Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn

The Use of Effective Core Potentials with Multiconfiguration Pair-Density Functional Theory

The reliable and accurate prediction of chemical properties is a key goal in quantum chemistry. Transition-metal-containing complexes can often pose difficulties to quantum mechanical methods for multiple reasons, including many electron configurations contributing to the overall electronic description of the system and the large number of electrons significantly increasing the amount of computational resources required. Often, multiconfigurational electronic structure methods are employed for such systems, and the cost of these calculations can be reduced by the use of an effective core potential (ECP). In this work, we explore both theoretical considerations and performances of ECPs applied in the context of multiconfiguration pair-density functional theory (MC-PDFT). A mixed-basis set approach is used, using ECP basis sets for transition metals and all-electron basis sets for nonmetal atoms. We illustrate the effects that an ECP has on the key parameters used in the computation of MC-PDFT energies, and we explore how ECPs affect the prediction of physical observables for chemical systems. The dissociation curve for a metal dimer was explored, and ionization energies for transition metal-containing diatomic systems were computed and compared to experimental values. In general, we find that ECP approaches employed with MC-PDFT are able to predict ionization energies with improved accuracy compared to traditional Kohn-Sham density functional theory approaches.

Targeting spectroscopic accuracy for dispersion bound systems from ab initio techniques: Translational eigenstates of Ne@C70

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Knudsen effusion mass spectrometry: Current and future approaches

RATIONALE

Knudsen effusion mass spectrometry (KEMS) has been a powerful tool in physical chemistry since 1954. There are many excellent reviews of the basic principles of KEMS in the literature. In this review, we focus on the current status and potential growth areas for this instrumental technique.

METHODS

We discuss (1) instrumentation, (2) measurement techniques, and (3) selected novel applications of the technique. Improved heating methods and temperature measurement allow for better control of the Knudsen cell effusive source. Accurate computer models of the effusive beam and its introduction to the ionizer allow optimization of such parameters as sensitivity and removal of background signals. Computer models of the ionizer allow for optimized sensitivity and resolution. Additionally, data acquisition systems specifically tailored to a KEMS system permit improved quantity and quality of data.

RESULTS

KEMS is traditionally utilized for thermodynamic measurements of pure compounds and solutions. These measurements can now be strengthened using first principles and model-based computational thermochemistry. First principles can be used to calculate accurate Gibbs energy functions (gefs) for improving third law calculations. Calculated enthalpies of formation and dissociation energies from ab initio methods can be compared to those measured using KEMS. For model-based thermochemistry, solution parameters can be derived from measured thermochemical data on metallic and nonmetallic solutions. Beyond thermodynamic measurements, KEMS has been used for many specific applications. We select examples for discussion: measurements of phase changes, measurement/control of low-oxygen potential systems, thermochemistry of ultrahigh-temperature ceramics, geological applications, nuclear applications, applications to organic and organometallic compounds, and thermochemistry of functional room temperature materials, such as lithium ion batteries.

CONCLUSIONS

We present an overview of the current status of KEMS and discuss ideas for improving KEMS instrumentation and measurements. We discuss selected KEMS studies to illustrate future directions of KEMS.

Relativistic Coupled Cluster with Completely Renormalized and Perturbative Triples Corrections

We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems change the dissociation energies by about 0.1-0.2 eV or about 4-7%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au2 than in Ag2 or Cu2.

Trapping the substrate radical of heme synthase AhbD

The heme synthase AhbD catalyzes the last step of the siroheme-dependent heme biosynthesis pathway, which is operative in archaea and sulfate-reducing bacteria. The AhbD-catalyzed reaction consists of the oxidative decarboxylation of two propionate side chains of iron-coproporphyrin III to the corresponding vinyl groups of heme b. AhbD is a Radical SAM enzyme employing radical chemistry to achieve the decarboxylation reaction. Previously, it was proposed that the central iron ion of the substrate iron-coproporphyrin III participates in the reaction by enabling electron transfer from the initially formed substrate radical to an iron-sulfur cluster in AhbD. In this study, we investigated the substrate radical that is formed during AhbD catalysis. While the iron-coproporphyrinyl radical was not detected by electron paramagnetic resonance (EPR) spectroscopy, trapping and visualization of the substrate radical was successful by employing substrate analogs such as coproporphyrin III and zinc-coproporphyrin III. The radical signals detected by EPR were analyzed by simulations based on density functional theory (DFT) calculations. The observed radical species on the substrate analogs indicate that hydrogen atom abstraction takes place at the β-position of the propionate side chain and that an electron donating ligand is located in proximity to the central metal ion of the porphyrin.

