Predissociation Measurements of Bond Dissociation Energies

Predissociation-based measurements of bond dissociation energies: US2, OUS, and USe

The uranium-containing molecules US2, OUS, and USe have been investigated using a pulsed laser ablation supersonic beam molecular source with time-of-flight mass spectrometric detection. Spectra have been recorded using the resonant two-photon ionization method over the spectroscopic range from 277 to 238 nm. These species have a myriad of excited electronic states in this spectroscopic region, leading to spectra that are highly congested and appear quasicontinuous. Sharp predissociation thresholds are observed, allowing precise bond dissociation energies to be measured. In the case of the triatomic molecules, it was necessary to use one laser for excitation and a delayed laser for ionization in order to observe a sharp predissociation threshold that allowed a precise bond dissociation energy to be measured. The resulting thermochemical values are D0(SU-S) = 4.910 ± 0.003 eV, D0(OU-S) = 5.035 ± 0.004 eV, and D0(USe) = 4.609 ± 0.009 eV. These results provide the first measurement of D0(USe) and reduce the error limits in the previous values of D0(SU-S) and D0(OU-S) by a factor of more than 70.

Quadruple bonds in MoC: Accurate calculations and precise measurement of the dissociation energy of low-lying states of MoC

In the present work, the electronic structure and chemical bonding of the MoC X3Σ- ground state and the six lowest excited states, A3Δ, a1Γ, b5Σ-, c1Δ, d1Σ+, and e5Π, have been investigated in detail using multireference configuration interaction methods and basis sets, including relativistic effective core potentials. In addition, scalar relativistic effects have been considered in the second order Douglas-Kroll-Hess approximation, while spin-orbit coupling has also been calculated. Five of the investigated states, X3Σ-, A3Δ, a1Γ, c1Δ, and d1Σ+, present quadruple σ2σ2π2π2 bonds. Experimentally, the predissociation threshold of MoC was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the dissociation energy of the ground state. Theoretically, the complete basis set limit of the calculated dissociation energy with respect to the atomic ground state products, including corrections for scalar relativistic effects, De(D0), is computed as 5.13(5.06) eV, in excellent agreement with our measured value of D0(MoC) of 5.136(5) eV. Furthermore, the calculated dissociation energies of the states having quadruple bonds with respect to their adiabatic atomic products range from 6.22 to 7.23 eV. The excited electronic states A3Δ2 and c1Δ2 are calculated to lie at 3899 and 8057 cm-1, also in excellent agreement with the experimental values of DaBell et al., 4002.5 and 7834 cm-1, respectively.

Chemical bonding in Uranium-based materials: A local vibrational mode case study of Cs 2 UO 2 Cl 4 and UCl 4 crystals

The Local Vibrational Mode Analysis, initially applied to diverse molecular systems, was extended to periodic systems in 2019. This work introduces an enhanced version of the LModeA software, specifically designed for the comprehensive analysis of two and three-dimensional periodic structures. Notably, a novel interface with the Crystal package was established, enabling a seamless transition from molecules to periodic systems using a unified methodology. Two distinct sets of uranium-based systems were investigated: (i) the evolution of the Uranyl ion (UO  2 2 + ) traced from its molecular configurations to the solid state, exemplified by Cs  2 UO  2 Cl  4 and (ii) Uranium tetrachloride (UCl  4 ) in both its molecular and crystalline forms. The primary focus was on exploring the impact of crystal packing on key properties, including IR and Raman spectra, structural parameters, and an in-depth assessment of bond strength utilizing local mode perspectives. This work not only demonstrates the adaptability and versatility of LModeA for periodic systems but also highlights its potential for gaining insights into complex materials and aiding in the design of new materials through fine-tuning.

Iron-histidine bonding in bishistidyl hemoproteins-A local vibrational mode study

We investigated the intrinsic strength of distal and proximal FeN bonds for both ferric and ferrous oxidation states of bishistidyl hemoproteins from bacteria, animals, human, and plants, including two cytoglobins, ten hemoglobins, two myoglobins, six neuroglobins, and six phytoglobins. As a qualified measure of bond strength, we used local vibrational force constants ka (FeN) based on local mode theory developed in our group. All calculations were performed with a hybrid QM/MM ansatz. Starting geometries were taken from available x-ray structures. ka (FeN) values were correlated with FeN bond lengths and covalent bond character. We also investigated the stiffness of the axial NFeN bond angle. Our results highlight that protein effects are sensitively reflected in ka (FeN), allowing one to compare trends in diverse protein groups. Moreover, ka (NFeN) is a perfect tool to monitor changes in the axial heme framework caused by different protein environments as well as different Fe oxidation states.

