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

Vibrational Entanglement through the Lens of Quantum Information Measures

We introduce a quantum information analysis of vibrational wave functions to understand complex vibrational spectra of molecules with strong anharmonic couplings and vibrational resonances. For this purpose, we define one- and two-modal entropies to guide the identification of strongly coupled vibrational modes and to characterize correlations within modal basis sets. We evaluate these descriptors for multiconfigurational vibrational wave functions which we calculate with the n-mode vibrational density matrix renormalization group algorithm. Based on the quantum information measures, we present a vibrational entanglement analysis of the vibrational ground and excited states of CO2, which display strong anharmonic effects due to the symmetry-induced and accidental (near-) degeneracies. We investigate the entanglement signature of the Fermi resonance and discuss the maximally entangled state arising from the two degenerate bending modes.

Unravelling the 6sp ← 6s absorption spectra of Bi(III) complexes

We report a spectroscopic and computational study that investigates the absorption spectra of Bi(III) complexes, which often show an absorption band in the UV region (∼270-350 nm) due to 6sp ← 6s transitions. We investigated the spectra of three simple complexes, [BiCl5]2-, [BiCl6]3- and [Bi(DMSO)8]3+, which show absorption maxima at 334, 326 and 279 nm due to 3P1 ← 1S0 transitions. Theoretical calculations based on quasi-degenerate N-electron valence perturbation theory to second order (QD-NEVPT2) provide an accurate description of the absorption spectra when employing CAS(2,9) wave functions. We next investigated the absorption spectra of the [Bi(NOTA)] complex (H3NOTA = 1,4,7-triazacyclononane-1,4,7-triacetic acid), which forms ternary complexes [Bi(NOTA)X]- (X = Cl, Br or I) in the presence of excess halide in aqueous solutions. Halide binding has an important impact on the position of the 3P1 ← 1S0 transition, which shifts progressively to longer wavelengths from 282 nm ([Bi(NOTA)]) to 298 nm (X = Cl), 305 nm (X = Br) and 325 nm (X = I). Subsequent QD-NEVPT2 calculations indicate that this effect is related to the progressive stabilization of the spin-orbit free states associated with the 6s16p1 configuration on increasing the covalent character of the metal-ligand(s) bonds, rather than with significant differences in spin-orbit coupling (SOC). These studies provide valuable insight into the coordination chemistry of Bi(III), an ion with increasing interest in targeted alpha therapy due to the possible application of bismuth isotopes bismuth-212 (212Bi, t1/2 = 60.6 min) and bismuth-213 (213Bi, t1/2 = 45.6 min).

Simulations of the Aqueous "Brown-Ring" Complex Reveal Fluctuations in Electronic Character

Ab initio molecular dynamics (AIMD) simulations of the aqueous [Fe(H2O)5(NO)]2+ "brown-ring" complex in different spin states, in combination with multiconfigurational quantum chemical calculations, show a structural dependence on the electronic character of the complex. Sampling in the quartet and sextet ground states show that the multiplicity is correlated with the Fe-N distance. This provides a motivation for a rigid Fe-N scan in the isolated "brown-ring" complex to investigate how the multiconfigurational wave function and the electron density change around the FeNO moiety. Our results show that subtle changes in the Fe-N distance produce a large response in the electronic configurations underlying the quartet wave function. However, while changes in spin density and potential energy are pronounced, variations in charge are negligible. These trends within the FeNO moiety are preserved in structural sampling of the AIMD simulations, despite distortions present in other degrees of freedom in the bulk solution.

Conformation, hydration, and ligand exchange process of ruthenium nitrosyl complexes in aqueous solution: Free-energy calculations by a combination of molecular-orbital theories and different solvent models

Distribution of solvent molecules near transition-metal complex is key information to comprehend the functionality, reactivity, and so forth. However, polarizable continuum solvent models still are the standard and conventional partner of molecular-orbital (MO) calculations in the solution system including transition-metal complex. In this study, we investigate the conformation, hydration, and ligand substitution reaction between NO₂ ^- and H₂ O in aqueous solution for [Ru(NO)(OH)(NO₂ )₄ ]^2- (A), [Ru(NO)(OH)(NO₂ )₃ (ONO)]^2- (B), and [Ru(NO)(OH)(NO₂ )₃ (H₂ O)]^- (C) using a combination method of MO theories and a state-of-the-art molecular solvation technique (NI-MC-MOZ-SCF). A dominant species is found in the complex B conformers and, as expected, different between the solvent models, which reveals that molecular solvation beyond continuum media treatment are required for a reliable description of solvation near transition-metal complex. In the stability constant evaluation of ligand substitution reaction, an assumption that considers the direct association between the dissociated NO₂ ^- and complex C is useful to obtain a reliable stability constant.

Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N₂, F₂, C₂, CN⁺, CO, BN, BO⁺, and Cr₂) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

A DMRG/CASPT2 Investigation of Metallocorroles: Quantifying Ligand Noninnocence in Archetypal 3d and 4d Element Derivatives

Hybrid density functional theory (B3LYP) and density matrix renormalization group (DMRG) theory have been used to quantitatively compare the degree of ligand noninnocence (corrole radical character) in seven archetypal metallocorroles. The seven complexes, in decreasing order of corrole noninnocent character, are Mn[Cor]Cl > Fe[Cor]Cl > Fe[Cor](NO) > Mo[Cor]Cl2 > Ru[Cor](NO) ≈ Mn[Cor]Ph ≈ Fe[Cor]Ph ≈ 0, where [Cor] refers to the unsubstituted corrolato ligand. DMRG-based second-order perturbation theory calculations have also yielded detailed excited-state energetics data on the compounds, shedding light on periodic trends involving middle transition elements. Thus, whereas the ground state of Fe[Cor](NO) (S = 0) is best described as a locally S = 1/2 {FeNO}7 unit antiferromagnetically coupled to a corrole A' radical, the calculations confirm that Ru[Cor](NO) may be described as simply {RuNO}6-Cor3-, that is, having an innocent corrole macrocycle. Furthermore, whereas the ferromagnetically coupled S = 1{FeNO}7-Cor•2- state of Fe[Cor](NO) is only ∼17.5 kcal/mol higher than the S = 0 ground state, the analogous triplet state of Ru[Cor](NO) is higher by a far larger margin (37.4 kcal/mol) relative to the ground state. In the same vein, Mo[Cor]Cl2 exhibits an adiabatic doublet-quartet gap of 36.1 kcal/mol. The large energy gaps associated with metal-ligand spin coupling in Ru[Cor](NO) and Mo[Cor]Cl2 reflect the much greater covalent character of 4d-π interactions relative to analogous interactions involving 3d orbitals. As far as excited-state energetics is concerned, DMRG-CASPT2 calculations provide moderate validation for hybrid density functional theory (B3LYP) for qualitative purposes, but underscore the possibility of large errors (>10 kcal/mol) in interstate energy differences.

Origin of the different reactivity of the high-valent coinage-metal complexes [RCuIIIMe3]- and [RAgIIIMe3]- (R = allyl)

High‐valent tetraalkylcuprates(iii) and ‐argentates(iii) are key intermediates of copper‐ and silver‐mediated C−C coupling reactions. Here, we investigate the previously reported contrasting reactivity of [RMⁱⁱⁱMe₃]⁻ complexes (M=Cu, Ag and R=allyl) with energy‐dependent collision‐induced dissociation experiments, advanced quantum‐chemical calculations and kinetic computations. The gas‐phase fragmentation experiments confirmed the preferred formation of the [RCuMe]⁻ anion upon collisional activation of the cuprate(iii) species, consistent with a homo‐coupling reaction, whereas the silver analogue primarily yielded [AgMe₂]⁻, consistent with a cross‐coupling reaction. For both complexes, density functional theory calculations identified one mechanism for homo coupling and four different ones for cross coupling. Of these pathways, an unprecedented concerted outer‐sphere cross coupling is of particular interest, because it can explain the formation of [AgMe₂]⁻ from the argentate(iii) species. Remarkably, the different C−C coupling propensities of the two [RMⁱⁱⁱMe₃]⁻ complexes become only apparent when properly accounting for the multi‐configurational character of the wave function for the key transition state of [RAgMe₃]⁻. Backed by the obtained detailed mechanistic insight for the gas‐phase reactions, we propose that the previously observed cross‐coupling reaction of the silver complex in solution proceeds via the outer‐sphere mechanism.

Multi-configuration electron-nuclear dynamics: An open-shell approach

The multi-configuration electron-nuclear dynamics for open shell systems with a spin-unrestricted formalism is described. The mean fields are evaluated using second-order reduced density matrices for electronic and nuclear degrees of freedom. Applications to light-element diatomics including equilibrium geometries, electronic energies, dipole moments, and absorption spectra are presented. The von Neumann entropies for different spin states of a LiH molecule are compared.

