Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure

Pentacycloundecanylidene and pentacycloundecanone - hyperconjugatively stabilized carbene and ketone

Pentacycloundecanylidene was spectroscopically identified during the photolysis of the corresponding aziridine and its aerial oxidation results in the corresponding ketone. Here we report the role of hyperconjugative interactions in stabilizing the singlet pentacycloundecanylidene and its corresponding ketone pentacycloundecanone. The pentacycloundecanylidene possesses a singlet ground state with two possible geometrical isomers based on the orientation of the carbene bridge (U1 and U2). The energy difference between U1 and U2 is minimal (0.9 kcal mol-1) and the triplet state is 5.6 kcal mol-1 energetically higher than the more stable singlet state U1. The proximal C-C bonds of the carbene bridge in the singlet state are significantly elongated as compared to the distal C-C bonds. The bending of the carbene bridge in the triplet state and the carbonyl group in the ketone are minimal as compared to the parent pentacycloundecane. The molecular orbital (MO), natural bond orbital (NBO) and energy decomposition analysis (EDA) show that both Cieplak-type hyperconjugation viz. donation of electrons from the proximal C-C σ bonds to the empty p-orbital on the carbene centre and Felkin-Anh type hyperconjugation viz. donation of the lone pair of carbene carbon to the distal C-C σ* orbitals exist in carbene systems. The bending of the carbene bridge in singlet carbene is to enhance the Cieplak-type hyperconjugative interaction. The ketone is also stabilized by Cieplak-type hyperconjugative interaction but to a lower extent as compared to the singlet carbene. The reactivity study suggests that the singlet pentacycloundecanylidene is ambiphilic in nature.

Complexation of Hexavalent Neptunium(VI) with Oxydiacetic Acid and Its Amide Derivatives in Aqueous Solution: Spectrophotometry and DFT Calculations

Unfolding the solution coordination chemistry of high-valent transuranium elements with the "CHON"-type ligands is important to understand the fundamental chemistry of actinides and to design more efficient extractants for partitioning of transuranium elements in advanced nuclear fuel cycles. Here, the complexation of a hexavalent neptunyl ion (NpO22+ or Np(VI)) with oxydiacetic acid (ODA) has been systematically investigated in comparison with its amide analogues N,N-dimethyl-3-oxa-glutaramic acid (DMOGA) and N,N,N',N'-tetramethyl-3-oxa-glutaramide (TMOGA) both experimentally and computationally. The formation of both 1:1 and 1:2 complexes between Np(VI) and the three ligands was identified by spectrophotometry, and their stability constants were obtained and compared with those of hexavalent U(VI) and Pu(VI). The corresponding bonding nature is elucidated by using energy decomposition analysis (EDA), electrostatic potential (ESP), ELF contours, and natural orbitals for chemical valence (NOCV) methods, which shows that the Np-O bonds are essentially ionic in character and the unoccupied 6d orbitals of Np play a key role in enhancing the covalent interactions between Np(VI) and the three ligands.

Generalized Foldy-Wouthuysen transformation for relativistic two-component methods: Systematic analysis of two-component Hamiltonians

The generalized Foldy-Wouthuysen (GFW) transformation was proposed as a generic form that unifies four types of transformations in relativistic two-component methods: unnormalized GFW(UN), and normalized form 1, form 2, and form 3 (GFW(N1), GFW(N2), and GFW(N3)). The GFW transformation covers a wide range of transformations beyond the simple unitary transformation of the Dirac Hamiltonian, allowing for the systematic classification of all existing two-component methods. New two-component methods were also systematically derived based on the GFW transformation. These various two-component methods were applied to hydrogen-like and helium-like ions. Numerical errors in energy were evaluated and classified into four types: the one-electron Hamiltonian approximation, the two-electron operator approximation, the newly defined "picture difference error (PDE)," and the error in determining the transformation, and errors in multi-electron systems were discussed based on this classification.

PhenTAA: A Redox-Active N4-Macrocyclic Ligand Featuring Donor and Acceptor Moieties

Here, we present the development and characterization of the novel PhenTAA macrocycle as well as a series of [Ni(R2PhenTAA)]n complexes featuring two sites for ligand-centered redox-activity. These differ in the substituent R (R = H, Me, or Ph) and overall charge of the complex n (n = -2, -1, 0, +1, or +2). Electrochemical and spectroscopic techniques (CV, UV/vis-SEC, X-band EPR) reveal that all redox events of the [Ni(R2PhenTAA)] complexes are ligand-based, with accessible ligand charges of -2, -1, 0, +1, and +2. The o-phenylenediamide (OPD) group functions as the electron donor, while the imine moieties act as electron acceptors. The flanking o-aminobenzaldimine groups delocalize spin density in both the oxidized and reduced ligand states. The reduced complexes have different stabilities depending on the substituent R. For R = H, dimerization occurs upon reduction, whereas for R = Me/Ph, the reduced imine groups are stabilized. This also gives electrochemical access to a [Ni(R2PhenTAA)]2- species. DFT and TD-DFT calculations corroborate these findings and further illustrate the unique donor-acceptor properties of the respective OPD and imine moieties. The novel [Ni(R2PhenTAA)] complexes exhibit up to five different ligand-based oxidation states and are electrochemically stable in a range from -2.4 to +1.8 V for the Me/Ph complexes (vs Fc/Fc+).