A physical organic strategy to predict and interpret stabilities of chemical bonds in energetic compounds for the discovery of thermal-resistant properties

CONTEXT

The in-depth understanding about the stability of chemical bonds in energetic compounds plays a central role for molecular design and safety-related evaluations. Most energetic compounds contain nitro as explosophores, and nitro cleavage is fundamental for thermal and mechanical stability. However, the quantum chemistry approach to accurately predict energy and temperature properties related to bond stability is challenging, due to the tradeoff between computational costs and deviations. Herein, the bond orders are proposed as accurate and computational-cost efficient descriptors for predicting the chemical bond stability and thermal-resistant properties. The intrinsic bond strength index (IBSI) demonstrates the best prediction for experimental homolytic bond dissociation energies (R2 > 0.996), which is on par with the results from high-precision quantum chemistry methods. The effects from bond connectivity and steric hindrance hierarchy were analyzed to reveal underlying mechanisms. Additionally, the IBSI descriptors are successfully applied to predict the thermal decomposition temperatures of 24 heat-resistant energetic compounds (R2 = 0.995), thus validating the effectiveness for the prediction and interpretation of chemical bond stability in energetic compounds via a physical organic approach.

METHODS

All DFT calculations were performed with Gaussian 09 software. To investigate the dependence of the method on functionals and basis sets, 9 DFT methods were considered (B3LYP/6-31G(d,p), B3LYP/6-311G(d,p), B3LYP/def2-TZVP, M062X/6-31G(d,p), M062X/6-311G(d,p), M062X/def2-TZVP, ωB97XD/6-31G(d,p), ωB97XD/6-311G(d,p), and ωB97XD/def2-TZVP). The bond order descriptors LBO and IBSI are obtained through the bond order analysis module in the Multiwfn software.

Bond dissociation energy of FeCr+ determined through threshold photodissociation in a cryogenic ion trap

The bond dissociation energy of FeCr+ is measured using resonance enhanced photodissociation spectroscopy in a cryogenic ion trap. The onset for FeCr+ → Fe + Cr+ photodissociation occurs well above the lowest Cr+(6S, 3d5) + Fe(5D, 3d64s2) dissociation limit. In contrast, the higher energy FeCr+ → Fe+ + Cr photodissociation process exhibits an abrupt onset at the energy of the Cr(7S, 3d54s1) + Fe+(6D, 3d64s1) limit, enabling accurate dissociation energies to be extracted: D(Fe-Cr+) = 1.655 ± 0.006 eV and D(Fe+-Cr) = 2.791 ± 0.006 eV. The measured D(Fe-Cr+) bond energy is 10%-20% larger than predictions from accompanying CAM (Coulomb Attenuated Method)-B3LYP and NEVPT2 and coupled cluster singles, doubles, and perturbative triples electronic structure calculations, which give D(Fe-Cr+) = 1.48, 1.40, and 1.35 eV, respectively. The study emphasizes that an abrupt increase in the photodissociation yield at threshold requires that the molecule possesses a dense manifold of optically accessible, coupled electronic states adjacent to the dissociation asymptote. This condition is not met for the lowest Cr+(6S, 3d5) + Fe(5D, 3d64s2) dissociation limit of FeCr+ but is satisfied for the higher energy Cr(7S, 3d54s1) + Fe+(6D, 3d64s1) dissociation limit.

Observation of Continuum State Dissociation Enables the Determination of N2 Bond Dissociation Energy to Spectroscopic Accuracy

Nitrogen (N) is one of the most fundamental elements of life. Precise determination of the bond dissociation energy (BDE) of the corresponding homonuclear diatomic molecule N2 is not only important for calculating the enthalpies of formation for any N-containing molecules but also provides the best benchmark for evaluating theoretical computational methods. Thus, it has attracted many experimental and theoretical studies, while controversies still exist. Here, we report the observation of continuum state dissociation of N2 into the channel N(2D5/2,3/2)+N(2D5/2,3/2) for the first time by using the vacuum ultraviolet (VUV)-pump-VUV-probe time-sliced velocity-mapped imaging setup. The quantum-state-resolved images enable the direct visualization of the dissociation onsets corresponding to each of the correlated spin-orbit fine-structure channels within a few tenths of wavenumber. The BDEs of 14N2 and 15N2 are directly determined to be 78691.8 ± 0.3 cm-1 and 78731.5 ± 0.3 cm-1, respectively, which should represent the most accurate BDE of N2 thus far.

CrN, CuB, and AuB: A Tale of Two Dissociation Limits

Predissociation thresholds corresponding to dissociation at ground state separated atom limits (SALs) have been recorded in this group for more than 100 d- and f-block metal-containing molecules. The metal atom electronic degeneracies in these molecules generate a dense manifold of electronic states that allow high-lying vibronic levels to couple to pathways leading to dissociation. However, CrN, CuB, and AuB fail to dissociate at their ground SAL. Instead, the molecules remain bound at energies that far surpass their bond dissociation energies (BDEs), and their bonds break only when excited at or above an excited SAL. Sharp predissociation thresholds at excited SALs nevertheless allowed BDEs to be derived: D0(CrN): 3.941(22) eV; D0(CuB): 2.26(15) eV; D0(Au11B): 3.724(3) eV. A previous measurement of D0(AlCr) is re-evaluated as dissociating to a higher energy limit, giving a revised value of D0(AlCr) = 1.32(2) eV. A discussion of this physical behavior is presented.

