The Complete Active Space Self-Consistent Field Method and its Applications in Electronic Structure Calculations

Impact of Parametrizations of the One-Body Reduced Density Matrix on the Energy Landscape

Many electronic structure methods rely on the minimization of the energy of the system with respect to the one-body reduced density matrix (1-RDM). To formulate a minimization algorithm, the 1-RDM is often expressed in terms of its eigenvectors via an orthonormal transformation and its eigenvalues. This transformation drastically alters the energy landscape. Especially in 1-RDM functional theory this means that the convexity of the energy functional is lost. We show that degeneracies in the occupation numbers can lead to additional critical points which are classified as saddle points. Using a Cayley or Householder parametrization for the orthonormal transformation, no extra critical points arise. In the case of Given's rotations or the exponential, additional critical points can arise, which are of no concern in practical minimization. These findings provide an explanation for the success of recent minimization procedures using second-order information.

Multiscale Embedding for Quantum Computing

We present a novel multiscale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that facilitates BE calculations on extended systems using classical computers with limited memory resources. Benchmark data suggest the combination of these two strategies as a robust path in attaining the correlation energies of large realistic systems, combining the proven accuracy of BE with chemical and biological systems of interest in a lower computational cost method. Due to the flexible tunability of the resource requirements and systematic fragment construction, future developments in the realization of quantum computers naturally offer improved accuracy for multiscale BE calculations.

Improving Aufbau Suppressed Coupled Cluster through Perturbative Analysis

Guided by perturbative analysis, we improve the accuracy of Aufbau suppressed coupled cluster theory in simple single excitations, multiconfigurational single excitations, and charge transfer excitations while keeping the cost of its leading-order terms precisely in line with ground-state coupled cluster. Combining these accuracy improvements with a more efficient implementation based on spin adaptation, we observe high accuracy in a large test set of single excitations and, in particular, a mean unsigned error for charge transfer states that outperforms equation-of-motion coupled cluster theory by 0.25 eV. We discuss how these results are achieved via a systematic identification of which amplitudes to prioritize for single- and multiconfigurational excited states, and how this prioritization differs in important ways from the ground-state theory. In particular, our data show that a partial linearization of the theory increases accuracy by mitigating unwanted side effects of Aufbau suppression.

Generalized Velocity Sampling at a Transition State and Nonadiabatic Dynamics of Four-Membered Heterocyclic Peroxides

We propose the generalized initial velocity sampling algorithm at a transition state, in which the total initial kinetic energy and extra positive initial velocity along the reaction coordinate have been introduced to improve the accuracy and efficiency of nonadiabatic dynamics simulation. This sampling algorithm is very useful for chemical reactions with multiple transition states, e.g., two transition states in the thermolysis of four-membered heterocyclic peroxides. The dependence of the chemiexcitation yields, dissociation times, and other quantities on the total initial kinetic energy and extra positive initial velocity has been investigated. By taking different CASPT2 corrections and additional positive initial velocities into account, we found that the resulting triplet quantum yield matches the experimental result perfectly. In most ensembles, the secondary primary intersystem crossing, i.e., the first singlet excited state to the first triplet state, is a major direct production channel for the first triplet state product trajectories.

Ab Initio Speciation of Tc-Gluconate Complexes in Aqueous Systems

Tc-gluconate complexes in aqueous systems were recently reported and characterized by Tc L3-edge X-ray absorption near-edge structure (XANES) measurements [Dardenne, K.; Inorg. Chem. 2021, 60, 12285-12298]. The puzzling result was reported that the Tc L3-edge XANES of the sample containing Tc(IV)-gluconate species differs substantially from that of the Tc(IV)O2(am,hyd) hydrous oxide reference sample, whereas the Tc K-edge XANES spectra did not differ significantly. We studied this observation theoretically and tracked the unknown Tc(IV)-gluconate species in a three-step procedure: (1) developing chemical models, (2) optimizing the equilibrium structures of the models, and (3) simulating the corresponding Tc L3-edge XANES spectra. We identified the [Tc(IV)(Glu-2H)2(H2O)2]2- structure as the most likely Tc(IV)-gluconate species present in our samples and explain the substantial difference between the two Tc L3-edge XANES spectra. Additionally, we revisited the Tc(V)-gluconate species and identified the [Tc(V)O(Glu-H)2]- structure as the most likely Tc(V)-gluconate species in our sample.

Can ΔSCF and ROKS DFT-Based Methods Predict the Inversion of the Singlet-Triplet Gap in Organic Molecules?

Inverted singlet-triplet gap systems (INVEST) have emerged as an intriguing class of materials with potential applications as emitters in Organic Light Emitting Diodes (OLEDs). Indeed, this type of material exhibits a negative singlet-triplet energy gap (ΔEST), i.e., an inversion of the lowest singlet (S1) and triplet (T1) excited states, that goes against Hund's rule. In this study, the ΔEST of a set of 15 INVEST molecules has been computed within the framework of Restricted Open-Shell Kohn-Sham (ROKS) and Delta Self-Consistent Field (ΔSCF) methods and the results were benchmarked against wavefunction-based calculations performed at the EOM-CCSD, NEVPT2, and SCS-CC2 levels. We find that ROKS always (and wrongly) predicts a positive ΔEST with global hybrid, meta-GGA, and long-range corrected functionals and that this is almost functional-independent. We also show that the only way to obtain an inverted gap was to resort to double hybrid functionals. In contrast, using the above-mentioned functionals, ΔSCF usually gives a negative ΔEST, although the results are largely functional-dependent. Overall, applying a ΔSCF method based on the PBE0 functional provides the lowest MSD and MAD with respect to the EOM-CCSD results. We further show that the singlet-triplet inversion is driven by different degrees of orbital relaxation in the singlet versus triplet state and that this is well captured by ΔSCF calculations. As a matter of fact, this orbital relaxation in ΔSCF somehow mimics the involvement of double and higher-order excitations in EOM-CCSD, which leads to a difference in spatial localization of the α and β spins, and thus introduces (local) spin polarization effects sourcing the negative ΔEST. However, care should be taken when using the ΔSCF method to screen materials with potential INVEST behavior in view of their limited quantitative correlation with reference EOM-CCSD results on the molecular data basis used here.