Scalar Relativistic Effects with Multiwavelets: Implementation and Benchmark

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.

Organometallic Allene [(μ-C)(Fe(CO)4 )2 ]: Bridging Carbon Showing Transformation from Classical Electron-Sharing Bonding to Double σ-Donor and Double π-Acceptor Ligation

Allenes (R2 C=C=CR2 ) have been traditionally perceived to feature localized orthogonal π-bonds between the carbon centres. We have carried out quantum-mechanical studies of the organometallic allenes envisioned by the isolobal replacement of the terminal CH2 groups by the d8 Fe(CO)4 fragment. Our studies have identified two organometallic allenes viz. D2d symmetric [(μ-C)(Fe(CO)4 )2 ] (2) and D3 symmetric [(μ-C)(Fe(CO)4 )2 ] (3) with trigonal bipyramidal coordination at the Fe atoms. Compound 2 features the bridging carbon atom in an equatorial position with respect to the ligands on the TM centre, while 3 features the central carbon atom in an axial position. The bis-pseudoallylic anionic delocalisation proposed in the C2-C1-C3 spine of organic allene is retained in the organometallic allene 2, and is transformed to a typical three-centre bis-allylic anionic delocalisation in the organometallic allene 3. The topological analysis of electron density also indicates a bis-allylic anionic type delocalisation in the organometallic allenes. The quantitative bonding analysis using the EDA-NOCV method suggests a transition from classical electron-sharing bonding between the central carbon atom and the terminal groups in 1 to donor-acceptor bonding in 3. Meanwhile, both electron-sharing and donor-acceptor bonding models are found to be probable heuristic bonding representations in the organometallic allene 2.

Inorganometallic allenes [(Mn(η5-C5H5)(CO)2)2(μ-E)] (E = Si-Pb): bis-allylic anionic delocalisation similar to organometallic allene but differential σ-donation and π-backdonation

The chemistry of heavy group-14 tetrel atoms is known to diverge from that of the lighter congener carbon. Here, we report the structure and bonding in inorganometallic allenes [(MnCp(CO)2)2(μ-E)] (2E, E = Si-Pb; Cp = η5-C5H5). These inorganometallic allenes are structurally similar to the lighter organometallic analog [(MnCp(CO)2)2(μ-C)] (2C). The bonding analysis of these compounds at the M06/def2-TZVPP//BP86/def2-SVP level of theory identifies a linear Mn-E-Mn spine with delocalised, mutually orthogonal π-systems across this back-bone. This results in a bis-allylic anionic bonding scenario. However, the strength of the Mn-E bonding is found to be weaker in these inorganometallic allenes. The energy decomposition analysis at the BP86/TZ2P//BP86/def2-SVP level of theory further reveals that the bonding in these compounds cannot be represented by one unique heuristic bonding model, but multiple bonding models. For all 2E (E = C-Pb), the Dewar-Chatt-Duncanson bonding model is one of the best bonding representations, where the central tetrel atom acts as a 4e- σ-donor and 4e- π-acceptor. The bonding analysis indicates that the carbon atom in the organometallic allene acts as a better π-acceptor than σ-donor, while the heavier tetrel atoms in the inorganometallic allenes are better σ-donors than π-acceptors. The npz-orbital is found to be a better σ-donor than the valence ns-orbital. However, when the bonding representation is changed to a traditional electron-sharing model, the contribution from the ns-orbital was found to be the largest in comparison to the interaction from the remaining three valence np-orbitals. It can be suggested that the ns-orbitals contribute more towards chemical bonding when participating via an electron-sharing interaction than a donor-acceptor interaction.

Reactivity Analysis of the [2 + 2] Cycloaddition between Group-6 ≡ Group-14 Triple-Bonded Complexes and Acetylene: Insights from Theoretical Studies

Theoretical examinations of reactivity for the formal [2 + 2] cycloaddition of Me-C≡C-Ph to Group-6(G6)≡Group-14(G14) triple-bonded organometallic complexes have been carried out using the M06-2X-D3/def2-TZVP level of theory. Our theoretical findings suggest that Me-C≡C-Ph can undergo adduct formation with all G6≡Si complexes, resulting in the generation of four-membered ring structures. However, among the W≡Group-14 complex reactants, only W≡Si-based, W≡Ge-based, and W≡Sn-based organometallic molecules are capable of undergoing a [2 + 2] cycloaddition reaction with Me-C≡C-Ph. Based on energy decomposition analysis, our theoretical investigations demonstrate that the bonding mechanism in such [2 + 2] cycloaddition reactions involves the creation of two dative bonds between singlet fragments (the donor-acceptor model), as opposed to two electron-sharing bonds between triplet fragments. In addition, the examinations based on the activation strain model indicate that the activation barrier of the [2 + 2] cycloaddition reaction is predominantly governed by the geometric deformation energy of the two reactants (G6≡G14-Rea and Me-C≡C-Ph). Our research using the M06-2X method shows that the barrier heights of [2 + 2] cycloaddition reactions between Me-C≡C-Ph and G6≡Si-Rea are dependent on the geometric changes occurring in both fragments during the transition states, consistent with Hammond's postulate.

