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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 (\ie, 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 to assess the clear improvement brought by the dynamical correction for both singlet and triplet optical transitions.

By combining density-functional theory (DFT) and wave function theory (WFT) 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 (SCI) known as \emph{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 $\mu=0.5$~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.

In this work we show the advantages of using the Coulomb-hole plus screened-exchange (COHSEX) approach in the calculation of potential energy surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and partial self-consistent $GW$ approaches, such as eigenvalue-self-consistent $GW$ and quasi-particle self-consistent $GW$, the COHSEX approach yields smooth potential energy surfaces without irregularities and discontinuities. Moreover, we show that the ground-state potential energy surfaces (PES) obtained from the Bethe-Salpeter equation, within the adiabatic connection fluctuation dissipation theorem, built with quasi-particle energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance. When self-consistent COHSEX quasi-particle energies and orbitals are used to build the BSE equation the results become independent of the starting point. We show that self-consistency worsens the total energies but improves the equilibrium distances with respect to BSE@COHSEX@HF. This is mainly due to changes in the screening inside the BSE.

We discuss the physical properties and accuracy of three distinct dynamical (ie, 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 (TDDFT) kernel proposed by Maitra and coworkers, ii) the dynamical kernel stemming from the Bethe-Salpeter equation (BSE) formalism derived originally by Strinati , and iii) the second-order BSE kernel derived by Yang and coworkers . 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 to 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. Using a simple two-level model, prototypical examples of valence, charge-transfer, and Rydberg excited states are considered.

The many-body Green's function Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In particular, the combination of the so-called $GW$ approximation of many-body perturbation theory, giving access to reliable ionization energies and electron affinities, and the BSE formalism, able to model UV/Vis spectra by catching excitonic effects, has shown to provide accurate singlet excitation energies in many chemical scenarios with a typical error of $0.1$--$0.3$ eV. With a similar computational cost as time-dependent density-functional theory (TD-DFT), the BSE formalism is able to provide an accuracy on par with the most accurate global and range-separated hybrid functionals without the unsettling choice of the exchange-correlation functional, resolving further known issues (e.g., charge-transfer excitations) and offering a well-defined path to dynamical kernels. In this \textit{Perspective} article, we provide a historical overview of the BSE formalism, with a particular focus on its condensed-matter roots. We also propose a critical review of its strengths and weaknesses in different chemical situations. Future directions of developments and improvements are also discussed.

While Diffusion Monte Carlo (DMC) has the potential to be an exact stochastic method for ab initio electronic structure calculations, in practice the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. 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 wave-functions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method, which iteratively selects the most relevant Slater determinants from the full configuration interaction (FCI) space. By introducing a simple protocol combining both exact and approximate finite-supercell results and a controlled extrapolation procedure to reach the thermodynamic limit, we show accurate DMC energies can be obtained using a manageable number of Slater determinants. This approach is illustrated by computing the cohesive energy of carbon diamond in the thermodynamic limit using Slater-Jastrow trial wavefunctions including up to one million Slater determinants.

We present a detailed non-relativistic study of the atoms H, He, C and K and the molecule CH4 in the center of a spherical soft confinement potential of the form VN (r) = (r/r0) N with stiffness parameter N and confinement radius r0. The soft confinement potential approaches the hard-wall limit as N → ∞, giving a more detailed picture of spherical confinement. The confined hydrogen atom is considered as a base model: it is treated numerically to obtain ground-and excited-state energies and nodal positions of the eigenstates to study the convergence towards the hard-wall limit. We also derive some important analytical relations. The use of Gaussian basis sets is analyzed. We find that, for increasing stiffness parameter N , the convergence towards the basis-set limit becomes problematic. As an application, we report dipole polarizabilities for different values of N and r0 of hydrogen. For helium, we determine electron correlation effects with varying N and r0, and discuss the virial theorem for both soft and hard confinements in the limit r0 → 0. For carbon, a change in the orbital population from 2s 2 2p 2 to 2s 0 2p 4 is observed with decreasing r0, while, for potassium, we observe a change from the 2 S to 2 D ground state at small r0 values. For CH4, we show that the one-particle density becomes more spherical with increasing confinement. A possible application of soft confinement to atoms and molecules under high pressure is discussed. Dedicated to Prof. Jürgen Gauss on the occasion of his 60th birthday