Electronic Structure of Heteronuclear Cerium-Platinum Clusters

Beyond the now well-known strong catalyst-support interactions reported for ceria-supported platinum catalysts, intermetallic Ce-Pt compounds exhibit fascinating properties such as heavy fermion behavior and magnetic instability. Small heterometallic Ce-Pt clusters, which can provide insights into the local features that govern bulk phenomena, have been less explored. Herein, the anion photoelectron spectra of three small mixed Ce-Pt clusters, Ce2OPt-, Ce2Pt-, and Ce3Pt-, are presented and interpreted with supporting density functional theory calculations. The calculations, which are readily reconciled with the experimental spectra, suggest the presence of numerous close-lying spin states, including states in which the Ce 4f electrons are ferromagnetically coupled or antiferromagnetically coupled. The Pt center is consistently in a nominal -2 charge state in all cluster neutrals and anions, giving the Ce-Pt bond ionic character. Ce-Pt bonds are stronger than Ce-Ce bonds, and the O atom in Ce2OPt- coordinates only with the Ce centers. The energy of the singly occupied Ce-local 4f orbitals relative to the Pt-local orbitals changes with cluster composition. Discussion of the results includes potential implications for Ce-rich intermetallic materials.

Probing the Chemical Bond between Lanthanides and Carbon: CeC, PrC, NdC, LuC, and TmC2

Resonant two-photon ionization experiments have been conducted to probe the bond dissociation energy (BDE) of the lanthanide-carbon bond, allowing the BDEs of CeC, PrC, NdC, LuC, and Tm-C₂ to be measured to high precision. Values of D₀(CeC) = 4.893(3) eV, D₀(PrC) = 4.052(3) eV, D₀(NdC) = 3.596(3) eV, D₀(LuC) = 3.685(4) eV, and D₀(Tm-C₂) = 4.797(6) eV are obtained. Additionally, the adiabatic ionization energy of LuC was measured, giving IE(LuC) = 7.05(3) eV. The electronic structure of these species, along with the previously measured LaC, has been further investigated using quantum chemical calculations. Despite LaC, CeC, PrC, and NdC having ground electronic configurations that differ only in the number of 4f electrons present and have virtually identical bond orders, bond lengths, fundamental stretching frequencies, and metallic oxidation states, a peculiar 1.30 eV range in bond dissociation energies exists for these molecules. A natural bond orbital analysis shows that the metal atoms in these molecules have a natural charge of +1 with a 5d² 4fⁿ 6s⁰ configuration while the carbon atom has a natural charge of -1 and a 2p³ configuration. The diabatic bond dissociation energies, calculated with respect to the lowest energy level of this separated ion configuration, show a greatly reduced energy range of 0.32 eV, with the diabatic BDE decreasing as the amount of 4f character in the σ-bond increases. Thus, the wide range of measured BDEs for these molecules is a consequence of the variation in atomic promotion energies at the separated ion limit. TmC₂ has a smaller BDE than the other LnC₂ molecules, due to the tiny amount of 5d participation in the valence molecular orbitals.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N⁷) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N³ - N⁴) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Bond dissociation energies of diatomic transition metal nitrides

Resonant two-photon ionization (R2PI) spectroscopy has been used to measure the bond dissociation energies (BDEs) of the diatomic transition metal nitrides ScN, TiN, YN, MoN, RuN, RhN, HfN, OsN, and IrN. Of these, the BDEs of only TiN and HfN had been previously measured. Due to the many ways electrons can be distributed among the d orbitals, these molecules possess an extremely high density of electronic states near the ground separated atom limit. Spin-orbit and nonadiabatic interactions couple these states quite effectively, so that the molecules readily find a path to dissociation when excited above the ground separated atom limit. The result is a sharp drop in ion signal in the R2PI spectrum when the molecule is excited above this limit, allowing the BDE to be readily measured. Using this method, the values D₀(ScN) = 3.905(29) eV, D₀(TiN) = 5.000(19) eV, D₀(YN) = 4.125(24) eV, D₀(MoN) = 5.220(4) eV, D₀(RuN) = 4.905(3) eV, D₀(RhN) = 3.659(32) eV, D₀(HfN) = 5.374(4) eV, D₀(OsN) = 5.732(3) eV, and D₀(IrN) = 5.115(4) eV are obtained. To support the experimental findings, ab initio coupled-cluster calculations extrapolated to the complete basis set limit (CBS) were performed. With a semiempirical correction for spin-orbit effects, these coupled-cluster single double triple-CBS calculations give a mean absolute deviation from the experimental BDE values of 0.20 eV. A discussion of the periodic trends, summaries of previous work, and comparisons to isoelectronic species is also provided.

Dihydrogen Bonding-Seen through the Eyes of Vibrational Spectroscopy

In this work, we analyzed five groups of different dihydrogen bonding interactions and hydrogen clusters with an H3+ kernel utilizing the local vibrational mode theory, developed by our group, complemented with the Quantum Theory of Atoms-in-Molecules analysis to assess the strength and nature of the dihydrogen bonds in these systems. We could show that the intrinsic strength of the dihydrogen bonds investigated is primarily related to the protonic bond as opposed to the hydridic bond; thus, this should be the region of focus when designing dihydrogen bonded complexes with a particular strength. We could also show that the popular discussion of the blue/red shifts of dihydrogen bonding based on the normal mode frequencies is hampered from mode-mode coupling and that a blue/red shift discussion based on local mode frequencies is more meaningful. Based on the bond analysis of the H3+(H2)n systems, we conclude that the bond strength in these crystal-like structures makes them interesting for potential hydrogen storage applications.

