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At least 415 records · Page 23

Electron impact excitation of N-like ions from the ICFT R-matrix calculation

We carried out intermediate coupling frame transformation (ICFT) R-matrix calculations on N-like ions (11≤Z≤20), which included a total of 272 fine structure levels in both the configuration interaction (CI) and close-coupling (CC) collision expansions. Comparisons with previous theoretical values were made in terms of energy levels, radiative transition rates, and oscillator strengths. The effective collision strengths (ϒ) were estimated in the temperature range of 10{sup 4}–10{sup 7} K. An excellent agreement with available computations was reached for dipole-allowed transitions, while differences in ϒ were found for non-dipole allowed and forbidden transitions. This discrepancy is mainly attributed to the difference in CC expansions. Our calculations provide a good supplement to the electron impact excitation data on N-like ions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Energy levels and radiative rates for transitions in Cr-like Kr XIII, Tc XX and Xe XXXI

Energy levels, radiative transition probabilities, Landé g-factors, and radiative lifetimes are reported for 144 levels of the 3p{sup 6}3d{sup 6} and 3p{sup 5}3d{sup 7} configurations of the Cr-like ions Kr XIII, Tc XX and Xe XXXI. Since to our knowledge no prior data for energy levels or A-values, experimental or theoretical, are available in the literature for these ions, calculations have been performed with three independent atomic structure codes, namely GRASP, FAC and a code implementing the QR approach, with increasing configuration interaction (CI) basis with each code. This is to establish the accuracy of the calculated results so that data can be confidently applied in the modeling of plasmas. Our recommended data are determined within the QR approach, because not only has the largest CI basis been included in this calculation, the reliability has already been established in our earlier work for other Cr-like ions, for which some experimental and theoretical data were available for comparison. Results for radiative rates (A-values) and transition wavelengths (λ) are listed for all strong E1, E2 and M1 transitions among the 144 levels of each ion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Level density of the sd-nuclei—Statistical shell-model predictions

Accurate knowledge of the nuclear level density is important both from a theoretical viewpoint as a powerful instrument for studying nuclear structure and for numerous applications. For example, astrophysical reactions responsible for the nucleosynthesis in the universe can be understood only if we know the nuclear level density. We use the configuration-interaction nuclear shell model to predict nuclear level density for all nuclei in the sd-shell, both total and for individual spins (only with positive parity). To avoid the diagonalization in large model spaces we use the moments method based on statistical properties of nuclear many-body systems. In the cases where the diagonalization is possible, the results of the moments method practically coincide with those from the shell-model calculations. Using the computed level densities, we fit the parameters of the Constant Temperature phenomenological model, which can be used by practitioners in their studies of nuclear reactions at excitation energies appropriate for the sd-shell nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

K- and L-edge X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) determination of differential orbital covalency (DOC) of transition metal sites

Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as Kα resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3d orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of σ and π donor bonding and π back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. Here, the application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relativistic opacities for astrophysical applications

Here, we report on the use of the Los Alamos suite of relativistic atomic physics codes to generate radiative opacities for the modeling of astrophysically relevant plasmas under local thermodynamic equilibrium (LTE) conditions. The atomic structure calculations are carried out in fine-structure detail, including full configuration interaction. Three example applications are considered: iron opacities at conditions relevant to the base of the solar convection zone, nickel opacities for the modeling of stellar envelopes, and samarium opacities for the modeling of light curves produced by neutron star mergers. In the first two examples, comparisons are made between opacities that are generated with the fully and semi-relativistic capabilities in the Los Alamos suite of codes. As expected for these highly charged, iron-peak ions, the two methods produce reasonably similar results, providing confidence that the numerical methods have been correctly implemented. However, discrepancies greater than 10% are observed for nickel and investigated in detail. In the final application, the relativistic capability is used in a preliminary investigation of the complicated absorption spectrum associated with cold lanthanide elements.

79 ASTRONOMY AND ASTROPHYSICS↗

Low-lying states and total internal partition sums of CH

The electronic structure and spin-orbit states of the CH radical have been systematically investigated using multi-reference configuration interaction (MRCI) and single-reference coupled-cluster (CC) methods. These calculations were performed in conjunction with large correlation-consistent basis sets of quadruple-, quintuple-, and sextuple-ζ quality. To achieve high accuracy, electronic energies for all states were extrapolated to the complete basis set (CBS) limit, enabling the detailed construction of potential energy curves and determination of reliable spectroscopic constants. Spin-orbit coupling effects were explicitly incorporated, and vibrational energy levels were computed via Numerov analysis. Furthermore, the resulting values exhibit good to excellent agreement with available experimental data. Dipole moment and transition dipole moment curves were evaluated to assess the opacity characteristics of CH, revealing that transitions such as Χ 2 Π (u′′ = 0) → Α 2 Δ (u′ = 0), Χ 2 Π (u′′ = 0) → Β 2 Σ − (u′ = 0), Χ 2 Π (u′′ = 0) → C 2 Σ + (u′ = 0), and Χ 2 Π (u′′ = 0) → D 2 Σ + (u′ = 3) are particularly probable. Finally, the total internal partition function sum (TIPS) of CH was computed over a broad temperature range (10–30,000 K) based on our high-accuracy ab initio results.

