Electronic structure of diatomic molecules composed of a first-row transition metal and main-group element (h-f)

Structures, simulated photoelectron spectroscopy, and electronic properties of CuASix(A = Sc, Cu, x ≤ 13) clusters: Relatively stable neutral pentagonal bipyramid structures of CuASi5

Structural design and optimization, simulated photoelectron spectroscopy, electronic properties and chemical bond analysis of CuASix(A = Sc, Cu, x ≤ 13) clusters were systematically studied using the PBE scheme to integrate with global search program of ABCluster. Firstly, neutral MS (the most stable structures) of CuASi5 of the basic 1 + 5 + 1 structures (1 metal + 5 silicons + 1 metal atoms) can be found as the basic units for assembling more lager clusters under the condition of neglecting distortions and minor changes. If the Cu atoms in Cu2Six(x ≤ 13) systems was replaced by one Sc atom, the geometries of MS will be reconstructed. Compared with the wheel geometries of Cu2Si12 and Cu2Si13, CuScSi12 and CuScSi13 clusters belong to near-wheel geometries with peripheral metal atoms. The neutral CuScSi5 and Cu2Si5 clusters possess relatively higher stability in all of cluster sizes. A combination of NPA analysis of CuASi5, sp of the Cu atom and spd of the Sc atom hybridizations were crucial to the chemical bonds of A-Si in the neutral CuASi5 clusters. In view of the higher SED value of the Cu2Si5 molecule, chemical bond analysis was carried out using MO, HLg and AdNDP analysis. 18 localized bonds and four delocalized bonds can play a positive role for the relative stabilities of neutral pentagonal bipyramid structures of Cu2Si5. Thus, the Cu2Si5 cluster with a lager HLg(1.80 eV) may be a good candidate for the basic unit of silicon-based semiconductor material assembly.

Wavefunction theory and density functional theory analysis of ground and excited electronic states of TaB and WB

Several low-lying electronic states of TaB and WB molecules were studied using ab initio multireference configuration interaction (MRCI), Davidson corrected MRCI (MRCI+Q), and coupled cluster singles doubles and perturbative triples [CCSD(T)] methods. Their full potential energy curves (PECs), equilibrium electron configurations, equilibrium bond distances (res), dissociation energies (Des), excitation energies (Tes), harmonic vibrational frequencies (ωes), and anharmonicities (ωexes) are reported. The MRCI dipole moment curves (DMCs) of the first 5 electronic states of both TaB and WB are also reported and the equilibrium dipole moment (μ) values are compared with the CCSD(T) μ values. The most stable 13Π (1σ22σ23σ11π3) and 15Δ (1σ22σ23σ11π21δ1) electronic states of TaB lie close in energy with ∼62 kcal mol-1De with respect to the Ta(4F) + B(2P) asymptote. However, spin-orbit coupling effects make the 15Δ0+ state the true ground state of TaB. The ground electronic state of WB (16Π) has the 1σ22σ13σ11π31δ2 electron configuration and is followed by the excited 16Σ+ and 14Δ states. Finally, the MRCI De, re, ωe, and ωexe values of the 13Π state of TaB and 16Π and 14Δ states of WB are used to assess the density functional theory (DFT) errors on a series of exchange-correlation functionals that span multiple-rungs of the Jacob's ladder of density functional approximations (DFA).

Ab initio electronic structure analysis of ground and excited states of HfN0,

High-level ab initio electronic structure analysis of third-row transition metal (TM)-based diatomic species is challenging and has been perpetually lagging. In this work, fourteen and eighteen electronic states of HfN and HfN+ respectively are studied, employing multireference configuration interaction (MRCI) and coupled cluster singles doubles and perturbative triples [CCSD(T)] theories under larger correlation-consistent basis sets. Their potential energy curves (PECs), energetics, and spectroscopic parameters are reported. Core electron correlation effects on their properties are also investigated. Chemical bonding patterns of several low-lying electronic states are introduced based on the equilibrium electron configurations. The ground state of HfN (X2Σ+) has the 1σ22σ23σ11π4 electronic configuration, and the ionization of the 3σ1 electron produces the ground state of HfN+ (X1Σ+). Ground states of both HfN and HfN+ are triple bonded in nature and bear 124.86 and 109.10 kcal mol-1 binding energies with respect to their ground state fragments. The findings of this work agree well with the limited experimental literature available and provide useful reference values for future experimental analysis of HfN and HfN+.