Reactivity of the Intramolecular Vicinal Group-13/P- and B/Group-15-Based Frustrate Lewis Pairs with Sulfur Dioxide: Mechanistic Insight from DFT

The emission of SO2 gas by industrialized societies contributes to the occurrence of acid rain in natural environments. In this study, we put forward a theoretical investigation into the capture reactions of SO2. Our analysis centers on the energy profiles of intramolecular 1,2-cyclohexylene-bridged FLP-associated molecules. We will particularly examine the reactions involving G13/P-based (with G13 denoting Group 13 element) and B/G15-based (with G15 representing Group 15 element) FLP-associated molecules. Except for Tl/P-FLP, B/N-FLP, and B/Bi-FLP, our theoretical examinations indicate that the remaining six FLP-associated molecules, namely G13'/P-FLP (G13' = B, Al, Ga, and In) and B/G15 ' -FLP (G15' = P, As, and Sb), can easily undergo SO2 capture reactions due to their energetic feasibility. Particularly, our theoretical findings suggested that 1,2-cyclohexylene-bridged Al/P-FLP, Ga/P-FLP, B/As-FLP, and B/Sb-FLP are capable of undergoing a reversible reaction and returning to the initial reactant state. Our theoretical evidence indicates that the G13-G15 bond length in the 1,2-cyclohexylene-linked G13/G15-FLP can serve as a basis for evaluating the free activation barrier associated with its reaction with SO2. Two theoretical methods, namely, the frontier molecular orbital theory and the energy decomposition analysis-natural orbitals of chemical valence approach, are utilized to investigate the electronic structure and bonding nature of the reactions under consideration. Moreover, the analyses based on the activation strain model revealed that it is the geometrical deformation energies of G13/G15-FLP, which is the key factor that greatly influences the activation barriers of such SO2 capture reactions. Further, our theoretical computations indicate that such capturing reactions of SO2 by intramolecular 1,2-cyclohexylene-linked G13/G15-based FLP-type molecules obey the Hammond postulate.

Reversible Modulation of the Electronic and Spatial Environment around Ni(0) Centers Bearing Multifunctional Carbene Ligands with Triarylaluminum

Designing and modulating the electronic and spatial environments surrounding metal centers is a crucial issue in a wide range of chemistry fields that use organometallic compounds. Herein, we demonstrate a Lewis-acid-mediated reversible expansion, contraction, and transformation of the spatial environment surrounding nickel(0) centers that bear N-phosphine oxide-substituted N-heterocyclic carbenes (henceforth referred to as (S)PoxIms). Reaction between tetrahedral (syn-κ-C,O-(S)PoxIm)Ni(CO)₂ and Al(C₆F₅)₃ smoothly afforded heterobimetallic Ni/Al species such as trigonal-planar {κ-C-Ni(CO)₂}(μ-anti-(S)PoxIm){κ-O-Al(C₆F₅)₃} via a complexation-induced rotation of the N-phosphine oxide moieties, while the addition of 4-dimethylaminopyridine resulted in the quantitative regeneration of the former Ni complexes. The corresponding interconversion also occurred between (SPoxIm)Ni(η²:η²-diphenyldivinylsilane) and {κ-C-Ni(η²:η²-diene)}(μ-anti-SPoxIm){κ-O-Al(C₆F₅)₃} via the coordination and dissociation of Al(C₆F₅)₃. The shape and size of the space around the Ni(0) center was drastically changed through this Lewis-acid-mediated interconversion. Moreover, the multinuclear NMR, IR, and XAS analyses of the aforementioned carbonyl complexes clarified the details of the changes in the electronic states on the Ni centers; i.e., the electron delocalization was effectively enhanced among the Ni atom and CO ligands in the heterobimetallic Ni/Al species. The results presented in this work thus provide a strategy for reversibly modulating both the electronic and spatial environment of organometallic complexes, in addition to the well-accepted Lewis-base-mediated ligand-substitution methods.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Influence of Group 15 elements on the [3 + 2] cycloaddition reactivity of G15 = G15-G15-based 1,3-dipoles with cyclooctyne

The influence of Group 15 elements (G15s) on the reactivity of the cycloaddition reactions of inorganic 1,3-dipolar analogs with cyclooctyne was computationally explored with density functional theory. To this end, the G15G15G15'-based 1,3-dipole, an interestingly representative model molecule of 1,3-dipole chemistry, was selected. The present computational investigations suggest that all NNG15-Rea and G15G15P-Rea molecules can be energetically feasible to undergo 1,3-dipolar cycloaddition reactions with cyclic alkynes, except for only the NNN-Rea 1,3-dipole molecule. The key factor, which can greatly affect the activation barriers, is quantitatively analyzed in detail through the frontier molecular orbital (FMO) theory, the activation strain model (ASM), and the energy decomposition analysis (EDA) approach. Our theoretical findings based on the FMO theory and the EDA suggest that two types of bonding interactions occur in such 1,3-dipolar cycloaddition reactions: forward bonding (filled p-π orbital (cyclooctyne) → the empty p-π* orbital (G15 = G15)) and back bonding (empty p-π* orbital (cyclooctyne) ← the lone pair (G15')). Notably, the bonding interactions of the former mechanism are much stronger than those of the latter mechanism. Evidence from the ASM reveals that the activation barriers of G15G15G15'-based 1,3-dipolar cycloaddition reactions strongly depend on the atomic radius of the G15 element. These theoretical conclusions allow a number of predictions to be made.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L_2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.