Ab initio composite strategies and multireference approaches for lanthanide sulfides and selenides

The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas-Kroll-Hess Hamiltonian. Spin-orbit coupling was addressed with the Breit-Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin-orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.

Early Transition Metals Strengthen the B2 Bond in MB2 Complexes

The bond dissociation energies of early transition metal diborides (M-B₂, M = Sc, Ti, V, Y, Mo) have been measured by observation of the sharp onset of predissociation in a highly congested spectrum. Density functional and CCSD(T) ab initio calculations, extrapolated to the complete basis set limit, have been used to examine the electronic structure of these species. The computations demonstrate the formation of bonding orbitals between the metal d orbitals and the 1π_u bonding orbitals of B₂, leading to the transfer of metallic electron density into the bonding 1π_u orbitals, strengthening both the M-B and B-B bonds in the molecule. This runs counter to most metal-ligand π interactions, where electron density is generally transferred into π antibonding orbitals of the ligand.

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T₀) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T₀) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T₀). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Molybdenum-Sulfur Bond: Electronic Structure of Low-Lying States of MoS

The molybdenum-sulfur bond plays an important role in many processes such as nitrogen-fixation, and it is found as a building block in layered materials such as MoS₂, known for its various shapes and morphologies. Here, we present an accurate theoretical and experimental investigation of the chemical bonding and the electronic structure of 20 low-lying states of the MoS molecule. Multireference and coupled cluster methodologies, namely, MRCISD, MRCISD + Q, RCCSD(T), and RCCSD[T], were employed in conjunction with basis sets up to aug-cc-pwCV5Z-PP/aug-cc-pwCV5Z for the study of these states. We note the significance of including the inner 4s²4p⁶ electrons of Mo and 2s²2p⁶ of S in the correlated space to obtain accurate results. Experimentally, the predissociation threshold of MoS was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the bond dissociation energy. Our extrapolated computational D₀ value for the ground state is 3.936 eV, in excellent agreement with our experimental measurement of 3.932 ± 0.004 eV. The largest calculated adiabatic D₀ (5.74 eV) and the largest dipole moment (6.50 D) were found for the ⁵Σ⁺ state, where a triple bond is formed. Finally, the connection of the chemical bonding of the isolated MoS species to the relevant solid, MoS₂, is emphasized. The low-lying septet states of the diatomic molecule are involved in the material as a building block, explaining the stability and the variety of the shapes and morphologies of the material.

Bond Dissociation Energies Reveal the Participation of d Electrons in f-Element Halide Bonding

Bond dissociation energies (BDEs) reported in the literature for lanthanide monofluorides and lanthanide monochlorides LnX, where X = F or Cl, exhibit substantial irregular variations across the Ln series. It is demonstrated here that correlations of these variations with reported experimentally based atomic energies to prepare the Ln constituent for bonding reveal the nature of the bonding. Whereas some molecular characteristics are well understood in the context of highly ionic bonding, with LnX considered to be (Ln⁺)(X^-), some significant variations in BDEs are not well rationalized simply by ionization to convert Ln to Ln⁺ for bonding. Focusing here on lanthanide monofluorides LnF, a consideration of alternative Ln preparation schemes shows that a particularly good rationalization of BDEs is obtained by invoking the participation of a lanthanide 5d electron in bonding. This 5d participation could be in ionic (Ln⁺)(F^-) via π-donation from F^- 2p to empty Ln⁺ 5d orbitals or in covalent π-bonded Ln:F via polarization from Ln 5d to F 2p, with these ionic and polar covalent perspectives ultimately being equivalent. The inference of lanthanide 5d involvement suggests that the valence 4f and 6s electrons do not effectively participate in some key aspects of the bonding, presumably due to poor spatial overlap with F 2p orbitals. An extension to actinide monofluorides, AnF, assumes analogous ionic or polar covalent bonding involving a valence 6d electron and results in predictions for BDEs that include a general decrease from left to right across the series, except for a distinctive local minimum at AmF. Determining the BDE for AmF would serve to evaluate the predictions and the underlying assumption of 6d bonding. The BDE assessments/predictions for neutral monofluorides, LnF and AnF, are also applied to cationic LnF⁺ and AnF⁺, and it is noted that the approach can be directly extended to f-element monochlorides, monobromides, and monoiodides.

Advancing Inorganic Coordination Chemistry by Spectroscopy of Isolated Molecules: Methods and Applications

A unique feature of the work carried out in the Collaborative Research Center 3MET continues to be its emphasis on innovative, advanced experimental methods which hyphenate mass-selection with further analytical tools such as laser spectroscopy for the study of isolated molecular ions. This allows to probe the intrinsic properties of the species of interest free of perturbing solvent or matrix effects. This review explains these methods and uses examples from past and ongoing 3MET studies of specific classes of multicenter metal complexes to illustrate how coordination chemistry can be advanced by applying them. As a corollary, we will show how the challenges involved in providing well-defined, for example monoisomeric, samples of the molecular ions have helped to further improve the methods themselves thus also making them applicable to many other areas of chemistry.