A framework for designing main-group single-molecule magnets

Single-molecule magnets (SMMs) are molecular entities with strongly anisotropic magnetic moment. As a result, SMMs display slow relaxation of magnetization at the macroscopic scale. Up to date all experimentally characterized SMMs are based on either d- or f-block metals with lanthanides proving to be the most successful. In the present work, a framework for constructing SMMs consisting purely of main-group elements will be outlined by computational and theoretical means. The proposed main-group SMMs utilize the strong spin-orbit coupling of a single heavy p-block atom or ion that can lead to strong magnetic anisotropy and pronounced SMM properties. A theoretical crystal-field model is developed to describe the magnetic properties of p-block SMMs with a minimal set of parameters related to the chemical structure of the SMMs. The model is used to establish which p-block elements and oxidation states can lead to SMM behavior. A large number of model structures are studied to establish general features of optimal chemical structures. These include one- and two-coordinate structures involving ligands with different coordination modes and all group 13 to 17 elements in periods 4 to 6. The results show that the most viable structures are based on mono-coordinated complexes of bismuth in oxidation state 0 with σ-donor ligands. Structures with bulkier ligands that sterically protect the bismuth atoms are then proposed as a starting point for the practical realization of main-group SMMs. The calculations show that minimizing the anagostic interactions with the bismuth atom is essential in the ligand design, which along with the low oxidation state of bismuth introduces significant synthetic challenges. The results do, however, show that main-group SMMs are plausible from a practical point of view within a limited set of heavier p-block elements in specific oxidation states. Furthermore, the proposed SMMs display much larger energy barriers for the relaxation of magnetization than even the best lanthanide-based SMMs do. This indicates that it is possible that main-group SMMs can supersede even the best currently known SMMs based on d- or f-block elements.

Energy decomposition analysis for excited states: an extension based on TDDFT

To enhance the understanding of photochemical reactivity and its mechanisms, it is essential to analyze bonding interactions in excited-state reactions. Such insights can aid in optimizing these reactions. This paper presents an energy decomposition analysis method for excited states (exc-EDA), integrating the ground state EDA approach by Morokuma, Ziegler and Rauk with time-dependent density functional theory (TDDFT). The methodology focuses on calculating excitation energies, particularly for the intermediate states of the EDA. We introduce two variants: the first uses non-relaxed excitation coefficients (exc-u-EDA), where the excitation coefficients of the excited fragment are used directly; the second optimizes these coefficients for the intermediate states (exc-r-EDA). Exc-EDA can be applied with various density functionals, but the accuracy depends on the functional's ability to describe the excited state properly. Smaller basis sets result in lower energy values due to fewer virtual orbitals, while larger basis sets produce consistent relative results but may involve different excited states in intermediate steps leading to artificial increase of energy terms in the EDA. The method's convergence behavior resembles that of TDDFT, with a computational cost approximately three times that of the underlying TDDFT calculation. At the current stage, the method requires that the excitation is localized on one of the fragments, but it also enables an analysis of the subsequent charge-transfer effects. Application of exc-EDA to singlet fission in pentacene clusters demonstrates its practical value, offering quantitative insights into excited-state bonding and revealing clear, intuitive trends.

Static and Dynamic Studies of Excitation in a Fullerene-Anthracene Complex

We investigate the static and dynamic aspects of an anthracene-fullerene complex. Our detailed investigation includes (a) systematic scrutiny of the complex in its stable state through the examination of its chemical reactivity parameters and absorption spectra and (b) exploration of its dynamic behavior in excited states at a femtosecond time scale. To achieve this, we employ a combination of ab initio molecular dynamics (AIMD) and time-dependent density functional theory (TDDFT) to study not only the system's behavior in the excited state but also the temporal evolution of chemical reactivity parameters when it moves in a particular excited state. It shows greater reactivity in the excited state as compared to that in the ground state. Interestingly, our findings reveal that the complex can even switch between excited states during its movement in certain trajectories. Accordingly, we conduct an extensive examination of the interactions among coupling components, which coincides with the occurrence of trajectory surface hopping.

Excited state relaxation mechanisms and tautomerism effects in 2,6-Diamino-8-Azapurine

The photochemistry of 9H-2,6-diamino-8-azapurine (9H-8AZADAP), a promising fluorescent probe, was investigated using the Multi-State Complete-Active-Space Second-Order Perturbation Theory (MS-CASPT2) quantum chemical method, along with the Average Solvent Electrostatic Configuration and Free Energy Gradient (ASEC-FEG) and Polarizable Continuum Model (PCM) to take into account water solvation effects. For both isolated and solvated species, the main photochemical event is initiated by the absorption of light from ground-state to the bright 1(ππ* La) state, which undergoes barrierless evolution to its minimum energy region (1(ππ* La)min) without crossing any other potential energy surface (PES). Subsequently, the excess of energy is released through fluorescence. From the 1(ππ* La)min region, two radiationless decay pathways back to the initial ground state, mediated by two distinct conical intersections between the ground and 1(ππ* La) states, are found to be unlikely due to the presence of high energy barriers in both environments. Our results also indicate that the solvation effects are more pronounced when using the ASEC-FEG method, which predicts larger structural and energy changes, especially concerning energetic barriers. Based on the free energy perturbation theory (FEP), a hypothetical thermodynamic cycle was devised, from which we infer that in an aqueous environment the N3 site is the most favorable for protonation. We also conclude that the 8H-8AZADAP tautomer is responsible for the fluorescent band observed experimentally at 410 nm and elucidates the mechanism of phototautomerism.

Minimum Energy Conical Intersection Optimization Using DFT/MRCI(2)

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a semiempirical electronic structure approach that is both computationally efficient and has predictive accuracy for the calculation of electronic excited states and for the simulation of electronic spectroscopies. However, given that the reference space is generated via a selected-CI procedure, a challenge arises in the construction of smooth potential energy surfaces. To address this issue, we treat the local discontinuities that arise as noise within the Gaussian progress regression framework and learn the surfaces by explicitly incorporating and optimizing a white-noise kernel. The characteristic polynomial coefficient surfaces of the potential matrix, which are smooth functions of nuclear coordinates even at conical intersections, are learned in place of the adiabatic energies and are used to optimize the DFT/MRCI(2) minimum energy conical intersection geometries for representative intersection motifs in the molecules ethylene, butadiene, and fulvene. One consequence of explicitly treating the noise in the surfaces is that the energy difference cannot be made arbitrarily small at points of nominal intersection. Despite the limitations, however, we find the structures as well as the branching spaces to compare well with ab initio MRCI and conclude that this approach is a viable method to learn a smooth representation of DFT/MRCI(2) surfaces.

