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ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [Malone et al., J. Chem. Theory Comput. 19(1), 109–121 (2023)]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations of large systems that otherwise would not fit on a single central processing unit node or graphics processing unit (GPU) card. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals with multi-GPUs. Using CUDA and cupy for NVIDIA GPUs, ipie supports GPU-accelerated multi-slater determinant trial wavefunctions [Huang et al. arXiv:2406.08314 (2024)] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu2O2]2+ and [Fe2S2(SCH3)4]2−. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron–phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications. [ABSTRACT FROM AUTHOR]

Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI method, the scaling of their computational cost with respect to the system size remains inherently exponential. In addition, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing us to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects. [ABSTRACT FROM AUTHOR]

Due to the infinite summation of bubble diagrams, the GW approximation of Green's function perturbation theory has proven particularly effective in the weak correlation regime, where this family of Feynman diagrams is important. However, the performance of GW in multireference molecular systems, characterized by strong electron correlation, remains relatively unexplored. In the present study, we investigate the ability of GW to handle closed-shell multireference systems in their singlet ground state by examining four paradigmatic scenarios. First, we analyze a prototypical example of a chemical reaction involving strong correlation: the potential energy curve of BeH2 during the insertion of a beryllium atom into a hydrogen molecule. Second, we compute the electron detachment and attachment energies of a set of molecules that exhibit a variable degree of multireference character at their respective equilibrium geometries: LiF, BeO, BN, C2, B2, and O3. Third, we consider a H6 cluster with a triangular arrangement, which features a notable degree of spin frustration. Finally, the dissociation curve of the HF molecule is studied as an example of single bond breaking. These investigations highlight a nuanced perspective on the performance of GW for strong correlation depending on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking at the Hartree–Fock level. [ABSTRACT FROM AUTHOR]

Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from the first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies. [ABSTRACT FROM AUTHOR]

We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known GW self-energy, as well as the particle–particle and electron–hole T-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory. The performance of these schemes on strongly correlated systems (B2 and C2) is also discussed. [ABSTRACT FROM AUTHOR]

In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established GW approximation provides accurate ionization potentials and electron affinities and can be extended to neutral excitations using the Bethe–Salpeter equation (BSE) formalism. Here, we investigate the connections between various Green's function methods and evaluate their performance for charged and neutral excitations. Comparisons with other widely known second-order wave function methods are also reported. Additionally, we calculate the singlet-triplet gap of cycl[3,3,3]azine, a model molecular emitter for thermally activated delayed fluorescence, which has the particularity of having an inverted gap thanks to a substantial contribution from the double excitations. We demonstrate that, within the GW approximation, a second-order BSE kernel with dynamical correction is required to predict this distinctive characteristic. [ABSTRACT FROM AUTHOR]

In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci.2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge‐transfer, Rydberg, singlet, and triplet) in a dozen of mono‐ and di‐substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled‐cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high‐level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM‐MP2, STEOM‐CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a) ⋆, and CCSDT‐3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT‐3 can provide very consistent estimates, whereas among less expensive methods SCS‐CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds. [ABSTRACT FROM AUTHOR]

The Faraday Discussions article discusses the general discussion on stochastic and low-scaling techniques for extended systems. Researchers explored various kernels and global descriptors to predict energy accurately. They found that global descriptors performed better for energy prediction, especially in homogeneous systems. The methodology was tested on hydrogen chains and showed promise for accurately representing wavefunctions and potential energy surfaces. The approach was found to be data-efficient and could potentially be applied to more complex systems in the future. [Extracted from the article]

The article "Novel perturbative and variational methods for stronger correlations: general discussion" delves into the quantification of electron correlation through quantum states and molecular Hamiltonians. It emphasizes the challenges of predicting correlation levels and the significance of kinematic measures in understanding quantum state structures. Various quantum chemistry methods like singlet excitations and coupled cluster theory are explored to study electronic states in molecular systems, with a focus on accuracy and efficiency through chemical intuition and symmetry constraints. The text showcases different researchers' efforts in developing and applying these methods to enhance the understanding of electronic structures and properties in molecular systems. [Extracted from the article]

The cumulant expansion of the Green's function is a computationally efficient beyond-GW approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous GW approximation of many-body perturbation theory, ab initio cumulant expansions performed on top of GW (GW + C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of GW + C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (Ne, HF, H2O, NH3, and CH4) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available. [ABSTRACT FROM AUTHOR]

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe–Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe–Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks. [ABSTRACT FROM AUTHOR]

Based on 280 reference vertical transition energies of various excited states (singlet, triplet, valence, Rydberg, n → π*, π → π*, and double excitations) extracted from the QUEST database, we assess the accuracy of complete-active-space third-order perturbation theory (CASPT3), in the context of molecular excited states. When one applies the disputable ionization-potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction in the mean absolute error to 0.09 eV when the IPEA shift is switched off. [ABSTRACT FROM AUTHOR]

