Renzo Cimiraglia

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.

Second order perturbation correction to CI energies by use of diagrammatic techniques: An improvement to the CIPSI algorithm

A usual procedure to get a large fraction of the correlation energy consists in the evaluation of the second order perturbation contribution to the electronic energy by utilizing as zeroth order state a moderate size CI wave function (CIPSI algorithm). A scheme of calculation based on a hole‐particle formulation of the Hamiltonian, leading to a diagrammatic pattern quite similar to the one used for the one‐determinant case, is proposed and discussed.

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 free energy changes of a solution in light absorption or emission processes

Abstract A simple model to evaluate energy changes in dilute solutions produced by absorption or emission of light is proposed. The computational scheme exploits some characteristics of the continuum model of liquids and is inserted into ab initio quantum-mechanical programs for isolated molecules. The model is addressed to evaluate changes in thermodynamic properties of the whole solution — while earlier models often consider the solute only — and it presents a detailed decomposition of the phenomenon into successive steps.

A novel perturbation-based complete active space–self-consistent-field algorithm: Application to the direct calculation of localized orbitals

A complete active space–self-consistent-field (CAS–SCF) algorithm based on molecular orbitals that conserve their physical nature during the iterative process is proposed. The algorithm consists of an iterative procedure based on the imposition of the generalized Brillouin theorem to a complete active space-configuration interaction wave function. At convergence, the wave function is identical to the corresponding one obtained using canonical CAS–SCF orbitals, provided the nature of the active space is the same. If localized guess orbitals are used, the locality property is conserved by the final orbitals. Test calculations illustrate the interest of the proposed approach, that permits to control the nature of the active space.