Influence of the Element and Substituent Effects on the Reactivity of Catching Reactions of Difluorocarbene by Benzene-Bridged and Group-13/Group-15-Based Frustrated Lewis Pairs

The trapping reactions of CF₂ by benzene-bridged Group-13/P-based and B/Group-15-based frustrated Lewis pairs (FLPs) have been computationally investigated based on density functional theory. Interestingly, our theoretical calculations predict that the capture of CF₂ by all five Group-13/P-based FLPs is energetically feasible. However, in the B/Group-15-based FLPs, only the phosphorus-based B/P-FLP can trap CF₂ from kinetic and thermodynamical viewpoints. According to the analyses of the activation strain model, it can be known that the atomic radius of the G15 element (Lewis base) of benzene-bridged B/Group-15-FLP plays an important role in controlling the reactivity of the CF₂ catching reactions, whereas the atomic radius of the Group-13 center (Lewis acid) does not play a role in influencing the activation barrier of these CF₂ catching reactions. Our theoretical findings based on sophisticated methods suggest that the forward bonding is the FLP-to-CF₂ interaction, the LP (Group-15-donor) → vacant p-π-orbital (CF₂), which was quantitatively proved to be strong in such present CF₂ catching reactions. However, the back bonding is the CF₂-to-FLP interaction, the empty σ-orbital (Group-13-acceptor) ← sp²-σ-orbital (CF₂), which was verified to be relatively weak. Our theoretical pieces of evidence reveal that the stronger electron-donating ability of the substituents is attached to the Lewis basic center and can make the reaction barrier of the benzene-bridged Group-13/Group-15-based FLP-related compound catching CF₂ smaller and more exothermic.

Two-Site O-H Addition to an Iridium Complex Featuring a Nonspectator Tricoordinate Phosphorus Ligand

The synthesis and reactivity of an ambiphilic iridium complex IrCl(PPh3)(L1) (1; L1 = P(N(o-N(2-pyridyl)C6H4)2)) featuring a chelating nontrigonal phosphorus triamide ligand is reported. The tandem Lewis basic Ir and Lewis acidic P of 1 achieve a two-site oxidative addition of phenol giving the iridaphenoxyphosphorane species IrHCl(PPh3)(L1OPh) (3'). In contrast, reactions of 1 with benzenethiol and benzeneselenol do not engage L1 and instead proceed via metal-centered oxidative addition of the chalcogen-hydrogen bond. These findings establish metal-ligand cooperation involving nonspectator reactivity of tricoordinate phosphorus ligands.

Classical vs. Non-Classical Cyclometalated Pt(II) Complexes

Rollover cyclometalated complexes constitute a family of derivatives which differ from classical cyclometalated species in certain aspects. Various potential application fields have been developed for both classes of compounds, which have both similarities and differences. In order to uncover the relationships and distinctions between these two families of compounds, four Pt(II) cyclometalated complexes derived from 2-phenylpyridine (ppy) and 2,2'-bipyridine (bpy), assumed as prototypical ligands, were compared. For this study, an electron rich isostructural and isoelectronic pair of compounds, [Pt(N^C)Me(PPh3)], and an electron-poorer compound, [Pt(N^C)Cl(PPh3)] were chosen (N^C = ppy or bpy). DFT calculations, cyclic voltammetry, and UV-Vis spectra also helped to shed light into these species. Due to the presence of the more electronegative nitrogen in place of a C-H group, the rollover bpy-H ligand becomes a slightly weaker donor than the classical ppy-H ligand, and hence, generates (slightly) more stable cyclometalated complexes, lower energy frontier molecular orbitals, and electron-poorer platinum centers. On the whole, it was revealed that classical and rollover complexes have overall structural similarity, which contrasts to their somewhat different chemical behavior.

Environmental Control of the Magnetic Behavior of Transition Metal Complexes: Density Functional Theory Study of Zeolite Y Embedded Complexes [M(bpy)3]2+@Y (M = Fe2+, Co2+)

