Celestino Angeli

Introduction of n-electron valence states for multireference perturbation theory

The present work presents three second-order perturbative developments from a complete active space (CAS) zero-order wave function, which are strictly additive with respect to molecular dissociation and intruder state free. They differ by the degree of contraction of the outer-space perturbers. Two types of zero-order Hamiltonians are proposed, both are bielectronic, incorporating the interactions between electrons in the active orbitals, therefore introducing a rational balance between the zero-order wave function and the outer-space. The use of Dyall’s Hamiltonian, which puts the active electrons in a fixed core field, and of a partially contracted formalism seems a promising compromise. The formalism is generalizable to multireference spaces which are parts of a CAS. A few test applications of the simplest variant developed in this paper illustrate its potentialities.

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.

n-Electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants

The n-electron valence state perturbation theory is reformulated in a spin-free formalism, concentrating on the “strongly contracted” and “partially contracted” variants. The new formulation is based on the introduction of average values in the unperturbed state of excitation operators which bear resemblance with analogous ones occurring in the extended Koopmans’ theorem and in the equations-of-motion technique. Such auxiliary quantities, which allow the second-order perturbation contribution to the energy to be evaluated very efficiently, can be calculated at the outset provided the unperturbed four-particle spinless density matrix in the active orbital space is available. A noticeable inequality concerning second-order energy contributions of the same type between the strongly and partially contracted versions is proven to hold. An example concerning the successful calculation of the potential energy curve for the Cr2 molecule is discussed.

N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant

Abstract In this work we reconsider the strongly contracted variant of the n -electron valence state perturbation theory (SC NEV-PT) which uses Dyalls Hamiltonian to define the zero-order energies (SC NEV-PT(D)). We develop a formalism in which the key quantities used for the second-order perturbation correction to the energy are written in terms of the matrix elements of suitable operators evaluated on the zero-order wavefunction, without the explicit knowledge of the perturbation functions. The new formalism strongly improves the computation performances. As test cases we present two preliminary studies: (a) on N 2 where the convergence of the spectroscopic properties as a function of the basis set and CAS-CI space is discussed and (b) on Cr 2 where it is shown that the SC NEV-PT(D) method is able to provide the correct profile for the potential energy curve.

A quasidegenerate formulation of the second order n-electron valence state perturbation theory approach.

The n-electron valence state perturbation theory (NEVPT) is reformulated in a quasidegenerate (QD) approach. The new theory allows the treatment of cases where the proximity of the energies causes artifacts in the zero order description. Problems of quasidegeneration are relevant in the dynamics involving regions at avoided crossings (or conical intersections) and in spectroscopy where the energies and oscillator strengths can be strongly influenced by the mixing of states of different nature. Two test cases are analyzed concerning (a) the ionic-neutral avoided crossing in LiF and (b) the valence/Rydberg mixing in the excited states of ethene. The QD-NEVPT2 is shown to be a useful tool for such systems.

Third-order multireference perturbation theory: The n-electron valence state perturbation-theory approach

A formulation of the n-electron valence state perturbation theory (NEVPT) at the third order of perturbation is presented. The present implementation concerns the so-called strongly contracted variant of NEVPT, where only a subspace of the first-order interacting space is taken into account. The resulting strongly contracted NEVPT3 approach is discussed in three test cases: (a) the energy difference between the 3B1 and 1A1 states of the methylene molecule, (b) the potential-energy curve of the N2 molecule ground state, and (c) the chromium dimer (Cr2) ground-state potential-energy profile. Particular attention is devoted to the last case where large basis sets comprising also h orbitals are adopted and where remarkable differences between the second- and third-order results show up.

Dynamic Electron Correlation Effects on the Ground State Potential Energy Surface of a Retinal Chromophore Model.