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Previously reported ferromagnetic triangles (N n Bu 4) 2 [Cu 3 (μ 3-Cl) 2 (μ-4-NO 2-pz) 3 Cl 3 ] (1), (PPN) 2 [Cu 3 (μ 3-Cl) 2 (μ-pz) 3 Cl 3 ] (2), (bmim) 2 [Cu 3 (μ 3-Cl) 2 (μ-pz) 3 Cl 3 ] (3) and newly reported (PPh 4) 2 [Cu 3 (μ 3-Cl) 2 (μ-4-Ph-pz) 3 Cl 3 ] (4) were studied by magnetic susceptometry, Electron Paramagnetic Resonance (EPR) spectroscopy and ab initio calculations to assess the origins of their ferromagnetism and of the magnetic anisotropy of their ground S = 3/2 state (PPN + = bis(triphenylphosphine)iminium, bmim + = 1-butyl-3-methylbenzimidazolium). Ab initio studies revealed the 2 d z character of the magnetic orbitals of the compressed trigonal bipyramidal copper(II) ions. Ferromagnetic interactions were attributed to weak orbital overlap via the pyrazolate bridges. From the wavefunctions expansions, the ratios of the magnetic couplings was determined, which was indeterminate by magnetic susceptometry. Single-crystal EPR studies of 1 were carried out to extend the spin Hamiltonian with terms which induce zero-field splitting (zfs), namely dipolar interactions, anisotropic exchange and Dzyaloshinskii-Moriya interactions (DMI). The data were treated through both a giant-spin model and through a multispin exchange-coupled model. The latter indicated that ~62% of the zfs is due to anisotropic and ~38% due to dipolar interactions. The powder EPR data of all complexes were fitted to a simplified form of the multispin model and the anisotropic and dipolar contributions to the ground state zfs were estimated. 2

DIRAC is a freely distributed general-purpose program system for 1-, 2- and 4-component relativistic molecular calculations at the level of Hartree--Fock, Kohn--Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, coupled cluster and electron propagator theory. At the self-consistent-field level a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding, and frozen density embedding models. DIRAC was one of the earliest codes for relativistic molecular calculations and remains a reference in its field.

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 (GOK) 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 many-electron systems in the weak, intermediate and strong correlation regimes. Although the present weight-dependent functional has been specifically designed for one-dimensional 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.

Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{independent} extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a \textit{weight-dependent} exchange-correlation functional in order to model the infamous ensemble derivative contribution to the excitation energies. In the present article, we discuss the construction of first-rung (i.e., local) weight-dependent exchange-correlation density-functional approximations for two-electron atomic and molecular systems (He and H$_2$) specifically designed for the computation of double excitations within GOK-DFT. In the spirit of optimally-tuned range-separated hybrid functionals, a two-step system-dependent procedure is proposed to obtain accurate energies associated with double excitations.

A new absorption spectroscopy method which enables rapid measurement of the diffusion coefficient of Fe 3+ in gelatin gel used in dosimetry was investigated. The physical approach, the preparation and the experimental application of this new method were tested on the EasyDosit dosimetry gel and the results were validated by MRI measurement. The diffusion coefficients measured on this gel were then compared with those of the other gels presented in the literature. This gel, which is considered stable, has a small post-irradiation ion diffusion, despite the absence of a complexing or crosslinking agent. The diffusion coefficients of a range of dosimetry gels containing different proportions of gelatin were also measured and the results show diffusion coefficients D from 3.21.10 −10 m 2 .s −1 to 2.41.10 −10 m 2 .s −1 .

We investigate the use of different variational principles in quantum Monte Carlo, namely energy and variance minimization, prompted by the interest in the robust and accurate estimate of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardless of the symmetry, we encounter severe problems for a variety of wave functions: as the variance converges, the energy drifts away from that of the selected state. This unexpected behavior is sometimes observed even when the target is the ground state, and generally prevents the robust estimate of total and excitation energies. We analyze this problem using a very simple wave function and infer that the optimization finds little or no barrier to escape from a local minimum or local plateau, eventually converging to the unique lowest-variance state instead of the target state. While the loss of the state of interest can be delayed and possibly avoided by reducing the statistical error of the gradient, for the full optimization of realistic wave functions, variance minimization with current functionals appears to be an impractical route.