The electronic structure of diatomic nickel oxide

The nature of the Ni-O bond is relevant to catalytic and environmental applications. The vibrational frequency and electronic structure of NiO were calculated using CASSCF, icMRCI+Q, CCSD(T), and DFT. CASSCF predicted a quintet state (5Σ-) ground state for the equilibrium bond distance with a state crossing at 1.65 Å, where the triplet (3Σ-) state becomes of lower energy. These states arise from the 3d8(3F)4s2 (3F) and 3d9(2D)4s1 (3D) configurations of Ni. The icMRCI+Q method predicts a triplet (3Σ-) ground state and does not predict a state crossing with the quintet. This state has significant ionic character with the 2pz of O bonding with the 4s/3dz2 of the Ni to form a σ bond. The NiO frequency at the icMRCI+Q level of 835.0 cm-1 is in excellent agreement with experiment; the value of re is 1.5992 Å at this computational level. CCSD(T) predicts ωe = 888.80 cm-1 when extrapolated to the complete basis set limit. Frequencies predicted using CCSD(T) deviate from experiment consistent with the calculations showing large multireference character. A wide array of density functionals were benchmarked. Of the 43 functionals tested, the ones that gave the best prediction of the frequency are ωB97XD, CAM-B3LYP, and τ-HCTH with respective values of 831.8, 838.3, and 837.4 cm-1 respectively. The bond dissociation energy (BDE) of NiO is predicted to be 352.4 kJ mol-1 at the Feller-Peterson-Dixon (FPD) level in good agreement with one of the experimental values. The calculated BDEs at the DFT level are sensitive to the choice of functional and atomic asymptote. Sixteen functionals predicted the BDE within 20 kJ mol-1 of the FPD value.

Towards reliable and efficient modeling of [Cu2O2]2+-based compound electronic structures with the partially fixed reference space protocols

This work reports a computationally efficient approach for reliable modeling of complex electronic structures based on [Cu2O2]2+ moieties. Specifically, we explore the recently developed partially fixed reference space (PFRS) protocol to minimize the active space size, taking into account the double d-shell effects. We show that the ground-state electronic structure of the core [Cu2O2]2+ model system is dominated by the d9/d10 occupations. The PFRS-crafted active spaces are further used to generate the reference wave functions for the multi-reference coupled cluster, configuration interaction, and multi-reference perturbation theory calculations. Specifically, we demonstrate that the bare [Cu2O2]2+ core can be modeled qualitatively using active spaces as small as CAS(2,2)PFRS. To obtain quantitative agreement with the reference DMRG(32,62)CI calculations, the CAS(4,4) has to be used in conjunction with the MRCCSD correction on top of it. This reliable and computationally efficient protocol is further used to model the electronic structure and properties of ammonia coordinated [Cu2O2]2+ complexes. Finally, based on the large amount of available experimental data regarding the oxo-peroxo equilibrium of [Cu2O2]2+-based systems, it is possible to formulate educated guesses regarding the effect of each experimental variable over each d-occupancy-specific state. With a large sample size of d-occupancy-specific state dependence with ligands and solvents, it should be possible to propose new ligands with specific d-occupancy and, therefore, oxidative properties based on the d-occupancy energy gaps of relatively low-cost calculations.

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.

Efficient Spin-Adapted Implementation of Multireference Algebraic Diagrammatic Construction Theory. I. Core-Ionized States and X-ray Photoelectron Spectra

We present an efficient implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulating core-ionized states and X-ray photoelectron spectra (XPS). Taking advantage of spin adaptation, automatic code generation, and density fitting, our implementation can perform calculations for molecules with more than 1500 molecular orbitals, incorporating static and dynamic correlation in the ground and excited electronic states. We demonstrate the capabilities of MR-ADC methods by simulating the XPS spectra of substituted ferrocene complexes and azobenzene isomers. For the ground electronic states of these molecules, the XPS spectra computed using the extended second-order MR-ADC method (MR-ADC(2)-X) are in a very good agreement with available experimental results. We further show that MR-ADC can be used as a tool for interpreting or predicting the results of time-resolved XPS measurements by simulating the core ionization spectra of azobenzene along its photoisomerization, including the XPS signatures of excited states and the minimum energy conical intersection. This work is the first in a series of publications reporting the efficient implementations of MR-ADC methods.

The trials and triumphs of modelling X-ray absorption spectra of transition metal phthalocyanines

This study explores the electronic structure of Co, Fe and Mn phthalocyanines (TMPcs) as well as their perfluorinated counterparts through a series of electronic structure calculations utilizing multireference methods and by simulating their metal L-edge and ligand (nitrogen and fluorine) K-edge X-ray absorption spectra (XAS) in an angle-resolved manner. Simulations targeting different ground-state symmetries, where relevant, have been conducted to observe changes in the N K-edge lineshape. The applicability of the quasi-degenerate formulation of n-electron valence state perturbation theory (QD-NEVPT2) for L-edge X-ray absorption spectroscopy (XAS) is evaluated, alongside the use of a restricted active space (RAS) formalism to describe the final-state multiplets generated by L-shell X-ray processes. Our findings provide valuable insights into the electronic properties of TMPcs, in particular with respect to the effect of fluorination, and demonstrate the broad applicability of various formulations of NEVPT2 in spectral simulations. Moreover, this study highlights the utility of manual truncation of the configuration spaces in order to allow for large active orbital spaces in aforementioned calculations.