The ground state potential energy surface of the retinal chromophore of visual pigments (e.g., bovine rhodopsin) features a low-lying conical intersection surrounded by regions with variable charge-transfer and diradical electronic structures. This implies that dynamic electron correlation may have a large effect on the shape of the force fields driving its reactivity. To investigate this effect, we focus on mapping the potential energy for three paths located along the ground state CASSCF potential energy surface of the penta-2,4-dieniminium cation taken as a minimal model of the retinal chromophore. The first path spans the bond length alternation coordinate and intercepts a conical intersection point. The other two are minimum energy paths along two distinct but kinetically competitive thermal isomerization coordinates. We show that the effect of introducing the missing dynamic electron correlation variationally (with MRCISD) and perturbatively (with the CASPT2, NEVPT2, and XMCQDPT2 methods) leads, invariably, to a stabilization of the regions with charge transfer character and to a significant reshaping of the reference CASSCF potential energy surface and suggesting a change in the dominating isomerization mechanism. The possible impact of such a correction on the photoisomerization of the retinal chromophore is discussed.

Analysis of the magnetic coupling in binuclear systems. III. The role of the ligand to metal charge transfer excitations revisited

In magnetic coordination compounds and solids the magnetic orbitals are essentially located on metallic centers but present some delocalization tails on adjacent ligands. Mean field variational calculations optimize this mixing and validate a single band modelization of the intersite magnetic exchange. In this approach, due to the Brillouins theorem, the ligand to metal charge transfer (LMCT) excitations play a minor role. On the other hand the extensive configuration interaction calculations show that the determinants obtained by a single excitation on the top of the LMCT configurations bring an important antiferromagnetic contribution to the magnetic coupling. Perturbative and truncated variational calculations show that contrary to the interpretation given in a previous article [C. J. Calzado et al., J. Chem. Phys. 116, 2728 (2002)] the contribution of these determinants to the magnetic coupling constant is not a second-order one. An analytic development enables one to establish that they contribute at higher order as a correlation induced increase in the LMCT components of the wave function, i.e., of the mixing between the ligand and the magnetic orbitals. This larger delocalization of the magnetic orbitals results in an increase in both the ferro- and antiferromagnetic contributions to the coupling constant.

On the applicability of multireference second-order perturbation theory to study weak magnetic coupling in molecular complexes.

The performance of multiconfigurational second‐order perturbation techniques is established for the calculation of small magnetic couplings in heterobinuclear complexes. Whereas CASPT2 gives satisfactory results for relatively strong magnetic couplings, the method shows important deviations from the expected Heisenberg spectrum for couplings smaller than 15–20 cm−1. The standard choice of the zeroth‐order CASPT2 Hamiltonian is compared to alternative definitions published in the literature and the stability of the results is tested against increasing level shifts. Furthermore, we compare CASPT2 with an alternative implementation of multiconfigurational perturbation theory, namely NEVPT2 and with variational calculations based on the difference dedicated CI technique.

On the nature of the π π* ionic excited states: The V state of ethene as a prototype†

This article addresses an analysis of the physical effects required for the correct description of the ionic π → π* excited states in the frame of ab initio quantum chemistry, using the ionic V state of the ethene molecule as an example. The importance of the dynamic σ polarization (absent in methods where the σ skeleton is treated at a mean‐field level) has been recognized by many authors in the past. In this article a new physical effect is described, i.e. the spatial contraction of the π and π* molecular orbitals (or of the local p atomic orbitals) originated from the reduction of the ionicity due to the dynamic σ polarization. Such an effect is a second‐order effect (it appears only as a consequence of the dynamic σ polarization) but it cannot be ignored. Many of the difficulties found in the past in the calculation of the vertical excitation energy of the ionic states are attributed to an incomplete description of this contraction, while the few successes have been obtained when it has been fortuitously introduced by ad hoc procedures or when it is described in a brute force approach. Various strategies are proposed to allow for the spatial contraction of the p atomic orbitals. If this effect is considered at the orbital optimization step, it is shown that for the V state of ethene no Rydberg/valence mixing occurs and a simple perturbation correction (to the second order in the energy) on the π → π* singly excited configuration gives stable results with respect to the computational parameters and in good agreement with the experimental findings and with the best theoretical calculations. Moreover, our results confirm the indication of Müller et al. (J Chem Phys 1999, 110, 7176) that the transition to the V state of ethene conforms to the Franck‐Condon principle and that it is not necessary to appeal to a nonvertical transition to interpret the experimental data. The strategy reported in this article for ethene can be in principle generalized to the π → π* ionic excited states of other molecules.