Spin-Orbit Coupling and Admixture Coefficients in SA-CASSCF and MS-CASPT2, and Triplet Excitation Yield Simulated via Trajectory Surface Hopping and Calibrated SA-CASSCF in 1,2-Dioxetane Derivatives

The energy gaps, spin-orbit coupling (SOC), and admixture coefficients over a series of the configurations are evaluated by the SA-CASSCF/6-31G, SA-CASSCF/6-31G*, SA-CASSCF/ANO-RCC-VDZP, and MS-CASPT2/ANO-RCC-VDZP to reveal the extent of the inaccuracy of the SA-CASSCF. By comparing the mean absolute errors for the energy gaps and the admixture coefficient magnitudes (ACMs) measured between the SA-CASSCF/6-31G, SA-CASSCF/6-31G*, or SA-CASSCF/ANO-RCC-VDZP and the MS-CASPT2/ANO-RCC-VDZP, the SA-CASSCF/6-31G is selected as the electronic structure method in the nonadiabatic molecular dynamics simulation. The major components of the ACMs of the SA-CASSCF/6-31G and MS-CASPT2/ANO-RCC-VDZP are identified and compared; we find that the ACMs are underestimated by the SA-CASSCF/6-31G, which is verified by the reasonable triplet quantum yield simulated by the trajectory surface hopping and the calibrated SA-CASSCF/6-31G. The magnitude of the singlet-triplet mixing positively correlates to the hopping probability between the mixed singlet and triplet states, which is confirmed by the computed S-T transition probability.

FragPT2: Multifragment Wave Function Embedding with Perturbative Interactions

Embedding techniques allow the efficient description of correlations within localized fragments of large molecular systems while accounting for their environment at a lower level of theory. We introduce FragPT2: a novel embedding framework that addresses multiple interacting active fragments. Fragments are assigned separate active spaces, constructed by localizing canonical molecular orbitals. Each fragment is then solved with a multireference method, self-consistently embedded in the mean field from other fragments. Finally, interfragment correlations are reintroduced through multireference perturbation theory. Our framework provides an exhaustive classification of interfragment interaction terms, offering a tool to analyze the relative importance of various processes such as dispersion, charge transfer, and spin exchange. We benchmark FragPT2 on challenging test systems, including N2 dimers, multiple aromatic dimers, and butadiene. We demonstrate that our method can be successful even for fragments defined by cutting through a covalent bond.

Modulation of the Magnetic Anisotropy via the Ligand Field in Sandwiched Erbium Complexes

Among lanthanide-based single-molecule magnets (SMMs), erbium(III) is a Kramers ion, apart from dysprosium(III), which provides magnetic bistability in the presence of a suitable coordination environment. However, Er-based SMMs exhibit significantly less magnetic anisotropy than Dy because their prolate electronic density necessitates equatorially correlated ligands to minimize the charge contact with the Er atom. Here, in this work, we have computationally investigated the heteroleptic organometallic complexes with an Er(III) atom sandwiched between two distinct cyclic rings (five- and eight-membered) with the aim of tuning the magnetic anisotropy via exploiting the ligand field. The ligand field is manipulated by substituting one of the C atoms from the five-membered ring with heteroatoms (groups 14 and 15), while the other (eight-membered) ring remains intact. The electronic and magnetic properties have been investigated using first-principles-based ab initio approaches. The distortion in the planarity of the five-membered ring generated by the larger heteroatom affects the bonding with magnetic Er and consequently the electronic structure. This is observed to modify the ligand field and the magnetic axis, thereby improving the magnetic relaxation barrier.

Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers

The promise of quantum computing to circumvent the exponential scaling of quantum chemistry has sparked a race to develop chemistry algorithms for quantum architecture. However, most works neglect the quantum-inherent shot noise, let alone the effect of current noisy devices. Here, we present a comprehensive study of quantum linear response (qLR) theory obtaining spectroscopic properties on simulated fault-tolerant quantum computers and present-day near-term quantum hardware. This work introduces novel metrics to analyze and predict the origins of noise in the quantum algorithm, proposes an Ansatz-based error mitigation technique, and reveals the significant impact of Pauli saving in reducing measurement costs and noise in subspace methods. Our hardware results using up to cc-pVTZ basis set serve as proof of principle for obtaining absorption spectra on quantum hardware in a general approach with the accuracy of classical multi-configurational methods. Importantly, our results exemplify that substantial improvements in hardware error rates and measurement speed are necessary to lift quantum computational chemistry from proof of concept to an actual impact in the field.

A cross-entropy corrected hybrid multiconfiguration pair-density functional theory for complex molecular systems

Hybrid density functionals, such as B3LYP and PBE0, have achieved remarkable success by substantially improving over their parent methods, namely Hartree-Fock and the generalized gradient approximation, and generally outperforming the second-order Møller-Plesset perturbation theory (MP2) that is more expensive. Here, we extend the linear scheme of hybrid multiconfiguration pair-density functional theory (HMC-PDFT) by incorporating a cross-entropy ingredient to balance the description of static and dynamic correlation effects, leading to a consistent improvement on both exchange and correlation energies. The B3LYP-like translated on-top functional (tB4LYP) developed along this line not only surpasses the accuracy of its parent methods, the complete active space self-consistent field (CASSCF) and the original MC-PDFT functionals (tBLYP and tB3LYP), but also outperforms the widely used complete active space second-order perturbation theory (CASPT2). Remarkably, while remaining satisfactory for general purpose, tB4LYP shows superior accuracy for challenging cases like the Cr2 dissociation and the associated low-lying vibrational energies, the ethylene torsional rotation and the ethyne diabatic colinear dissociations, with the significantly lower computational cost than CASPT2.

QM/MM Calculations on Excited-State Proton Transfer and Photoisomerization of a Red Fluorescent Protein mKeima with Large Stokes Shift

Large Stokes shift red fluorescent proteins (LSS-RFPs) are of growing interest for multicolor bioimaging applications. However, their photochemical mechanisms are not fully understood. Here, we employed the QM(XDW-CASPT2//CASSCF)/MM method to investigate the excited-state proton transfer and photoisomerization processes of the LSS-RFP mKeima starting from its cis neutral isomer. Upon excitation to the bright S1 state in the Franck-Condon region, mKeima relaxes to a metastable minimum-energy state. From this short-lived species, two competing deactivation pathways are available: the excited-state proton transfer in the S1 state, and the S1 decay via the S1/S0 conical intersection as a result of the cis-trans photoisomerization. In comparison, the former is a dominant excited-state relaxation pathway, leading to the cis anionic isomer of mKeima in the S1 state. This anionic intermediate then undergoes cis-trans photoisomerization after overcoming a barrier of approximately 10 kcal/mol in the S1 state, which is followed by an excited-state decay via the S1/S0 conical intersection region. The efficient nonadiabatic decay of the cis anionic isomer of mKeima in the S1 state inhibits the radiative process, leading to a weak emission around 520 nm observed experimentally. These findings shed important mechanistic light on the experimental observations and provide valuable insights that could help in the design of LSS-RFPs with superior fluorescence properties.