Going for Gold(-Standard): Attaining Coupled Cluster Accuracy in Oxide-Supported Nanoclusters

The structure of oxide-supported metal nanoclusters plays an essential role in their sharply enhanced catalytic activity over that of bulk metals. Simulations provide the atomic-scale resolution needed to understand these systems. However, the sensitive mix of metal-metal and metal-support interactions, which govern their structure, puts stringent requirements on the method used, requiring calculations beyond standard density functional theory (DFT). The method of choice is coupled cluster theory [specifically CCSD(T)], but its computational cost has so far prevented its application to these systems. In this work, we showcase two approaches to make CCSD(T) accuracy readily achievable in oxide-supported nanoclusters. First, we leverage the SKZCAM protocol to provide the first benchmarks of oxide-supported nanoclusters, revealing that it is specifically metal-metal interactions that are challenging to capture with DFT. Second, we propose a CCSD(T) correction (ΔCC) to the metal-metal interaction errors in DFT, reaching accuracy comparable to that of the SKZCAM protocol at significantly lower cost. This approach forges a path toward studying larger systems at reliable accuracy, which we highlight by identifying a ground-state structure in agreement with experiments for Au20 on MgO, a challenging system where DFT models have yielded conflicting predictions.

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

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.

"On-the-fly" Crystal : How to reliably and automatically characterize and construct potential energy surfaces

In this work, the Crystal  code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of Crystal  over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, Crystal  is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H2 O), (reduced-dimensional) methane (CH4 ), and methylene imine (CH2 NH).

Theoretical prediction of closed-shell paramagnetism for scandium and yttrium hydride

Following chemical intuition, one would expect that all closed-shell molecules are diamagnetic. However, it is known that this is not the case for some second-row hydrides with low-lying unoccupied π orbitals due to an unquenching of the total angular momentum in the presence of an external magnetic field. In this article, the transition-metal hydrides ScH and YH are investigated, assuming a similar unquenching effect involving low-lying unoccupied π and δ orbitals formed from the metal d orbitals rather than the p orbitals. We are comparing results obtained with various quantum-chemical methods (HF, CCSD, CCSD(T), CCSDT) and basis sets. The obtained positive values for the magnetizabilities clearly indicate paramagnetic behavior. Vibrational effects on the magnetizability tensor are also considered, but these effects are small and do not change the overall conclusion that both ScH and YH are further examples for closed-shell paramagnetism.

Triptycene as a scaffold in metallocene catalyzed olefin polymerization

A set of metallocene olefin polymerization catalysts bearing triptycene moieties in either position 4-5 (complexes Ty1-Ty5) or in position 5-6 (complexes Ty6-Ty8) of the basic dimethylsilyl-bridged bis(indenyl) system has been tested in propene polymerization and in ethene/1-hexene copolymerization. Comparison of the results with QSPR (quantitative structure-property relationship) predictions not parametrized for these exotic ligand variations demonstrates that trends can still be identified by extrapolation. Interestingly, Ty7, upon suitable activation, provides a highly isotactic polypropylene with an exceptional amount of 2,1 regio-errors (8%). The previously developed QSPR type models successfully predicted the low regioselectivity of this catalyst, despite the fact that the catalyst structure differs significantly from the benchmark set.

In Search of the Best Low-Cost Methods for Efficient Screening of Conformers

Locating the lowest energy conformer is crucial for the accurate computation of equilibrium properties of molecular systems. This paper examines the performance of efficient low-cost methods in terms of the alignment and relative energies of their energy minima against the benchmark revDSD-PBEP86-D4/def2-TZVPP//MP2/cc-pVTZ potential energy surface. The low-cost methods considered include GFN-FF, GFN2-xTB, DFTB3, HF-3c, B97-3c, PBEh-3c, and r2SCAN-3c composite methods against a diverse test set of 20 compounds including alkanes, perfluoroalkyl molecules, peptides, open-shell radicals, and Zn(II) complexes of varying sizes. The "3c" composite methods are generally more accurate, but are at least 2-3 orders of magnitude more expensive than tight-binding methods which have energy minima that align well with the benchmark potential energy surface. The findings of this paper were further exploited to introduce a simple strategy involving Grimme's CENSO energy-sorting algorithm that resulted in up to an order of magnitude reduction in computational time for locating the lowest energy conformer on the revDSD-PBEP86-D4/def2-TZVPP//MP2/cc-pVTZ surface.

Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

Ab Initio Computation of Auger Decay in Heavy Metals: Zinc about It

We report the first coupled-cluster study of Auger decay in heavy metals. The zinc atom is used as a case study due to its relevance to the Auger emission properties of the 67Ga radionuclide. Coupled-cluster theory combined with complex basis functions is used to describe the transient nature of the core-ionized zinc atom. We also introduce second-order Møller-Plesset perturbation theory as an alternative method for computing partial Auger decay widths. Scalar-relativistic effects are included in our approach for computing Auger electron energies by means of the spin-free exact two-component one-electron Hamiltonian, while spin-orbit coupling is treated by means of perturbation theory. We center our attention on the K-edge Auger decay of zinc dividing the spectrum into three parts (K-LL, K-LM, and K-MM) according to the shells involved in the decay. The computed Auger spectra are in good agreement with experimental results. The most intense peak is found at an Auger electron energy of 7432 eV, which corresponds to a 1D2 final state arising from K-L2L3 transitions. Our results highlight the importance of relativistic effects for describing Auger decay in heavier nuclei. Furthermore, the effect of a first solvation shell is studied by modeling Auger decay in the hexaaqua-zinc(II) complex. We find that K-edge Auger decay is slightly enhanced by the presence of the water molecules as compared to the bare atom.

