Multireference Approaches Research Articles

Time-Dependent Density Functional Theory Study of Copper(II) Oxo Active Sites for Methane-to-Methanol Conversion in Zeolites.

Copper-exchanged zeolites are useful materials for step-wise methane-to-methanol conversion (MMC). However, methanol yields on copper-exchanged zeolites are often modest, spurring interest in the development of active-site species that are activated at moderate temperatures, afford greater yields, and provide excellent methanol selectivities. Ultraviolet-visible (UV-vis) spectroscopy is a major tool for characterizing the active-sites and their evolution during the step-wise MMC process. However, computation of the UV-vis spectra of the copper-oxo active sites using Tamm-Dancoff time-dependent density functional theory (TDA-DFT) can be quite problematic. This has led to utilization of expensive methods based on multireference approaches, Green functions, and the Bethe-Salpeter equation. In this work, we examined the optical spectra of [CuO]+, [Cu2O]2+, [Cu2O2]2+, and [Cu3O3]2+ species implicated in MMC in zeolites. For the larger species, we examined how agreement with experimental data is improved with increasingly larger cluster models. For [CuO]+, we compared TDA-DFT against restricted active space 2nd-order perturbation theory, RASPT2. We found that signature peaks for [CuO]+ have multireference behavior. The excited states have many configuration state functions with a double excitation character. These effects are likely responsible for the poor utility of conventional TDA-DFT methods. Indeed, we obtain good agreement with experimental data and RASPT2 after accounting for 2h/2p excitations within TDA-DFT with a previously described configuration interaction singles and doubles, CIS(D)-style scheme. This was the case for [CuO]+, [Cu2O]2+, as well as a [Cu2O2]2+ species. Using a long-range corrected double-hybrid, ωB2PLYP, we provide for the first time computational evidence for the experimental UV-vis spectrum of the [Cu3O3]2+ active site motif.

Intrastrand Photolesion Formation in Thio-Substituted DNA: A Case Study Including Single-Reference and Multireference Methods.

The substitution of canonical nucleobases by thiated analogues in natural DNA has been exploited in pharmacology, photochemotherapy, and structural biology. Thionucleobases react with adjacent thymines leading to 6-4 pyrimidine-pyrimidone photoproducts (6-4PPs), which are a major source of DNA photodamage, in particular intrastrand cross-linked photolesions. Here, we study the mechanism responsible for the formation of 6-4PPs in thionucleobases by employing quantum-mechanical calculations. We use multiconfiguration pair-density functional theory, complete active space second-order perturbation theory, and Kohn-Sham density functional theory. Scrutinizing the photochemistry of thionucleobases can elucidate the reaction mechanism of these prodrugs and identify the role that triplet excited states play in the generation of photolesions in the natural biopolymer. Three different possible mechanisms to generate the 6-4PPs are presented, and we conclude that the use of multireference approaches is indispensable to capture important features of the potential energy surface.

New benzene dimers: a benchmark theoretical investigation

A wide variety of methods have been used to study the retro-dimerization reactions of one cis-fused (1) and four new trans-fused benzene dimers (2–5). These methods, which included both single-reference and multi-reference approaches, were benchmarked against multi-reference Moller-Plesset perturbation theory of the second order (MRMP2) based on CASSCF(12,12) wavefunctions. Each of the single-reference approaches was found to be overestimating the activation barrier for retro-dimerization process. Interestingly, N-electron valence perturbation theory (NEVPT2) energies also diverged for these reactions from MRMP2 values. Canonical MP2 barriers were in better agreement with MRMP2 results than the NEVPT2 numbers, with mean unsigned deviations (MUD) of 5.4 kcal/mol and 6.6 kcal/mol, respectively. The behavior of each of the methods is discussed and compared with the application of the same methods to the standard pericyclic reaction set proposed by Houk et al. (J Phys Chem A 107:11445, 2003). The comparison between NEVPT2 and MRMP2 reaction barriers, when applied to the cycloadditions in the Houk set and the synchronous symmetry-allowed retro-dimerization of the benzene dimer 1, showed that these two methods give almost identical results for these reaction types (MUD of 0.5 kcal/mol).