Using the supramolecular approach developed for the study of the guest-host interactions in the zeolite Y encapsulated [Fe(bpy)₃]²⁺ compound: [Fe(bpy)₃]²⁺@Y (bpy = 2,2'-bipyridine) [Vargas et al., J. Chem. Theory Comput. 2009, 5, 97-115], we apply density functional theory (DFT) to the study of the influence of zeolite Y encapsulation on the structural and energetic properties of [Co(bpy)₃]²⁺ in the low-spin (LS) and high-spin (HS) states, while revisiting [Fe(bpy)₃]²⁺@Y. Although the accurate prediction of the HS-LS energy difference ΔE_HL^el remains challenging for current DFT methods, they give accurate estimates of its variation Δ(ΔE_HL^el) in a series of complexes of a given transition metal ion. Therefore, denoting [M(bpy)₃]²⁺@Y_SM as the supramolecular model of the inclusion compounds, the values of ΔE_HL^el for the bpy complexes in the gas phase and in the supercage of zeolite Y were determined by combining the DFT estimates of Δ(ΔE_HL^el) in the series {[M(NCH)₆]²⁺, [M(bpy)₃]²⁺, and [M(bpy)₃]²⁺@Y_SM}, with accurate CCSD(T) estimates of ΔE_HL^el in the benchmark complexes [M(NCH)₆]²⁺ (M = Fe, Co) [Lawson Daku et al., J. Chem. Theory Comput., 2012, 8, 4216-4231]. Generalized gradient approximations as well as global and range-separated hybrids were employed. In order to better account for the key role of dispersion, they were also augmented with the semiempirical D2, D3BJ, and D3BJM dispersion corrections when available. The use of the D3BJ and D3BJM corrections led to similar results, and this is only with the use of the D2 scheme that (i) the free and encapsulated [Fe(bpy)₃]²⁺ are correctly predicted as LS species and that (ii) the encapsulation of both complexes translates into a destabilization of their HS state with respect to their LS state. The increase of the HS-LS energy difference is smaller for [Co(bpy)₃]²⁺ than [Fe(bpy)₃]²⁺ because the HS-LS molecular volume difference ΔV_HL in [Co(bpy)₃]²⁺ is ∼50% smaller than in [Fe(bpy)₃]²⁺. Periodic DFT calculations performed on crystalline [M(bpy)₃]²⁺@Y show that the employed [M(bpy)₃]²⁺@Y_SM supramolecular model allows the influence of encapsulation on the geometry and the spin-state energetics of [M(bpy)₃]²⁺ (M = Fe, Co) to be quantitatively captured.

The reactivity of the trapping reaction of the benzene-bridged boron/phosphorus-based frustrated Lewis pair with difluorocarbene and its group 14 analogs: A theoretical investigation

The trapping reactions of carbene analogs G14F₂ (G14 = group 14 element) by the benzene-bridged B/P-Rea frustrated Lewis pair (FLPs) molecule are studied using density functional theory (B3LYP-D3(BJ)/def2-TZVP). Our theoretical investigations predict that only the CF₂ intermediate rather than other heavy carbene analogs can be trapped by the B/P-Rea FLP-type molecule. Energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) analyses indicate that the bonding nature of the G14F₂ catching reactions by the B/P-Rea FLP-type molecule is a donor-acceptor (singlet-singlet) interaction rather than an electron-sharing (triplet-triplet) interaction. Moreover, EDA-NOCV and frontier molecular orbital (FMO) theory findings strongly suggest that the lone pair (LP) (P) → vacant p-π-orbital (G14F₂ ) interaction rather than the empty σ-orbital (B) ← sp² -σ-orbital (G14F₂ ) interaction plays a predominant role in establishing its bonding condition during the G14F₂ trapping reaction with the B/P-Rea FLP-associated molecule. Our activation strain model findings reveal that the atomic radius of the G14 element of G14F₂ plays a key role in determining the activation barrier of the G14F₂ trapping reactions by the benzene-bridged B/P-Rea FLP. The valence bond state correlation diagram (VBSCD) model developed by Shaik is used to rationalize the calculated results. The VBSCD findings demonstrate that in the present trapping reactions, the singlet triplet splitting of G14F₂ plays a significant role in influencing its reaction barrier and reaction enthalpy. Our theoretical results demonstrate that the relationship between the geometrical parameters of the transition states and the corresponding reaction free energy barriers agrees well with the findings based on the Hammond postulate.

Understanding the Reactivity of Combination Reactions of Intramolecular Geminal Group 13 Element/Phosphorus and Gallium/Group 15 Element Frustrated Lewis Pairs with CS2

The reactions of CS₂ captured by intramolecular geminal G13/P-based (G13 = group 13 elements) and Ga/G15-based (G15 = group 15 elements) frustrated Lewis pairs have been theoretically examined by using density functional theory (DFT) computations. With regard to the nine FLP-related compounds, our DFT calculated results reveal that only Al/P-Rea and Ga/P-Rea can kinetically and thermodynamically precede the energetically feasible combination reactions with CS₂ to form the five-membered heterocyclic adducts. Our activation strain model analyses on the nine aforementioned model molecules indicate that the atomic radius of the Lewis acceptor (G13) and the Lewis donor (G15) plays a role in controlling their barrier heights to obtain good orbital overlaps among G13/P-Rea, Ga/G15-Rea, and CS₂. Our theoretical observations based on the energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) approach strongly indicate that the donor-acceptor bonding (i.e., singlet-singlet bonding) rather than the electron-sharing bonding (i.e., triplet-triplet bonding) plays a central role in determining the bonding conditions of the transition states, G13/P-TS and Ga/G15-TS. In addition, the theoretical evidence obtained by the frontier molecular orbital theory and EDA-NOCV analyses reveals that the best description for the bonding natures of the combination reactions of intramolecular geminal G13/P-Rea and Ga/G15-Rea with CS₂ is the lone pair(G15) → p-π*(C) interaction rather than the p-π*(G13) ← p-π(S) interaction. Moreover, our present DFT computations concerning the calculated structures and corresponding relative energetics of the stationary points connected with the aforementioned sophisticated approaches are in accordance with the Hammond postulate.