By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, it is shown that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group is proposed to avoid such issues and speed up the convergence of partially self-consistent GW calculations. [ABSTRACT FROM AUTHOR]

While the well-established GW approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly correlated systems, the T-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe–Salpeter equations when one considers T-matrix quasiparticle energies and a T-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems. A comparison with more conventional schemes as well as other wave function methods is also reported. Our results suggest that the T-matrix-based formalism performs best in few-electron systems where the electron density remains low. [ABSTRACT FROM AUTHOR]

Following our recent work on the benzene molecule [P.-F. Loos, Y. Damour, and A. Scemama, J. Chem. Phys. 153, 176101 (2020)], motivated by the blind challenge of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for 12 five- and six-membered ring molecules (cyclopentadiene, furan, imidazole, pyrrole, thiophene, benzene, pyrazine, pyridazine, pyridine, pyrimidine, s-tetrazine, and s-triazine) in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with an estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction calculations performed with the configuration interaction using a perturbative selection made iteratively algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of (i) the Møller–Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), (ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and (iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), is also investigated. We show that MP4 provides an interesting accuracy/cost ratio, while MP5 systematically worsens the correlation energy estimates. In addition, CC3 outperforms CCSD(T) and CR-CC(2,3), as well as its more expensive parent CCSDT. A similar trend is observed for the methods including quadruple excitations, where the CC4 model is shown to be slightly more accurate than CCSDTQ, both methods providing correlation energies within 2 millihartree of the FCI limit. [ABSTRACT FROM AUTHOR]

In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes that are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, for reference Slater determinants made of ground- or excited-state Hartree–Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated. [ABSTRACT FROM AUTHOR]

Fractional-spin errors are inherent in all current approximate density functionals, including Hartree–Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree–Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree–Fock representation. By considering the hydrogen atom and H+2 cation, we analyze how the unrestricted and generalized Hartree–Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller–Plesset adiabatic connection, excited states, and functional- and density-driven errors. [ABSTRACT FROM AUTHOR]

We report the first investigation of the performance of EOM-CC4—an approximate equation-of-motion coupled-cluster model, which includes iterative quadruple excitations—for vertical excitation energies in molecular systems. By considering a set of 28 excited states in 10 small molecules for which we have computed CC with singles, doubles, triples, quadruples, and pentuples and full configuration interaction reference energies, we show that, in the case of excited states with a dominant contribution from the single excitations, CC4 yields excitation energies with sub-kJ mol−1 accuracy (i.e., error below 0.01 eV), in very close agreement with its more expensive CC with singles, doubles, triples, and quadruples parent. Therefore, if one aims at high accuracy, CC4 stands as a highly competitive approximate method to model molecular excited states, with a significant improvement over both CC3 and CC with singles, doubles, and triples. Our results also evidence that, although the same qualitative conclusions hold, one cannot reach the same level of accuracy for transitions with a dominant contribution from the double excitations. [ABSTRACT FROM AUTHOR]

We discuss the physical properties and accuracy of three distinct dynamical (i.e., frequency-dependent) kernels for the computation of optical excitations within linear response theory: (i) an a priori built kernel inspired by the dressed time-dependent density-functional theory kernel proposed by Maitra et al. [J. Chem. Phys. 120, 5932 (2004)], (ii) the dynamical kernel stemming from the Bethe–Salpeter equation (BSE) formalism derived originally by Strinati [Riv. Nuovo Cimento 11, 1–86 (1988)], and (iii) the second-order BSE kernel derived by Zhang et al. [J. Chem. Phys. 139, 154109 (2013)]. The principal take-home message of the present paper is that dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated with higher-order excitations (such as the infamous double excitations), an unappreciated feature of dynamical quantities. We also analyze, for each kernel, the appearance of spurious excitations originating from the approximate nature of the kernels, as first evidenced by Romaniello et al. [J. Chem. Phys. 130, 044108 (2009)]. Using a simple two-level model, prototypical examples of valence, charge-transfer, and Rydberg excited states are considered. [ABSTRACT FROM AUTHOR]

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes. [ABSTRACT FROM AUTHOR]

Following the recent work of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)], we report the performance of the configuration interaction using a perturbative selection made iteratively method on the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis. Following our usual protocol, we obtain a correlation energy of −863.4 mEh, which agrees with the theoretical estimate of −863 mEh proposed by Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] using an extensive array of highly accurate new electronic structure methods. [ABSTRACT FROM AUTHOR]

By combining density-functional theory (DFT) and wave function theory via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction known as configuration interaction using a perturbative selection made iteratively (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron–electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of μ = 0.5 bohr−1 provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems. [ABSTRACT FROM AUTHOR]

