A Density Matrix Renormalization Group Study of the Low-Lying Excited States of a Molybdenum Carbonyl-Nitrosyl Complex.

A density matrix renormalization group-self consistent field (DMRG-SCF) study has been carried out to calculate the low-lying excited states of CpMo(CO)2 NO, a molybdenum complex containing NO and CO ligands. In order to automatically select an appropriate active space, a novel procedure employing the maximum single-orbital entropy for several states has been introduced and shown to be efficient and easy-to-implement when several electronic states are simultaneously considered. The analysis of the resulting natural transition orbitals and charge-transfer numbers shows that the lowest five excited electronic states are excitation into metal-NO antibonding orbitals, which offer the possibility for nitric oxide (NO) photorelease after excitation with visible light. Higher excited states are metal-centered excitations with contributions of metal-CO antibonding orbitals, which may serve as a gateway for carbon monoxide (CO) delivery. Time-dependent density functional theory calculations done for comparison, show that the state characters agree remarkably well with those from DMRG-SCF, while excitation energies are 0.4-1.0 eV red-shifted with respect to the DMRG-SCF ones.

Tailored coupled cluster theory in varying correlation regimes.

The tailored coupled cluster (TCC) approach is a promising ansatz that preserves the simplicity of single-reference coupled cluster theory while incorporating a multi-reference wave function through amplitudes obtained from a preceding multi-configurational calculation. Here, we present a detailed analysis of the TCC wave function based on model systems, which require an accurate description of both static and dynamic correlation. We investigate the reliability of the TCC approach with respect to the exact wave function. In addition to the error in the electronic energy and standard coupled cluster diagnostics, we exploit the overlap of TCC and full configuration interaction wave functions as a quality measure. We critically review issues, such as the required size of the active space, size-consistency, symmetry breaking in the wave function, and the dependence of TCC on the reference wave function. We observe that possible errors caused by symmetry breaking can be mitigated by employing the determinant with the largest weight in the active space as reference for the TCC calculation. We find the TCC model to be promising in calculations with active orbital spaces which include all orbitals with a large single-orbital entropy, even if the active spaces become very large and then may require modern active-space approaches that are not restricted to comparatively small numbers of orbitals. Furthermore, utilizing large active spaces can improve on the TCC wave function approximation and reduce the size-consistency error because the presence of highly excited determinants affects the accuracy of the coefficients of low-excited determinants in the active space.

Modern quantum chemistry with [Open]Molcas.

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.

Shedding Light on the Nature of Photoinduced States Formed in a Hydrogen-Generating Supramolecular RuPt Photocatalyst by Ultrafast Spectroscopy.

Photoinduced electronic and structural changes of a hydrogen-generating supramolecular RuPt photocatalyst are studied by a combination of time-resolved photoluminescence, optical transient absorption, and X-ray absorption spectroscopy. This work uses the element specificity of X-ray techniques to focus on the interplay between the photophysical and -chemical processes and the associated time scales at the catalytic Pt moiety. We observe very fast (<30 ps) photoreduction of the Pt catalytic site, followed by an ∼600 ps step into a strongly oxidized Pt center. The latter process is likely induced by oxidative addition of reactive iodine species. The oxidized Pt species is long-lived and fully recovers to the original ground state complex on a >10 µs time scale. However, the photosensitizing Ru moiety is fully restored on a much shorter ∼300 ns time scale. This reaction scheme implies that we may withdraw two electrons from a catalyst that is activated by a single photon.

Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex.

Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru-NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru-NO π bonds show static and dynamic correlation, while other Ru-ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru-NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru-NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

Theoretical spectroscopy and photodynamics of a ruthenium nitrosyl complex.

Photoactive transition-metal nitrosyl complexes are particularly interesting as potential drugs that deliver nitric oxide (NO) upon UV-light irradiation to be used, e.g., in photodynamic therapy. It is well-recognized that quantum-chemical calculations can guide the rational design and synthesis of molecules with specific functions. In this contribution, it is shown how electronic structure calculations and dynamical simulations can provide a unique insight into the photodissociation mechanism of NO. Exemplarily, [Ru(PaPy3)(NO)](2+) is investigated in detail, as a prototype of a particularly promising class of photoactive metal nitrosyl complexes. The ability of time-dependent density functional theory (TD-DFT) to obtain reliable excited-state energies compared with more sophisticated multiconfigurational spin-corrected calculations is evaluated. Moreover, a TD-DFT-based trajectory surface-hopping molecular dynamics study is employed to reveal the details of the radiationless decay of the molecule via internal conversion and intersystem crossing. Calculations show that the ground state of [Ru(PaPy3)(NO)](2+) includes a significant admixture of the Ru(III)(NO)(0) electronic configuration, in contrast to the previously postulated Ru(II)(NO)(+) structure of similar metal nitrosyls. Moreover, the lowest singlet and triplet excited states populate the antibonding metal d → πNO* orbitals, favoring NO dissociation. Molecular dynamics show that intersystem crossing is ultrafast (<10 fs) and dissociation is initiated in less than 50 fs. The competing relaxation to the lowest S1 singlet state takes place in less than 100 fs and thus competes with NO dissociation, which mostly takes place in the higher-lying excited triplet states. All of these processes are accompanied by bending of the NO ligand, which is not confined to any particular state.

Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: geometry optimization and spin-state energetics of a ruthenium nitrosyl complex.

We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S0 and 0.11 Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.

Mechanism elucidation of the cis-trans isomerization of an azole ruthenium-nitrosyl complex and its osmium counterpart.

Synthesis and X-ray diffraction structures of cis and trans isomers of ruthenium and osmium metal complexes of general formulas (nBu4N)[cis-MCl4(NO)(Hind)], where M = Ru (1) and Os (3), and (nBu4N)[trans-MCl4(NO)(Hind)], where M = Ru (2) and Os (4) and Hind = 1H-indazole are reported. Interconversion between cis and trans isomers at high temperatures (80-130 °C) has been observed and studied by NMR spectroscopy. Kinetic data indicate that isomerizations correspond to reversible first order reactions. The rates of isomerization reactions even at 110 °C are very low with rate constants of 10(-5) s(-1) and 10(-6) s(-1) for ruthenium and osmium complexes, respectively, and the estimated rate constants of isomerization at room temperature are of ca. 10(-10) s(-1). The activation parameters, which have been obtained from fitting the reaction rates at different temperatures to the Eyring equation for ruthenium [ΔH(cis-trans)‡ = 122.8 ± 1.3; ΔH(trans-cis)‡ = 138.8 ± 1.0 kJ/mol; ΔS(cis-trans)‡ = -18.7 ± 3.6; ΔS(trans-cis)‡ = 31.8 ± 2.7 J/(mol·K)] and osmium [ΔH(cis-trans)‡ = 200.7 ± 0.7; ΔH(trans-cis)‡ = 168.2 ± 0.6 kJ/mol; ΔS(cis-trans)‡ = 142.7 ± 8.9; ΔS(trans-cis)‡ = 85.9 ± 3.9 J/(mol·K)] reflect the inertness of these systems. The entropy of activation for the osmium complexes is highly positive and suggests the dissociative mechanism of isomerization. In the case of ruthenium, the activation entropy for the cis to trans isomerization is negative [-18.6 J/(mol·K)], while being positive [31.0 J/(mol·K)] for the trans to cis conversion. The thermodynamic parameters for cis to trans isomerization of [RuCl4(NO)(Hind)]-, viz. ΔH° = 13.5 ± 1.5 kJ/mol and ΔS° = -5.2 ± 3.4 J/(mol·K) indicate the low difference between the energies of cis and trans isomers. The theoretical calculation has been carried out on isomerization of ruthenium complexes with DFT methods. The dissociative, associative, and intramolecular twist isomerization mechanisms have been considered. The value for the activation energy found for the dissociative mechanism is in good agreement with experimental activation enthalpy. Electrochemical investigation provides further evidence for higher reactivity of ruthenium complexes compared to that of osmium counterparts and shows that intramolecular electron transfer reactions do not affect the isomerization process. A dissociative mechanism of cis↔trans isomerization has been proposed for both ruthenium and osmium complexes.

The Role of Triplet States in the Photodissociation of a Platinum Azide Complex by a Density Matrix Renormalization Group Method.

Platinum azide complexes are appealing anticancer photochemotherapy drug candidates because they release cytotoxic azide radicals upon light irradiation. Here we present a density matrix renormalization group self-consistent field (DMRG-SCF) study of the azide photodissociation mechanism of trans,trans,trans-[Pt(N3)2(OH)2(NH3)2], including spin-orbit coupling. We find a complex interplay of singlet and triplet electronic excited states that falls into three different dissociation channels at well-separated energies. These channels can be accessed either via direct excitation into barrierless dissociative states or via intermediate doorway states from which the system undergoes non-radiative internal conversion and intersystem crossing. The high density of states, particularly of spin-mixed states, is key to aid non-radiative population transfer and enhance photodissociation along the lowest electronic excited states.

Simplified State Interaction for Matrix Product State Wave Functions.

We present an approximation to the state-interaction approach for matrix product state (MPS) wave functions (MPSSI) in a nonorthogonal molecular orbital basis, first presented by Knecht et al. [J. Chem. Theory Comput., 2016, 28, 5881], that allows for a significant reduction of the computational cost without significantly compromising its accuracy. The approximation is well-suited if the molecular orbital basis is close to orthogonality, and its reliability may be estimated a priori with a single numerical parameter. For an example of a platinum azide complex, our approximation offers up to 63-fold reduction in computational time compared to the original method for wave function overlaps and spin-orbit couplings, while still maintaining numerical accuracy.

Approximate Analytical Gradients and Nonadiabatic Couplings for the State-Average Density Matrix Renormalization Group Self-Consistent-Field Method.