Investigating the Origin of Automatic Rhodopsin Modeling Outliers Using the Microbial Gloeobacter Rhodopsin as Testbed

The automatic rhodopsin modeling (ARM) approach is a computational workflow devised for the automatic buildup of hybrid quantum mechanics/molecular mechanics (QM/MM) models of wild-type rhodopsins and mutants, with the purpose of establishing trends in their photophysical and photochemical properties. Despite the success of ARM in accurately describing the visible light absorption maxima of many rhodopsins, for a few cases, called outliers, it might lead to large deviations with respect to experiments. Applying ARM toGloeobacter rhodopsin (GR), a microbial rhodopsin with important applications in optogenetics, we analyze the origin of such outliers in the absorption energies obtained for GR wild-type and mutants at neutral pH, with a total root-mean-square deviation (RMSD) of 0.42 eV with respect to the experimental GR excitation energies. Having discussed the importance and the uncertainty of one particular amino-acid pKa, namely histidine at position 87, we propose and test several modifications to the standard ARM protocol: (i) improved pKa predictions along with the consideration of several protonation microstates, (ii) attenuation of the opsin electrostatic potential at short-range, (iii) substitution of the state-average complete active space (CAS) electronic structure method by its state-specific approach, and (iv) complete replacement of CAS with mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT). The best RMSD result we obtain is 0.2 eV combining the protonation of H87 and using MRSF/CAMH-B3LYP.

Computational Investigations of the Detailed Mechanism of Reverse Intersystem Crossing in Inverted Singlet-Triplet Gap Molecules

Inverted singlet-triplet gap (INVEST) materials have promising photophysical properties for optoelectronic applications due to an inversion of their lowest singlet (S1) and triplet (T1) excited states. This results in an exothermic reverse intersystem crossing (rISC) process that potentially enhances triplet harvesting, compared to thermally activated delayed fluorescence (TADF) emitters with endothermic rISCs. However, the processes and phenomena that facilitate conversion between excited states for INVEST materials are underexplored. We investigate the complex potential energy surfaces (PESs) of the excited states of three heavily studied azaphenalene INVEST compounds, namely, cyclazine, pentazine, and heptazine using two state-of-the-art computational methodologies, namely, RMS-CASPT2 and SCS-ADC(2) methods. Our findings suggest that ISC and rISC processes take place directly between the S1 and T1 electronic states in all three compounds through a minimum-energy crossing point (MECP) with an activation energy barrier between 0.11 to 0.58 eV above the S1 state for ISC and between 0.06 and 0.36 eV above the T1 state for rISC. We predict that higher-lying triplet states are not populated, since the crossing point structures to these states are not energetically accessible. Furthermore, the conical intersection (CI) between the ground and S1 states is high in energy for all compounds (between 0.4 to 2.0 eV) which makes nonradiative decay back to the ground state a relatively slow process. We demonstrate that the spin-orbit coupling (SOC) driving the S1-T1 conversion is enhanced by vibronic coupling with higher-lying singlet and triplet states possessing vibrational modes of proper symmetry. We also rationalize that the experimentally observed anti-Kasha emission of cyclazine is due to the energetically inaccessible CI between the bright S2 and the dark S1 states, hindering internal conversion. Finally, we show that SCS-ADC(2) is able to qualitatively reproduce excited state features, but consistently overpredict relative energies of excited state structural minima compared to RMS-CASPT2. The identification of these excited state features elaborates design rules for new INVEST emitters with improved emission quantum yields.

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe-2S] Systems: A Benchmark Study of the [Fe2S2(SCH3)4]2-,3-,4-, [Fe2S2(SCys)4]2-, [Fe2S2(S-p-tol)4]2-, and [Fe2S2(S-o-xyl)4]2- Complexes

Iron-sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Using a [2Fe-2S] model complex with FeII and FeIII oxidation states, which leads to different charges, i.e., [Fe2S2(SMe)4]2-,3-,4-, we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree-Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe2S2(SCys)4]2-, [Fe2S2(S-o-tol)4]2-, and [Fe2S2(S-o-xyl)4]2-, via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the FeIII/FeIII → FeII/FeIII (4.27 eV) and FeII/FIII → FeII/FII (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

Duality of Particle-Hole and Particle-Particle Theories for Strongly Correlated Electronic Systems

We propose a novel approach to electron correlation for multireference systems. It is based on particle-hole (ph) and particle-particle (pp) theories in the second-order, developed in the random phase approximation (RPA) framework for multireference wave functions. We show a formal correspondence (duality), between contributions to the correlation energy in the ph and pp pictures. It allows us to describe correlation energy by rigorously combining pp and ph terms, avoiding correlation double counting. The multireference ph, pp, and the combined correlation methods are applied to ground and excited states of systems in the intermediate and strong correlation regimes and compared with the multireference second-order perturbation method (MRPT2). It is shown that the pp approximation fails to describe dissociation of multiple bonds. The ph-pp combined method is overall superior to both ph and pp alone. It parallels good accuracy of the second-order perturbation theory for ground states and singlet excitation energies. For the singlet-triplet gaps of biradicals its accuracy is significantly better. This is impressive, taking into account that it relies only on one- and two-body density matrices, while MRPT2 methods typically require density matrices up to the four-body.

Phase-dependent polymerization isomerism in the coordination complexes of a flexible bis(β-diketonato) ligand

First prepared in the late 70s, the pro-ligand 1,3-bis(3,5-dioxo-1-hexyl)benzene (H2bdhb) contains two acetoacetyl terminations linked to a central 1,3-phenylene unit through dimethylene bridges. Since each termination can be either in diketonic or keto-enolic form, in organic solution it exists as a mixture of three spectroscopically resolvable tautomers. In the presence of pyridine, Co2+ and the bdhb2- anion form a crystalline dimeric compound with formula [Co2(bdhb)2(py)4] (2) and a Co⋯Co separation of more than 11 Å. Complex 2 contains two pseudo-octahedrally coordinated and non-interacting high-spin cobalt(II) ions (S = 3/2) displaying a large easy-plane anisotropy (D ∼ 70 cm-1), as consistently indicated by magnetic measurements, X-band EPR spectra, and complete active space self-consistent field/N-electron valence state perturbation theory (CASSCF/NEVPT2) calculations. At cryogenic temperatures (T < 7 K) and in an applied static magnetic field, the compound shows detectably slow magnetic relaxation, which occurs through direct and Raman mechanisms. Combined mass spectrometry, UV-Vis, and 1H/2H NMR data, including an isotopic labelling experiment and a determination of molecular weight by diffusion ordered spectroscopy (DOSY), show that 2 rearranges to monomeric high-spin [Co(bdhb)(py)x] species (x = 0, 1, or 2) in organic solution (CH2Cl2, THF) with concomitant partial dissociation of the py ligands. The X-band EPR spectra in a frozen CH2Cl2/toluene matrix concurrently suggest a significant alteration of the coordination environment upon dissolution. These observations are fairly well reproduced by density functional theory (DFT) and CASSCF/NEVPT2 calculations on the lowest Gibbs free energy conformers of each species, as provided by an extensive conformational search based on meta-dynamics simulations and semiempirical tight-binding methods. After the vanadyl analogue, compound 2 provides the second example of polymerization isomerism in the 1 : 1 adducts of bdhb2- with divalent metal ions.