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.

Electronic structure with spin-orbit coupling effect of HfH molecule for laser cooling investigations

The electronic structure, including the spin-orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ - Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission [Formula: see text] , and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.

Reference Vertical Excitation Energies for Transition Metal Compounds

To enrich and enhance the diversity of the quest database of highly accurate excitation energies [Véril, M.; et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with a singlet or doublet ground state containing a fourth-row transition metal (CuCl, CuF, CuH, ScF, ScH, ScO, ScS, TiN, ZnH, ZnO, and ZnS) are considered, and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely, CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In many cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of the CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported.

Diving into the optoelectronic properties of Cu(II) and Zn(II) curcumin complexes: a DFT and wavefunction benchmark

CONTEXT

Curcumin is a popular food additive around the world whose medicinal properties have been known since ancient times. The literature has recently highlighted several biological properties, but besides the health-related usages, its natural yellowish color may also be helpful for light-harvesting applications. This research aims to close a knowledge gap regarding the photophysical description of curcumin and its metallic complexes.

METHODS

We conducted benchmark experiments comparing NEVPT calculations with several DFT functionals (B3LYP, M06-L, M06-2X, CAM-B3LYP, and ωB97X-D) for describing the UV spectra of curcumin and its metallo-derivative, curcumin-copper(II). Once we determined the most suitable functional, we performed tests with different basis sets and conditions, such as solvation and redox state, to identify their impact on excited state properties. These results are also reported for the curcumin-zinc(II) derivative. We found that the accuracy of DFT functionals depends strongly on the nature of curcumin's excitations. Intra-ligand transitions dominate the absorption spectra of the complexes. Curcumin absorption is marginally affected by solvation and chelation, but when combined with redox processes, they may result in significant modifications. This is because copper cation changes its coordination geometry in response to redox conditions, changing the spectrum. We found that, compared to a NEVPT reference, B3LYP is the best functional for a general description of the compounds, despite not being appropriate for charge transfer transitions. M06-L was the best for LMCT transitions. However, compared with NEVPT2 and PNO-LCCSD(T)-F12 results, no functional achieved acceptable accuracy for MLCT transitions.

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.

Structural evolution and electronic properties of neutral and anionic TiASil (A = Sc, Ti; l ≤ 12): relatively stable TiASi4 as a structural unit

Molecular orbitals (MO) and the HOMO–LUMO energy gaps (HLgs) of neutral TiASi4 clusters (A = Sc, Ti).

Applying Generalized Variational Principles to Excited-State-Specific Complete Active Space Self-consistent Field Theory

We employ a generalized variational principle to improve the stability, reliability, and precision of fully excited-state-specific complete active space self-consistent field theory. Compared to previous approaches that similarly seek to tailor this ansatz's orbitals and configuration interaction expansion for an individual excited state, we find the present approach to be more resistant to root flipping and better at achieving tight convergence to an energy stationary point. Unlike state-averaging, this approach allows orbital shapes to be optimal for individual excited states, which is especially important for charge-transfer states and some doubly excited states. We demonstrate the convergence and state-targeting abilities of this method in LiH, ozone, and MgO, showing in the latter that it is capable of finding three excited-state energy stationary points that no previous method has been able to locate.

Gaseous transport properties of the ground and excited Cr, Co and Ni cations in He: Ab initio study of electronic state chromatography

The electronic state chromatography (ESC) effect allows the differentiation of ions in their ground and metastable states by their gaseous mobilities in the limit of low electrostatic fields. It is investigated here by means of accurate transport calculations with ab initio ion-atom potentials for the Cr, Co and Ni cations in He buffer gas near room temperature. The values for the open-shell ions in degenerate states are shown to be well approximated by using the single isotropic interaction potential. Minimalistic implementation of the multireference configuration interaction (MRCI) method is enough to describe the zero-field transport properties of metastable ions in the 3dm-14s configuration, such as Cr+(a6D), Co+(a5F) and Ni+(4F), due to their weak and almost isotropic interaction with He atom and the low sensitivity of the measured mobilities to the potential well region. By contrast, interactions involving the ions in the ground 3dm states, such as Cr+(a6S), Co+(a3F) and Ni+(2D), are strong and anisotropic; the MRCI potentials poorly describe their transport coefficients. Even the coupled cluster with singles, doubles and non-iterative triples [CCSD(T)] approach taking into account vectorial spin-orbit coupling may not be accurate enough, as shown here for Ni+(2D). The sensitivity of ion mobility and the ESC effect to interaction potentials, similarities in ion-He interactions of the studied ions in distinct configurations, accuracy and possible improvements of the ab initio schemes, and control of the ESC effect by macroscopic parameters are discussed. Extensive sets of improved interaction potentials and transport data are generated.

