Predissociation measurements of bond dissociation energies: VC, VN, and VS

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.

Adiabatic ionization energies of RuC, RhC, OsC, IrC, and PtC

The ionization energies (IEs) of RuC, RhC, OsC, IrC, and PtC are assigned by the measurement of their two-photon ionization thresholds. Although late transition metal-carbon bonds are of major importance in organometallic chemistry and catalysis, accurate and precise fundamental thermochemical data on these chemical bonds are mainly lacking in the literature. Based on their two-photon ionization thresholds, in this work, we assign IE(RuC) = 7.439(40) eV, IE(RhC) = 7.458(32) eV, IE(OsC) = 8.647(25) eV, IE(IrC) = 8.933(74) eV, and IE(PtC) = 9.397(32) eV. These experimentally derived IEs are further confirmed through quantum chemical calculations using coupled-cluster single double perturbative triple methods that are extrapolated to the complete basis set limit using a three-parameter mixed Gaussian/exponential extrapolation scheme and corrected for spin-orbit effects using a semiempirical method. The electronic structure and chemical bonding of these MC species are discussed in the context of these ionization energy measurements. The IEs of RuC, RhC, OsC, and IrC closely mirror the IEs of the corresponding transition metal atoms, suggesting that for these species, the (n + 1)s electrons of the transition metals are not significantly involved in chemical bonding.

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.

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.

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.

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.

Comparative Analysis of the Phase Interaction in Plasma Surfaced NiBSi Overlays with IVB and VIB Transition Metal Carbides

Important applications of transition metal carbides (TMCs) are as wear resistant composite layers deposited by plasma transferred arc welding (PTAW) and laser methods. Growing interest in them has also been observed in additive manufacturing and in HEA technology (bulk composite materials and layers), and in the area of energy conversion and storage. This paper presents the results of comparative studies on interfacial interactions in the NiBSi−TMCs system for two border IVB and VIB TM groups of the periodic table. Model (wettability and spreadability) and application experiments (testing of the PTAW-obtained carbide particle−matrix boundaries) were performed. Fe from partially melted steel substrates is active in the liquid NiBSi−TMCs system. It was revealed that the interaction of TMCs with the liquid NiBSi matrix tends to increase with the group number, and from the top to bottom inside individual groups. Particles of IVB TMCs are decomposed by penetration of the liquid along the grain boundaries, whereas those of VIB are decomposed by solubility in the matrix and secondary crystallization. No transition zones formed at the interfacial boundaries of the matrix−IVB group TMCs, unlike in the case of the VIB group. The experimental results are discussed using the data on the TMC electronic structure and the physicochemical properties.

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.

Chemical Bonding and Electronic Structure of the Early Transition Metal Borides: ScB, TiB, VB, YB, ZrB, NbB, LaB, HfB, TaB, and WB

The predissociation thresholds of the early transition metal boride diatomics (MB, M = Sc, Ti, V, Y, Zr, Nb, La, Hf, Ta, W) have been measured using resonant two-photon ionization (R2PI) spectroscopy, allowing for a precise assignment of the bond dissociation energy (BDE). No previous experimental measurements of the BDE exist in the literature for these species. Owing to the high density of electronic states arising from the ground and low-lying separated atom limits in these open d-subshell species, a congested spectrum of vibronic transitions is observed as the energy of the ground separated atom limit is approached. Nonadiabatic and spin-orbit interactions among these states, however, provide a pathway for rapid predissociation as soon as the ground separated atom limit is reached, leading to a sharp decrease in signal to background levels when this limit is reached. Accordingly, the BDEs of the early transition metal borides have been assigned as D₀(ScB) 1.72(6) eV, D₀(TiB) 1.956(16) eV, D₀(VB) 2.150(16) eV, D₀(YB) 2.057(3) eV, D₀(ZrB) 2.573(5) eV, D₀(NbB) 2.989(12) eV, D₀(LaB) 2.086(18) eV, D₀(HfB) 2.593(3) eV, D₀(TaB) 2.700(3) eV, and D₀(WB) 2.730(4) eV. Additional insight into the chemical bonding and electronic structures of these species has been achieved by quantum chemical calculations.

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.

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.