Discovery of a New Polymorph of 5-Methoxy-1H-Indole-2-Carboxylic Acid: Characterization by X-ray Diffraction, Infrared Spectroscopy, and DFT Calculations

This study presents a new 5-methoxy-1H-indole-2-carboxylic acid (MI2CA) polymorph investigated by single-crystal X-ray diffraction, infrared spectroscopy, and density functional theory (ωB97X-D) calculations employing two basis sets (6-31++G(d,p) and aug-cc-pVTZ). The compound crystallizes in the monoclinic system, space group P21/c (a = 4.0305(2) Å, b = 13.0346(6) Å, c = 17.2042(9) Å, β = 91.871(5)°, Z = 4). In the crystalline structure, the formation of cyclic dimers via double hydrogen bonds O-H⋯O between MI2CA molecules was observed. Interactions between the NH groups of the indole rings and the adjacent methoxy groups, as well as C-H⋯O contacts, significantly influence the spatial arrangement of molecules. The results from DFT calculations, including dimeric and trimeric structures, agree well with the experimental structural and spectroscopic data. Analysis of the infrared spectra confirms the conclusions drawn from X-ray diffraction studies and reveals differences between the IR spectra of the newly obtained polymorph and that reported earlier in the literature. This comprehensive study sheds some light on the MI2CA polymorphism and is important for a potential pharmacological applications of this compound.

Searching for stable copper borozene complexes in CuB7- and CuB8. Phys Chem Chem Phys 2024;26:12928-12938. [PMID: 38456623 DOI: 10.1039/d4cp00296b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Copper has been shown to be an important substrate for the growth of borophenes. Copper-boron binary clusters are ideal platforms to study the interactions between copper and boron, which may provide insight about the underlying growth mechanisms of borophene on copper substrates. Here we report a joint photoelectron spectroscopy and theoretical study on two copper-doped boron clusters, CuB7- and CuB8-. Well resolved photoelectron spectra are obtained for the two clusters at different wavelengths and are used to understand the structures and bonding properties of the two CuBn- clusters. We find that CuB8- is a highly stable borozene complex, which possesses a half-sandwich structure with a Cu+ species interacting with the doubly aromatic η8-B82- borozene. The CuB7- cluster is found to consist of a terminal copper atom bonded to a double-chain B7 motif, but it has a low-lying isomer composed of a half-sandwich structure with a Cu+ species interacting with an open-shell η7-B72- borozene. Both ionic and covalent interactions are found to be possible in the binary Cu-B clusters, resulting in different structures.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

Unraveling the electronic structure of LuH, LuN, and LuNH: building blocks of new materials

Advances in superconductor technology have been pursued for decades, moving towards room temperature models, such as a postulated nitrogen-doped lutetium hydride network. While experimental observations have been contradictory, insight into the building blocks of potential new superconductor materials can be gained theoretically, unravelling the fascinating electronic structure of these compounds at a molecular level. Here, the fundamental building blocks of lutetium materials (LuH, LuN, and LuNH) have been examined. The structures, spectroscopic constants for the ground and excited states, and the potential energy curves have been obtained for these species using complete active self-consistent field (CASSCF) and multireference configuration interaction with Davidson's correction (MRCI+Q) methods. For LuNH, the energetic properties of its isomers are determined. The bond dissociation energies of the three building blocks are calculated with the state-of-the-art f-block ab initio correlation consistent composite approach (f-ccCA) and the high accuracy extrapolated ab initio thermochemistry (HEAT) scheme. As well, an analysis of different formation pathways of LuNH has been provided.

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals

σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12 000 basis functions.

Translational eigenstates of He@C60 from four-dimensional ab initio potential energy surfaces interpolated using Gaussian process regression

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two ab initio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]- Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the ΔE is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect ΔE. Our best revised single-reference CC estimates for ΔE are 85-91 kJ/mol, including energy corrections to account for contributions beyond triples, core-valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree-Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82-84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, r2SCAN with 10-13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The r2SCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC ΔE results within 2 kJ/mol.

Confined Lewis Pairs: Investigation of the X- →Si20 Interaction in Halogen-Encapsulating Silafulleranes

A joint theoretical and experimental study on 32 endohedral silafullerane derivatives [X@Si20 Y20 ]- (X=F-I; Y=F-I, H, Me, Et) andT h ${T_h }$ -[Cl@Si20 H12 Y8 ]- (Y=F-I) is presented. First, we evaluated the structure-determining template effect of Cl- in a systematic series of concave silapolyquinane model systems. Second, we investigated the X- →Si20 interaction energy (E int ${E_{{\rm{int}}} }$ ) as a function of X- and Y and found the largestE int ${E_{{\rm{int}}} }$ values for electron-withdrawing exohedral substituents Y. Given that X- ions can be considered as Lewis bases and empty Si20 Y20 clusters as Lewis acids, we classify our inseparable host-guest complexes [X@Si20 Y20 ]- as "confined Lewis pairs". Third, 35 Cl NMR spectroscopy proved to be highly diagnostic for an experimental assessment of the Cl- →Si20 interaction as the paramagnetic shielding and, in turn, δ ${\delta }$ (35 Cl) of the endohedral Cl- ion correlate inversely withE int ${E_{{\rm{int}}} }$ . Finally, we disclose the synthesis of [PPN][Cl@Si20 Y20 ] (Y=Me, Et, Br) and provide a thorough characterization of these new silafulleranes.

Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n-block (n = 1-4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.

Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods

An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.

Influence of Steric and Dispersion Interactions on the Thermochemistry of Crowded (Fluoro)alkyl Compounds

ConspectusAlkanes play a pivotal role in industrial, environmental, and biological processes. They are characterized by their carbon-carbon single-bond structure, remarkable stability, and conformational diversity. Fluorination of such compounds imparts unique physicochemical properties that often enhance pharmacokinetic profiles, metabolic stability, and receptor interactions while keeping beneficial properties. However, such per- and polyfluoroalkyl substances (PFAS) show a persistent presence in the environment and potential adverse health effects, which propelled them to the forefront of global environmental and health discussions. Alkyl compounds are also prototypical for stereoelectronic (SE) effects that are widely applied in chemistry. Substituents are typically described as electron-density-donating/withdrawing and/or responsible for sterically interacting with reagents or strategic groups in the molecule. That alkane branching can result in higher stability compared to less-branched isomers has been investigated in detail also by testing quantum chemical methods, in particular density functional theory (DFT). Alkane branching results in spatially compact structures with close intramolecular contacts so that at a specific size the detailed balance of attractive London dispersion and covalent versus repulsive Pauli exchange interactions shifts to new, chemically unfragile situations. This may lead to dissociation at room temperature and opens the central question: what is the smallest crowed alkane that cannot be made synthetically? In this Account, we try to shed light on the interplay among the various (free) energy components for crowded (fluoro)alkane dissociation. In this context, homolytic cleavage of the central C-C bond in a series of model alkanes of increasing size with tert-butyl (tBu), adamantyl (Ad), and [1.1.1]propellanyl (Prop) substituents is investigated. Reference energies are calculated at the PNO-LCCSD(T)-F12b level and used to benchmark the performance of contemporary DFT functionals. In line with previous conclusions, the application of dispersion corrections to density functionals is mandatory. For crowed structures, the accurate description of the midrange correlation effects, specifically repulsive van der Waals interactions, is crucial, and we observed that the density-dependent VV10 correction is superior to D4 in this context, although the asymptotic region is better described by the latter. The best available dispersion-inclusive functionals show systematic and reasonably small residual errors and can be safely applied to large systems (>100 atoms), for which coupled cluster methods with large basis sets are not computationally feasible anymore. For qualitatively correct predictions of synthetic accessibility under equilibrium conditions (free energy), the inclusion of thermostatistical (entropy) contributions is also essential. According to our results, tetra-tert-butylmethane (C17tBu) is the largest and most crowded system with a positive dissociation free energy and should be synthesizable. The difference between hydrogenated and perfluorinated systems originates from the increase in the steric repulsion of spatially close substituents, which is not compensated to the same extent by attractive orbital and dispersion interactions. A sometimes-assumed similar steric demand for fluorine and hydrogen atoms is not corroborated by our investigations on crowded systems. Perfluorination is found to substantially decrease thermal stability, rendering perfluorinated hexamethylethane (C8tBuF) the last potentially stable representative.

Element effects in endohedral metal-metal-bonding fullerenes M2@C82 (M = Sc, Y, La, Lu)

Endohedral metal-metal-bonding fullerenes have recently emerged, in which encapsulated metals form a metal-metal bond. However, the physical reasons why some metal elements prefer to form metal-metal bonds inside fullerene are still unclear. Herein, we reported first-principles calculations on electronic structures, bonding properties, dynamics, and thermodynamic stabilities of endohedral metallofullerenes M2@C82 (M = Sc, Y, La, Lu). Multiple bonding analysis approaches unambiguously reveal the existence of one two-center two-electron σ covalent metal-metal bond in M2@C82 (M = Sc, Y, Lu); however, the La-La bonding interaction in La2@C82 is weaker and could not be categorized as one metal-metal covalent bond. The energy decomposition analysis on bonding interactions between an encapsulated metal dimer and fullerene cages suggested that there exist two electron-sharing bonds between a metal dimer and fullerene cages. The reasons why La2 prefers to donate electrons to fullerene cages rather than form a standard σ covalent metal-metal bond are mainly attributed to two following facts: La2 has a lower ionization potential, while the hybridization of ns, (n - 1)d, and np atomic orbitals in La2 is higher. Ab initio molecular dynamic simulations reveal that the M-M bond length at room temperature follows the trend of Sc < Lu < Y. The statistical thermodynamics calculations at different temperatures reveal that the experimentally observed endohedral metal-metal-bonding fullerenes M2@C82 have high concentrations in the endohedral fullerene formation temperature range.

M11pz: A Nonlocal Meta Functional with Zero Hartree-Fock Exchange and with Broad Accuracy for Chemical Energies and Structures

The accuracy of Kohn-Sham density functional theory depends strongly on the approximation to the exchange-correlation functional. In this work, we present a new exchange-correlation functional called M11pz (M11 plus rung-3.5 terms with zero Hartree-Fock exchange) that is built on the M11plus functional with the goal of using its rung-3.5 terms without a Hartree-Fock exchange term, especially to improve the accuracy for strongly correlated systems. The M11pz functional is optimized with the same local and rung-3.5 ingredients that are used in M11plus but without any percentage of Hartree-Fock exchange. The performance of M11pz is compared with eight local functionals, and M11pz is found to be in top three when the errors or ranks are averaged over eight grouped and partially overlapping databases: AME418/22, atomic and molecular energies; MGBE172, main-group bond energies; TMBE40, transition-metal bond energies; SR309, single-reference systems; MR54, multireference systems; BH192, barrier heights; NC579, noncovalent interaction energies; and MS20, molecular structures. For calculations of band gaps of solids, M11pz is the second best of the nine tested functionals that have zero Hartree-Fock exchange.