74 ATOMIC AND MOLECULAR PHYSICS↗

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this “on-the-fly” approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. Furthermore, this approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH 2 O → H 2 + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Precise Control of Noncovalent Interactions in Semiconducting Polymers for High-Performance Organic Field-Effect Transistors

Performed through side-chain engineering or by incorporating intramolecular locking units, the directionality and dynamic nature of noncovalent interactions are particularly attractive for the design of novel semiconducting materials in a wide variety of applications. This work investigates the nature and position of hydrogen bonding (intra- versus intermolecular), with the objective of developing a rational approach to the design of new semiconducting materials with improved properties in the solid state. To control the polymer chains’ self-assembly, a π-conjugated polymer incorporating a moiety capable of generating intramolecular hydrogen bonding is evaluated against a polymer that allows for intermolecular hydrogen bonding. Characterization through various techniques, optical spectroscopies, grazing incidence wide-angle x-ray scattering, and solution small-angle neutron scattering showed that intramolecular hydrogen bonds resulted in materials with improved crystallinity and higher effective conjugation in the solid state. Additionally, the effect of the noncovalent interaction configuration on the optoelectronic properties was analyzed in organic field-effect transistor fabrication. Devices prepared from the materials with intramolecular hydrogen bonds showed significantly higher performance, with three orders of magnitude higher charge mobility than their counterparts fabricated from polymers with intermolecular hydrogen bonds. These results confirm the importance of chemical design on polymer structures and offer a novel route for the design of high-efficiency semiconducting polymers for next-generation electronics.

36 MATERIALS SCIENCE↗

Combining Wave Function Methods with Density Functional Theory for Excited States

Here, we review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn–Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe–Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

[(MeCN)Ni(CF 3 ) 3 ] - and [Ni(CF 3 ) 4 ] 2– : Foundations toward the Development of Trifluoromethylations at Unsupported Nickel

Nickel anions [(MeCN)Ni(CF 3 ) 3 ] - and [Ni(CF 3 ) 4 ] 2– were prepared by the formal addition of 3 and 4 equiv, respectively, of AgCF 3 to [(dme)NiBr 2 ] in the presence of the [PPh 4 ] + counterion. Detailed insights into the electronic properties of these new compounds were obtained through the use of density functional theory (DFT) calculations, spectroscopy-oriented configuration interaction (SORCI) calculations, X-ray absorption spectroscopy, and cyclic voltammetry. The data collectively show that trifluoromethyl complexes of nickel, even in the most common oxidation state of nickel(II), are highly covalent systems whereby a hole is distributed on the trifluoromethyl ligands, surprisingly rendering the metal to a physically more reduced state. In the cases of [(MeCN)Ni(CF 3 ) 3 ] - and [Ni(CF 3 ) 4 ] 2- , these complexes are better physically described as d 9 metal complexes. [(MeCN)Ni(CF 3 ) 3 ] - is electrophilic and reacts with other nucleophiles such as phenoxide to yield the unsupported [(PhO)Ni(CF 3 ) 3 ] 2– salt, revealing the broader potential of [(MeCN)Ni(CF 3 ) 3 ] - in the development of “ligandless” trifluoromethylations at nickel. Proof-in-principle experiments show that the reaction of [(MeCN)Ni(CF 3 ) 3 ] - with an aryl iodonium salt yields trifluoromethylated arene, presumably via a high-valent, unsupported, and formal organonickel(IV) intermediate. Evidence of the feasibility of such intermediates is provided with the structurally characterized [PPh 4 ] 2 [Ni(CF 3 ) 4 (SO 4 )], which was derived through the two-electron oxidation of [Ni(CF 3 ) 4 ] 2– .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Single-Determinant Ground State in Ce 4+ Imidophosphorane Complexes

X-ray spectroscopy techniques are critical in the electronic structure analysis of high-valent lanthanides. The interpretation of multipeaked features at the lanthanide L 3 -edge has remained a challenging question, as it is observed across a range of material classes. A series of structurally related Ce 4+ complexes were prepared to probe the potential ligand field perturbation of the ground state within the series. The tuning of relative 4f and ligand orbital energies in homoleptic and heteroleptic tetravalent Ce imidophosphorane complexes is achieved through ligand derivatization and is clearly demonstrated by UV−vis spectroscopy and electrochemically measured redox potentials. However, Ce L 3 - edge high-energy resolution fluorescence-detected (HERFD) X-ray absorption near-edge structure (XANES) spectra present features at consistent numbers and energies across the range of complexes. Resonant inelastic X-ray scattering (RIXS) is employed to visualize the observed features in the HERFD-XANES spectra. Large complete active space configuration interaction singles and doubles (CASCISD) calculations demonstrate that the ground-state wave function of all complexes can be described employing a single determinant. As a result, the multielectron feature at the L 3 -edge observed in this study for the Ce 4+ imidophosphorane complexes is described as excited-state multiconfigurational behavior that is independent of ligand variation, in systems where the ground state is described using the simple single determinant wave function.