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 sulfides: ScS, YS, TiS, ZrS, HfS, NbS, and TaS

The early transition metal diatomic sulfides, MS, M = Sc, Y, Ti, Zr, Hf, Nb, and Ta, have been investigated using resonant two-photon ionization spectroscopy in the vicinity of their bond dissociation energies (BDEs). Due to the high density of vibronic states in this energy range, the molecular spectra appear quasicontinuous, and when the excitation energy exceeds the ground separated atom limit, excited state decay by dissociation becomes possible. The dissociation process typically occurs so rapidly that the molecule falls apart before a second photon can be absorbed to ionize the species, leading to a sharp drop in ion signal, which is identified as the 0 K BDE. The observed predissociation thresholds yield BDEs of 4.852(10) eV (ScS), 5.391(3) eV (YS), 4.690(4) eV (TiS), 5.660(4) eV (ZrS), 5.780(20) eV (HfS), 5.572(3) eV (NbS), and 5.542(3) eV (TaS). Utilizing thermochemical cycles, the enthalpies of formation, Δ_fH_0K ^o(g), of 182.7(4.3) kJ mol^-1 (ScS), 178.3(4.2) kJ mol^-1 (YS), 293.1(16.7) kJ mol^-1 (TiS), 337.3(8.4) kJ mol^-1 (ZrS), 335.0(6.6) kJ mol^-1 (HfS), 467.0(8.0) kJ mol^-1 (NbS), and 521.5(2.1) kJ mol^-1 (TaS) are obtained. Another thermochemical cycle has been used to combine the previously measured M⁺-S BDEs with the M-S BDEs and atomic ionization energies to obtain the MS ionization energies of 6.44(5) eV (ScS), 6.12(8) eV (YS), 6.78(7) eV (TiS), 6.60(10) eV (ZrS), and 6.88(9) eV (NbS). Using this same cycle, we obtain D₀(Hf⁺-S) = 4.926(20) eV. The bonding trends of the early transition metal sulfides, along with the corresponding selenides, are discussed.

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.

High-Level Ab Initio Predictions for the Ionization Energy, Bond Dissociation Energies, and Heats of Formation of Vanadium Methylidyne Radical and Its Cation (VCH/VCH+)

The ionization energy (IE) of VCH, the 0 K V-CH/VC-H bond dissociation energies (D₀s), and the heats of formation at 0 K (ΔH_f0^°) and 298 K (ΔH_f298^°) for VCH/VCH⁺ are predicted by the wave function-based CCSDTQ/CBS approach. This composite-coupled cluster method includes full quadruple excitations in conjunction with the approximation to the complete basis set (CBS) limit. The contributions of zero-point vibrational energy, core-valence (CV) correlation, spin-orbit coupling, and scalar relativistic corrections are taken into account. The present calculations show that adiabatic IE(VCH) = 6.785 eV and demonstrate excellent agreement with an IE value of 6.774 7 ± 0.000 1 eV measured with two-color laser-pulsed field ionization-photoelectron spectroscopy. The CCSDT and MRCI+Q methods which include CV correlations give the best predictions of harmonic frequencies: ω₂ (ω₂⁺) (bending) = 534 (650) and 564 (641) cm^-1 and the V-CH stretching ω₃ (ω₃⁺) = 835 (827) and 856 (857) cm^-1 compared with the experimental values. In this work, we offer a streamlined CCSDTQ/CBS approach which shows an error limit (≤20 meV) matching with previous benchmarking efforts for reliable IE and D₀ predictions for VCH/VCH⁺. The CCSDTQ/CBS D₀(V⁺-CH) - D₀(V-CH) = -0.012 eV and D₀(VC⁺-H) - D₀(VC-H) = 0.345 eV are in good accord with the experimentally derived values of -0.028 4 ± 0.000 1 and 0.355 9 ± 0.000 1 eV, respectively. The present study has demonstrated that the CCSDTQ/CBS protocol can be readily extended to investigate triatomic molecules containing 3d-metals.

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.