Isolation and characterization of a triplet nitrene

Nitrene radical compounds are short-lived intermediates in a variety of nitrogen-involved transformations. They feature either a singlet or a triplet ground state, depending on the electronic properties of the substituents. Triplet nitrenes are highly reactive and their isolation in the condensed phase under ambient conditions is challenging. Here we report the synthesis and isolation of a triplet arylnitrene supported by a bulky hydrindacene ligand. The arylnitrene is fully characterized by various spectroscopic and structural techniques including electron paramagnetic resonance spectroscopy and single-crystal X-ray diffraction. Its high stability is largely attributed to the steric hindrance and effective electron delocalization provided by the supporting ligand. Electron paramagnetic resonance spectroscopy in conjunction with highly correlated wavefunction-based ab initio calculations provides support for a triplet ground state nitrene with axial zero-field splitting D = 0.92 cm-1 and vanishing rhombicity E/D = 0.002.

Stereoelectronic Tuning of Bioinspired Nonheme Iron(IV)-Oxo Species by Amide Groups in Primary and Secondary Coordination Spheres for Selective Oxygenation Reactions

Two mononuclear iron(II) complexes, [(6-amide2-BPMEN)FeII](OTf)2 (1) and [(6-amide-Me-BPMEN)FeII(OTf)](OTf) (2), supported by two BPMEN-derived (BPMEN = N1,N2-dimethyl-N1,N2-bis(pyridine-2-yl-methyl)ethane-1,2-diamine) ligands bearing one or two amide functionalities have been isolated to study their reactivity in the oxygenation of C-H and C═C bonds using isopropyl 2-iodoxybenzoate (iPr-IBX ester) as the oxidant. Both 1 and 2 contain six-coordinate high-spin iron(II) centers in the solid state and in solution. The 6-amide2-BPMEN ligand stabilizes an S = 1 iron(IV)-oxo intermediate, [(6-amide2-BPMEN)FeIV(O)]2+ (1A). The oxidant (1A) oxygenates the C-H and C═C bonds with a high selectivity. Oxidant 1A, upon treatment with 2,6-lutidine, is transformed into another oxidant [{(6-amide2-BPMEN)-(H)}FeIV(O)]+ (1B) through deprotonation of an amide group, resulting in a stronger equatorial ligand field and subsequent stabilization of the triplet ground state. In contrast, no iron-oxo species could be observed from complex 2 and [(6-Me2-BPMEN)FeII(OTf)2] (3) under similar experimental conditions. The iron(IV)-oxo oxidant 1A shows the highest A/K selectivity in cyclohexane oxidation and 3°/2° selectivity in adamantane oxidation reported for any synthetic nonheme iron(IV)-oxo complexes. Theoretical investigation reveals that the hydrogen bonding interaction between the -NH group of the noncoordinating amide group and Fe═O core smears out the equatorial charge density, reducing the triplet-quintet splitting, and thus helping complex 1A to achieve better reactivity.

Semiclassical Nonadiabatic Molecular Dynamics Using Linearized Pair-Density Functional Theory

Nonadiabatic molecular dynamics is an effective method for modeling nonradiative decay in electronically excited molecules. Its accuracy depends strongly on the quality of the potential energy surfaces, and its affordability for long direct-dynamic simulations with adequate ensemble averaging depends strongly on the cost of the required electronic structure calculations. Linearized pair-density functional theory (L-PDFT) is a recently developed post-self-consistent-field multireference method that can model potential energy surfaces with an accuracy similar to expensive multireference perturbation theories but at a computational cost similar to the underlying multiconfiguration self-consistent field method. Here, we integrate the SHARC dynamics and PySCF electronic structure code to utilize L-PDFT for electronically nonadiabatic calculations and use the combined programs to study the photoisomerization reaction of cis-azomethane. We show that L-PDFT is able to successfully simulate the photoisomerization without crashes, and it yields results similar to the more expensive extended multistate complete active space second-order perturbation theory. This shows that L-PDFT can model internal conversion, and it demonstrates its promise for broader photodynamics applications.

Rank-Reduced Equation-of-Motion Coupled Cluster Triples: an Accurate and Affordable Way of Calculating Electronic Excitation Energies

In the present work, we report an implementation of the rank-reduced equation-of-motion coupled cluster method with approximate triple excitations (RR-EOM-CC3). The proposed variant relies on tensor decomposition techniques in order to alleviate the high cost of computing and manipulating the triply excited amplitudes. In the RR-EOM-CC3 method, both ground-state and excited-state triple-excitation amplitudes are compressed according to the Tucker-3 format. This enables factorization of the working equations such that the formal scaling of the method is reduced to N6, where N is the system size. An additional advantage of our method is the fact that the accuracy can be strictly controlled by proper choice of two parameters defining sizes of triple-excitation subspaces in the Tucker decomposition for the ground and excited states. Optimal strategies of selecting these parameters are discussed. The developed method has been tested in a series of calculations of electronic excitation energies and compared to its canonical EOM-CC3 counterpart. Errors several times smaller than the inherent error of the canonical EOM-CC3 method (in comparison to FCI) are straightforward to achieve. This conclusion holds both for valence states dominated by single excitations and for states with pronounced doubly excited character. Taking advantage of the decreased scaling, we demonstrate substantial computational costs reductions (in comparison with the canonical EOM-CC3) in the case of two large molecules - l-proline and heptazine. This illustrates the usefulness of the RR-EOM-CC3 method for accurate determination of excitation energies of large molecules.

Complete Active Space Iterative Coupled Cluster Theory

In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected CC. This is accomplished by establishing a feedback loop between the CC and CAS parts of a calculation through a similarity transformation of the Hamiltonian with those CC amplitudes that are not encompassed by the active space. We denote this approach as the complete active space iterative coupled cluster (CASiCC) ansatz. We investigate its efficiency and accuracy in the singles and doubles approximation by studying the prototypical molecules H4, H8, H2O, and N2. Our results demonstrate that CASiCC systematically improves on the single-reference CCSD and the externally corrected CCSD methods across entire potential energy curves while retaining modest computational costs. However, the tailored coupled cluster method shows superior performance in the strong correlation regime, suggesting that its accuracy is based on error compensation. We find that the iterative versions of externally corrected and tailored coupled cluster methods converge to the same results.