Understanding the Regioselectivity of Ion-Pair-Assisted Meta-Selective C(sp2)-H Activation in Conformationally Flexible Arylammonium Salts

The lack of directionality and the long-range nature of Coulomb interactions have been a bottleneck to achieve chemically precise C-H activation using ion-pairs. Recent report by Phipps and co-workers of the ion-pair-directed regioselective Iridium-catalyzed borylation opens a new direction toward harnessing noncovalent interactions for C-H activation. In this article, the mechanism and specific role of ion-pairing are investigated using density functional theory (DFT). Computational studies reveal that meta C-H activation is kinetically more favorable than the para analogue due to stronger electrostatic interactions between the ion-pairs in closer proximity [d(NMe₃⁺···SO₃^-)_TSP1m = 3.93 Å versus d(NMe₃⁺···SO₃^-)_TSP1p = 4.30 Å]. The electrostatic interactions overwhelm the Pauli repulsion and distortion interactions incurred in bringing the oppositely charged ions in close contact for the rate-limiting meta transition state (TSP1_m). Multiple linear regression shows that the free energies of activation correlate well with descriptors like the charge densities on the meta carbon and Ir atom along with that on the cation and anion with R² = 0.74. Tuned range-separated DFT calculations demonstrate accurately the localization of charge separation in the reactant complex and transition state for the meta selectivity.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding tensors and shifts in a nonrelativistic and scalar-relativistic density functional theory framework. For the latter, we make use of the scalar exact two-component Hamiltonian in its local approximation, and generally we apply the well established (multipole-accelerated) resolution of the identity approximation and the seminumerical exchange approximation. The perturbed density matrix of a paramagnetic NMR shielding calculation is further used to study the magnetically induced current density and ring currents of open-shell systems as illustrated for [U@Bi₁₂]^3-. [U@Bi₁₂]^3- features delocalized highest occupied molecular orbitals and sustains a net diatropic ring current of ca. 18 nA/T through the Bi₁₂ torus similar to the all-metal aromatic heavy-element cluster [Th@Bi₁₂]^4-.

Significant Insight into the Origin of Reaction Barriers Determining Dihydrogen Activation by G13-P-P (G13 = Group 13 Element) and G15-P-Ga (G15 = Group 15 Element) Frustrated Lewis Pairs

The heterolytic cleavage of H₂ by multiply bonded phosphorus-bridged G13-P-P-Rea (G13 = B, Al, Ga, In, and Tl) and G15-P-Ga-Rea (G15 = N, P, As, Sb, and Bi) frustrated Lewis pairs (FLPs) has been theoretically investigated using density functional theory calculations. For the above nine FLP-type molecules, our theoretical findings suggest that only Al-P-P-Rea, Ga-P-P-Rea, and In-P-P-Rea can undergo the energetically feasible H₂ activation reaction from kinetic and thermodynamic viewpoints. Our study based on the activation strain model (ASM) reveals that gaining a better orbital overlap between G13-P-P-Rea and G15-P-Ga-Rea molecules and H₂ affected the reaction barriers through the atomic radius of G13 and G15. According to our energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) results, the bonding of these H₂ activation reactions involving G13-P-P-Rea and G15-P-Ga-Rea is dominated by the donor-acceptor interaction (singlet-singlet interaction) rather than the electron-sharing interaction (triplet-triplet interaction). Moreover, our EDA-NOCV evidence reveals that the best description for the above bonding situations is the lone pair(G15) → σ*(H₂) interaction rather than the empty p-π-orbital(G13) ← σ(H₂) interaction. In particular, the findings in this work based on theoretically calculated geometries and the corresponding relative free energies of the stationary points combined with the results from the above sophisticated methods nicely agree with the famous Hammond postulate.

NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 10¹⁹ T J^-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the ¹J(¹¹⁹Sn, ³¹P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

Donor-acceptor duality of the transition-metal-like B2 core in core-shell-like metallo-borospherenes La3&[B2@B17]- and La3&[B2@B18]. RSC Adv 2020;10:34225-34230. [PMID: 35519037 PMCID: PMC9056772 DOI: 10.1039/d0ra06769e]

Transition-metal doping induces dramatic structural changes and leads to earlier planar → tubular → spherical → core–shell-like structural transitions in boron clusters. Inspired by the newly discovered spherical trihedral metallo-borospherene D_3h La₃&B₁₈⁻ (1) (Chen, et al., Nat. Commun., 2020, 11, 2766) and based on extensive first-principles theory calculations, we predict herein the first and smallest core–shell-like metallo-borospherenes C_2v La₃&[B₂@B₁₇]⁻ (2) and D_3h La₃&[B₂@B₁₈]⁻ (3) which contain a transition-metal-like B₂ core at the cage center with unique donor–acceptor duality in La₃&B_n⁻ spherical trihedral shells (n = 17, 18). Detailed energy decomposition and bonding analyses indicate that the B₂ core in these novel complexes serves as a π-donor in the equatorial direction mainly to coordinate three La atoms on the waist and a π/σ-acceptor in the axial direction mainly coordinated by two B₆ triangles on the top and bottom. These highly stable core–shell complexes appear to be spherically aromatic in nature in bonding patterns. The IR, Raman, and photoelectron spectra of 2 and 3 are computationally simulated to facilitate their spectroscopic characterizations.