Predissociation Measurements of Bond Dissociation Energies

A fundamental need in chemistry is understanding the chemical bond, for which the most quantitative measure is the bond dissociation energy (BDE). While BDEs of chemical bonds formed from the lighter main group elements are generally well-known and readily calculated by modern computational chemistry, chemical bonds involving the transition metals, lanthanides, and actinides remain computationally extremely challenging. This is due to the simultaneous importance of electron correlation, spin-orbit interaction, and other relativistic effects, coupled with the large numbers of low-lying states that are accessible in systems with open d or f subshells. The development of efficient and accurate computational methods for these species is currently a major focus of the field. An obstacle to this effort has been the scarcity of highly precise benchmarks for the BDEs of M-X bonds. For most of the transition metal, lanthanide, or actinide systems, tabulated BDEs of M-X bonds have been determined by Knudsen effusion mass spectrometric measurements of high-temperature equilibria. The measured ion signals are converted to pressures and activities of the species involved in the equilibrium, and the equilibrium constants are then analyzed using a van't Hoff plot or the third-law method to extract the reaction enthalpy, which is extrapolated to 0 K to obtain the BDE. This procedure introduces errors at every step and ultimately leads to BDEs that are typically uncertain by 2-20 kcal mol^-1 (0.1-1 eV). A second method in common use employs a thermochemical cycle in which the ionization energies of the MX molecule and M atom are combined with the BDE of the M⁺-X bond, obtained via guided ion beam mass spectrometry, to yield the BDE of the neutral, M-X. When accurate values of all three components of the cycle are available, this method yields good results-but only rarely are all three values available. We have recently implemented a new method for the precise measurement of BDEs in molecules with large densities of electronic states that is based on the rapid predissociation of these species as soon as the ground separated atom limit is exceeded. When a sharp predissociation threshold is observed, its value directly provides the BDE of the system. With this method, we are able in favorable cases to determine M-X BDEs to an accuracy of ∼0.1 kcal mol^-1 (0.004 eV). The method is generally applicable to species that have a high density of states at the ground separated atom limit and has been used to measure the BDEs of more than 50 transition metal-main group MX molecules thus far. In addition, a number of metal-metal BDEs have also been measured with this method. There are good prospects for the extension of the method to polyatomic systems and to lanthanide and actinide-containing molecules. These precise BDE measurements provide chemical trends for the BDEs across the transition metal series, as well as crucial benchmarks for the development of efficient and accurate computational methods for the d- and f-block elements.

Bond dissociation energies of FeSi, RuSi, OsSi, CoSi, RhSi, IrSi, NiSi, and PtSi

Resonant two-photon ionization spectroscopy has been used to investigate the spectra of the diatomic late transition metal silicides, MSi, M = Fe, Ru, Os, Co, Rh, Ir, Ni, and Pt, in the vicinity of the bond dissociation energy. In these molecules, the density of vibronic states is so large that the spectra appear quasicontinuous in this energy range. When the excitation energy exceeds the ground separated atom limit, however, a new decay process becomes available-molecular dissociation. This occurs so rapidly that the molecule falls apart before it can absorb another photon and be ionized. The result is a sharp drop to the baseline in the ion signal, which we identify as occurring at the thermochemical 0 K bond dissociation energy, D₀. On this basis, the measured predissociation thresholds provide D₀ = 2.402(3), 4.132(3), 4.516(3), 2.862(3), 4.169(3), 4.952(3), 3.324(3), and 5.325(9) eV for FeSi, RuSi, OsSi, CoSi, RhSi, IrSi, NiSi, and PtSi, respectively. Using thermochemical cycles, the enthalpies of formation of the gaseous MSi molecules are derived as 627(8), 700(10), 799(10), 595(8), 599(8), 636(10), 553(12), and 497(8) kJ/mol for FeSi, RuSi, OsSi, CoSi, RhSi, IrSi, NiSi, and PtSi, respectively. Likewise, combining these results with other data provides the ionization energies of CoSi and NiSi as 7.49(7) and 7.62(7) eV, respectively. Chemical bonding trends among the diatomic transition metal silicides are discussed.