Theoretical Investigation on One-Electron ϕ···ϕ Bonding in Diuranium Inverse Sandwich U2B6 Complex Enabled by a B6 Ring

Traditional σ, π, and δ types of covalent chemical bonding have been extensively studied for nearly a century. In contrast, ϕ-type bonding involving nf (n = 4, 5) orbitals has received less attention due to their high contraction and minimal orbital overlap. Herein, we theoretically predict a singly occupied ϕ···ϕ bonding between two 5f orbitals, facilitated by B6 group orbitals in the hexa-boron diuranium inverse sandwich structure of U2B6. From ab initio quantum chemical calculations, the global minimum structure has a septuplet state with D6h symmetry. Chemical bonding analyses reveal that the 5f and 6d atomic orbitals of the two uranium atoms interact with the ligand orbitals of the central B6 ring, exhibiting favorable energy matching and symmetry compatibility to form delocalized σ-, π-, δ-, and ϕ-type bonding orbitals. Notably, even though the ϕ···ϕ bonding orbital is singly occupied, it still has a significant role in stability and cannot be overlooked. Furthermore, the U2B6 cluster model can be viewed as a building block of UB2 solid materials from both geometric and electronic perspectives. This work predicts the first example of ϕ···ϕ bonding, highlighting the complexity and diversity of chemical bonds formed in actinide boride clusters.

Attosecond impulsive stimulated X-ray Raman scattering in liquid water

We report the measurement of impulsive stimulated x-ray Raman scattering in neutral liquid water. An attosecond pulse drives the excitations of an electronic wavepacket in water molecules. The process comprises two steps: a transition to core-excited states near the oxygen atoms accompanied by transition to valence-excited states. Thus, the wavepacket is impulsively created at a specific atomic site within a few hundred attoseconds through a nonlinear interaction between the water and the x-ray pulse. We observe this nonlinear signature in an intensity-dependent Stokes Raman sideband at 526 eV. Our measurements are supported by our state-of-the-art calculations based on the polarization response of water dimers in bulk solvation and propagation of attosecond x-ray pulses at liquid density.

Investigation of the Nonradiative Photoprocesses of Unnatural DNA Base: 7-(2-Thienyl)-imidazo[4,5-b]pyridine (Ds)─A Computational Study

7-(2-Thienyl)-imidazo[4,5-b]pyridine (Ds) is an unnatural nucleic acid that forms a stable pair with pyrrole-2-carbaldehyde (Pa) in DNA. This Ds-Pa pair gets stabilized via van der Waals interaction and shape fitting. In our previous study [Ghosh, P. J. Phys. Chem. A 2021, 125, 5556-5561], we investigated the nonradiative photoprocesses of the unnatural DNA base Pa, and also there are some studies on its stability and reactivity in the ground state. But, to consider it as a good unnatural base pair, one has to understand its stability not only in the ground state but also in the excited states after absorbing ultraviolet (UV) radiation. Therefore, in this study, the excited-state photoprocesses of Ds on UV irradiation and its nonradiative decay channels have been investigated using state-of-the-art multireference methods, and this investigation finally leads the molecule to access the minimum energy crossing point (MECP) via a downhill pathway.

Photocyclization and Photoisomerization Mechanisms of an Indolylfulgide Derivative in Acetonitrile Solution by Using the QM (MS-CASPT2)/MM Method

The indolylfulgide systems have been extensively investigated due to their potential applications as photochromic materials. In this work, the photoinduced ring-closure/opening and isomerization reactions of a photochromic indolylfulgide in vacuum and acetonitrile solvent have been investigated by means of MS-CASPT2//CASSCF and QM(MS-CASPT2)//CASSCF/MM. The deactivation mechanisms of indolylfulgide have been proposed based on the optimized structures in the S0 and S1 states, S1/S0 conical intersections, and the calculated minimum-energy paths. After excitation into the first singlet excited-state, which is spectroscopically bright in the Franck-Condon point of the E, the photoprocesses proceed toward a nearby S1 minimum. Then, two possible nonadiabatic relaxation paths exist to repopulate the ground state. In the ring closure reaction, the S1 E isomer evolves directly into one S1/S0 conical intersection and decays to the ground state with bifurcation toward C or E. In the E → Z tautomerization pathway, the excited system can deactivate to the S0 state via a distinct conical intersection. The minimum-energy paths of the indolylfulgide revealed that the ring closure reaction in the solvent is more facile to take place than the E → Z isomerization after irradiation of the same E. Furthermore, for the ring opening reaction from the C side, there exists an energy barrier (11.1 kcal/mol) in the S1 state before arriving at the conical intersection. The computational results showed that the solvent has some influence on the system compared with that in the gas phase. The present work could contribute to comprehending the photoreactions of indolylfulgide and its derivatives in solution.

Photochemical Mechanism of Co-C Bond Activation via Triplet Energy Transfer in Ethyl(aqua)cobaloxime

The photochemical decomposition of ethyl(aqua)cobaloxime, [EtCoIII(dmgH)2H2O], a vitamin B12 derivative model complex, was investigated to understand the mechanism of the Co-CEt bond scission induced by light. Upon irradiation of [EtCoIII(dmgH)2H2O], the Co-CEt bond undergoes homolytic scission, resulting in Et/Co(II) radical pair (RP) formation in a similar fashion observed in alkylcobalamins. The [EtCoIII(dmgH)2H2O] complex acts as a potent quencher of a wide variety of excited states in the presence of organic molecules such as benzophenone. It has been proposed that the reaction mechanism involves Dexter energy transfer, resulting in the bond dissociation process. Two issues associated with the proposed mechanism have been investigated, namely, (i) how the energy transfer occurs from benzophenone to cobaloxime and (ii) how the Co-CEt bond is activated and cleaved. Both TD-DFT and CASSCF/NEVPT2 methods have been applied to show the feasibility of the energy transfer reaction via the triplet pathway from photocatalyst to substrate.

A homoleptic Fe(iv) ketimide complex with a low-lying excited state

The reaction of 4 equiv. of Li(N[double bond, length as m-dash]C( t Bu)Ph) with FeIICl2 results in isolation of [Li(Et2O)]2[FeII(N[double bond, length as m-dash]C( t Bu)Ph)4] (1), in good yields. The reaction of 1 with 1 equiv. of I2 leads to formation of [FeIV(N[double bond, length as m-dash]C( t Bu)Ph)4] (2), in moderate yields. 57Fe Mössbauer spectroscopy confirms the Fe(iv) oxidation state of 2, and X-ray crystallography reveals that 2 has a square planar coordination geometry along with several intramolecular H⋯C interactions. Furthermore, SQUID magnetometry indicates a small magnetic moment at room temperature, suggestive of an accessible S = 1 state. Both density functional theory and multiconfigurational calculations were done to elucidate the nature of the ground state. Consistent with the experimental results, the ground state was found to be an S = 0 state with an S = 1 excited state close in energy.