Lanthanides↗

A Macrocyclic Chelator That Selectively Binds Ln 4+ over Ln 3+ by a Factor of 10 29

A tetravalent cerium macrocyclic complex (CeLK 4 ) was prepared with an octadentate terephthalamide ligand comprised of hard catecholate donors and characterized in the solution state by spectrophotometric titrations and electrochemistry and in the crystal by X-ray diffraction. The solution-state studies showed that L exhibits a remarkably high affinity toward Ce 4+ , with log β 110 = 61(2) and ΔG = -348 kJ/mol, compared with log β 110 = 32.02(2) for the analogous Pr 3+ complex. In addition, L exhibits an unusual preference for forming CeL 4- relative to formation of the analogous actinide complex, ThL 4- , which has β 110 = 53.7(5). The extreme stabilization of tetravalent cerium relative to its trivalent state is also evidenced by the shift of 1.91 V in the redox potential of the Ce 3+ /Ce 4+ couple of the complex (measured at -0.454 V vs SHE). The unprecedented behavior prompted an electronic structure analysis using L 3 - and M 5,4 -edge X-ray absorption near-edge structure (XANES) spectroscopies and configuration interaction calculations, which showed that 4f-orbital bonding in CeLK 4 has partial covalent character due to ligand-to-metal charge transfer (LMCT) in the ground state. The experimental results are presented in the context of earlier measurements on tetravalent cerium compounds, indicating that the amount of LMCT for CeLK 4 is similar to that observed for [Et 4 N] 2 [CeCl 6 ] and CeO 2 and significantly less than that for the organometallic sandwich compound cerocene, (C 8 H 8 ) 2 Ce. A simple model to rationalize changes in 4f orbital bonding for tri- and tetravalent lanthanide and actinide compounds is also provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes

Iron–sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. Here, to provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III) 4 S 4 (SMe) 4 ] -2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Methods to Calculate Electronic Excited-State Dynamics for Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase

Here, we present an efficient set of methods for propagating excited-state dynamics involving a large number of configuration interaction singles (CIS) or Tamm-Dancoff approximation (TDA) single-reference excited states. Specifically, (i) following Head-Gordon et al., we implement an exact evaluation of the overlap of singly-excited CIS/TDA electronic states at different nuclear geometries using a biorthogonal basis and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states, where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Systematic Improvement of Quantum Monte Carlo Calculations in Transition Metal Oxides: sCI-Driven Wavefunction Optimization for Reliable Band Gap Prediction

Accurate determination of the electronic properties of correlated oxides remains a significant challenge for computational theory. Traditional Hubbard-corrected density functional theory (DFT+U) frequently encounters limitations in precisely capturing electron correlation, particularly in predicting band gaps. We introduce a systematic methodology to enhance the accuracy of diffusion Monte Carlo (DMC) simulations for both ground and excited states, focusing on LiCoO 2 as a case study. By employing a selected configuration interaction (sCI) approach, we demonstrate the capability to optimize wavefunctions beyond the constraints of single-reference DFT+U trial wavefunctions. Here, we show that the sCI framework enables accurate prediction of band gaps in LiCoO 2 , closely aligning with experimental values and substantially improving traditional computational methods. The study uncovers a nuanced mixed state of t 2g and e g orbitals at the band edges that is not captured by conventional single-reference methods, further elucidating the limitations of PBE+U in describing d-d excitations. Our findings advocate for the adoption of beyond-DFT methodologies, such as sCI, to capture the essential physics of excited-state wavefunctions in strongly correlated materials. The improved accuracy in band gap predictions and the ability to generate more reliable trial wavefunctions for DMC calculations underscore the potential of this approach for broader applications in the study of correlated oxides. This work not only provides a pathway for more accurate simulations of electronic structures in complex materials but also suggests a framework for future investigations of the excited states of other challenging systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Capturing Correlation Effects in Positron Binding to Atoms and Molecules

A major challenge in contemporary electronic structure theory involves the development of methods to describe in a balanced manner the contribution of correlation effects to energy differences. This challenge can be even greater for multicomponent systems containing more than one type of quantum particle. In the present work, we describe a flexible code for carrying out self-consistent field and configuration interaction (CI) calculations on multicomponent systems and use it to generate trial wave functions for use in diffusion Monte Carlo (DMC) calculations of the positron affinity of Be, Be 2 , Be 4 , Mg, CS 2 , and benzene. The resulting positron affinities (PAs) are in good agreement with the best values from the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (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. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (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, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (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 Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Beyond CCSD(T) Accuracy at Lower Scaling with Auxiliary Field Quantum Monte Carlo

We introduce a black-box auxiliary field quantum Monte Carlo (AFQMC) approach to perform highly accurate electronic structure calculations using configuration interaction singles and doubles (CISD) trial states. This method consistently provides more accurate energy estimates than coupled cluster singles and doubles with perturbative triples (CCSD(T)), often regarded as the gold standard in quantum chemistry. This level of precision is achieved at a lower asymptotic computational cost, scaling as O(N 6 ) compared to the O(N 7 ) scaling of CCSD(T). Furthermore, we provide numerical evidence supporting these findings through results for challenging main group and transition metal-containing molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