Bond dissociation energies of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi

Predissociation thresholds have been observed in the resonant two-photon ionization spectra of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi. It is argued that because of the high density of electronic states at the ground separated atom limit in these molecules, the predissociation threshold in each case corresponds to the thermochemical bond dissociation energy. The resulting bond dissociation energies are D₀(TiSi) = 2.201(3) eV, D₀(ZrSi) = 2.950(3) eV, D₀(HfSi) = 2.871(3) eV, D₀(VSi) = 2.234(3) eV, D₀(NbSi) = 3.080(3) eV, and D₀(TaSi) = 2.999(3) eV. The enthalpies of formation were also calculated as Δ_f,0KH°(TiSi(g)) = 705(19) kJ mol^-1, Δ_f,0KH°(ZrSi(g)) = 770(12) kJ mol^-1, Δ_f,0KH°(HfSi(g)) = 787(10) kJ mol^-1, Δ_f,0KH°(VSi(g)) = 743(11) kJ mol^-1, Δ_f,0KH°(NbSi(g)) = 879(11) kJ mol^-1, and Δ_f,0KH°(TaSi(g)) = 938(8) kJ mol^-1. Using thermochemical cycles, ionization energies of IE(TiSi) = 6.49(17) eV and IE(VSi) = 6.61(15) eV and bond dissociation energies of the ZrSi^- and NbSi^- anions, D₀(Zr-Si^-) ≤ 3.149(15) eV, D₀(Zr^--Si) ≤ 4.108(20) eV, D₀(Nb-Si^-) ≤ 3.525(31) eV, and D₀(Nb^--Si) ≤ 4.017(39) eV, have also been obtained. Calculations on the possible low-lying electronic states of each species are also reported.

Comparative Study of Nonhybrid Density Functional Approximations for the Prediction of 3d Transition Metal Thermochemistry

The utility of several nonhybrid density functional approximations (DFAs) is considered for the prediction of gas phase enthalpies of formation for a large set of 3d transition metal-containing molecules. Nonhybrid DFAs can model thermochemical values for 3d transition metal-containing molecules with accuracy comparable to that of hybrid functionals. The GAM-generalized gradient approximation (GGA); the TPSS, M06-L, and MN15-L meta-GGAs; and the Rung 3.5 PBE+ΠLDA(s) DFAs all give root-mean-square deviations below that of the widely used B3LYP hybrid. Modern nonhybrid DFAs continue to show utility for transition metal thermochemistry.

Predicting Bond Dissociation Energies of Transition-Metal Compounds by Multiconfiguration Pair-Density Functional Theory and Second-Order Perturbation Theory Based on Correlated Participating Orbitals and Separated Pairs

We study the performance of multiconfiguration pair-density functional theory (MC-PDFT) and multireference perturbation theory for the computation of the bond dissociation energies in 12 transition-metal-containing diatomic molecules and three small transition-metal-containing polyatomic molecules and in two transition-metal dimers. The first step is a multiconfiguration self-consistent-field calculation, for which two choices must be made: (i) the active space and (ii) its partition into subspaces, if the generalized active space formulation is used. In the present work, the active space is chosen systematically by using three correlated-participating-orbitals (CPO) schemes, and the partition is chosen by using the separated-pair (SP) approximation. Our calculations show that MC-PDFT generally has similar accuracy to CASPT2, and the active-space dependence of MC-PDFT is not very great for transition-metal-ligand bond dissociation energies. We also find that the SP approximation works very well, and in particular SP with the fully translated BLYP functional SP-ftBLYP is more accurate than CASPT2. SP greatly reduces the number of configuration state functions relative to CASSCF. For the cases of FeO and NiO with extended-CPO active space, for which complete active space calculations are unaffordable, SP calculations are not only affordable but also of satisfactory accuracy. All of the MC-PDFT results are significantly better than the corresponding results with broken-symmetry spin-unrestricted Kohn-Sham density functional theory. Finally we test a perturbation theory method based on the SP reference and find that it performs slightly worse than CASPT2 calculations, and for most cases of the nominal-CPO active space, the approximate SP perturbation theory calculations are less accurate than the much less expensive SP-PDFT calculations.

Theoretical Study of Low-Lying Electronic States of PtX (X = F, Cl, Br, and I) Including Spin-Orbit Coupling

The low-lying electronic states of platinum ions (Pt(+)) and platinum monohalides (PtX; X = F, Cl, Br, and I) are calculated using the multireference configuration interaction method with relativistic effective core potentials. The spin-orbit coupling is taken into account through the perturbative state-interaction approach. For the Ω states of PtX below 35000 cm(-1), the potential energy curves and the corresponding spectroscopic constants are reported. It is found that the lowest Ω = 3/2 state is the ground one for the four species of PtX. Overall, the theoretical results are in reasonable agreement with the available experimental data.