Multi-d-Occupancy as an Alternative Definition for the Double d-Shell Effect.

Despite the prevalence of first-row transition metal-containing compounds in virtually all areas of chemistry, the accurate modeling of these systems is a known challenge for the theoretical chemistry community. Such a challenge is shown in a myriad of facets; among them are difficulties in defining ground-state multiplicities, disagreement in the results from methods considered highly accurate, and convergence problems in calculations for excited states. These problems cause a scarcity of reliable theoretical data for transition metal-containing systems. In this work, we explore the double d-shell effect that plagues and makes the application of multireference methods to this type of system difficult. We propose an alternative definition for this effect based on the mixing among d-occupancy configurations or the multi-d-occupancy character of the wave function. Moreover, we present a protocol able to include this effect in multireference calculations using an active space smaller than that usually used in the literature. A molybdenum-copper model system and its copper subsystem are used as example study cases, in particular, the molybdenum-copper charge transfer of the former and the electron affinity of the latter. We have shown that our alternative definition can be used to analyze their reference wave functions qualitatively. Based on this qualitative description, it is possible to optimize an active space without a second d-shell able to obtain relative energies accurately. Seeing the double d-shell effect through the lens of a multi-d-occupancy character, it is possible to correctly describe the wave function, improve the accuracy of the relative energies, and reduce the computational cost of multireference calculations. That way, we believe that this alternative definition has the potential to improve the modeling of first-row transition metal-containing compounds both for their ground and excited electronic structures.

Diving into the optoelectronic properties of Cu(II) and Zn(II) curcumin complexes: a DFT and wavefunction benchmark.

CONTEXT: Curcumin is a popular food additive around the world whose medicinal properties have been known since ancient times. The literature has recently highlighted several biological properties, but besides the health-related usages, its natural yellowish color may also be helpful for light-harvesting applications. This research aims to close a knowledge gap regarding the photophysical description of curcumin and its metallic complexes. METHODS: We conducted benchmark experiments comparing NEVPT calculations with several DFT functionals (B3LYP, M06-L, M06-2X, CAM-B3LYP, and ωB97X-D) for describing the UV spectra of curcumin and its metallo-derivative, curcumin-copper(II). Once we determined the most suitable functional, we performed tests with different basis sets and conditions, such as solvation and redox state, to identify their impact on excited state properties. These results are also reported for the curcumin-zinc(II) derivative. We found that the accuracy of DFT functionals depends strongly on the nature of curcumin's excitations. Intra-ligand transitions dominate the absorption spectra of the complexes. Curcumin absorption is marginally affected by solvation and chelation, but when combined with redox processes, they may result in significant modifications. This is because copper cation changes its coordination geometry in response to redox conditions, changing the spectrum. We found that, compared to a NEVPT reference, B3LYP is the best functional for a general description of the compounds, despite not being appropriate for charge transfer transitions. M06-L was the best for LMCT transitions. However, compared with NEVPT2 and PNO-LCCSD(T)-F12 results, no functional achieved acceptable accuracy for MLCT transitions.

Geometric interpretation for coupled-cluster theory. A comparison of accuracy with the corresponding configuration interaction model.

Although coupled-cluster theory is well-known for its accuracy, the geometry associated with the manifold of wave functions reached by the coupled-cluster Ansatz has not been deeply explored. In this article, we look for an interpretation for the high accuracy of coupled-cluster theory based on how the manifold of coupled-cluster wave functions is embedded within the space of n-electron wave functions. We define the coupled-cluster and configuration interaction manifolds and measure the distances from the full-configuration interaction (FCI) wave function to these manifolds. We clearly observe that the FCI wave function is closer to the coupled-cluster manifold that is curved than to the configuration interaction manifold that is flat for the selected systems studied in this work. Furthermore, the decomposition of the distances among these manifolds and wave functions into excitation ranks gives insights into the failure of the coupled-cluster approach for multireference systems. The present results show a new interpretation for the quality of the coupled-cluster method, as contrasted to the truncated configuration interaction approach, besides the well-established argument based on size extensivity. Furthermore, we show how a geometric description of wave function methods can be used in electronic structure theory.

Can one use the electronic absorption spectra of metalloporphyrins to benchmark electronic structure methods? A case study on the cobalt porphyrin.