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.

Modern multireference methods and their application in transition metal chemistry

Transition metal chemistry is a challenging playground for quantum chemical methods owing to the simultaneous presence of static and dynamic electron correlation effects in many systems. Wavefunction based multireference (MR) methods constitute a physically sound and systematically improvable Ansatz to deal with this complexity but suffer from some conceptual difficulties and high computational costs. The latter problem partially arises from the unfavorable scaling of the Full Configuration Interaction (Full-CI) problem which in the majority of MR methods is solved for a subset of the molecular orbital space, the so-called active space. In the last years multiple methods such as modern variants of selected CI, Full-CI Quantum Monte Carlo (FCIQMC) and the density matrix renormalization group (DMRG) have been developed that solve the Full-CI problem approximately for a fraction of the computational cost required by conventional techniques thereby significantly extending the range of applicability of modern MR methods. This perspective review outlines recent advancements in the field of MR electronic structure methods together with the resulting chances and challenges for theoretical studies in the field of transition metal chemistry. In light of its emerging importance a special focus is put on the selection of adequate active spaces and the concomitant development of numerous selection aides in recent years.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

Electronic structure and mechanism for the uptake of nitric oxide by the Ru(iii) antitumor complex NAMI-A

Nitric oxide (NO) has well known vasodilation effects in living organisms and its participation in the metastasis of cancer cells through the angiogenesis process has been demonstrated experimentally. Therefore, the uptake of NO has become one focus of investigation to produce anti-metastatic drugs. In this article we have investigated the uptake of NO by the ruthenium based metallodrug trans-tetrachloride(dimethylsulfoxide)imidazole ruthenate(iii) [Im]trans-[RuCl4(Im)(DMSO)], known as New Anti-tumor Metastasis Inhibitor-A (NAMI-A). Electronic structure calculations using Density Functional Theory, DFT, and State-Averaged Complete Active Space Self Consistent Field, SA-CASSCF, with second order perturbation theory corrections, NEVPT2 were carried out to investigate the mechanism involved in the uptake of NO by the Ru-based anticancer metallodrug NAMI-A. The calculations revealed that the reaction takes place at the triplet potential energy surface, with the singlet surface being ∼15 kcal mol-1 shifted to higher energies, and there is a surface crossing to form the most stable singlet product after the reaction takes place at the triplet surface. The spin pairing and electron transfer from the nitric oxide to the metallic fragment takes place at the region of the minimum energy crossing point between the two surfaces. The Ru-NO bond in the {Ru-NO}6 product has ∼10% of the RuIII-NO0 character. The SA-CASSCF/NEVPT2 calculations revealed that the uptake of NO by NAMI-A has a small energy barrier of ∼8 kcal mol-1 and, therefore a rate constant of 11.3 × 106 s-1 at 300 K. In addition, the reaction is thermodynamically favorable, with a Gibbs free energy of ∼30 kcal mol-1. These results show that the uptake of nitric oxide by the NAMI-A complex is kinetically and thermodynamically feasible in biological medium and, therefore, gives support to the anti-angiogenesis theory associated to the mode of action of NAMI-A and other related compounds.

Concept of Orbital Entanglement and Correlation in Quantum Chemistry

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements in numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement seen previously. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.

Portably parallel construction of a configuration-interaction wave function from a matrix-product state using the Charm++ framework

The construction of configuration-interaction (CI) expansions from a matrix product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations in a large Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS employing the parallel object-oriented Charm++ programming framework, upon which automatic load-balancing and object migrating facilities can be employed. This procedure was employed in the MPS-to-CI utility (Moritz et al., J. Chem. Phys. 2007, 126, 224109), the sampling-reconstructed complete active-space algorithm (SR-CAS, Boguslawski et al., J. Chem. Phys. 2011, 134, 224101), and the entanglement-driven genetic algorithm (EDGA, Luo et al., J. Chem. Theory Comput. 2017, 13, 4699). It enhances productivity and allows the sampling programs to evolve to their population-expansion versions, for example, EDGA with population expansion (PE-EDGA). Further, examples of 1,2-dioxetanone and firefly dioxetanone anion (FDO^- ) molecules demonstrated the following: (a) parallel efficiencies can be persistently improved by simply by increasing the proportions of the asynchronous executions and (b) a sampled CAS-type CI wave function of a bi-radical-state FDO^- molecule utilizing the full valence (30e,26o) active space can be constructed within a few hours with using thousands of cores.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