The Bethe–Salpeter equation (BSE) formalism is a computationally affordable method for the calculation of accurate optical excitation energies in molecular systems. Similar to the ubiquitous adiabatic approximation of time-dependent density-functional theory, the static approximation, which substitutes a dynamical (i.e., frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the BSE formalism. Here, going beyond the static approximation, we compute the dynamical correction of the electron–hole screening for molecular excitation energies, thanks to a renormalized first-order perturbative correction to the static BSE excitation energies. The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random-phase approximation. Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing one to assess the clear improvement brought by the dynamical correction for both singlet and triplet optical transitions. [ABSTRACT FROM AUTHOR]

We report a local, weight-dependent correlation density-functional approximation that incorporates information about both ground and excited states in the context of density functional theory for ensembles (eDFT). This density-functional approximation for ensembles is specially designed for the computation of single and double excitations within Gross–Oliveira–Kohn DFT (i.e., eDFT for neutral excitations) and can be seen as a natural extension of the ubiquitous local-density approximation in the context of ensembles. The resulting density-functional approximation, based on both finite and infinite uniform electron gas models, automatically incorporates the infamous derivative discontinuity contributions to the excitation energies through its explicit ensemble weight dependence. Its accuracy is illustrated by computing single and double excitations in one-dimensional (1D) many-electron systems in the weak, intermediate, and strong correlation regimes. Although the present weight-dependent functional has been specifically designed for 1D systems, the methodology proposed here is general, i.e., directly applicable to the construction of weight-dependent functionals for realistic three-dimensional systems, such as molecules and solids. [ABSTRACT FROM AUTHOR]

We extend to strongly correlated molecular systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner et al., J. Chem. Phys. 149, 194301 (2018)]. This basis-set correction relies on a mapping between wave-function calculations in a finite basis set and range-separated DFT (RSDFT) through the definition of an effective non-divergent interaction corresponding to the electron–electron Coulomb interaction projected in the finite basis set. This enables the use of RSDFT-type complementary density functionals to recover the dominant part of the short-range correlation effects missing in this finite basis set. To study both weak and strong correlation regimes, we consider the potential energy curves of the H10, N2, O2, and F2 molecules up to the dissociation limit, and we explore various approximations of complementary functionals fulfilling two key properties: spin-multiplet degeneracy (i.e., independence of the energy with respect to the spin projection Sz) and size consistency. Specifically, we investigate the dependence of the functional on different types of on-top pair densities and spin polarizations. The key result of this study is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin polarization without any significant loss of accuracy. Quantitatively, we show that the basis-set correction reaches chemical accuracy on atomization energies with triple-ζ quality basis sets for most of the systems studied here. In addition, the present basis-set incompleteness correction provides smooth potential energy curves along the whole range of internuclear distances. [ABSTRACT FROM AUTHOR]

The ΔNO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results and on par with conventional multireference approaches. [ABSTRACT FROM AUTHOR]

The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of density-functional theory (DFT) and the foundation of the most acclaimed approximation of DFT, the local-density approximation (LDA). In the last thirty years, the knowledge of analytical parametrizations of the infinite UEG (IUEG) exchange-correlation energy has allowed researchers to perform a countless number of approximate electronic structure calculations for atoms, molecules, and solids. Recently, it has been shown that the traditional concept of the IUEG is not the unique example of UEGs, and systems, in their lowest-energy state, consisting of electrons that are confined to the surface of a sphere provide a new family of UEGs with more customisable properties. Here, we show that, some of the excited states associated with these systems can be classified as transient UEGs (TUEGs) as their electron density is only homogenous for very specific values of the radius of the sphere even though the electronic wave function is not rotationally invariant. Concrete examples are provided in the case of two-electron systems. [ABSTRACT FROM AUTHOR]

By combining extrapolated selected configuration interaction (sCI) energies obtained with the Configuration Interaction using a Perturbative Selection made Iteratively algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [E. Giner et al., J. Chem. Phys. 149, 194301 (2018)], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-ζ basis sets. We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer, and ethylene). The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set. [ABSTRACT FROM AUTHOR]

Processes related to electronically excited states are central in many areas of science; however, accurately determining excited-state energies remains a major challenge in theoretical chemistry. Recently, higher energy stationary states of non-linear methods have themselves been proposed as approximations to excited states, although the general understanding of the nature of these solutions remains surprisingly limited. In this letter, we present an entirely novel approach for exploring and obtaining excited stationary states by exploiting the properties of non-Hermitian Hamiltonians. Our key idea centres on performing analytic continuations of conventional quantum chemistry methods. Considering Hartree–Fock theory as an example, we analytically continue the electron-electron interaction to expose a hidden connectivity of multiple solutions across the complex plane, revealing a close resemblance between Coulson–Fischer points and non-Hermitian degeneracies. Finally, we demonstrate how a ground-state wave function can be morphed naturally into an excited-state wave function by constructing a well-defined complex adiabatic connection. [ABSTRACT FROM AUTHOR]