In this article, we describe calculations on the absorption spectrum of cobalt(ii) porphyrin, using density functional (DFT) and multireference n-electron valence perturbation (NEVPT) theories. With these calculations, we describe the lowest-energy states of doublet and quartet spin multiplicities, the excited states that originate the Q and B bands of porphyrins, some higher-energy π-π* excitations and charge-transfer states, HOMO-LUMO gaps, and ionisation potentials. Results undoubtedly show that the position of B band is essentially independent on the DFT functional, while the Q band is better described by pure functionals, and these bands do not depend on the initial state of the transition (whether doublet or quartet) as well. However, other excitation energies, orbital energies, and ionisation potentials strongly depend on the functional, in some cases varying more than 2 eV. Based on these results we conclude that one should not use the UV-Vis spectrum of metalloporphyrins to benchmark density functionals, mainly those properties related to coordination with the metallic ion. Furthermore, the results show that functionals that yield correct spectra may be based on an incorrect ground state description. Moreover, we reinforce that one must be skeptical about the reference chosen to benchmark electronic structure calculations, such as DFT functionals and active spaces for multireference calculations.

Perturbation Expansion of Internally Contracted Coupled-Cluster Theory up to Third Order.

The internally contracted multireference coupled-cluster (icMRCC) method is analyzed through third order in perturbation theory. Up to second order, the icMRCC perturbation expansion is equivalent to that of the standard Rayleigh-Schrödinger perturbation theory, which is based on a linear ansatz for the wave function, and the resulting theory is, depending on the employed zeroth-order Hamiltonian, equivalent to either second-order complete active space perturbation theory (CASPT2), N-electron valence perturbation theory (NEVPT2), or Fink's retention of the excitation degree perturbation theory (REPT2). At third order, the icMRCC perturbation expansion features additional terms in comparison to the Rayleigh-Schrödinger perturbation theory, but these are shown to be nearly negligibly small by both analytic arguments and numerical examples. Considering these systematic cancellations, however, may be important in future work on approximations to icMRCC theory. In addition, we provide an extensive set of tests of the second and third-order perturbation theories based on three different zeroth-order Hamiltonians, namely, the projected effective Fock operator as used for CASPT, the Dyall Hamiltonian as used for NEVPT, and the Fink Hamiltonian used for REPT. While the third-order variant of REPT often gives absolute energies that are rather close to values from higher level calculations, the results for relative energies and spectroscopic constants such as harmonic frequencies, give a less clear picture and a general conclusion about any best zeroth-order Hamiltonian does not emerge from our data. For small active spaces, REPT is rather prone to intruder state problems.

Revisiting the F + HCl → HF + Cl reaction using a multireference coupled-cluster method.

We have constructed a new potential energy surface for the title reaction, based on the internally contracted multireference coupled-cluster method. The calculated barrier height is 1.59 ± 0.08 kcal mol-1. This value is much lower than that obtained in previous ab initio calculations and it is close to the experimentally suggested value. Other features of the [F,H,Cl] system are also analysed, such as van der Waals minima and conical intersections. The rate constant and the vibrational and rotational distributions of the products were calculated using a fully converged time independent quantum mechanical approach. The calculated rate constant agrees well with the experimental values. Qualitative agreement for the vibrational distribution is obtained and it is shown that it is strongly influenced by the initial rotational state distribution.

Internally contracted multireference coupled-cluster theory in a multistate framework.

The internally contracted multireference coupled cluster (icMRCC) theory is reexamined in a multistate framework. The new derivation starts from the Bloch equations employing a wave operator similar to the one originally employed by Jeziorski and Monkhorst [Phys. Rev. A 24, 1668 (1981)], but allows for a multideterminantal model-space basis. The resulting working equations are a generalization of state-universal multireference coupled-cluster (SU-MRCC) theory. In the case of truncated cluster operators, energies and wave functions depend on the choice of the model-space basis. It is shown that the state-specific solutions of the original icMRCC theory exactly diagonalize the effective Hamiltonian of the multistate theory and thus decouple the multistate equations. While this in principle means that icMRCC is a multistate theory, we find that truncated icMRCC theory still shows minor artifacts close to avoided crossings, which can be removed by considering a true multistate ansatz. The results also shed new light on the orbital variance of the original SU-MRCC theory.

Metastable BrO2+ and NBr2+ molecules in the gas phase.

