Assessment of Multireference Perturbation Methods for Chemical Reaction Barrier Heights

A few flavors of multireference perturbation theory, two variants of the <i>n</i>-electron valence state perturbation theory and two of the complete active space perturbation theory, are here tested for the calculation of barrier heights for the set of chemical reactions included in the DBH24/08 database, for which very accurate values are available. The comparison of the results obtained with these approaches with those already published for other theoretical models indicates that multireference perturbation theory is a valuable tool for the description of a chemical reaction. Moreover, limiting the comparison to the perturbation theory approaches, one observes that the bad behavior found for single reference methods (such as Møller–Plesset to second and fourth order in the energy) is markedly improved upon moving to the multireference generalizations

Density Relaxation in Time-Dependent Density Functional Theory: Combining Relaxed Density Natural Orbitals and Multireference Perturbation Theories for an Improved Description of Excited States

Making use of the recently developed excited state charge displacement analysis [E. Ronca et al., <i>J</i>. <i>Chem</i>. <i>Phys</i>. <b>140</b>, 054110 (2014)], suited to quantitatively characterize the charge fluxes coming along an electronic excitation, we investigate the role of the density relaxation effects in the overall description of electronically excited states of different nature, namely, valence, ionic, and charge transfer (CT), considering a large set of prototypical small and medium-sized molecular systems. By comparing the response densities provided by time-dependent density functional theory (TDDFT) and the corresponding relaxed densities obtained by applying the Z-vector postlinear-response approach [N. C. Handy and H. F. Schaefer, <i>J</i>. <i>Chem</i>. <i>Phys</i>. <b>81</b>, 5031 (1984)] with those obtained by highly correlated state-of-the-art wave function calculations, we show that the inclusion of the relaxation effects is imperative to get an accurate description of the considered excited states. We also examine what happens at the quality of the response function when an increasing amount of Hartree–Fock (HF) exchange is included in the functional, showing that the usually improved excitation energies in the case of CT states are not always the consequence of an improved description of their overall properties. Remarkably, we find that the relaxation of the response densities is always able to reproduce, independently of the extent of HF exchange in the functional, the benchmark wave function densities. Finally, we propose a novel and computationally convenient strategy, based on the use of the natural orbitals derived from the relaxed TDDFT density to build zero-order wave function for multireference perturbation theory calculations. For a significant set of different excited states, the proposed approach provided accurate excitation energies, comparable to those obtained by computationally demanding ab initio calculations

Behavior of the Position–Spread Tensor in Diatomic Systems

The behavior of the Position–Spread Tensor (<b>Λ</b>) in a series of light diatomic molecules (either neutral or negative ions) is investigated at a Full Configuration Interaction level. This tensor, which is the second moment cumulant of the total position operator, is invariant with respect to molecular translations, while its trace is also rotationally invariant. Moreover, the tensor is additive in the case of noninteracting subsystems and can be seen as an intrinsic property of a molecule. In the present work, it is shown that the longitudinal component of the tensor, <b>Λ</b>_∥, which is small for internuclear distances close to the equilibrium, tends to grow if the bond is stretched. A maximum is reached in the region of the bond breaking, then <b>Λ</b>_∥ decreases and converges toward the isolated-atom value. The degenerate transversal components, <b>Λ</b>_⊥, on the other hand, usually have a monotonic growth toward the atomic value. The Position Spread is extremely sensitive to reorganization of the molecular wave function, and it becomes larger in the case of an increase of the electron mobility, as illustrated by the neutral-ionic avoided crossing in LiF. For these reasons, the Position Spread can be an extremely useful property that characterizes the nature of the wave function in a molecular system

Beryllium Dimer: A Bond Based on Non-Dynamical Correlation

The bond nature in beryllium dimer has been theoretically investigated using high-level <i>ab initio</i> methods. A series of ANO basis sets of increasing quality, going from sp to spdf ghi contractions, has been employed, combined with HF, CAS-SCF, CISD, and MRCI calculations with several different active spaces. The quality of these calculations has been checked by comparing the results with valence Full-CI calculations, performed with the same basis sets. It is shown that two quasi-degenerated partly occupied orbitals play a crucial role to give a qualitatively correct description of the bond. Their nature is similar to that of the edge orbitals that give rise to the quasi-degenerated singlet–triplet states in longer beryllium chains