Description of Two-Particle One-Hole Electronic Resonances Using Orbital Stabilization Methods.

Two-particle one-hole (2p-1h) resonances are elusive to accurate characterization, their decay to the neutral state being a two-electron process. Although in limited cases, single reference methods can be used, a proper description of a 2p-1h resonant state entails a multiconfigurational treatment of the reference wavefunction. In this work, we test the performance of the orbital stabilization method to characterize the 2p-1h resonances found in water and benzene. We employ a set of two multireference approaches, namely, the restricted active space self-consistent field and the multireference configuration interaction, as well as the single reference method equation of motion for electron attachment coupled-cluster with singles and doubles, in the case of benzene. We further explore the resonant channel mixing in benzene between the B2g shape resonance and 2p-1h resonance, a phenomenon which has been explored quite often in experimental studies.

Extension of the Fock-space coupled-cluster method with singles and doubles to the three-valence sector.

The single-reference coupled-cluster method has proven very effective in the ab initio description of atomic and molecular systems, but its successful application is limited to states dominated by a single Slater determinant, which is used as the reference. In cases where several determinants are important in the wave function expansion, i.e., we have to deal with nondynamic correlation effects, a multi-reference version of the coupled-cluster method is required. The multi-reference coupled-cluster approaches are based on the effective Hamiltonian formulation providing a two-step procedure, in which dynamic correlation effects can be efficiently evaluated by the wave operator, while nondynamic correlation contributions are given by diagonalization of the effective Hamiltonian in the final step. There are two classical multi-reference coupled-cluster formulations. In this paper, the focus is on the so-called Fock-space coupled-cluster method in its basic version with one- and two-particle operators in the exponent. Computational schemes using this truncation of the cluster operator have been successfully applied in calculations in one- and two-valence sectors of the Fock space. In this paper, we show that the approach can be easily extended and effectively employed in the three-valence sector calculations.

DFT, DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine.

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T1 and T2 diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.

Multireference Ground and Excited State Electronic Structures of Free- versus Iron Porphyrin-Carbenes.

Iron porphyrin carbenes (IPCs) are important reaction intermediates in engineered carbene transferase enzymes and homogeneous catalysis. However, discrepancies between theory and experiment complicate the understanding of IPC electronic structure. In the literature, this has been framed as whether the ground state is an open- vs closed-shell singlet (OSS vs CSS). Here we investigate the structurally dependent ground and excited spin-state energetics of a free carbene and its IPC analogs with variable trans axial ligands. In particular, for IPCs, multireference ab initio wave function methods are more consistent with experiment and predict a mixed singlet ground state that is dominated by the CSS (Fe(II) ← {:C(X)Y}0) configuration (i.e., electrophilic carbene) but that also has a small, non-negligible contribution from an Fe(III)-{C(X)Y}-• configuration (hole in d(xz), i.e., radical carbene). In the multireference approach, the "OSS-like" excited states are metal-to-ligand charge transfer (MLCT) in nature and are energetically well above the CSS-dominated ground state. The first, lowest energy of these "OSS-like" excited states is predicted to be heavily weighted toward the Fe(III)-{C(X)Y}-• (hole in d(yz)) configuration. As expected from exchange considerations, this state falls energetically above a triplet of the same configuration. Furthermore, potential energy surfaces (PESs) along the IPC Fe-C(carbene) bond elongation exhibit increasingly strong mixings between CSS/OSS characters, with the Fe(III)-{C(X)Y}-• configuration (hole in d(xz)) growing in weight in the ground state during bond elongation. The relative degree of electrophilic/radical carbene character along this structurally relevant PES can potentially play a role in reactivity and selectivity patterns in catalysis. Future studies on IPC reaction coordinates should evaluate contributions from ground and excited state multireference character.

Comparison of Spin-Flip TDDFT-Based Conical Intersection Approaches with XMS-CASPT2.