Renormalized Internally Contracted Multireference Coupled Cluster with Perturbative Triples

In this work, we combine the many-body formulation of the internally contracted multireference coupled cluster (ic-MRCC) method with Evangelista's multireference formulation of the driven similarity renormalization group (DSRG). The DSRG method can be viewed as a unitary multireference coupled cluster theory, which renormalizes the amplitudes based on a flow equation approach to eliminate numerical instabilities. We extend this approach by demonstrating that the unitary flow equation approach can be adapted for nonunitary transformations, rationalizing the renormalization of ic-MRCC amplitudes. We denote the new approach, the renormalized ic-MRCC (ric-MRCC) method. To achieve high accuracy with a reasonable computational cost, we introduce a new approximation to the Baker-Campbell-Hausdorff expansion. We fully consider the linear commutator while approximating the quadratic commutator, for which we neglect specific contractions involving amplitudes with active indices. Moreover, we introduce approximate perturbative triples to obtain the ric-MRCCSD[T] method. We demonstrate the accuracy of our approaches in comparison to advanced multireference methods for the potential energy curves of H8, F2, H2O, N2, and Cr2. Additionally, we show that ric-MRCCSD and ric-MRCSSD[T] match the accuracy of CCSD(T) for evaluating spectroscopic constants and of full configuration interaction energies for a set of small molecules.

Carbene-Decorated Geometrically Constrained Borylenes for Bond Activations

While metal-ligand cooperativity is well-known, studies on element-ligand cooperativity involving main group species are comparatively much less explored. In this study, we computationally designed a few geometrically constrained borylenes supported by different carbenes. Our density functional theory studies indicate that they possess enhanced nucleophilicity as well as electrophilicity, thus rendering them promising candidates for exhibiting borylene-ligand cooperativity. The cooperation between the boron and adjacent carbene centers facilitates different bond activation processes, including the cycloaddition of acetylene across the boron-carbene bond as well as B-H/Si-H bond activation reactions, which have been analyzed in detail. To the best of our knowledge, the borylenes proposed in this study represent the first examples of theoretically proposed geometrically constrained bis(carbene)-stabilized borylenes capable of cooperative activation of enthalpically strong bonds.

Unraveling the Geometry-Driven C═C Epoxidation and C-H Hydroxylation Reactivity of Tetra-Coordinated Nonheme Iron(IV)-Oxo Complexes

The electronic structure and reactivity of tetra-coordinated nonheme iron(IV)-oxo complexes have remained unexplored for years. The recent synthesis of a closed-shell iron(IV)-oxo complex [(quinisox)FeIV(O)]+ (1) has set up a platform to understand how such complexes compare with the celebrated open-shell iron-oxo chemistry. Herein, using density functional theory and ab initio calculations, we present an in-depth electronic structure investigation of the C═C epoxidation [oxygen atom transfer (OAT)] and C-H hydroxylation [hydrogen atom transfer (HAT)] reactivity of 1. Using a solvent-coordinated geometry of 1 (1') and other potential tetra-coordinated iron(IV)-oxo complexes bearing rigid ligands (2 and 3), we established the geometric origin of spin-state energetics and reactivity of 1. Complex 1 featuring a strong Fe-O bond exhibits OAT and HAT reactivity in its quintet state. The lowest quintet OAT pathway has a lower barrier by ∼4 kcal/mol than the quintet HAT pathway, corroborating the experimentally observed gas-phase OAT reactivity preference. A conventional HAT reactivity preference for 2 and a comparable OAT and HAT reactivity for 3 are observed. This further supports the geometry-driven reactivity preference for 1. Noncovalent interaction analyses reveal a pronounced π-π interaction between the substrate and ligand in the OAT transition state, rationalizing the origin of the observed reactivity preference for 1.

Triplet-Singlet Emission of d-Block Metal Complexes Characterized by Spin-Orbit Natural Transition Orbitals

Spin-orbit natural transition orbital (SO-NTO) methodology, recently developed in our group for complete and restricted active space (CAS/RAS) wavefunction calculations, is applied to analyze triplet-to-singlet emission in transition metal complexes. The lowest-energy (longest-wavelength) spin-forbidden transitionT 1 → S 0 ${{{\rm T}}_{1}\to {{\rm S}}_{0}}$ is studied for for [Ir(pbt)2(acac)] and [Re(CO)4(pbt)] and the complexes [W(CO)4(bpy)] and [Mo(CO)4(bpy)]. For the latter complexes, spin-forbidden transitions from higher spin-triplet levels are additionally analyzed. SO-NTOs are compared with spin-free NTOs for the transitions under consideration. The major assignment of a spin-forbidden transition is obtained from the spin-free NTO analysis, while the source of intensity of the electronic transition is revealed by the SO-NTOs.

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

Dynamical Electron Correlation and the Chemical Bond. IV. Covalent Bonds in A2 Molecules (A = N-As and F-Br)

In a series of recent papers, we investigated the effect of dynamical electron correlation on the potential energy curves and spectroscopic constants of several diatomic molecules, including the simple diatomic hydrides (AH) and the more complex diatomic fluorides (AF) and homonuclear diatomic molecules (A2) with A = B-F (AF) or A = C-F (A2), respectively. Our goal was to understand the dependence of the dynamical electron correlation energy, EDEC, on the internuclear distance, R, and quantify how dynamical electron correlation influences the spectroscopic constants (De, Re, and ωe) of these molecules. At large R, we found that the magnitude of EDEC(R) had a simple dependence on R, with EDEC(R) increasing nearly exponentially with decreasing R. However, as R continued to decrease, there were significant variations in EDEC(R). These variations led to differing changes in the predicted spectroscopic constants of the molecules. In many molecules, the changes in EDEC(R) could be correlated with changes in the underlying spin-coupled generalized valence bond wave function, either in the orbitals or the spin-coupling coefficients. In the current paper, we extend these studies to higher main group elements, comparing the effects of EDEC(R) on P2 and As2 versus N2, and on Cl2 and Br2 versus F2. We find that there are significant differences between the effects of dynamical electron correlation on the molecules in the first and subsequent rows of the periodic table.

Beyond a Richardson-Gaudin Mean-Field: Slater-Condon Rules and Perturbation Theory

Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Thermal Jahn-Teller Distortion Changes and Slow Relaxation of Magnetization in Mn(III) Schiff Base Complexes

The impact that the anion and alkyl group has on the electronic structures and magnetic properties of four mononuclear Mn(III) complexes is explored in [Mn(salEen-Br)2]Y (salEen-Br = 2-{[2-(ethylamino)ethylimino]methyl}-4-Br-phenol; Y = ClO4- 1 and BF4-·1/3CH2Cl2 2) and [Mn(salBzen-Br)2]Y (salBzen-Br = 2-{[2-(benzylamino)ethylimino]methyl}-4-Br-phenol; Y = ClO4- 3 and BF4- 4). X-ray structures of [Mn(salEen-Br)2]ClO4·0.45C6H14 1-hexane, [Mn(salEen-Br)2]BF4·0.33CH2Cl2·0.15C6H14 2-dcm-hexane, and 3-4 reveal that they crystallize in ambient conditions in the monoclinic P21/c space group. Lowering the temperature, 2-dcm-hexane uniquely exhibits a structural phase transition toward a monoclinic P21/n crystal structure determined at 100 K with the unit cell trebling in size. Remarkably, at room temperature, the axially elongated Jahn-Teller axis in 2-dcm-hexane is poorly defined but becomes clearer at low temperature after the phase transition. Magnetic susceptibility measurements of 1-4 reveal that only 3 and 4 show slow relaxation of magnetization with Δeff/kB = 27.9 and 20.7 K, implying that the benzyl group is important for observing single-molecule magnet (SMM) properties. Theoretical calculations demonstrate that the alkyl group subtly influences the orbital levels and therefore very likely the observed SMM properties.