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 <i>cis</i> isomer and the <i>trans</i> 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

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

Metal–Metal Interactions in Trinuclear Copper(II) Complexes [Cu₃(RCOO)₄(H₂TEA)₂] and Binuclear [Cu₂(RCOO)₂(H₂TEA)₂]. Syntheses and Combined Structural, Magnetic, High-Field Electron Paramagnetic Resonance, and Theoretical Studies

The trinuclear [Cu₃­(RCOO)₄­(H₂TEA)₂] copper­(II) complexes, where RCOO^– = 2-furo­ate (<b>1</b>), 2-methoxy­benzo­ate (<b>2</b>), and 3-methoxy­benzo­ate (<b>3</b>, <b>4</b>), as well as dimeric species [Cu₂­(H₂TEA)₂­(RCOO)₂]·​2H₂O, have been prepared by adding tri­ethanol­amine (H₃TEA) at ambient conditions to hydrated Cu­(RCOO)₂ salts. The newly synthesized complexes have been characterized by elemental analyses, spectroscopic techniques (IR and UV–visible), magnetic susceptibility, single crystal X-ray structure determination and theoretical calculations, using a Difference Dedicated Configuration Interaction approach for the evaluation of magnetic coupling constants. In <b>1</b> and <b>2</b>, the central copper atom lies on an inversion center, while in the polymorphs <b>3</b> and <b>4</b>, the three metal centers are crystallographically independent. The zero-field splitting parameters of the trimeric compounds, <i>D</i> and <i>E</i>, were derived from high-field, high-frequency electron paramagnetic resonance spectra at temperatures ranging from 3 to 290 K and were used for the interpretation of the magnetic data. It was found that the dominant inter­action between the terminal and central Cu sites <i>J</i>₁₂ is ferro­magnetic in nature in all complexes, even though differences have been found between the symmetrical or quasi-symmetrical complexes <b>1</b>–<b>3</b> and non-symmetrical complex <b>4</b>, while the inter­action between the terminal centers, <i>J</i>₂₃, is negligible

Metal–Metal Interactions in Trinuclear Copper(II) Complexes [Cu₃(RCOO)₄(H₂TEA)₂] and Binuclear [Cu₂(RCOO)₂(H₂TEA)₂]. Syntheses and Combined Structural, Magnetic, High-Field Electron Paramagnetic Resonance, and Theoretical Studies

The trinuclear [Cu₃­(RCOO)₄­(H₂TEA)₂] copper­(II) complexes, where RCOO^– = 2-furo­ate (<b>1</b>), 2-methoxy­benzo­ate (<b>2</b>), and 3-methoxy­benzo­ate (<b>3</b>, <b>4</b>), as well as dimeric species [Cu₂­(H₂TEA)₂­(RCOO)₂]·​2H₂O, have been prepared by adding tri­ethanol­amine (H₃TEA) at ambient conditions to hydrated Cu­(RCOO)₂ salts. The newly synthesized complexes have been characterized by elemental analyses, spectroscopic techniques (IR and UV–visible), magnetic susceptibility, single crystal X-ray structure determination and theoretical calculations, using a Difference Dedicated Configuration Interaction approach for the evaluation of magnetic coupling constants. In <b>1</b> and <b>2</b>, the central copper atom lies on an inversion center, while in the polymorphs <b>3</b> and <b>4</b>, the three metal centers are crystallographically independent. The zero-field splitting parameters of the trimeric compounds, <i>D</i> and <i>E</i>, were derived from high-field, high-frequency electron paramagnetic resonance spectra at temperatures ranging from 3 to 290 K and were used for the interpretation of the magnetic data. It was found that the dominant inter­action between the terminal and central Cu sites <i>J</i>₁₂ is ferro­magnetic in nature in all complexes, even though differences have been found between the symmetrical or quasi-symmetrical complexes <b>1</b>–<b>3</b> and non-symmetrical complex <b>4</b>, while the inter­action between the terminal centers, <i>J</i>₂₃, is negligible

OpenMolcas: From source code to insight

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with post calculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory and new electronic and muonic basis sets