Predissociation measurements of the bond dissociation energies of EuO, TmO, and YbO

The observation of a sharp predissociation threshold in the resonant two-photon ionization spectra of EuO, TmO, and YbO has been used to measure the bond dissociation energies of these species. The resulting values, D₀(EuO) = 4.922(3) eV, D₀(TmO) = 5.242(6) eV, and D₀(YbO) = 4.083(3) eV, are in good agreement with previous values but are much more precise. In addition, the ionization energy of TmO was measured by the observation of a threshold for one-color two-photon ionization of this species, resulting in IE(TmO) = 6.56(2) eV. The observation of a sharp predissociation threshold for EuO was initially surprising because the half-filled 4f⁷ subshell of Eu in its ground state generates fewer potential energy curves than in the other molecules we have studied by this method. The observation of a sharp predissociation threshold in YbO was even more surprising, given that the ground state of Yb is nondegenerate (4f¹⁴6s², ¹S_g) and the lowest excited state of Yb is over 2 eV higher in energy. It is suggested that these molecules possess a high density of electronic states at the energy of the ground separated atom limit because ion-pair states drop below the ground limit, providing a sufficient electronic state density to allow predissociation to set in at the thermochemical threshold.

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

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

Bond dissociation energies of low-valent lanthanide hydroxides: lower limits from ion-molecule reactions and comparisons with fluorides

Despite that bond dissociation energies (BDEs) are among the most fundamental and relevant chemical properties they remain poorly characterized for most elementary lanthanide hydroxides and halides. Lanthanide ions Ln+ = Eu+, Tm+ and Yb+ are here shown to react with H2O to yield hydroxides LnOH+. Under low-energy conditions such reactions must be exothermic, which implies a lower limit of 499 kJ mol-1 for the Ln+-OH BDEs. This limit is significantly higher than previously reported for YbOH+ and is unexpectedly similar to the BDE for Yb+-F. To explain this apparent anomaly, it is considered feasible that the inefficient hydrolysis reactions observed here in a quadrupole ion trap mass spectrometer may actually be endothermic. More definitive and broad-based evaluations and comparisons require additional and more reliable BDEs and ionization energies for key lanthanide molecules, and/or energies for ligand-exchange reactions like LnF + OH ↔ LnOH + F. The hydroxide results motivated an assessment of currently available lanthanide monohalide BDEs. Among several intriguing relationships is the distinctively higher BDE for neutral LuF versus cationic LuF+, though quantifying this comparison awaits a more accurate value for the anomalously high ionization energy of LuF.

Multiconfiguration Pair-Density Functional Theory for Transition Metal Silicide Bond Dissociation Energies, Bond Lengths, and State Orderings

Transition metal silicides are promising materials for improved electronic devices, and this motivates achieving a better understanding of transition metal bonds to silicon. Here we model the ground and excited state bond dissociations of VSi, NbSi, and TaSi using a complete active space (CAS) wave function and a separated-pair (SP) wave function combined with two post-self-consistent field techniques: complete active space with perturbation theory at second order and multiconfiguration pair-density functional theory. The SP approximation is a multiconfiguration self-consistent field method with a selection of configurations based on generalized valence bond theory without the perfect pairing approximation. For both CAS and SP, the active-space composition corresponds to the nominal correlated-participating-orbital scheme. The ground state and low-lying excited states are explored to predict the state ordering for each molecule, and potential energy curves are calculated for the ground state to compare to experiment. The experimental bond dissociation energies of the three diatomic molecules are predicted with eight on-top pair-density functionals with a typical error of 0.2 eV for a CAS wave function and a typical error of 0.3 eV for the SP approximation. We also provide a survey of the accuracy achieved by the SP and extended separated-pair approximations for a broader set of 25 transition metal–ligand bond dissociation energies.

Halogen Bonding Involving I2 and d8 Transition-Metal Pincer Complexes

We systematically investigated iodine–metal and iodine–iodine bonding in van Koten’s pincer complex and 19 modifications changing substituents and/or the transition metal with a PBE0–D3(BJ)/aug–cc–pVTZ/PP(M,I) model chemistry. As a novel tool for the quantitative assessment of the iodine–metal and iodine–iodine bond strength in these complexes we used the local mode analysis, originally introduced by Konkoli and Cremer, complemented with NBO and Bader’s QTAIM analyses. Our study reveals the major electronic effects in the catalytic activity of the M–I–I non-classical three-center bond of the pincer complex, which is involved in the oxidative addition of molecular iodine I2 to the metal center. According to our investigations the charge transfer from the metal to the σ* antibonding orbital of the I–I bond changes the 3c–4e character of the M–I–I three-center bond, which leads to weakening of the iodine I–I bond and strengthening of the metal–iodine M–I bond, facilitating in this way the oxidative addition of I2 to the metal. The charge transfer can be systematically modified by substitution at different places of the pincer complex and by different transition metals, changing the strength of both the M–I and the I2 bonds. We also modeled for the original pincer complex how solvents with different polarity influence the 3c–4e character of the M–I–I bond. Our results provide new guidelines for the design of pincer complexes with specific iodine–metal bond strengths and introduce the local vibrational mode analysis as an efficient tool to assess the bond strength in complexes.