Anharmonic Vibrational Spectroscopy of Germanium-Containing Clusters, GexC4-x and GexSi4-x (x = 0-4), for Interstellar Detection

An extensive, high-level theoretical study on tetra-atomic germanium carbide/silicide clusters is presented. Accurate harmonic and anharmonic vibrational frequencies and rotational constants are calculated at the CCSD(T)-F12a(b)/cc-pVT(Q)Z-F12 levels of theory. With growing capabilities to discern more of the chemical composition of the interstellar medium (ISM), an accurate database of reference material is required. The presence of carbon is ubiquitous in the ISM, and silicon is known to be present in interstellar dust grains; however, germanium-containing molecules remain elusive. To begin understanding the presence and role of germanium in the ISM, we present this study of the vibrational and rotational spectroscopic properties of various germanium-containing molecules to aid in their potential identification in the ISM with modern observational tools such as the James Webb Space Telescope. Structures studied herein include rhomboidal (r-), diamond (d-), and trapezoidal (t-) tetra-atomic molecules of the form GexC4-x and GexSi4-x, where x = 0-4. The most promising structure for detection is r-Ge2C2 via the ν4 mode with a frequency of 802.7 cm-1 (12.5 μm) and an intensity of 307.2 km mol-1. Other molecules that are potentially detectable, i.e., through vibrational modes or rotational transitions, include r-Ge3C, r-GeSi3, d-GeC3, r-GeC3, and t-Ge2C2.

A Merger of the Spin-Flip ORMAS Approach and the MC-PDFT Method

The SF-ORMAS-PDFT (spin-flip occupation restricted multiple active space-pair density functional theory) approach combines the SF-ORMAS-CI method with the MC-PDFT method to treat both static and dynamic correlation in multiconfigurational systems. The static correlation description is generated via the spin-flip approach, which uses a high-spin single reference determinant to treat excited states with multiconfigurational characters. The on-top pair density functional theory uses a translation scheme applied to GGA density functionals. The SF-ORMAS-PDFT scheme has also been combined with virtual valence orbitals (VVO), a well-defined subspace of the virtual molecular orbitals, giving rise to significant speedups relative to the use of the full virtual space. The accuracy of the SF-ORMAS-PDFT method is tested by calculating 65 vertical excitation energies of 12 small- and medium-sized organic molecules. The SF-ORMAS-PDFT vertical excitation energies calculated with VVOs are comparable to those calculated with the full virtual space. The SF-ORMAS-PDFT/6-31G(d) level of theory predicts the rotational barrier of ethylene to be 65.5 and 65.9 kcal/mol, with full virtual space and VVOs, respectively. These predicted barrier heights compare well with the experimental value of 65 kcal/mol.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Multiconfigurational actinide nitrides assisted by double Möbius aromaticity

Understanding the bonding nature between actinides and main-group elements remains a key challenge in actinide chemistry due to the involvement of f orbitals. Herein, we propose a unique "aromaticity-assisted multiconfiguration" (AAM) model to elucidate the bonding nature in actinide nitrides (An2N2, An = Ac, Th, Pa, U). Each planar four-membered An2N2 with equivalent An-N bonds possesses four delocalized π electrons and four delocalized σ electrons, forming a new family of double Möbius aromaticity that contributes to the molecular stability. The unprecedented aromaticity further supports actinide nitrides to exhibit multiconfigurational characters, where the unpaired electrons (2, 4 or 6 in naked Th2N2, Pa2N2 or U2N2, respectively) either are spin-free and localized on metal centres or form metal-ligand bonds. High-level multiconfigurational computations confirm an open-shell singlet ground state for actinide nitrides, with small energy gaps to high spin states. This is consistent with the antiferromagnetic nature observed experimentally in uranium nitrides. The novel AAM bonding model can be authenticated in both experimentally identified compounds containing a U2N2 motif and other theoretically modelled An2N2 clusters and is thus expected to be a general chemical bonding pattern between actinides and main-group elements.

Comments on "Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding"

In a recent communication (Angew. Chem. Int. Ed. 2024, 63, e202317312), Kalita et al. studied In4H+ system within the frame of single-reference approximation (SRA) and found that the global energy minimum (1 a) adopted the singlet state and a planar tetracoordinate hydrogen (ptH), while the second lowest isomer (1 b) located 3.0 kcal/mol above 1 a and adopted the triplet state as well as non-planar structure with a quasi-ptH. They assessed the reliability of SRA by checking the T1-diagnostic values of coupled cluster calculations. However, according to our multi-configurational second-order perturbation theory calculations at the CASPT2(12,13)/aug-cc-pVQZ (aug-cc-pVQZ-PP for In) level, both 1 a and 1 b exhibit obvious multi-referential characters, as reflected by their largest reference coefficients of 0.928 (86.1 %) and 0.938 (88.0 %), respectively. Moreover, 1 b is 5.05 kcal/mol lower than 1 a at this level, that is, what can be observed in In4H+ system is the quasi-ptH.

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear-electronic coupling in addition to accurately predicting Franck-Condon vertical excitations. In this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

Flexible Ansatz for N-Body Perturbation Theory

We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrödinger equation for arbitrary wave functions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly nonlinear wave functions.

Synthesis and Reactivity of a Dialane-Bridged Diradical

Radicals of the lightest group 13 element, boron, are well established and observed in numerous forms. In contrast to boron, radical chemistry involving the heavier group 13 elements (aluminum, gallium, indium, and thallium) remains largely underexplored, primarily attributed to the formidable synthetic challenges associated with these elements. Herein, we report the synthesis and isolation of planar and twisted conformers of a doubly CAAC (cyclic alkyl(amino)carbene)-radical-substituted dialane. Extensive characterization through spectroscopic analyses and X-ray crystallography confirms their identity, while quantum chemical calculations support their open-shell nature and provide further insights into their electronic structures. The dialane-connected diradicals exhibit high susceptibility to oxidation, as evidenced by electrochemical measurements and reactions with o-chloranil and a variety of organic azides. This study opens a previously uncharted class of dialuminum systems to study, broadening the scope of diradical chemistry and its potential applications.