We present an approximate scheme for analytical gradients and nonadiabatic couplings for calculating state-average density matrix renormalization group self-consistent-field wave function. Our formalism follows closely the state-average complete active space self-consistent-field (SA-CASSCF) ansatz, which employs a Lagrangian, and the corresponding Lagrange multipliers are obtained from a solution of the coupled-perturbed CASSCF (CP-CASSCF) equations. We introduce a definition of the matrix product state (MPS) Lagrange multipliers based on a single-site tensor in a mixed-canonical form of the MPS, such that a sweep procedure is avoided in the solution of the CP-CASSCF equations. We apply our implementation to the optimization of a conical intersection in 1,2-dioxetanone, where we are able to fully reproduce the SA-CASSCF result up to arbitrary accuracy.

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 postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes.

The accurate calculation of ligand dissociation (or equivalently, ligand binding) energies is crucial for computational coordination chemistry. Despite its importance, obtaining accurate ab initio reference data is difficult, and density-functional methods of uncertain reliability are chosen for feasibility reasons. Here, we consider advanced coupled-cluster and multiconfigurational approaches to reinvestigate our WCCR10 set of 10 gas-phase ligand dissociation energies [ J. Chem. Theory Comput. 2014, 10, 3092]. We assess the potential multiconfigurational character of all molecules involved in these reactions with a multireference diagnostic [ Mol. Phys. 2017, 115, 2110] in order to determine where single-reference coupled-cluster approaches can be applied. For some reactions of the WCCR10 set, large deviations of density-functional results including semiclassical dispersion corrections from experimental reference data had been observed. This puzzling observation deserves special attention here, and we tackle the issue (i) by comparing to ab initio data that comprise dispersion effects on a rigorous first-principles footing and (ii) by a comparison of density-functional approaches that model dispersion interactions in various ways. For two reactions, species exhibiting nonnegligible static electron correlation were identified. These two reactions represent hard problems for electronic structure methods and also for multireference perturbation theories. However, most of the ligand dissociation reactions in WCCR10 do not exhibit static electron correlation effects, and hence, we may choose standard single-reference coupled-cluster approaches to compare with density-functional methods. For WCCR10, the Minnesota M06-L functional yielded the smallest mean absolute deviation of 13.2 kJ mol-1 out of all density functionals considered (PBE, BP86, BLYP, TPSS, M06-L, PBE0, B3LYP, TPSSh, and M06-2X) without additional dispersion corrections in comparison to the coupled-cluster results, and the PBE0-D3 functional produced the overall smallest mean absolute deviation of 4.3 kJ mol-1. The agreement of density-functional results with coupled-cluster data increases significantly upon inclusion of any type of dispersion correction. It is important to emphasize that different density-functional schemes available for this purpose perform equally well. The coupled-cluster dissociation energies, however, deviate from experimental results on average by 30.3 kJ mol-1. Possible reasons for these deviations are discussed.

Multireference 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.

Assessing Excited State Energy Gaps with Time-Dependent Density Functional Theory on Ru(II) Complexes.

A set of density functionals coming from different rungs on Jacob's ladder is employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical excitation energies, in this work we focus on the energy gaps between the electronic excited states, of the same and different multiplicity. Excited state energy gaps are important for example to determine radiationless transition probabilities. Besides energies, a functional should deliver the correct state character and state ordering. Therefore, wave function overlaps are introduced to systematically evaluate the effect of different functionals on the character of the excited states. As a reference, the energies and state characters from multistate second-order perturbation theory complete active space (MS-CASPT2) are used. In comparison to MS-CASPT2, it is found that while hybrid functionals provide better vertical excitation energies, pure functionals typically give more accurate excited state energy gaps. Pure functionals are also found to reproduce the state character and ordering in closer agreement to MS-CASPT2 than the hybrid functionals.

Peripheral ligands as electron storage reservoirs and their role in enhancement of photocatalytic hydrogen generation.

The contrasting early-time photodynamics of two related Ru/Pt photocatalysts with very different photocatalytic H2 generation capabilities are reported. Ultrafast equilibration (535 ± 17 fs) creates an electron reservoir on the peripheral ligands of the ester substituted complex, allowing a dramatic increase in photocatalytic performance. This insight opens the way towards a novel design strategy for H2 generating molecular photocatalysts.

Dynamic theory of liquid junction potentials.

A Nernst-Planck-Poisson finite difference simulation system is used to model the dynamic evolution of a liquid junction from a nonequilibrium initial condition to a condition of steady potential difference, in a linear semi-infinite space. Liquid junctions of Lingane's type 1 (monophasic, unequal concentration) and type 2 (bi-ionic potential; biphasic, equal concentration) are considered, for the sake of simplicity. Analysis of the results shows consistency with known and novel asymptotic solutions. A comprehensive dynamic theory of the free liquid junction potential is presented, having considered the simulated concentration profiles and electric field in the system. This reveals a dynamically relaxing junction in which a diffuse layer continues to expand. This is advocated as physically realistic and shown to be consistent with a steady state potential difference, which arises after 10-1000 ns for typical aqueous systems, when the expanding diffuse layer has a corresponding size of 10-1000 nm. Hence, Planck's concept [Wied. Ann. 1890, 40, 561-576] that a steady state potential difference exclusively implies a static junction with equal fluxes of all species is shown to be false, for an unconstrained system.