Bond dissociation energies of lanthanide sulfides and selenides

Resonant two-photon ionization spectroscopy has been employed to observe sharp predissociation thresholds in the spectra of the lanthanide sulfides and selenides for the 4f metals Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, and Lu. As these molecules possess a large density of electronic states near the ground separated atom limit, these predissociation thresholds are argued to coincide with the true 0 K bond dissociation energies (BDEs). This is because spin-orbit and nonadiabatic couplings among these states allow the molecules to predissociate rapidly when the BDE is reached or exceeded. The measured BDEs, in eV, are as follows: 5.230(3) (PrS), 4.820(3) (NdS), 4.011(17) (SmS), 3.811(8) (EuS), 5.282(5) (GdS), 5.292(3) (TbS), 4.298(3) (DyS), 4.251(3) (HoS), 4.262(3) (ErS), 5.189(3) (LuS), 4.496(3) (PrSe), 4.099(3) (NdSe), 3.495(17) (SmSe), 3.319(3) (EuSe), 4.606(3) (GdSe), 4.600(6) (TbSe), 3.602(3) (DySe), 3.562(3) (HoSe), 3.587(3) (ErSe), and 4.599(6) (LuSe). Through the use of thermochemical cycles, the 0 K gaseous heat of formation, Δ_fH_0K ^○, is reported for each molecule. A threshold corresponding to the onset of two-photon ionization in EuSe was also observed, providing the ionization energy of EuSe as 6.483(10) eV. Through a thermochemical cycle and the above reported BDE of the neutral EuSe molecule, the BDE for the Eu⁺-Se cation was also determined as D₀(Eu⁺-Se) = 2.506(10) eV. Bonding trends of the lanthanide sulfides and selenides are discussed. Our previous observation that the transition metal sulfides are 15.6% more strongly bound than the corresponding selenides continues to hold true for the lanthanides as well.

Exceptionally Long Covalent CC Bonds-A Local Vibrational Mode Study

For decades one has strived to synthesize a compound with the longest covalent C−C bond applying predominantly steric hindrance and/or strain to achieve this goal. On the other hand electronic effects have been added to the repertoire, such as realized in the electron deficient ethane radical cation in its D3d form. Recently, negative hyperconjugation effects occurring in diamino-o-carborane analogs such as di-N,N-dimethylamino-o-carborane have been held responsible for their long C−C bonds. In this work we systematically analyzed CC bonding in a diverse set of 53 molecules including clamped bonds, highly sterically strained complexes such as diamondoid dimers, electron deficient species, and di-N,N-dimethylamino-o-carborane to cover the whole spectrum of possibilities for elongating a covalent C−C bond to the limit. As a quantitative intrinsic bond strength measure, we utilized local vibrational CC stretching force constants ka(CC) and related bond strength orders BSO n(CC), computed at the ωB97X-D/aug-cc-pVTZ level of theory. Our systematic study quantifies for the first time that whereas steric hindrance and/or strain definitely elongate a C−C bond, electronic effects can lead to even longer and weaker C−C bonds. Within our set of molecules the electron deficient ethane radical cation, in D3d symmetry, acquires the longest C−C bond with a length of 1.935 Å followed by di-N,N-dimethylamino-o-carborane with a bond length of 1.930 Å. However, the C−C bond in di-N,N-dimethylamino-o-carborane is the weakest with a BSO n value of 0.209 compared to 0.286 for the ethane radical cation; another example that the longer bond is not always the weaker bond. Based on our findings we provide new guidelines for the general characterization of CC bonds based on local vibrational CC stretching force constants and for future design of compounds with long C−C bonds.

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium-Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D_e and bond length r_e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15-0.19. For the single-reference methods, Kohn-Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D_e and r_e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core-valence terms; this results in highly accurate dissociation energies and good bond lengths. Averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

Computational analysis of vibrational frequencies and rovibrational spectroscopic constants of hydrogen sulfide dimer using MP2 and CCSD(T)

Previous studies have shown that the weakly bonded H₂S dimer demands high level quantum chemical calculations to reproduce experimental values. We investigated the hydrogen bonding of H₂S dimer using MP2 and CCSD(T) levels of theory in combination with aug-cc-pV(D,T,Q)Z basis sets. More precisely, the binding energies, potential energy curves, rovibrational spectroscopic constants, decomposition lifetime, and normal vibrational frequencies were calculated. In addition, we introduced the local mode analysis of Konkoli-Cremer to quantify the hydrogen bonding in the H₂S dimer as well as providing for the first time the comprehensive decomposition of normal vibrational modes into local modes contributions, and a decomposition lifetime based on rate constant. The local mode force constant of the H₂S dimer hydrogen bond is smaller than that of the water dimer, in accordance with the weaker hydrogen bonding in the H₂S dimer.

