Laboratoire de Chimie et Physique Quantiques

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.

A method is proposed to calculate the effect of configuration interaction by a Rayleigh-Schrödinger perturbation expansion when starting from a multiconfigurational wavefunction. It is shown that a careless choice of H0 may lead to absurd transition energies between two states, at the first orders of the perturbation, even when the perturbation converges for both states. A barycentric defintion of H0 is proposed, which ensures the cancellation of common diagrams in the calculated transition energies. A practical iterative procedure is defined which allows a progressive improvement of the unperturbed wavefunction ψ0; the CI matrix restricted to a subspace S of strongly interacting determinants is diagonalized. The desired eigenvector ψ0 of this matrix is perturbed by the determinants which do not belong to S. The most important determinants in ψ1 are added to S, etc. The energy thus obtained after the second-order correction is compared with the ordinary perturbation series where ψ0 is a single determinant. For the ground state, this procedure includes, besides the whole second-order correction, the most important terms of the third and fourth orders. The question of orthogonality of excited states is discussed. This technique, hereafter called CIPSI, has been tested on the ground and several excited states of H2, Ne, and MgO, showing both a rapid convergence of the calculated transition energy and the importance of correlation effects on transition energy.

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability ${A}_{k}$ which depends on the number of preexisting links $k$ to that site. For homogeneous connection kernels, ${A}_{k}\ensuremath{\sim}{k}^{\ensuremath{\gamma}}$, different behaviors arise for $\ensuremath{\gamma}<1$, $\ensuremath{\gamma}>1$, and $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. For $\ensuremath{\gamma}<1$, the number of sites with $k$ links, ${N}_{k}$, varies as a stretched exponential. For $\ensuremath{\gamma}>1$, a single site connects to nearly all other sites. In the borderline case ${A}_{k}\ensuremath{\sim}k$, the power law ${N}_{k}\ensuremath{\sim}{k}^{\ensuremath{-}\ensuremath{\nu}}$ is found, where the exponent $\ensuremath{\nu}$ can be tuned to any value in the range $2<\ensuremath{\nu}<\ensuremath{\infty}$.

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.

Entering Dirac territory: This Minireview provides a guide to two- and four-component relativistic Hamiltonians for use in quantum chemistry with particular emphasis on the recently developed eXact two-component (X2C) Hamiltonian.

We study the dynamics of a fully coupled network of N classical rotators, which can also be viewed as a mean-field XY Heisenberg (HMF) model, in the attractive (ferromagnetic) and repulsive (antiferromagnetic) cases. The exact free energy and the spectral properties of a Vlasov-Poisson equation give hints on the values of dynamical observables and on time relaxation properties. At high energy (high temperature T) the system relaxes to Maxwellian equilibrium with vanishing magnetization, but the relaxation time to the equilibrium momentum distribution diverges with N as ${\mathit{NT}}^{2}$ in the ferromagnetic case and as ${\mathit{NT}}^{3/2}$ in the antiferromagnetic case. The N dependence of the relaxation time is suggested by an analogy of the HMF model with gravitational and charged sheets dynamics in one dimension and is verified in numerical simulations. Below the critical temperature the ferromagnetic HMF mode shows a collective phenomenon where the rotators form a drifting cluster; we argue that the drifting speed vanishes as ${\mathit{N}}^{\mathrm{\ensuremath{-}}1/2}$ but increases as one approaches the critical point (a manifestation of critical slowing down). For the antiferromagnetic HMF model a two-cluster drifting state with zero magnetization forms spontaneously at very small temperatures; at larger temperatures an initial density modulation produces this state, which relaxes very slowly. This suggests the possibility of exciting magnetized states in a mean-field antiferromagnetic system.

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

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The effect of nonorthogonality in the broken symmetry approach to magnetic coupling has been explicitly considered for the first time in Hartree−Fock and a variety of DFT methods. On the basis of the results for three different systems, representative of a variety of physical situations it is shown that the most often quoted trend concerning the much larger degree of delocalization of magnetic orbitals obtained from DFT, as opposed to Hartree−Fock, is not fully justified. A new and simple way to relate the overlap integral entering into the calculation and the spin density is proposed and tested in a variety of model systems.

Femtosecond high-resolution pump-probe experiments have been used together with theoretical ab initio quantum calculations and wave packet dynamics simulations to decode an optimal femtosecond pulse that is generated from adaptive learning algorithms. This pulse is designed to maximize the yield of the organometallic ion CpMn(CO)3 while hindering the competing fragmentation. The sequential excitation and ionization of the target ion are accomplished by an optimized field consisting of two dominant subpulses with optimal frequencies and time delays.

The diffusion of protons through water is understood within the framework of the Grotthuss mechanism, which requires that they undergo structural diffusion in a stepwise manner throughout the water network. Despite long study, this picture oversimplifies and neglects the complexity of the supramolecular structure of water. We use first-principles simulations and demonstrate that the currently accepted picture of proton diffusion is in need of revision. We show that proton and hydroxide diffusion occurs through periods of intense activity involving concerted proton hopping followed by periods of rest. The picture that emerges is that proton transfer is a multiscale and multidynamical process involving a broader distribution of pathways and timescales than currently assumed. To rationalize these phenomena, we look at the 3D water network as a distribution of closed directed rings, which reveals the presence of medium-range directional correlations in the liquid. One of the natural consequences of this feature is that both the hydronium and hydroxide ion are decorated with proton wires. These wires serve as conduits for long proton jumps over several hydrogen bonds.

