Multi-reference 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.Comment: 9 pages, 4 figures, 2 table

The role of the magnetic orbitals in the calculation of the magnetic coupling constants from multireference perturbation theory methods

The use of multireference perturbation theory (MRPT) for the calculation of the magnetic coupling in binuclear complexes has shown to give poor results if applied on a minimal active space complete active space self-consistent field (CASSCF) wavefunction. In this work, we identify the origin of this problem in the starting CASSCF orbitals, which are exceedingly localized on the metal atoms. Focusing on the case of antiferromagnetic systems, it is shown that the form of the active orbitals has a dramatic effect on the relative description of the neutral and ionic structures. Finally, a simple and computational inexpensive strategy is proposed for the calculation of a set of magnetic orbitals describing in a more balanced way the neutral and ionic structures. The use of these orbitals, instead the CASSCF ones, in minimal active space MRPT2 calculations leads to a marked improvement of the J values, which become in reasonable agreement with those obtained with the expensive high level difference dedicated configuration interaction approach and with the experimental value

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 Jeziorsky-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. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction (FCI) 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.Comment: 4 figures, 18 page

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 Brillouin’s 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 ferroand antiferromagnetic contributions to the coupling constan

A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave functio

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

Mapping The Excited State Potential Energy Surface Of A Retinal Chromophore Model With Multireference And Equation-of-motion Coupled-cluster Methods

The photoisomerization of the retinal chromophore of visual pigments proceeds along a complex reaction coordinate on a multidimensional surface that comprises a hydrogen-out-of-plane (HOOP) coordinate, a bond length alternation (BLA) coordinate, a single bond torsion and, finally, the reactive double bond torsion. These degrees of freedom are coupled with changes in the electronic structure of the chromophore and, therefore, the computational investigation of the photochemistry of such systems requires the use of a methodology capable of describing electronic structure changes along all those coordinates. Here, we employ the penta-2,4-dieniminium (PSB3) cation as a minimal model of the retinal chromophore of visual pigments and compare its excited state isomerization paths at the CASSCF and CASPT2 levels of theory. These paths connect the cis isomer and the trans isomer of PSB3 with two structurally and energetically distinct conical intersections (CIs) that belong to the same intersection space. MRCISD+Q energy profiles along these paths provide benchmark values against which other ab initio methods are validated. Accordingly, we compare the energy profiles of MRPT2 methods (CASPT2, QD-NEVPT2, and XMCQDPT2) and EOM-SF-CC methods (EOM-SF-CCSD and EOM-SF-CCSD(dT)) to the MRCISD+Q reference profiles. We find that the paths produced with CASSCF and CASPT2 are topologically and energetically different, partially due to the existence of a locally excited region on the CASPT2 excited state near the Franck-Condon point that is absent in CASSCF and that involves a single bond, rather than double bond, torsion. We also find that MRPT2 methods as well as EOM-SF-CCSD(dT) are capable of quantitatively describing the processes involved in the photoisomerization of systems like PSB3

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

A 1D numerical study of the salt diffusion in a solar pond using finite difference tecniques

A simple one dimensional (1D) model for the study of the salt diffusion processes in a solar pond is presented together with the implementation in a computer program using standard finite differences technique. The convective motions are not explicitly taken into account in this model and comments on their importance are presented. Albeit its simplicity the approach here reported can shed light on the basic effects taking place in the dynamics of a solar pond. The importance of the temperature profile and of the Soret effect is discussed

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