Bond dissociation energies of transition metal oxides: CrO, MoO, RuO, and RhO

Through the use of resonant two-photon ionization spectroscopy, sharp predissociation thresholds have been identified in the spectra of CrO, MoO, RuO, and RhO. Similar thresholds have previously been used to measure the bond dissociation energies (BDEs) of many molecules that have a high density of vibronic states at the ground separated atom limit. A high density of states allows precise measurement of the BDE by facilitating prompt dissociation to ground state atoms when the BDE is exceeded. However, the number of states required for prompt predissociation at the thermochemical threshold is not well defined and undoubtedly varies from molecule to molecule. The ground separated atom limit generates 315 states for RuO, 252 states for RhO, and 63 states for CrO and MoO. Although comparatively few states derive from this limit for CrO and MoO, the observation of sharp predissociation thresholds for all four molecules nevertheless allows BDEs to be assigned as 4.863(3) eV (RuO), 4.121(3) eV (RhO), 4.649(5) eV (CrO), and 5.414(19) eV (MoO). Thermochemical cycles are used to derive the enthalpies of formation of the gaseous metal oxides and to obtain IE(RuO) = 8.41(5) eV, IE(RhO) = 8.56(6) eV, D₀(Ru-O^-) = 4.24(2) eV, D₀(Cr-O^-) = 4.409(8) eV, and D₀(Mo-O^-) = 5.243(20) eV. The mechanisms leading to prompt predissociation at threshold in the cases of CrO and MoO are discussed. Also presented is a discussion of the bonding trends for the transition metal oxides, which are compared to the previously measured transition metal sulfides.

The bond dissociation energy of VO measured by resonant three-photon ionization spectroscopy

The predissociation threshold of VO has been measured using resonant three-photon ionization (R3PI) spectroscopy. Given the high density of electronic states in the molecule, it is argued that the molecule dissociates rapidly as soon as the thermochemical bond dissociation energy (BDE) is exceeded, allowing the measured predissociation threshold to be assigned as the BDE. This is the first time a BDE has been measured using the R3PI method. The first photon is provided by an optical parametric oscillator (OPO) laser that promotes VO into a high-energy, discrete vibronic state. A tunable dye laser then excites the molecule further to a resonant state close to the dissociation limit where there is a quasi-continuum of states. A second photon from the same dye laser pulse ionizes the molecule, generating VO⁺ ions. The dye laser is then scanned to higher energies, and when the energy of one OPO photon plus one dye photon exceeds the BDE, the molecule dissociates before another dye photon can be absorbed to induce ionization. The combined photon energy at the sharp drop in the ion signal is assigned as the BDE. The experiment has been repeated using four different intermediate states, all yielding the same BDE, D₀(VO) = 6.545(2) eV. Using thermochemical cycles, a revised value for the BDE of cationic VO is obtained, D₀(V⁺-O) = 6.053(2) eV. The 0 K enthalpy of formation for VO(g) is also derived as Δ_fH_0K ⁰VO(g) = 128.6(1.0) kJ mol^-1. Previous spectroscopic and thermochemical studies of VO are reviewed.

Bond dissociation energies of the diatomic late transition metal sulfides: RuS, OsS, CoS, RhS, IrS, and PtS

The spectra of RuS, OsS, CoS, RhS, IrS, and PtS have been recorded near their respective bond dissociation energies using resonant two-photon ionization spectroscopy. The spectra display an abrupt drop to baseline when the bond dissociation energy (BDE) is exceeded. It is argued that spin-orbit and nonadiabatic interactions among the myriad of states that result from the ground and low-lying separated atom limits cause the molecules to predissociate rapidly as soon as the ground separated atom limit is exceeded in energy. Thus, the observed sharp predissociation thresholds are assigned as the 0 K BDEs of the molecules. With this assumption, the BDEs are assigned as follows: 4.071(8) eV (RuS), 4.277(3) eV (OsS), 3.467(5) eV (CoS), 3.611(3) eV (RhS), 4.110(3) eV (IrS), and 4.144(8) eV (PtS). Using thermochemical cycles, the gas-phase enthalpies of formation at 0 K, Δ_fH_{0 K}°, were calculated to be 531.8(4.3) kJ mol^-1 (RuS), 651.2(6.3) kJ mol^-1 (OsS), 365.3(2.2) kJ mol^-1 (CoS), 481.5(2.1) kJ mol^-1 (RhS), 546.7(6.3) kJ mol^-1 (IrS), and 438.9(1.5) kJ mol^-1 (PtS). The ionization energies of RuS, CoS, and RhS were also calculated using data on the BDEs of the associated cations and were found to be 8.39(10) eV (RuS), 8.40(9) eV (CoS), and 8.46(12) eV (RhS). Combining these data with predissociation measurements of other transition metal sulfide BDEs, the periodic trends in the transition metal sulfide BDEs are discussed and the BDEs of the transition metal sulfides are compared to those of the corresponding selenides. The BDEs of the sulfides are found to be 15.4% greater than those of the corresponding sulfides.