The smallest core–shell-like metallo-borospherenes C_2v La3&[B₂@B₁₇]⁻ and D_3h La₃&[B₂@B₁₈]⁻ have been predicted at first-principles theory level which contain a transition-metal-like B₂ core with unique donor–acceptor duality.

Quantum chemical topology at the spin-orbit configuration interaction level: Application to astatine compounds

We report a methodology that allows the investigation of the consequences of the spin-orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the "state-specific" natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin-orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = AtF) and trihalide anions (IAtI^- , BrAtBr^- , and IAtBr^- ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin-orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin-orbit couplings.

Combined Experimental and Theoretical Study on Hampered Phosphine Dissociation in Heteroleptic Ni/Zn Complexes

Heterometallic Ni/Zn complexes can serve as molecular models for the semihydrogenation of acetylene catalyzed by heterogeneous Ni/Zn phases. Pursuing this target, we present the synthesis of the series [Ni(ZnCp*)_n(ZnMe)_n(PEt₃)_4-n] (n = 1-3; 1, 2, 3) which is obtained via E/Zn exchange from [Ni(ECp*)_n(PEt₃)_4-n] (n = 1-3, E = Al, Ga; P1, P2, P3). The isolation of the intermediate compound [Ni(GaCp*)(ZnCp*)(ZnMe)(PEt₃)₂] (2a) supports the assumption of a stepwise Ga/Zn exchange in the formation of 3. The dissociation behavior of PEt₃ in 2 and 3 was investigated experimentally using variable temperature (VT) UV-vis spectroscopy indicating suppressed phosphine dissociation in both cases. For comparison, the absorption spectra of the saturated and unsaturated compounds were calculated using time dependent DFT calculations (TDDFT). Energy decomposition analysis with the natural orbital for chemical valence extension (EDA NOCV) calculations shows a bond strengthening of the Ni-P bond by successive substitution of the phosphines with (ZnR)₂ units. The influence of different phosphines (PMe₃, PEt₃, PPh₃, P(OEt)₃) on Ni-P bond length and on Zn-Zn interactions in [Ni(ZnR)_2n(PR')_4-n] (R = Cp*, Me; R' = Me, Et, Ph, OEt) was also studied by DFT calculations. A correlation of increasing sterical demand of the phosphine ligand and a shortening of the Zn-Zn distances is observed.

Similarity-transformed equation-of-motion coupled-cluster singles and doubles method with spin-orbit effects for excited states

The similarity transformed equation-of-motion coupled-cluster method (STEOM-CCSD) for excited states is extended to treat spin-orbit coupling interactions (SOIs) using the spin-orbit mean field approximation of the Breit-Pauli Hamiltonian. Two possible schemes to include the spin-orbit splittings of excited states within the STEOM-CCSD model are formulated. They are identified as "diagonalize-then-perturb" and "perturb-then-diagonalize" approaches. The second approach is more suited for cases where SOI is larger, and the first approach breaks down. With the aid of the standard many-body diagrammatic techniques, expressions for all the necessary matrix elements can be derived. These new formulations are implemented in the ACES III suite of parallel coupled cluster programs, and benchmark studies are performed. Numerical tests for several atoms and molecules show a good agreement of calculated spin-orbit splittings to experiment, while also documenting the numerical differences between the two approaches.

Resolution-of-identity accelerated relativistic two- and four-component electron dynamics approach to chiroptical spectroscopies

We present an implementation and application of electron dynamics based on real-time time-dependent density functional theory (RT-TDDFT) and relativistic 2-component X2C and 4-component Dirac-Coulomb (4c) Hamiltonians to the calculation of electron circular dichroism and optical rotatory dispersion spectra. In addition, the resolution-of-identity approximation for the Coulomb term (RI-J) is introduced into RT-TDDFT and formulated entirely in terms of complex quaternion algebra. The proposed methodology was assessed on the dimethylchalcogenirane series, C₄H₈X (X = O, S, Se, Te, Po, Lv), and the spectra obtained by non-relativistic and relativistic methods start to disagree for Se and Te, while dramatic differences are observed for Po and Lv. The X2C approach, even in its simplest one-particle form, reproduces the reference 4c results surprisingly well across the entire series while offering an 8-fold speed-up of the simulations. An overall acceleration of RT-TDDFT by means of X2C and RI-J increases with system size and approaches a factor of almost 25 when compared to the full 4c treatment, without compromising the accuracy of the final spectra. These results suggest that one-particle X2C electron dynamics with RI-J acceleration is an attractive method for the calculation of chiroptical spectra in the valence region.