Quantum Information-Assisted Complete Active Space Optimization (QICAS)

We propose an effective quantum information-assisted complete active space optimization scheme (QICAS). What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features, QICAS yields, for smaller correlated molecule, sets of optimized orbitals with respect to which the complete active space configuration interaction energy reaches the corresponding complete active space self-consistent field (CASSCF) energy within chemical accuracy. For more challenging systems such as the chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal nonactive spaces are predominantly those that contain the least entanglement.

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

Local Oxidation States in {FeNO}6-8 Porphyrins: Insights from DMRG/CASSCF-CASPT2 Calculations

A first DMRG/CASSCF-CASPT2 study of a series of paradigmatic {FeNO}6, {FeNO}7, and {FeNO}8 heme-nitrosyl complexes has led to substantial new insight as well as uncovered key shortcomings of the DFT approach. By virtue of its balanced treatment of static and dynamic correlation, the calculations have provided some of the most authoritative information available to date on the energetics of low- versus high-spin states of different classes of heme-nitrosyl complexes. Thus, the calculations indicate low doublet-quartet gaps of 1-4 kcal/mol for {FeNO}7 complexes and high singlet-triplet gaps of ≳20 kcal/mol for both {FeNO}6 and {FeNO}8 complexes. In contrast, DFT calculations yield widely divergent spin state gaps as a function of the exchange-correlation functional. DMRG-CASSCF calculations also help calibrate DFT spin densities for {FeNO}7 complexes, pointing to those obtained from classic pure functionals as the most accurate. The general picture appears to be that nearly all the spin density of Fe[P](NO) is localized on the Fe, while the axial ligand imidazole (ImH) in Fe[P](NO)(ImH) pushes a part of the spin density onto the NO moiety. An analysis of the DMRG-CASSCF wave function in terms of localized orbitals and of the resulting configuration state functions in terms of resonance forms with varying NO(π*) occupancies has allowed us to address the longstanding question of local oxidation states in heme-nitrosyl complexes. The analysis indicates NO(neutral) resonance forms [i.e., Fe(II)-NO0 and Fe(III)-NO0] as the major contributors to both {FeNO}6 and {FeNO}7 complexes. This finding is at variance with the common formulation of {FeNO}6 hemes as Fe(II)-NO+ species but is consonant with an Fe L-edge XAS analysis by Solomon and co-workers. For the {FeNO}8 complex {Fe[P](NO)}-, our analysis suggests a resonance hybrid description: Fe(I)-NO0 ↔ Fe(II)-NO-, in agreement with earlier DFT studies. Vibrational analyses of the compounds studied indicate an imperfect but fair correlation between the NO stretching frequency and NO(π*) occupancy, highlighting the usefulness of vibrational data as a preliminary indicator of the NO oxidation state.

G0W0 Ionization Potentials of First-Row Transition Metal Aqua Ions

We report computations of the vertical ionization potentials within the GW approximation of the near-complete series of first-row transition metal (V-Cu) aqua ions in their most common oxidation states, i.e., V3+, Cr3+, Cr2+, Mn2+, Fe3+, Fe2+, Co2+, Ni2+, and Cu2+. The d-orbital occupancy of these systems spans a broad range from d2 to d9. All of the structures were first optimized at the density functional theory level using a large cluster of explicit water molecules that are embedded in a continuum solvation model. Vertical ionization potentials were computed with the one-shot G0W0 approach on a range of transition metal ion clusters (6, 18, 40, and 60 explicit water molecules), wherein the convergence with respect to the basis set size was evaluated using the systems with 40 water molecules. We assess the results using three different density functional approximations as starting points for the vertical ionization potential calculations, namely, G0W0@PBE, G0W0@PBE0, and G0W0@r2SCAN. While the predicted ground-state structures are similar to all three exchange-correlation functionals, the vertical ionization potentials were in closer agreement with experiment when using the G0W0@PBE0 and G0W0@r2SCAN approaches, with the r2SCAN-based calculations being significantly less expensive. Computed bond distances and vertical ionization potentials for all structures are in good agreement with available experimental data.

Corrected density functional theory and the random phase approximation: Improved accuracy at little extra cost

We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory [DC(HF)-DFT] calculations and an extension to it we called "corrected" HF DFT [C(HF)-DFT] [Graf and Thom, J. Chem. Theory Comput. 19 5427-5438 (2023)]. In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA [C(HF)-RPA]. We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel, and RPA with second-order screened exchange. C(HF)-dRPA demonstrates very promising performance; for RPA with exchange methods, on the other hand, we often find over-corrections.