Determining conical intersection geometries is of key importance to understanding the photochemical reactivity of molecules. While many small- to medium-sized molecules can be treated accurately using multireference approaches, larger molecules require a less computationally demanding approach. In this work, minimum energy crossing point conical intersection geometries for a series of molecules have been studied using spin-flip TDDFT (SF-TDDFT), within the Tamm-Dancoff Approximation, both with and without explicit calculation of nonadiabatic coupling terms, and compared with both XMS-CASPT2 and CASSCF calculated geometries. The less computationally demanding algorithms, which do not require explicit calculation of the nonadiabatic coupling terms, generally fare well with the XMS-CASPT2 reference structures, while the relative energetics are only reasonably replicated with the MECP structure as calculated with the BHHLYP functional and full nonadiabatic coupling terms. We also demonstrate that, occasionally, CASSCF structures deviate quantitatively from the XMS-CASPT2 structures, showing the importance of including dynamical correlation.

Oxetan-3-one pyrolysis from the perspective of multireference approaches

The objective of this research is to provide a theoretical explanation of the thermal decomposition of the oxetan-3-one molecule. This process may proceed via at least two distinctive reaction pathways. One of them leads to the formation of ketene and formaldehyde and the other to oxirane and carbon monoxide. We examined, on the basis of multireference approaches, the reaction profiles of oxetan-3-one pyrolysis in terms of Gibb’s free energy. The geometries and thermodynamical parameters of the transition states were obtained and compared to the known experimental facts and calculations. We also show that as some transition states have broken spin-symmetry character in DFT calculations, incorporating multireference approaches seems to be necessary. On the basis of CASPT2 modelling we were able to explain the fundamental experimental finding that the reaction leading to oxirane and carbon monoxide becomes more and more pronounced in higher temperatures and rationalized in terms of entropic contributions.

The MRCC program system: Accurate quantum chemistry from water to proteins.

MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller-Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD.

The ΔNO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results and on par with conventional multireference approaches.

Numerical and experimental analysis of thermal penetration depth in bare reinforced concrete structures during fire accidents

This work faces the problem of fire resistance and temperature penetration depth in reinforced concrete under construction subjected to fire. Indeed, the design approaches always neglect the fire-induced effects on the structures under construction. In current applications, a lot of information about working boundary conditions during fire, actual material parameters and geometrical details lacks. The paper presents an original approach for the case study of a vertical reinforced concrete element (a stack under construction of the new bridge “Viadotto Polcevera”, Genoa) subjected to a fire accident. Lacking information was retrieved and integrated following a multi-reference approach (numerical simulation, design and operational data, norms). The critical areas of the stack, identified by means of a simplified numerical model, were compared to samples of materials extracted from the construction site and tested in laboratory. Particular attention was given to the model sensitivity to data uncertainties about component geometry, material thermophysical properties and possible thermal effects due to the reinforcement bars extruding from the cast of concrete, acting like fins. The very good agreement between the model and experimental data allowed to identify the minimum volume of stack to be demolished and rebuilt with a significant saving in time and money.

The intermediate Hamiltonian Fock-space coupled-cluster method with approximate evaluation of the three-body effects.

The exponential parametrization of the wave function used in the coupled-cluster approaches has proven very successful in the ab initio description of atomic and molecular systems. This concerns first of all the single-reference version of the method that is designed for states dominated by a single Slater determinant. Usually, the coupled-cluster methods with one- and two-body excitation operators in the exponent form the basic computational schemes. The inclusion of three-body effects in the cluster operator to increase the accuracy of the results is numerically expensive, so their approximate evaluation is rather used in practice. In the case of the single-reference coupled-cluster approach, the problem of approximate evaluation of three-body effects in the cluster operator has been well studied, and computational schemes of both noniterative and iterative nature have been proposed. The situation is different in the case of multireference coupled-cluster methods which are required to describe open shell and quasidegenerate states. The multireference approaches in their standard effective Hamiltonian formulations are more complicated and less frequently used in routine calculations; however, one of them, the so-called Fock-space coupled-cluster method, becomes very effective if reformulated within the intermediate Hamiltonian framework. Both the basic version of the method with one- and two-body clusters and the extended one that includes up to three-body operators in the exponent are implemented. The latter approach provides more accurate results, but its relatively high numerical cost limits its applicability. For this reason, going beyond the basic scheme with one- and two-body clusters through an approximate evaluation of the impact of three-body clusters is of great interest. In the paper, we investigate different ways of approximate inclusion of the three-body effects in the Fock-space coupled-cluster method designated for excitation energy calculations.