The theory of effective Hamiltonians is well established. However, limitations appear in its applicability for many problems in molecular physics and quantum chemistry. The standard effective Hamiltonians may become strongly non-Hermitian when there is a large coupling between the model space, in which they are defined, and the outer space Moreover, in the presence of intruder states, discontinuities appear in the matrix elements of these effective Hamiltonians as a function of the internuclear distances. To solve these difficulties, a new class of effective Hamiltonians (called intermediate Hamiltonians) is presented; only one part of their roots are exact eigen-energies of the full Hamiltonian. The theory of these intermediate Hamiltonians is presented by means of a new wave-operator R which is the analogue of the wave-operator Omega in the theory of effective Hamiltonians. Solutions are obtained by a generalised degenerate perturbation theory (GDPT) and by iterative procedures. Two model systems are numerically solved which demonstrate the good convergence properties of GDPT with respect to standard degenerate perturbation theory (DPT). Continuity of the solutions is also checked in the presence of an intruder state.

), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, CC3, CCSDT., and CCSDTQ. It turns out that CCSDTQ yields a negligible difference with the extrapolated CI values with a mean absolute error as small as 0.01 eV, whereas the coupled cluster approaches including iterative triples are also very accurate (mean absolute error of 0.03 eV). Consequently, CCSDT-3 and CC3 can be used to define reliable benchmarks. This observation does not hold for ADC(3) that delivers quite large errors for this set of small compounds, with a clear tendency to overcorrect its second-order version, ADC(2). Finally, we discuss the possibility to use basis set extrapolation approaches so as to tackle more easily larger compounds.

The recently proposed ab initio effective Hamiltonian technique is extended to polymer calculations and applied to various conformations of polyacetylene (all-trans, cis-transoid, and trans-cisoid) and polydiacetylene (acetylenic and butatrienic backbones). Band structures, density of states (DOS), and XPS theoretical spectra are presented. Comparison of the band structures and DOS with those obtained by ab initio SCF (self-consistent-field) Hartree–Fock calculations of double zeta quality is excellent. The XPS theoretical spectrum for all-trans polyacetylene is in good agreement with experiment. In polyacetylene, it is found that the π bands are quite similar for all three backbone conformations, though the σ bands differ significantly. For polydiacetylene, low ionization potentials are predicted—a few tenths of an eV larger than polyacetylene for the acetylenic backbone and a few tenths of an eV smaller than polyacetylene for the butatrienic backbone.

Monometallic Ni(II) and Co(II) complexes with large magnetic anisotropy are studied using correlated wave function based ab initio calculations. Based on the effective Hamiltonian theory, we propose a scheme to extract both the parameters of the zero-field splitting (ZFS) tensor and the magnetic anisotropy axes. Contrarily to the usual theoretical procedure of extraction, the method presented here determines the sign and the magnitude of the ZFS parameters in any circumstances. While the energy levels provide enough information to extract the ZFS parameters in Ni(II) complexes, additional information contained in the wave functions must be used to extract the ZFS parameters of Co(II) complexes. The effective Hamiltonian procedure also enables us to confirm the validity of the standard model Hamiltonian to produce the magnetic anisotropy of monometallic complexes. The calculated ZFS parameters are in good agreement with high-field, high-frequency electron paramagnetic resonance spectroscopy and frequency domain magnetic resonance spectroscopy data. A methodological analysis of the results shows that the ligand-to-metal charge transfer configurations must be introduced in the reference space to obtain quantitative agreement with the experimental estimates of the ZFS parameters.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster 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 for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Improved three-parameter atomic pseudopotentials are theoretically determined from lithium to krypton. In view of further molecular calculations, accurate expressions are given for the pseudopotential matrix elements between cartesian gaussian functions. These matrix elements are introduced into the standard IBMOL/H programme leading to the PSIBMOL algorithm. The method is tested on various hydrides of the first three rows of the Periodic Table at the independent particle approximation level. Satisfactory agreement is obtained between pseudopotential and all-electron molecular calculations.

Abstract The matrix elements of the total Hamiltonian between a multiconfigurational SCF wave function and some well‐defined linear combinations of excited Slater determinants are equal to zero. By means of this generalized Brillouin theorem it is possible to estimate the improvements to be expected from a subsequent configuration‐interaction treatment. The expression of the effective potential for the orbitals can be also derived in the frame of a given multiconfigurational theory. As an example, the case of the CMC‐SCF method recently suggested [9] is examined.

Abstract On décrit la méthode des orbitales cristallines, combinaisons linéaires d'orbitales atomiques ( LCAO  HCO ), inspirée des procédés classiques de la chimie quantique et permettant d'étudier théoriquement les systèmes périodiques. On déduit la forme explicite de quelques grandeurs caractéristiques dans l'approximation de Hückel. La méthode est comparée à l'approximation dite des électrons “quasi‐atomiques” et appliquée aux polyènes, aux polyacènes, et au graphite. La validité générale du procédé est discutée dans la conclusion.

R2P̈-C̈-X or R2P⊕  C⊖-X or R2PC-X—which form best describes the activity of the title compound 1? On the basis of its reactions with Me3SiCl, Me3SiN3 and DMSO as well as NMR data, 1 was hitherto regarded as a species with PC multibonding. That 1 is rather a carbene, could now be deduced, inter alia, from the addition of electron deficient alkenes (→2) and tert-butyl isocyanide (→3) (R=iPr2N, X = SiMe3).