CASPT2 Potential Energy Curves for NO Dissociation in a Ruthenium Nitrosyl Complex

Ruthenium nitrosyl complexes are fascinating photoactive compounds showing complex photoreactivity, such as N→O linkage photoisomerism and NO photorelease. This dual photochemical behavior has been the subject of many experimental studies in order to optimize these systems for applications as photoswitches or therapeutic agents for NO delivery. However, despite recent experimental and computational studies along this line, the underlying photochemical mechanisms still need to be elucidated for a more efficient design of these systems. Here, we present a theoretical contribution based on the calculations of excited-state potential energy profiles for NO dissociation in the prototype trans-[RuCl(NO)(py)4]2+ complex at the complete active space second-order perturbation theory (CASPT2). The results point to a sequential two-step photon absorption photorelease mechanism coupled to partial photoisomerization to a side-on intermediate, in agreement with previous density functional theory calculations.

Elucidating the multi-configurational character of the firefly dioxetanone anion and its prototypes in the biradical region using full valence active spaces

We analyzed the near-degenerate states of the firefly dioxetanone anion (FDO-) and its prototypes, especially in the biradical region, using multi-configurational approaches. The importance of utilizing full valence active spaces by means of density-matrix renormalization group self-consistent field (DMRG-SCF) calculations was described. Our results revealed that the neglect of some valence orbitals can affect the quantitative accuracy in later multi-reference calculations or the qualitative conclusion when optimizing conical intersections. Using all of the relevant valence orbitals of FDO-, we confirmed that there were two conical intersections, as reported in previous work, and that the intersecting states were changed when the active space was enlarged. Beyond these, we found that there were strong interactions between states in the biradical regions, in which the changes in entanglements can be used to visualize the interacting state evolution.

Tracking the role of trans-ligands in ruthenium–NO bond lability: computational insight

Ruthenium–NO tetraamine structures control the nitric oxide bioavailability. The ligand trans to NO modulates the Ru–NO bond stability.

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.

Structural and Optical Properties of Metal-Nitrosyl Complexes

The electronic, structural and optical properties (including Spin–Orbit Coupling) of metal nitrosyl complexes [M(CN)₅(NO)]²⁻ (M = Fe, Ru or Os) are investigated by means of Density Functional Theory, TD-DFT and MS-CASPT2 based on an RASSCF wavefunction. The energy profiles connecting the N-bound (η¹-N), O-bound (η¹-O) and side-on (η²-NO) conformations have been computed at DFT level for the closed shell singlet electronic state. For each structure, the lowest singlet and triplet states have been optimized in order to gain insight into the energy profiles describing the conformational isomerism in excited states. The energetics of the three complexes are similar—with the N-bound structure being the most stable—with one exception, namely the triplet ground state of the O-bound isomer for the iron complex. The conformation isomerism is highly unfavorable in the S₀ electronic state with the occurrence of two energy barriers higher than 2 eV. The lowest bands of the spectra are assigned to MLCT_NO/LLCT_NO transitions, with an increasing MLCT character going from iron to osmium. Two low-lying triplet states, T1 (MLCT_NO/LLCT_NO) and T2 (MLCT_NO/IL_NO), seem to control the lowest energy profile of the excited-state conformational isomerism.

[Fe(H2 O)5 (NO)]2+ , the "Brown-Ring" Chromophore

Although the "brown-ring" ion, [Fe(H₂ O)₅ (NO)]²⁺ (1), has been a research target for more than a century, this poorly stable species had never been isolated. We now report on the synthesis of crystals of a salt of 1 which allowed us to tackle the unique bonding situation on an experimental basis. As a result of the bonding analysis, two stretched, spin-polarised π-interactions provide the Fe-NO binding-and challenge the concept of "oxidation state".

Quantum information-based analysis of electron-deficient bonds

Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here, for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely, diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe the bonding situation in more exotic molecules which have been synthesized and characterized only recently, in particular, the diborane molecule with four hydrogen atoms [diborane(4)] and a neutral zerovalent s-block beryllium complex, whose surprising stability was attributed to a strong three-center two-electron π bond stretching across the C-Be-C core. Our approach is of high importance especially in the light of a constant chase after novel compounds with extraordinary properties where the bonding is expected to be unusual.

