Stefano Evangelisti

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.

Convergence of an improved CIPSI algorithm

Abstract The configuration interaction CIPSI algorithm defines three classes of determinants of decreasing importance; the most important ones (∼ 100) are generators, the mean class (∼ 10 3 ) is treated variationally or to the fourth order, while the less important ones (∼ 10 5 ) are treated to the second order only. The accuracy of the result is studied as a function of the borders between the classes in the case of H 2 O (double-zeta basis set), where the exact solution is known, and for the nearly degenerate CN + problem.

A vector and parallel full configuration interaction algorithm

A full configuration interaction (FCI) algorithm is presented and discussed. It is an integral driven formalism based on the explicit construction of tables which realize the correspondence between the FCI vector x and the vector Hx, H being the Hamiltonian matrix of the system. In this way no decomposition of the identity is needed, and in the simplest implementation only the two vectors x and Hx need to be kept on disk. The main test has been done on the cyclic polyene C18H18 in the Pariser–Parr–Pople approximation, where the size of the FCI vector can be reduced to about 73 million components. Running on a CRAY Y‐MP with 4 CPU and 32 MW of core memory, we obtained an elapsed CPU time per iteration of about 300 s and a total elapsed time of 1000 s, which correspond to about 4 and 14 s per million determinants, respectively. The parallel CPU speed‐up obtained by running with the 4 CPU is greater than 3, without any substantial increasing of the memory or disk requirements.

Direct generation of local orbitals for multireference treatment and subsequent uses for the calculation of the correlation energy

We present a method that uses the one-particle density matrix to generate directly localized orbitals dedicated to multireference wave functions. On one hand, it is shown that the definition of local orbitals making possible physically justified truncations of the CAS (complete active space) is particularly adequate for the treatment of multireference problems. On the other hand, as it will be shown in the case of bond breaking, the control of the spatial location of the active orbitals may permit description of the desired physics with a smaller number of active orbitals than when starting from canonical molecular orbitals. The subsequent calculation of the dynamical correlation energy can be achieved with a lower computational effort either due to this reduction of the active space, or by truncation of the CAS to a shorter set of references. The ground- and excited-state energies are very close to the current complete active space self-consistent field ones and several examples of multireference singles and doubles calculations illustrate the interest of the procedure.

3,5-Bis(ethynyl)pyridine and 2,6-bis(ethynyl)pyridine spanning two Fe(Cp*)(dppe) units: role of the nitrogen atom on the electronic and magnetic couplings.

The role of the nitrogen atom on the electronic and magnetic couplings of the mono-oxidized and bi-oxidized pyridine-containing complex models [2,6-{Cp(dpe)Fe-C≡C-}(2)(NC(5)H(3))](n+) and [3,5-{Cp(dpe)Fe-C≡C-}(2)(NC(5)H(3))](n+) is theoretically tackled with the aid of density-functional theory (DFT) and multireference configuration interaction (MR-CI) calculations. Results are analyzed and compared to those obtained for the reference complex [1,3-{Cp*(dppe)Fe-C≡C-)}(2)(C(6)H(4))](n+). The mono-oxidized species show an interesting behavior at the borderline between spin localization and delocalization and one through-bond communication path among the two involving the central ring, is favored. Investigation of the spin state of the dicationic complexes indicates ferromagnetic coupling, which can differ in magnitude from one complex to the other. Very importantly, electronic and magnetic properties of these species strongly depend not only upon the location of the nitrogen atom in the ring versus that of the organometallic end-groups but also upon the architectural arrangement of one terminus, with respect to the other and/or vis-à-vis the central ring. To help validate the theoretical results, the related families of compounds [1,3-{Cp*(dppe)Fe-C≡C-)}(2)(C(6)H(4))](n+), [2,6-{Cp*(dppe)Fe-C≡C-}(2)(NC(5)H(3))](n+), [3,5-{Cp*(dppe)Fe-C≡C-}(2)(NC(5)H(3))](n+) (n = 0-2) were experimentally synthesized and characterized. Electrochemical, spectroscopic (infrared (IR), Mössbauer), electronic (near-infrared (NIR)), and magnetic properties (electron paramagnetic resonance (EPR), superconducting quantum interference device (SQUID)) are discussed and interpreted in the light of the theoretical data. The set of data obtained allows for many strong conclusions to be drawn. A N atom in the long branch increases the ferromagnetic interaction between the two Fe(III) spin carriers (J > 500 cm(-1)), whereas, when placed in the short branch, it dramatically reduces the magnetic exchange in the di-oxidized species (J = 2.14(5) cm(-1)). In the mixed-valence compounds, when the N atom is positioned on the long branch, the intermediate excited state is higher in energy than the different ground-state conformers and the relaxation process provides exclusively the Fe(II)/Fe(III) localized system (H(ab) ≠ 0). Positioning the N atom on the short branch modifies the energy profile and the diabatic mediating state lies just above the reactant and product diabatic states. Consequently, the LMCT transition becomes less energetic than the MMCT transition. Here, the direct coupling does not occur (H(ab) = 0) and only the coupling through the bridge (c) and the reactant (a) and product (b) diabatic states is operating (H(ac) = H(bc) ≠ 0).

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.

A theoretical study of the nitrogen clusters formed from the ions N3−, N5+, and N5−

The results of a theoretical study on the formation of the nitrogen cluster N10 from the ionic species N5+ and N5− are presented. The possibility to form N8 from N5+ and N3− has also been studied but no stable form was found. Structural and vibrational data are given for the different clusters. It is suggested that the anion N5− might be stable enough to be synthesized. The calculations have been carried out using multiconfigurational self-consistent-field wave functions and second-order perturbation theory.

A full-configuration benchmark for the N2 molecule

Abstract A full-configuration interaction (FCI) calculation has been performed for the nitrogen molecule using an ANO [4s3p1d] basis set. The FCI space for such a system contains about 9.68×109 symmetry-adapted Slater determinants. The FCI results are compared with several approximate methods, both of single- and multi-reference type, in order to test their accuracy.

A theoretical study of ten N8 isomers

The HF/3s2pld and MP2/3s2pld structures, energies and vibrational frequencies were calculated for ten N8 isomers, corresponding to ten analogous CH structures. Comparative calculations using density functional theory (DFT), with a cc-pVTZ basis set, were also performed. All ten structures were found to be local minima on the energy hypersurface at the Hartree-Fock (HF) level, whereas at the second-order Moller-Plesset (MP2) level nine structures were stable. At the DFT level, eight local minima were found. The total energies were recomputed using 4s3p2dlf basis sets at the HF and MP2 levels of theory.

The use of local orbitals in multireference calculations

CAS-SCF-type algorithms based on molecular orbitals that preserve their physical nature during the iterative process have been proposed recently by our groups. Our approach is based on the iterative partial diagonalization of the one-body reduced density matrix. If localized guess orbitals are used, the locality property is kept by the final orbitals. The use of local orbitals in multiference calculations has several advantages. It can be used to reduce the number of active orbitals in CAS-SCF calculations on large systems, and in general to have a better control on the physical nature of the active space. The reduction from a complete to a selected reference space is also possible in the case of configuration interaction calculations. The technique is illustrated through applications to the description of bond breaking and n → π* excited states in conjugated systems. The efficiency of selection of local excitations is shown on a magnetic complex.