Bond dissociation energies of diatomic transition metal selenides: ScSe, YSe, RuSe, OsSe, CoSe, RhSe, IrSe, and PtSe

The diatomic transition metal selenides, MSe (M = Sc, Y, Ru, Os, Co, Rh, Ir, and Pt), were studied by resonant two-photon ionization spectroscopy near their respective bond dissociation energies. As these molecules exhibit high densities of vibronic states near their dissociation limits, the spectra typically appear quasicontinuously at these energies. Spin-orbit and nonadiabatic couplings among the multitudes of potential curves allow predissociation to occur on a rapid timescale when the molecule is excited to states lying above the ground separated atom limit. This dissociation process occurs so rapidly that the molecules are dissociated before they can be ionized by the absorption of a second photon. This results in an abrupt drop in the ion signal that is assigned as the 0 K bond dissociation energy for the molecule, giving bond dissociation energies of 4.152(3) eV (ScSe), 4.723(3) eV (YSe), 3.482(3) eV (RuSe), 3.613(3) eV (OsSe), 2.971(6) eV (CoSe), 3.039(9) eV (RhSe), 3.591(3) eV (IrSe), and 3.790(31) eV (PtSe). The enthalpies of formation, Δ_fH_0K° (g), for each diatomic metal selenide were calculated using thermochemical cycles, yielding Δ_fH_0K° (g) values of 210.9(4.5) kJ mol^-1 (ScSe), 203.5(4.5) kJ mol^-1 (YSe), 549.2(4.5) kJ mol^-1 (RuSe), 675.9(6.5) kJ mol^-1 (OsSe), 373.9(2.6) kJ mol^-1 (CoSe), 497.4(2.7) kJ mol^-1 (RhSe), 557.4(6.5) kJ mol^-1 (IrSe), and 433.7(3.6) kJ mol^-1 (PtSe). Utilizing a thermochemical cycle, the ionization energy for ScSe is estimated to be about 7.07 eV. The bonding trends of the transition metal selenides are discussed.

Metal-Halogen Bonding Seen through the Eyes of Vibrational Spectroscopy

Incorporation of a metal center into halogen-bonded materials can efficiently fine-tune the strength of the halogen bonds and introduce new electronic functionalities. The metal atom can adopt two possible roles: serving as halogen acceptor or polarizing the halogen donor and acceptor groups. We investigated both scenarios for 23 metal–halogen dimers trans-M(Y₂)(NC₅H₄X-3)₂ with M = Pd(II), Pt(II); Y = F, Cl, Br; X = Cl, Br, I; and NC₅H₄X-3 = 3-halopyridine. As a new tool for the quantitative assessment of metal–halogen bonding, we introduced our local vibrational mode analysis, complemented by energy and electron density analyses and electrostatic potential studies at the density functional theory (DFT) and coupled-cluster single, double, and perturbative triple excitations (CCSD(T)) levels of theory. We could for the first time quantify the various attractive contacts and their contribution to the dimer stability and clarify the special role of halogen bonding in these systems. The largest contribution to the stability of the dimers is either due to halogen bonding or nonspecific interactions. Hydrogen bonding plays only a secondary role. The metal can only act as halogen acceptor when the monomer adopts a (quasi-)planar geometry. The best strategy to accomplish this is to substitute the halo-pyridine ring with a halo-diazole ring, which considerably strengthens halogen bonding. Our findings based on the local mode analysis provide a solid platform for fine-tuning of existing and for design of new metal–halogen-bonded materials.

Bond dissociation energies of ScSi, YSi, LaSi, ScC, YC, LaC, CoC, and YCH

Predissociation thresholds of the ScSi, YSi, LaSi, ScC, YC, LaC, CoC, and YCH molecules have been measured using resonant two-photon ionization spectroscopy. It is argued that the dense manifold of electronic states present in these molecules causes prompt dissociation when the bond dissociation energy (BDE) is exceeded, allowing their respective predissociation thresholds to provide precise values of their bond energies. The BDEs were measured as 2.015(3) eV (ScSi), 2.450(2) eV (YSi), 2.891(5) eV (LaSi), 3.042(10) eV (ScC), 3.420(3) eV (YC), 4.718(4) eV (LaC), 3.899(13) eV (CoC), and 4.102(3) eV (Y-CH). Using thermochemical cycles, the enthalpies of formation, Δ_fH_0K°(g), were calculated as 627.4(9.0) kJ mol^-1 (ScSi), 633.1(9.0) kJ mol^-1 (YSi), 598.1(9.0) kJ mol^-1 (LaSi), 793.8(4.3) kJ mol^-1 (ScC), 805.0(4.2) kJ mol^-1 (YC), 687.3(4.2) kJ mol^-1 (LaC), 760.1(2.5) kJ mol^-1 (CoC), and 620.8(4.2) kJ mol^-1 (YCH). Using data for the BDEs of the corresponding cations allows ionization energies to be obtained through thermochemical cycles as 6.07(11) eV (ScSi), 6.15(13) eV (YSi), 5.60(10) eV (LaSi), 6.26(6) eV (ScC), 6.73(12) or 5.72(11) eV [YC, depending on the value of D₀(Y⁺-C) employed], and 5.88(35) eV (LaC). Additionally, a new value of D₀(Co⁺-C) = 4.045(13) eV was obtained based on the present work and the previously determined ionization energy of CoC. An ionization onset threshold allowed the measurement of the LaSi ionization energy as 5.607(10) eV, in excellent agreement with a prediction based on a thermochemical cycle. Chemical bonding trends are also discussed.