including disordered quantum spin systems among others. In this work, we employ a numerical technique referred to as multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) to evaluate the ground state of several disordered spin models. ML-MCTDH has previously been used to study problems of high-dimensional quantum dynamics in molecular and ultracold physics but is here applied to study spin systems for the first time. We exploit the inherent flexibility of the method to present results in one and two spatial dimensions and treat challenging setups that incorporate long-range interactions as well as disorder. Our results suggest that the hierarchical multi-layering inherent to ML-MCTDH allows to tackle a wide range of quantum many-body problems such as spin dynamics of varying dimensionality.

Theoretical insights into the spectroscopic properties of ferrocenyl hetaryl ketones

Quantum chemical calculations have been carried out to elucidate the electronic structure as well as to draw structure-property relationships for a series of ferrocenyl hetaryl ketones by means of simulated NMR, IR and UV–vis spectra. In this series, the list of hetaryl groups included furan-2-yl, thiophen-2-yl, selenophen-2-yl, 1H-pyrrol-2-yl and N-methylpyrrol-2-yl. Density functional theory was employed to determine the ground-state properties of the five ketones while their excited-state properties were modeled using a broad range of theoretical methods, namely from time-dependent density functional theory to multiconfigurational and multireference ab initio approaches. The patterns in the 13C and 17O chemical shifts of the carbonyl group were explained by the geometrical twist of hetaryl rings and by the electronic parameters corresponding to π-bonds conjugation and group hardness. Furthermore, the corresponding 13C and 17O shielding constants were analyzed in terms of both their dia/paramagnetic and Lewis/non-Lewis contributions within the framework of natural chemical shielding theory. The pattern in the vibrational frequency of the carbonyl bond was connected with changes in its bond length and bond order. It was established that the electronic absorption spectra of the studied ketones are largely characterized by low-intensity d → π* transitions in the visible region and the dominant high-intensity π → π* transition in the UV region. Finally, the theoretical methods best suited for modeling the excited-state properties of such ketones were designated.

Design and Optical Analysis of a Refractive Aspheric Intraocular Lens with Extended Depth of Focus

To obtain a continuous range of clear vision for pseudophakic eyes, a design of intraocular lens (IOL) with extended depth of focus (EDoF) was proposed. The IOL was optimized with a multi-configuration approach based on a pseudophakic eye model and the optical performances of the designed IOL were analyzed. The modulation transfer function (MTF) values remain above 0.2 at 50 lp/mm for object distance ranging from 0.35 m to infinity in both photopic vision and mesopic vision over a field of 4°. The optical performances remain stable when the pupil diameter changes from 2.25 mm to 5 mm. Besides, the presented theoretical analyses show the designed IOL has good optical performances for polychromatic light and corneal asphericity. The above shows that the IOL exhibits an excellent ability for pseudophakic eyes to see the object in a continuous range of distance.

A multiconfigurational approach to the electronic structure of electro‐generated species of the Re2(μ‐Ph2PCH2PPh2)(S2CNEt2)4 complex

AbstractThe nature of Re−Re bonding in Re2(μ‐Ph2PCH2PPh2)(S2CNEt2)4 complex, including its neutral (10) and two oxidized (1+ and 12+) species, was explored utilizing state‐of‐the‐art quantum chemical methodologies within density functional theory (DFT) and complete active space self‐consistent field (CASSCF). Our results show that the ground state electron configuration of the 10 is with an effective bond order (EBO) of 2.73 computed with CASSCF. The oxidation discloses an electron removal from a metal‐based orbital, giving 1+ and 12+ with an EBO of 2.71 and 2.64, respectively. The relative similarity in EBO values among neutral and oxidized species suggests that the oxidation processes have almost no effect on the Re−Re bond strength even though electrons removal from metal‐based orbitals because the electrons that occupied the components of Re−Re bonds in 1+ and 12+ localized on the two Re ions, thus, they were excluded from EBO estimation.

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization.

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (-F) and donating (-CH3 ) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the -CH3 substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to -F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with -F or -CH3 , the conversion proceeds via the conrotatory pathway.

Active Spaces and Non-Orthogonal Configuration Interaction Approaches for Investigating Molecules on Metal Surfaces.

We test a set of multiconfigurational wavefunction approaches for calculating the ground state electron population for a two-site Anderson model representing a molecule on a metal surface. In particular, we compare (i) a Hartree Fock like wavefunction where frontier orbitals are allowed to be nonorthogonal versus (ii) a fully non-orthogonal configuration interaction wavefunction based on constrained Hartree-Fock states. We test both the strong and weak metal-molecule hybridization (Γ) limits as well as the strong and weak electron-electron repulsion (U) limits. We obtain accurate results as compared with exact numerical renormalization group theory, recovering charge transfer states where appropriate. The current framework should open a path to run molecular non-adiabatic dynamics on metal surfaces.

Efficient Multiconfigurational Quantum Chemistry Approach to Single-Ion Magnets Based on Density Matrix Embedding Theory.