Externally-Contracted Multireference Configuration Interaction Method Using a DMRG Reference Wave Function

The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry makes it practical to evaluate static correlation in a large active space, while dynamic correlation provides a critical correction to the DMRG reference for strong-correlated systems and is usually obtained using multireference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use an active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with an active space larger than 30 orbitals and/or a large basis set because of high computation and storage costs of high-order reduced density matrices (RDMs) and the crucial dependence of the MRCI Hamiltonian dimension on the number of virtual orbitals. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use reconstructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA) [ Luo et al. J. Chem. Theory Comput. 2017 , 13 , 4699 - 4710 . ] and integrate it with MRCI by an external contraction (ec) scheme. This bypasses the bottleneck of computing high-order RDMs in traditional DMRG dynamic correlation methods with ic approximation, and the number of MRCI configurations is not dependent on the number of virtual orbitals. Therefore, the DMRG-ec-MRCI method is promising for dealing with a larger active space than 30 orbitals and large basis sets. We demonstrate the capability of our DMRG-ec-MRCI method in several benchmark applications, including the evaluation of the potential energy curve of Cr₂, single-triplet gaps of higher n-acene molecules, and the energy of the Eu-BTBP(NO₃)₃ complex.

Linkage Photoisomerization of an Isolated Ruthenium Sulfoxide Complex: Sequential versus Concerted Rearrangement

Ruthenium sulfoxide complexes undergo thermally reversible linkage isomerization of sulfoxide ligands from S- to O-bound in response to light. Here, we report photoisomerization action spectra for a ruthenium bis-sulfoxide molecular photoswitch, [Ru(bpy)₂(bpSO)]²⁺, providing the first direct evidence for photoisomerization of a transition metal complex in the gas phase. The linkage isomers are separated and isolated in a tandem drift tube ion mobility spectrometer and exposed to tunable laser radiation provoking photoisomerization. Direct switching of the S,S-isomer to the O,O-isomer following absorption of a single photon is the predominant isomerization pathway in the gas phase, unlike in solution, where stepwise isomerization is observed with each sulfoxide ligand switching in turn. The change in isomerization dynamics is attributed to rapid vibrational quenching that suppresses isomerization in solution. Supporting electronic structure calculations predict the wavelengths and intensities of the peaks in the photoisomerization action spectra of the S,S- and S,O-isomers, indicating that they correspond to metal-to-ligand charge transfer (MLCT) and ligand-centered ππ* transitions.

Photophysical properties and the NO photorelease mechanism of a ruthenium nitrosyl model complex investigated using the CASSCF-in-DFT embedding approach

A complete state-averaged active space self-consistent field (SA-CASSCF) calculation by means of the SA-CASSCF(18,14)-in-BP86 Miller-Manby embedding approach was performed to explore the ground and excited electronic states of the trans-[RuCl(NO)(NH₃)₄]²⁺ complex. Insights into the NO photodissociation mechanism and Ru-NO bonding properties are provided. In addition, spin-orbit (SO) interactions were taken into account to describe and characterize the spin-forbidden transitions observed at the low-energy regions of the trans-[RuCl(NO)(NH₃)₄]²⁺ UV-Vis spectrum. The SA-CASSCF(18,14)-in-BP86 electronic spectrum is in great agreement with the experimental data of Schreiner [Schreiner et al., Inorg. Chem., 1972, 11, 880].

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed-Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.

The correlation theory of the chemical bond

The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.

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.

Calculating NMR Chemical Shifts for Paramagnetic Metal Complexes from First-Principles

Paramagnetic effects on NMR shifts (pNMR) for paramagnetic metal complexes are calculated from first-principles, without recourse to spin Hamiltonian parameters. A newly developed code based on complete active space (CAS) and restricted active space (RAS) techniques in conjunction with treating spin-orbit (SO) coupling via state interaction is applied to (13)C NMR shifts of actinyl tris-carbonate complexes, specifically [UO2(CO3)3](5-) and [NpO2(CO3)3](4-). The experimental pNMR shifts as well as the sizable difference of the (13)C NMR shift for these iso-electronic species are well reproduced by the calculations. Approximations to the pNMR shift equations using spin Hamiltonian parameters or the magnetic susceptibility are calculated for the same systems at the same level of theory, and it is shown how the approximations relate to the ab initio data.

Singlet ground state actinide chemistry with geminals

We present the first application of the variationally orbital optimized antisymmetric product of 1-reference orbital geminals (vOO-AP1roG) method to singlet-state actinide chemistry.

The effect of nitrido, azide, and nitrosyl ligands on magnetization densities and magnetic properties of iridium PNP pincer-type complexes

The magnetisation density of different iridium PNP pincer-type complexes depends on the chosen quantum chemistry method.