The doubly positively charged gas-phase molecules BrO(2+) and NBr(2+) have been produced by prolonged high-current energetic oxygen (17 keV (16)O(-)) ion surface bombardment (ion beam sputtering) of rubidium bromide (RbBr) and of ammonium bromide (NH(4)Br) powdered ionic salt samples, respectively, pressed into indium foil. These novel species were observed at half-integer m∕z values in positive ion mass spectra for ion flight times of roughly ∼12 µs through a magnetic-sector secondary ion mass spectrometer. Here we present these experimental results and combine them with a detailed theoretical investigation using high level ab initio calculations of the ground states of BrO(2+) and NBr(2+), and a manifold of excited electronic states. NBr(2+) and BrO(2+), in their ground states, are long-lived metastable gas-phase molecules with well depths of 2.73 × 10(4) cm(-1) (3.38 eV) and 1.62 × 10(4) cm(-1) (2.01 eV); their fragmentation channels into two monocations lie 2.31 × 10(3) cm(-1) (0.29 eV) and 2.14 × 10(4) cm(-1) (2.65 eV) below the ground state minimum. The calculated lifetimes for NBr(2+) (v(") < 35) and BrO(2+) (v(") < 18) are large enough to be considered stable against tunneling. For NBr(2+), we predicted R(e) = 3.051 a(0) and ω(e) = 984 cm(-1); for BrO(2+), we obtained 3.033 a(0) and 916 cm(-1), respectively. The adiabatic double ionization energies of BrO and NBr to form metastable BrO(2+) and NBr(2+) are calculated to be 30.73 and 29.08 eV, respectively. The effect of spin-orbit interactions on the low-lying (Λ + S) states is also discussed.

New molecular species of potential interest to atmospheric chemistry: isomers on the [H, S2, Br] potential energy surface.

This work reports a state-of-the-art theoretical characterization of four new sulfur-bromine species and five transition states on the [H, S(2), Br] potential energy surface. Our highest level theoretical approach employed the method coupled cluster singles and doubles with perturbative contributions of connected triples, CCSD(T), along with the series of correlation-consistent basis sets and with extrapolation to the complete basis set (CBS) limit in the optimization of the geometrical parameters and to quantify the energetic quantities. The structural and vibrational frequencies here reported are unique and represent the most accurate investigation to date of these species. The global minimum corresponds to a skewed structure HSSBr with a disulfide bond; this is followed by a pyramidal-like structure, SSHBr, 18.85 kcal/mol above the minimum. Much higher in energy, we found another skewed structure, HSBrS (50.29 kcal/mol), with one S-Br dative-type bond, and another pyramidal-like one, HBrSS (109.80 kcal/mol), with two S-Br dative-type bonds. The interconversion of HSSBr into SSHBr can occur via a transfer of either the hydrogen or the bromine atom but involves a very high barrier of about 43 kcal/mol. These molecules are potentially a new route of coupling the sulfur and bromine chemistry in the atmosphere, and conditions of high concentration of H(2)S like in volcanic eruptions might contribute to their formation. We note that HSSBr can act as a reservoir molecule for the reaction between the radicals HSS and Br. Also, an assessment of the methods DFT/B3LYP/CBS and MP2/CBS relative to CCSD(T)/CBS provides insights on the expected performance of these methods on the characterization of polysulfides and also of more complex systems containing disulfide bridges.

Predicting new molecular species of potential interest to atmospheric chemistry: the isomers HSBr and HBrS.

Coupled cluster singles and doubles with perturbative contributions of connected triples CCSD(T) theory with a series of correlation consistent basis sets was used to predict the existence and characterize for the first time the structures, harmonic frequencies, and energetic quantities of the isomeric species HSBr and HBrS, as well as the transition state connecting them. These calculations consider extrapolation to the complete basis set (CBS) limit, corrections for scalar relativistic effects using the second-order Douglas-Kroll-Hess Hamiltonian, and also correlation of the bromine d electrons in addition to the 14 valence electrons. The species HSBr was found to be more stable than HBrS by 50.93 kcal/mol, with a high barrier height of 60.00 kcal/mol for the interconversion into HBrS. The smaller barrier of 7.90 kcal/mol (ZPE included) for the reverse process, however, should favor a rapid interconversion of HBrS into HSBr if HBrS can also be initially present in a potential synthetic route. If trapped in a matrix, their harmonic frequencies will allow for an unambiguous distinction between the two species. Scalar relativistic corrections and correlation of 24 electrons, although minor for the present purpose of a first time, but accurate, characterization of these species, are needed if chemical accuracy is also pursued. A test of the DFT/B3LYP approach in describing this type of system resulted in good energetic quantities, but geometric parameters and frequencies still lack spectroscopic accuracy. Whether HSBr can act as a temporary bromine reservoir and/or a source of reactive bromine and HS radicals requires further studies that are underway in our group.