Electronic Structure of the Low-Lying States of the Triatomic MoS2 Molecule: The Building Block of 2D MoS2

Molybdenum disulfide (MoS2 ) is the building component of 1D-monolayer, 2D-layered nanosheets and nanotubes having many applications in industry, and it is detected in various molecular systems observed in nature. Here, the electronic structure and the chemical bonding of sixteen low-lying states of the triatomic MoS2 molecule are investigated, while the connection of the chemical bonding of the isolated MoS2 molecule to the relevant 2D-MoS2 , is emphasized. The MoS2 molecule is studied via DFT and multireference methodologies, i. e., MRCISD(+Q)/aug-cc-pVQZ(-PP)Mo . The ground state,X ˜ ${\tilde{X}}$ 3 B1 , is bent (Mo-S=2.133 Å and ϕ(SMoS)=115.9°) with a dissociation energy to atomic products of 194.7 kcal/mol at MRCISD+Q. In the ground and in the first excited state a double bond is formed between Mo and each S atom, i. e.,a 1 2 a 1 2 b 2 2 a 2 2 ${{{\rm a}}_{1}^{2}{{\rm a}}_{1}^{2}{{\rm b}}_{2}^{2}{{\rm a}}_{2}^{2}}$ . These two states differ in which d electrons of Mo are unpaired. The Mo-S bond distances of the calculated states range from 2.108 to 2.505 Å, the SMoS angles range from 104.1 to 180.0°, and the Mo-S bonds are single or double. Potential energy curves and surfaces have been plotted for theX ˜ ${\tilde{X}}$ 3 B1 , 5 A1 and 5 B1 states. Finally, the low-lying septet states of the triatomic molecule are involved in the material as a building block, explaining the variety of its morphologies.

Further Understanding the Roles of Solvent, Brønsted Acids, and Hydrogen Bonding in Iron Porphyrin-Mediated Carbon Dioxide Reduction

Improving our understanding of how molecules and materials mediate the electrochemical reduction of carbon dioxide (CO2) to upgraded products is of great interest as a means to address climate change. A leading class of molecules that can facilitate the electrochemical conversion of CO2 to carbon monoxide (CO) is iron porphyrins. These molecules can have high rate constants for CO2-to-CO conversion; they are robust, and they rely on abundant and inexpensive synthetic building blocks. Important foundational work has been conducted using chloroiron 5,10,15,20-tetraphenylporphyrin (FeTPPCl) in N,N-dimethylformamide (DMF) solvent. A related and recent report points out that the corresponding perchlorate complex, FeTPPClO4, can have superior function due to its solubility in other organic solvents. However, the importance of hydrogen bonding and solvent effects was not discussed. Herein, we present a detailed kinetic study of the triflate (CF3SO3-) complex of FeTPP in DMF and in MeCN using a range of phenol Brønsted acid additives. We also detected the formation of Fe(III)TPP-phenolate complexes using cyclic voltammetry experiments. Importantly, our new analysis of apparent rate constants with different added phenols allows for a modification to the established mechanistic model for CO2-to-CO conversion. Critically, our improved model accounts for hydrogen bonding and solvent effects by using simple hydrogen bond acidity and basicity descriptors. We use this augmented model to rationalize function in other reported porphyrin systems and to make predictions about operational conditions that can enhance the CO2 reduction chemistry.

Electronic Structure of Small Isolated and Supported Manganese Oxide Clusters

In the present work, possible molecular models of the isolated manganese oxides and supported Mn3Ox/Al2O3 structures were built based on small clusters of passivated MnOx. The support was represented as a simplified model of the alumina tetramer cluster based on small fragments of AlOxHy. Combinations of MnOxHy and AlOxHy clusters were made to form both the isolated and supported manganese oxides clusters. The electronic structure of these systems was characterized by ab initio methods (DFT and CASPT2). It was observed that the vertical excitation energy of the isolated and supported Mn3OxHy clusters is significantly lower than that of the alumina cluster model, while both the isolated and supported Mn3OxHy wave function characters are qualitatively similar with respect to the ground state and electronic transition processes, suggesting that the alumina cluster behaves as an inert support, since there is little contribution of this component in the description of the low-lying electronic states. The present study also reports for the first time the spectroscopic parameters of several clusters containing the manganese transition metal atom.

Mobility and separation of linear and branched C5 alkanes in UiO-66 (Zr) probed by 2H NMR and MD simulations

The UiO-66 (Zr) metal-organic framework (MOF) is of notable interest due to its facile synthesis, robustness under a wide range of chemical and physical conditions and its capability to separate industrially relevant hydrocarbons mixtures. However, the knowledge of the molecular mechanisms behind these process remains limited. Here, we present a combined experimental (2H NMR) and computational study of the molecular mobility, transport and adsorption of C5 alkanes isomers in a dehydroxylated UiO-66 (Zr) MOF. We show that the tetrahedral cages of the MOF are the preferred adsorption location for both n-pentane and isopentane. In a binary mixture of the isomers, isopentane interacts more strongly with the material leading it to occupy more of the tetrahedral cages than n-pentane, resulting in an isopentane/n-pentane adsorption selectivity of αads = 2 (at 373 K). At the same time, the microscopic diffusivity for n-pentane, Dn (En = 18 kJ mol-1), is significantly lower than for isopentane, Diso (Eiso = 28 kJ mol-1), which results in a high separation selectivity for a n-pentane/isopentane mixture of α ≈ 13 (at 300 K). This shows that the UiO-66 MOF is indeed a promising active material for use in light hydrocarbon separation processes.