Density matrix embedding theory (DMET) provides a systematic framework to combine low-level (e.g., Hartree-Fock approximation) and high-level correlated quantum chemistry methods to treat strongly correlated systems. In this work, we propose an efficient quantum embedding approach that combines DMET with the complete active space self-consistent field and subsequent state interaction treatment of spin-orbit coupling (CASSI-SO) and apply it to a theoretical description of single-ion magnets (SIMs). We have developed a novel regularized direct inversion of iterative subspace (R-DIIS) technique that ensures restricted open-shell Hartree-Fock converging to a physically correct ground state, which is found to be crucial for the efficacy of subsequent CASSI-SO calculation. The DMET+CASSI-SO approach can produce reliable zero-field splitting parameters in typical 3d-SIMs with dramatically reduced computational cost compared to its all-electron counterpart. This work therefore demonstrates the great potential of DMET-based multiconfigurational approaches for efficient ab initio study of magneto-structural correlations in complex molecular magnetic systems.

Strong-field molecular ionization beyond the single active electron approximation.

This work explores quantitative limits to the single-active electron approximation, often used to deal with strong-field ionization and subsequent attosecond dynamics. Using a time-dependent, multiconfiguration approach, specifically the time-dependent configuration interaction method, we solve the time-dependent Schrödinger equation for the two-electron dihydrogen molecule with the possibility of tuning at will the electron-electron interaction by an adiabatic switch-on/switch-off function. We focus on signals of the single ionization of H2 under a strong near-infrared, four-cycle, linearly polarized laser pulse of varying intensity and within a vibrationally frozen molecular model. The observables we address are post-pulse total ionization probability profiles as a function of the laser peak intensity. Three values of the internuclear distance R taken as a parameter are considered, R = Req = 1.4 a.u. for the equilibrium geometry of the molecule, R = 5.0 a.u. for an elongated molecule, and R = 10.2 a.u. for a dissociating molecule. The most striking observation is the non-monotonous behavior of the ionization probability profiles at intermediate elongation distances with an instance of enhanced ionization and one of partial ionization quenching. We give an interpretation of this in terms of a resonance-enhanced-multiphoton ionization mechanism with interfering overlapping resonances resulting from excited electronic states.

Theoretical Evaluation of Metal-Ligand Bonding in Neptunium Compounds in Relation to 237Np Mössbauer Spectroscopy.

The 237Np Mössbauer isomer shift and quadrupole splitting (QS) are powerful probes for the metal-ligand bonding of neptunium, a 5f-element of vital importance in the nuclear fuel cycle. A large set of Np compounds with different oxidation states (III) to (VII) is studied to investigate, by first-principles calculations, isomer shifts and the QS trends in relation to the Np oxidation state. Natural Bond Orbital analysis reveals that in addition to donation bonding to the 5f shell, participation of the 6d and 7s neptunium shells in covalent (donation) bonding substantially impacts the isomer shifts. The isomer shift cannot be interpreted solely by the 5f shell electron count. The isomer shift for Np(II) compounds is estimated to be in the range of 31-34 mm/s, less positive than for Np(III) compounds. For the QS, density functional calculations fail to reproduce the quadrupole splitting for some Np(VI) ionic solids. A multiconfigurational wave function approach reproduces the observed QS trends. The calculations give a semiquantitative interpretation of the trends for Np oxidation states (V) to (VII). The contrasting QS for standard and "reverse" neptunyl(VI), at the opposite extremes of the observed QS scale, arises predominantly from the different crystal environments.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies.

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

Magnetostructural Dependencies in 3d2Systems: The Trigonal Bipyramidal V3+Complex

We introduce a multiconfigurational approach to study the magnetostructural correlations in systems. The theoretical framework represents a restricted active space self‐consistent field method, with active space optimized to the number of all non‐bonding orbitals. To demonstrate the validity and effectiveness of the method, we explore the physical properties of the trigonal bipyramidal spin‐one single‐ion magnet . The obtained theoretical results show good agreement with the experimental data available in the literature. This includes measurements for the magnetization, low‐field susceptibility, continuous wave electron paramagnetic resonance, and photoluminescence spectroscopy. The proposed method may be reliably applied to a variety of magnetic systems. To this end, and for the sake completeness, we provide detailed analytical and numerical representations for the generic Hamiltonian's effective matrix elements related to the crystal field, exchange, spin–orbit, and Zeeman interactions.

Benchmarking ANO-R basis set for multiconfigurational calculations

The selection of basis sets is very important for multiconfigurational wave function calculation, due to a balance between a desired accuracy and computational costs. Recently, the atomic natural orbital-relativistic (ANO-R) basis set was published as a suggested replacement for the ANO-RCC basis set for scalar-relativistic correlated calculations Zobel et al (2021 J. Chem. Theory Comput. 16 278–294). Benchmarking ANO-R basis set against ANO-RCC for atoms (from H to Rn) and their compounds is the goal of this study. Many of these compounds (for instance, diatomic molecules containing transition metals) have open shells, for which reason a multiconfigurational approach is necessary and was primarily used throughout this project. Performance of the ANO-R basis set in multiconfigurational calculations is similar to the ANO-RCC basis set for the ionisation potential of atoms, and the bond distance in diatomic molecules. Deficiencies are noted for atomic electron affinities and dissociation energies of fluoride diatomic molecules. ANO-R basis sets are more compact in comparison to the corresponding ANO-RCC basis sets leading to smaller computational costs, which was demonstrated by chloroiron corrole molecule as an example.