Mapping of Hückel zigzag carbon nanotubes onto independent polyene chains: Application to periodic nanotubes.

The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism. This introduces border effects, which prevent a fast convergence to the thermodynamic limit and can be eliminated within the formalism of periodic boundary conditions. Recently, we introduced an original approach to periodic boundary conditions, named Clifford boundary conditions. It considers a finite fragment extracted from a periodic system and the modification of its topology into that of a Clifford torus. The quantity representing the position is modified in order to fulfill the system periodicity. In this work, we apply the formalism of Clifford boundary conditions to the case of carbon nanotubes, whose treatment results in a particularly simple zigzag geometry. Indeed, we demonstrate that at the Hückel level, these nanotubes, either finite or periodic, are formally equivalent to a collection of non-interacting dimerized linear chains, thus simplifying their treatment. This equivalence is used to describe some nanotube properties as the sum of the contributions of the independent chains and to identify the origin of peculiar behaviors (such as conductivity). Indeed, if the number of hexagons along the circumference is a multiple of three, a metallic behavior is found, namely a divergence of both the (per electron) polarizability and total position spread of at least one linear chain. These results are in agreement with those in the literature from tight-binding calculations.

The localization spread and polarizability of rings and periodic chains.

The localization spread gives a criterion to decide between metallic and insulating behavior of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different operators are used for systems treated with open or periodic boundary conditions. In particular, in the case of periodic systems, we use the complex position definition, which was already used in similar contexts for the treatment of both classical and quantum situations. In this study, we show that the localization spread evaluated on a finite ring system of radius R with open boundary conditions leads, in the large R limit, to the same formula derived by Resta and co-workers [C. Sgiarovello, M. Peressi, and R. Resta, Phys. Rev. B 64, 115202 (2001)] for 1D systems with periodic Born-von Kármán boundary conditions. A second formula, alternative to Resta's, is also given based on the sum-over-state formalism, allowing for an interesting generalization to polarizability and other similar quantities.

OpenMolcas: From Source Code to Insight.

In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the Article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

A perturbation-based super-CI approach for the orbital optimization of a CASSCF wave function.

A perturbation theory-based algorithm for the iterative orbital update in complete active space self-consistent-field (CASSCF) calculations is presented. Following Angeli et al. (J. Chem. Phys. 2002, 117, 10525), the first-order contribution of singly excited configurations to the CASSCF wave function is evaluated using the Dyall Hamiltonian for the determination of a zeroth-order Hamiltonian. These authors employ an iterative diagonalization of the first-order density matrix including the first-order correction arising from single excitations, whereas the present approach uses the single-excitation amplitudes directly for the construction of the exponential of an anti-Hermitian matrix resulting in a unitary matrix which can be used for the orbital update. At convergence, the single-excitation amplitudes vanish as a consequence of the generalized Brillouin's theorem. It is shown that this approach in combination with direct inversion of the iterative subspace (DIIS) leads to very rapid convergence of the CASSCF iteration procedure. © 2019 Wiley Periodicals, Inc.

A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

Computation of the Isotropic Hyperfine Coupling Constant: Efficiency and Insights from a New Approach Based on Wave Function Theory.

The present paper reports an original computational strategy for the computation of the isotropic hyperfine coupling constants (hcc). The algorithm proposed here is based on an approach recently introduced by some of the authors, namely, the first-order breathing orbital self-consistent field (FOBO-SCF). The approach is an almost parameter-free wave function method capable to accurately treat the spin delocalization together with the spin polarization effects while staying in a restricted formalism and avoiding spin contamination. The efficiency of the method is tested on a series of small radicals, among which four nitroxide radicals and the comparison with high-level ab initio methods show very encouraging results. On the basis of these results, the method is then applied to compute the hcc of a challenging system, namely, the DEPMPO-OOH radical in various conformations. The reference values obtained on such a large system allows us to validate a cheap computational method based on density functional theory (DFT). Another interesting feature of the model applied here is that it allows for the rationalization of the results according to a relatively simple scheme based on a two-step mechanism. More precisely, the results are analyzed in terms of two separated contributions: first the spin delocalization and then the spin polarization.

Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group.

We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.

The "Fermi hole" and the correlation introduced by the symmetrization or the anti-symmetrization of the wave function.

The impact of the antisymmetrization is often addressed as a local property of the many-electron wave function, namely that the wave function should vanish when two electrons with parallel spins are in the same position in space. In this paper, we emphasize that this presentation is unduly restrictive: we illustrate the strong non-local character of the antisymmetrization principle, together with the fact that it is a matter of spin symmetry rather than spin parallelism. To this aim, we focus our attention on the simplest representation of various states of two-electron systems, both in atomic (helium atom) and molecular (H2 and the π system of the ethylene molecule) cases. We discuss the non-local property of the nodal structure of some two-electron wave functions, both using analytical derivations and graphical representations of cuttings of the nodal hypersurfaces. The attention is then focussed on the impact of the antisymmetrization on the maxima of the two-body density, and we show that it introduces strong correlation effects (radial and/or angular) with a non-local character. These correlation effects are analyzed in terms of inflation and depletion zones, which are easily identifiable, thanks to the nodes of the orbitals composing the wave function. Also, we show that the correlation effects induced by the antisymmetrization occur also for anti-parallel spins since all Ms components of a given spin state have the same N-body densities. Finally, we illustrate that these correlation effects occur also for the singlet states, but they have strictly opposite impacts: the inflation zones in the triplet become depletion zones in the singlet and vice versa.