Correction to "Systematic First-Principles Configuration-Interaction Calculations of Linear Optical Absorption Spectra in Silicon Hydrides: Si2H2n (n = 1-3)".

We have performed first-principles electron-correlated calculations employing large basis sets to optimize the geometries and to compute linear optical absorption spectra of various low-lying conformers of silicon hydrides: Si2H2n, n = 1, 2, 3. The geometry optimization for various isomers was carried out at the coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] level of theory, while their excited states and absorption spectra were computed using a large-scale multireference singles-doubles configuration-interaction approach, which includes electron-correlation effects at a sophisticated level. Our calculated spectra are the first ones for Si2H2 and Si2H4 conformers, while for Si2H6, we obtain excellent agreement with the experimental measurements, suggesting that our computational approach is reliable. Our calculated absorption spectra exhibit a strong structure-property relationship, suggesting the possibility of identifying various conformers based on their optical absorption fingerprints. Furthermore, we have also performed geometry optimization for the selected optically excited states, providing insights into their character.

On the Stability of Cu5 Catalysts in Air Using Multireference Perturbation Theory.

An ab initio study of the interaction of O2, the most abundant radical and oxidant species in the atmosphere, with a Cu5 cluster, a new generation atomic metal catalyst, is presented. The open-shell nature of the reactant species is properly accounted for by using the multireference perturbation theory, allowing the experimentally confirmed resistivity of Cu5 clusters toward oxidation to be investigated. Approximate reaction pathways for the transition from physisorption to chemisorption are calculated for the interaction of O2 with quasi-iso-energetic trapezoidal planar and trigonal bipyramidal structures. Within the multireference approach, the transition barrier for O2 activation can be interpreted as an avoided crossing between adiabatic states (neutral and ionic), which provides new insights into the charge-transfer process and gives better estimates for this hard to localize and therefore often neglected first intermediate state. For Cu5 arranged in a bipyramidal structure, the O–O bond cleavage is confirmed as the rate-determining step. However, for planar Cu5, the high energy barrier for O2 activation, related to a very pronounced avoided crossing when going from physisorption to chemisorption, determines the reactivity in this case.

Calculation of Chemical Reaction Barrier Heights by Multiconfiguration Pair-Density Functional Theory with Correlated Participating Orbitals.

The accurate description of reaction barrier heights is challenging for quantum mechanical methods due to the need for a balanced treatment of dynamic and static correlation energies because their importance varies during the course of a chemical reaction. While some regions of potential energy surfaces are well-described by a single-reference wave function or by Kohn-Sham density functional theory, in other cases a multireference treatment is needed. For systems with many active electrons, most accurate multireference methods have prohibitive computational scalings with system size. Multiconfiguration pair-density functional theory, MC-PDFT, is a more affordable multireference approach that computes the total electron correlation energy in a single step by using the multiconfiguration kinetic energy, density, and on-top pair density and an on-top density functional. In this work, we apply MC-PDFT to a benchmark database (DBH24/18) of 24 diverse reaction barrier heights. We explore the role of active space and basis set selection on the performance of MC-PDFT. We find that MC-PDFT is able to calculate reaction barrier heights with a similar accuracy to complete active space second order perturbation theory, CASPT2, but at a lower computational cost, and we find that MC-PDFT is less dependent on basis set selection than CASPT2.

Correlation effects in B1s core-excited states of boronic-acid derivatives: An experimental and computational study.