Atmospheric Chemistry of HOHg(II)O• Mimics That of a Hydroxyl Radical

HOHg(II)O•, formed from HOHg(I)• + O3, is a key intermediate in the OH-initiated oxidation of Hg(0) in the atmosphere. As no experimental data are available for HOHg(II)O•, we use computational chemistry (CCSD(T)//M06-2X/AVTZ) to characterize its reactions with atmospheric trace gases (NO, NO2, CH4, C2H4, CH2O and CO). In summary, HOHg(II)O•, like the analogous BrHg(II)O• radical, largely mimics the reactivity of •OH in reactions with NOx, alkanes, alkenes, and aldehydes. The rate constant for its reaction with methane (HOHg(II)O• + CH4 → Hg(II)(OH)2 + •CH3) is about four times higher than that of •OH at 298 K. All of these reactions maintain mercury as Hg(II), except for HOHg(II)O• + CO → HOHg(I)• + CO2. Considering only the six reactions studied here, we find that reduction by CO dominates the fate of HOHg(II)O• (79-93%) in many air masses (in the stratosphere and at ground level in rural, marine, and polluted urban regions) with only modest competition from HOHg(II)O• + CH4 (<15%). We expect that this work will help global modeling of atmospheric mercury chemistry.

Octahedral Zirconium Salan Catalysts for Olefin Polymerization: Substituent and Solvent Effects on Structure and Dynamics

Group 4 metal-Salan olefin polymerization catalysts typically have relatively low activity, being slowed down by a pre-equilibrium favoring a non-polymerization active resting state identified as a mer-mer isomer (MM); formation of the polymerization active fac-fac species (FF) requires isomerization. We now show that the chemistry is more subtle than previously realized. Salan variations bearing large, flat substituents can achieve very high activity, and we ascribe this to the stabilization of the FF isomer, which becomes lower in energy than MM. Detailed in situ NMR studies of a fast (o-anthracenyl) and a slow (o-tBu) Salan precursors, suitably activated, indicate that preferred isomers in solution are different: the fast catalyst prefers FF while the slow catalyst prefers a highly distorted MM geometry. Crystal structures of the activated o-anthracenyl substituted complex with a moderately (chlorobenzene) and, more importantly, a weakly coordinating solvent (toluene) in the first coordination sphere emphasize that the active FF isomer is preferred, at least for the benzyl species. Site epimerization (SE) barriers for the fast catalyst (ΔS > 0, dissociative) and the slow catalyst (ΔS < 0, associative) in toluene corroborate the solvent role. Diagnostic NMe 13C chemical shift differences allow unambiguous detection of FF or MM geometries for seven activated catalysts in different solvents, highlighting the role of solvent coordination strength and bulkiness of the ortho-substituent on the isomer equilibrium. For the first time, active polymeryl species of Zr-Salan catalysts were speciated. The slow catalyst is effectively trapped in the inactive MM state, as previously suggested. Direct observation of fast catalysts is hampered by their high reactivity, but the product of the first 1-hexene insertion maintains its FF geometry.

Semiempirical Methods for Molecular Systems in Strong Magnetic Fields

A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, |B | ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, |B | > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.

Unraveling the Spin-State Energetics of FeN4 Complexes with Ab Initio Methods

A systematic analysis was conducted to explore the spin-state energetics of a series of 19 FeN4 complexes. The performance of a large number of multireference methods was assessed, highlighting the significant challenges associated with accurately describing the spin-state energetics of FeN4 complexes. Most multireference methods were found to be susceptible to errors originating from the reference CASSCF wavefunction, leading to an overstabilization of high-spin states. Nonetheless, a few multireference methods, namely, CASPT2/CC, DSRG-MRPT3, and LDSRG(2), demonstrated promising performance compared to the benchmark CCSD(T) method. Furthermore, our study revealed that FeN4 complexes having a quintet ground state are exceedingly rare. Accordingly, only one specific model (Fe(L2)) and one synthesized complex (Fe(OTBP)) have the quintet ground state among the studied complexes. This scarcity of quintet FeN4 complexes highlights the unique nature of these systems and raises intriguing questions regarding the factors influencing spin states, such as the size of the macrocycle cavity, the introduction of substituents, or the induction of out-of-plane deformation.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac-Coulomb-Breit-Parameterized Effective Spin-Orbit Coupling

In photochemical processes, spin-orbit coupling plays a crucial role in determining the outcome of the reaction. However, the exact treatment of the Dirac-Coulomb-Breit two-electron operator required for rigorous inclusion of spin-orbit coupling is computationally prohibitive. To address this challenge, we present a Dirac-Coulomb-Breit-parameterized screened-nuclear spin-orbit factor to approximate two-electron spin-orbit couplings in the effective one-electron spin-orbit Hamiltonian. We propose two schemes, the universal and row-dependent parameterizations, to further improve the accuracy of the method. Benchmark calculations on both atomic and molecular systems are performed and compared to results from the computationally expensive four-component Dirac-Coulomb-Breit method. The Dirac-Coulomb-Breit-parameterized approach offers a more computationally feasible method for accurate spin-orbit coupling calculations.