Highly efficient perturbative + variational strategy based on orthogonal valence bond theory for the evaluation of magnetic coupling constants. Application to the trinuclear Cu(ii) site of multicopper oxidases.

A new strategy based on orthogonal valence-bond analysis of the wave function combined with intermediate Hamiltonian theory has been applied to the evaluation of the magnetic coupling constants in two AF systems. This approach provides both a quantitative estimate of the J value and a detailed analysis of the main physical mechanisms controlling the coupling, using a combined perturbative + variational scheme. The procedure requires a selection of the dominant excitations to be treated variationally. Two methods have been employed: a brute-force selection, using a logic similar to that of the CIPSI approach, or entanglement measures, which identify the most interacting orbitals in the system. Once a reduced set of excitations (about 300 determinants) is established, the interaction matrix is dressed at the second-order of perturbation by the remaining excitations of the CI space. The diagonalization of the dressed matrix provides J values in good agreement with experimental ones, at a very low-cost. This approach demonstrates the key role of d → d* excitations in the quantitative description of the magnetic coupling, as well as the importance of using an extended active space, including the bridging ligand orbitals, for the binuclear model of the intermediates of multicopper oxidases. The method is a promising tool for dealing with complex systems containing several active centers, as an alternative to both pure variational and DFT approaches.

Photoionization of furan from the ground and excited electronic states.

Here we present a comparative computational study of the photoionization of furan from the ground and the two lowest-lying excited electronic states. The study aims to assess the quality of the computational methods currently employed for treating bound and continuum states in photoionization. For the ionization from the ground electronic state, we show that the Dyson orbital approach combined with an accurate solution of the continuum one particle wave functions in a multicenter B-spline basis, at the density functional theory (DFT) level, provides cross sections and asymmetry parameters in excellent agreement with experimental data. On the contrary, when the Dyson orbitals approach is combined with the Coulomb and orthogonalized Coulomb treatments of the continuum, the results are qualitatively different. In excited electronic states, three electronic structure methods, TDDFT, ADC(2), and CASSCF, have been used for the computation of the Dyson orbitals, while the continuum was treated at the B-spline/DFT level. We show that photoionization observables are sensitive probes of the nature of the excited states as well as of the quality of excited state wave functions. This paves the way for applications in more complex situations such as time resolved photoionization spectroscopy.

The Spin-Partitioned Total-Position Spread Tensor: An Application To Diatomic Molecules.

The spin partition (SP) of the total-position spread (TPS) tensor is applied to the case of a few light diatomic molecules at full configuration interaction (FCI) level. It appears that the SP-TPS tensor gives informations that are complementary with respect to the corresponding spin-summed (SS) quantity. The spin-summed total position-spread tensor (SS-TPS, Λ) is defined as the second moment cumulant of the total position operator, and the SP-TPS is its partition in equal (Λαα+ßß) and different spin (Λαß+ßα) contributions. Then, the SS-TPS allows description of the molecule charge mobility, while the SP-TPS allows description of the spin delocalization. The most relevant Cartesian-component for both tensors (SS-TPS and SP-TPS) is the component along the chemical bond (Λ(∥)), and it was found that its behavior was related to the type of interaction involved. For covalent bonds the SP-TPS has a squared growth when the bond is stretched, while for ionic bonds there exists a faster-than-linear growth after the avoided-crossing between the covalent and the ionic states. Other exotic bonds, like He2 and Be2, were also considered, and a particular spin delocalization was able to describe the different character of the two weakly bonded molecules, and specially the multireference character of the wave function along the dissociative potential energy curve.

Spin density and orbital optimization in open shell systems: A rational and computationally efficient proposal.

The present work describes a new method to compute accurate spin densities for open shell systems. The proposed approach follows two steps: first, it provides molecular orbitals which correctly take into account the spin delocalization; second, a proper CI treatment allows to account for the spin polarization effect while keeping a restricted formalism and avoiding spin contamination. The main idea of the optimization procedure is based on the orbital relaxation of the various charge transfer determinants responsible for the spin delocalization. The algorithm is tested and compared to other existing methods on a series of organic and inorganic open shell systems. The results reported here show that the new approach (almost black-box) provides accurate spin densities at a reasonable computational cost making it suitable for a systematic study of open shell systems.

Metal-Metal Interactions in Trinuclear Copper(II) Complexes [Cu3(RCOO)4(H2TEA)2] and Binuclear [Cu2(RCOO)2(H2TEA)2]. Syntheses and Combined Structural, Magnetic, High-Field Electron Paramagnetic Resonance, and Theoretical Studies.