We performed a theoretical investigation on the influence of electronic correlation effects on the B1s NEXAFS spectrum of boronic acid derivatives, namely, boric acid [B(OH)3], phenyl boronic acid (PBA), and 1,4-phenyl diboronic acid (PDBA), employing different computational schemes of increasing complexity, ranging from the purely one-electron scheme based on the transition potential method of density functional theory (DFT-TP), time-dependent DFT (TDDFT), and multiconfigurational self-consistent field (MCSCF). We also report experimental measurements of the B1s NEXAFS spectra of the aforementioned molecules together with the high-resolution C1s NEXAFS spectrum of PBA. We demonstrate that due to the shallow B1s core energy levels compared to C, O, and N, the inclusion of static correlation effects, which can be incorporated by using multireference approaches to excited states, assumes a decisive role in reconciling experiment and theory on B1s core-electron excitation energies and oscillator strengths to valence states. This claim is corroborated by the good agreement that we find between the DFT-TP calculated C1s NEXAFS spectrum and that experimentally measured for PBA and by the failure of both DFT-TP and TDDFT approaches with a selection of xc functionals kernels to properly describe the B1s NEXAFS spectrum of PBA and PDBA, at variance with the good agreement with the experiment that is found by employing the MCSCF wave function approach.

Assessing the Reversed Exponential Decay of the Electrical Conductance in Molecular Wires: The Undeniable Effect of Static Electron Correlation.

An extraordinary new family of molecular junctions, inaccurately referred to as "anti-Ohmic" wires in the recent literature, has been proposed based on theoretical predictions. The unusual electron transport observed for these systems, characterized by a reversed exponential decay of their electrical conductance, might revolutionize the design of molecular electronic devices. This behavior, which has been associated with intrinsic diradical nature, is reexamined in this work. Since the diradical character arises from a near-degeneracy of the frontier orbitals, the employment of a multireference approach is mandatory. CASSCF calculations on a set of nanowires based on polycyclic aromatic hydrocarbons (PAHs) demonstrate that, in the frame of an appropriate multireference treatment, the ground state of these systems shows the expected exponential decay of the conductance. Interestingly, these calculations do evidence a reversed exponential decay of the conductance, although now in several excited states. Similar results have been obtained for other recently proposed candidates to "anti-Ohmic" wires. These findings open new horizons for possible applications in molecular electronics of these promising systems.

Analyses on Molecular Properties of the Diamidinate CrI-CrI Complex by Multireference and DFT Approaches.

The model system of the diamidinate CrI-CrI complex is investigated by wave function theory (WFT) and Kohn-Sham density functional theory (KS-DFT). The multireference perturbation theory (RASPT2) estimates a stabilization energy of ca. 20 kcal mol-1 for the δ bonding. The multiconfiguration pair-density functional theory (MC-PDFT) with the ftPBE functional well predicts the singlet energy curve comparable to the RASPT2 level. For the KS-DFT scheme based on a single determinant, seven functionals including BP86, BLYP, PBE, B3LYP, M06-L, M06, and ωB97X-D are assessed: two types of functionals are classified according to the nature of the restricted and broken symmetry potential energy curves. The broken symmetry scheme with the type I functionals can give good results for the energy curve in agreement with the multireference calculations. In regard to the metal-metal bonding, the restricted KS-DFT calculations performed by all of the seven functionals yield inferior description due to the lack of significant multiconfigurational character. The Mayer bond order, the electron localization function, and electron density predicted by the broken symmetry formalism with the type II functionals are consistent with those obtained with the multireference theory.

Ab Initio Calculations for Spin-Gaps of Non-Heme Iron Complexes

We employed our recently proposed multireference approach CASPT2/CC to calculate the quintet-triplet gaps ΔETQ of a series of non-heme FeIV═O species and subsequently used these results to benchmark density functional theory (DFT) as well as two variants of local coupled-cluster approaches (DLPNO-CCSD(T) and LUCCSD(T0)). We showed that current implementations of the local coupled-cluster method are not sufficiently accurate. DLPNO-CCSD(T) systematically overstabilizes the quintet state, whereas LUCCSD(T0) overestimates the triplet one. This sort of systematic bias may be helpful in improving local correlation methods and can also be used as the basis for a simple correction scheme.