Observation of alkaline earth complexes M(CO)8 (M = Ca, Sr, or Ba) that mimic transition metals

The alkaline earth metals calcium (Ca), strontium (Sr), and barium (Ba) typically engage in chemical bonding as classical main-group elements through their ns and np valence orbitals, where n is the principal quantum number. Here we report the isolation and spectroscopic characterization of eight-coordinate carbonyl complexes M(CO)₈ (where M = Ca, Sr, or Ba) in a low-temperature neon matrix. Analysis of the electronic structure of these cubic O_h -symmetric complexes reveals that the metal-carbon monoxide (CO) bonds arise mainly from [M(d_π)] → (CO)₈ π backdonation, which explains the strong observed red shift of the C-O stretching frequencies. The corresponding radical cation complexes were also prepared in gas phase and characterized by mass-selected infrared photodissociation spectroscopy, confirming adherence to the 18-electron rule more conventionally associated with transition metal chemistry.

Suppressed Phosphine Dissociation by Polarization Effects on the Donor-Acceptor Bonds in [Ni(PEt3)4- n(ECp*) n] (E = Al, Ga)

A series of heteroleptic complexes [Ni(PEt₃)_{4- n}(ECp*) _n] (E = Al, Ga, Cp* = pentamethylcyclopentadienyl, n = 0-4) was prepared and characterized by experimental as well as computational means. The series of compounds was studied with respect to ligand dissociation processes which are fundamental for reactivity. In contrast to the homoleptic complexes [Ni(PR₃) _n] phosphine dissociation is remarkably suppressed in the heteroleptic title complexes. Single crystal X-ray structures as well as density functional theory calculations reveal a gradual decrease of the Ni-PEt₃ distances with increasing number of coordinated group-13 ligands ECp*. Accordingly, variable-temperature UV-vis studies of [Ni(PEt₃)_{4- n}(AlCp*) _n] in solution indicate no ligand dissociation equilibrium for n ≥ 2. Energy decomposition analysis with the natural orbital for chemical valence extension shows higher Ni-P interaction energies for [Ni(PEt₃)_{4- n}(AlCp*) _n] than for [Ni(PEt₃)₄] which is mainly a result of an increase in columbic attraction forces induced by Ni-PEt₃ bond polarization upon ECp* coordination.

A Restricted Open Configuration Interaction with Singles Method To Calculate Valence-to-Core Resonant X-ray Emission Spectra: A Case Study

In this work, a new protocol for the calculation of valence-to-core resonant X-ray emission (VtC RXES) spectra is introduced. The approach is based on the previously developed restricted open configuration interaction with singles (ROCIS) method and its parametrized version, based on a ground-state Kohn-Sham determinant (DFT/ROCIS) method. The ROCIS approach has the following features: (1) In the first step approximation, many-particle eigenstates are calculated in which the total spin is retained as a good quantum number. (2) The ground state with total spin S and excited states with spin S' = S, S ± 1, are obtained. (3) These states have a qualitatively correct multiplet structure. (4) Quasi-degenerate perturbation theory is used to treat the spin-orbit coupling operator variationally at the many-particle level. (5) Transition moments are obtained between the relativistic many-particle states. The method has shown great potential in the field of X-ray spectroscopy, in particular in the field of transition-metal L-edge, which cannot be described correctly with particle-hole theories. In this work, the method is extended to the calculation of resonant VtC RXES [alternatively referred to as 1s-VtC resonant inelastic X-ray scattering (RIXS)] spectra. The complete Kramers-Dirac-Heisenerg equation is taken into account. Thus, state interference effects are treated naturally within this protocol. As a first application of this protocol, a computational study on the previously reported VtC RXES plane on a molecular managanese(V) complex is performed. Starting from conventional X-ray absorption spectra (XAS), we present a systematic study that involves calculations and electronic structure analysis of both the XAS and non-resonant and resonant VtC XES spectra. The very good agreement between theory and experiment, observed in all cases, allows us to unravel the complicated intensity mechanism of these spectroscopic techniques as a synergic function of state polarization and interference effects. In general, intense features in the RIXS spectra originate from absorption and emission processes that involve nonorthogonal transition moments. We also present a graphical method to determine the sign of the interference contributions.

Picosecond sulfur K-edge X-ray absorption spectroscopy with applications to excited state proton transfer

Picosecond X-ray absorption (XA) spectroscopy at the S K-edge (∼2.4 keV) is demonstrated and used to monitor excited state dynamics in a small organosulfur molecule (2-Thiopyridone, 2TP) following optical excitation. Multiple studies have reported that the thione (2TP) is converted into the thiol (2-Mercaptopyridine, 2MP) following photoexcitation. However, the timescale and photochemical pathway of this reaction remain uncertain. In this work, time-resolved XA spectroscopy at the S K-edge is used to monitor the formation and decay of two transient species following 400 nm excitation of 2TP dissolved in acetonitrile. The first transient species forms within the instrument response time (70 ps) and decays within 6 ns. The second transient species forms on a timescale of ∼400 ps and decays on a 15 ns timescale. Time-dependent density functional theory is used to identify the first and second transient species as the lowest-lying triplet states of 2TP and 2MP, respectively. This study demonstrates transient S K-edge XA spectroscopy as a sensitive and viable probe of time-evolving charge dynamics near sulfur sites in small molecules with future applications towards studying complex biological and material systems.