The trinuclear [Cu3(RCOO)4(H2TEA)2] copper(II) complexes, where RCOO(-) = 2-furoate (1), 2-methoxybenzoate (2), and 3-methoxybenzoate (3, 4), as well as dimeric species [Cu2(H2TEA)2(RCOO)2]·2H2O, have been prepared by adding triethanolamine (H3TEA) at ambient conditions to hydrated Cu(RCOO)2 salts. The newly synthesized complexes have been characterized by elemental analyses, spectroscopic techniques (IR and UV-visible), magnetic susceptibility, single crystal X-ray structure determination and theoretical calculations, using a Difference Dedicated Configuration Interaction approach for the evaluation of magnetic coupling constants. In 1 and 2, the central copper atom lies on an inversion center, while in the polymorphs 3 and 4, the three metal centers are crystallographically independent. The zero-field splitting parameters of the trimeric compounds, D and E, were derived from high-field, high-frequency electron paramagnetic resonance spectra at temperatures ranging from 3 to 290 K and were used for the interpretation of the magnetic data. It was found that the dominant interaction between the terminal and central Cu sites J12 is ferromagnetic in nature in all complexes, even though differences have been found between the symmetrical or quasi-symmetrical complexes 1-3 and non-symmetrical complex 4, while the interaction between the terminal centers, J23, is negligible.

Metal-ligand delocalization and spin density in the CuCl2 and [CuCl4](2-) molecules: Some insights from wave function theory.

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl2 and [CuCl4](2-) systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that each valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.

Electronic reorganization triggered by electron transfer: the intervalence charge transfer of a Fe³âº/Fe²âº bimetallic complex.

The key role of the molecular orbitals in describing electron transfer processes is put in evidence for the intervalence charge transfer (IVCT) of a synthetic nonheme binuclear mixed-valence Fe(3+)/Fe(2+) compound. The electronic reorganization induced by the IVCT can be quantified by controlling the adaptation of the molecular orbitals to the charge transfer process. We evaluate the transition energy and its polarization effects on the molecular orbitals by means of ab initio calculations. The resulting energetic profile of the IVCT shows strong similarities to the Marcus' model, suggesting a response behaviour of the ensemble of electrons analogue to that of the solvent. We quantify the extent of the electronic reorganization induced by the IVCT process to be 11.74 eV, a very large effect that induces the crossing of states reducing the total energy of the transfer to 0.89 eV.

Assessment of multireference perturbation methods for chemical reaction barrier heights.

A few flavors of multireference perturbation theory, two variants of the n-electron valence state perturbation theory and two of the complete active space perturbation theory, are here tested for the calculation of barrier heights for the set of chemical reactions included in the DBH24/08 database, for which very accurate values are available. The comparison of the results obtained with these approaches with those already published for other theoretical models indicates that multireference perturbation theory is a valuable tool for the description of a chemical reaction. Moreover, limiting the comparison to the perturbation theory approaches, one observes that the bad behavior found for single reference methods (such as Møller-Plesset to second and fourth order in the energy) is markedly improved upon moving to the multireference generalizations.

The Dalton quantum chemistry program system.

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Improving the calculation of magnetic coupling constants in MRPT methods.

The magnetic coupling in transition metal compounds with more than one unpaired electron per magnetic center has been studied with multiconfigurational perturbation theory. The usual shortcomings of these methodologies (severe underestimation of the magnetic coupling) have been overcome by describing the Slater determinants with a set of molecular orbitals that maximally resemble the natural orbitals of a high-level multiconfigurational reference configuration interaction calculation. These orbitals have significant delocalization tails onto the bridging ligands and largely increase the coupling strengths in the perturbative calculation.

Dynamical photoionization observables of the CS molecule: the role of electron correlation.

Highly correlated calculations are performed on the primary ionic states and the prominent satellite present in the outer valence photoelectron spectrum of carbon monosulfide (CS). Dyson orbitals are coupled to accurate one particle continuum orbitals to provide a correlated description of energy dependent cross sections, asymmetry parameters, branching ratios, and molecular frame photoelectron angular distributions. The comparison with results obtained at the Hartree-Fock and Density Functional Theory level shows the strong sensitivity of these observables to details of the correlation in the bound states. The behaviour of the well characterized satellite state is analyzed in detail, and shows differences from the relevant primary states, revealing the limitations of a simple intensity borrowing mechanism. The results resolve the intensity disagreement with experiment obtained at the level of the sudden approximation.

Some useful odds and ends from the n-electron valence state perturbation theory.

The n-electron valence state perturbation theory makes use of zero-order wave functions whose energies are endowed with a direct physical interest, describing various processes occurring in the active space (removal/addition of one or two electrons, electronic excitations). It is shown that the zero-order energies related to the process of removal of an electron from the active space provide a reasonable and cheap approximation to the vertical ionization potentials. The zero-order energies referring to the process of an electronic excitation within the active space can also provide a first approximation to electronic transition energies, provided that a careful choice of the active molecular orbitals is performed. Test calculations have been carried out on the molecules N2 and H2CO.