First detection and analysis of an electronic spectrum of vanadium hydride: The D5Π-X5Δ (0,0) band

The D5Π-X5Δ (0,0) band of vanadium hydride at 654 nm has been recorded by laser excitation spectroscopy and represents the first analyzed spectrum of VH in the gas phase. The molecules were generated using a hollow cathode discharge source, with laser-induced fluorescence detected via the D5Π-A5Π (0,0) transition. All five main (ΔΩ = ΔΛ) subbands were observed as well as with several satellite ones, which together create a rather complex and overlapped spectrum covering the region 15180-15500 cm-1. The D5Π state displays the effects of three strong local perturbations, which are likely caused by interactions with high vibrational levels of the B5Σ- and c3Σ- states, identified in a previous multiconfigurational self-consistent field study by Koseki et al. [J. Phys. Chem. A 108, 4707 (2004)]. Molecular constants describing the X5Δ, A5Π, and D5Π states were determined in three separate least-squares fits using effective Hamiltonians written in a Hund's case (a) basis. The fine structure of the ground state is found to be consistent with its assignment as a σπ2δ, 5Δ electronic state. The fitted values of its first-order spin-orbit and rotational constants in the ground state are A = 36.5378 cm-1 and B = 5.7579 cm-1, the latter of which yields a bond length of R0 = 1.7212(2) Å. This experimental value is in good agreement with previous computational studies of the molecule and fits well within the overall trend of decreasing bond length across the series of 3d transition metal monohydrides.

Functional-Based Description of Electronic Dynamic and Strong Correlation: Old Issues and New Insights

Approximate functionals in Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT) have advantages in dealing with dynamic correlation and strong correlation, respectively; their combination can benefit from complementarity while suffering from the problem of correlation double-counting. Herein, a short-range corrected reduced density matrix (1-RDM) functional is developed to take advantage of the functionals in KS-DFT and RDMFT without double-counting. The resulting functional, denoted as ωP22, outperforms other 1-RDM functionals for the tests of thermochemistry, nonbonded interactions, and bond dissociation energy. In particular, ωP22 shows much less systematic error for systems involving fractional spins, and it can properly predict the energies at both equilibrium and dissociated distances for different single and multiple bonds, which cannot be achieved by commonly used KS-DFT and RDMFT functionals. Therefore, ωP22 is demonstrated effective in balance handling dynamic and strong correlation, and the advances in this work would create new possibilities for the development and application of approximate functionals.

Theoretical Electronic Structure with a Feasibility Study of Laser Cooling of LaNa Molecule with Spin Orbit Effect

The electronic structure with the spin orbit effect of the molecule LaNa has been studied in the present work using the Multi-Reference Configuration Interaction MRCI calculations including Davidson correction (+Q)....

Photoelectron velocity-map imaging spectroscopy of nickel carbide: Examination of the low-lying electronic states

The photoelectron detachment of nickel carbide anion has been characterized using the photoelectron velocity-map imaging spectroscopy, allowing for a precise assignment of the electron affinity, vibrational frequencies, energy spacing and...

Experiment and Theory Clarify: Sc+ Receives One Oxygen Atom from SO2 to Form ScO+, which Proves to be a Catalyst for the Hidden Oxygen-Exchange with SO2

Using Fourier‐transform ion cyclotron resonance mass spectrometry, it was experimentally determined that Sc⁺ in the highly diluted gas phase reacts with SO₂ to form ScO⁺ and SO. By ¹⁸O labeling, ScO⁺ was shown to play the role of a catalyst when further reacting with SO₂ in a Mars‐van Krevelen‐like (MvK) oxygen exchange process, where a solid catalyst actively reacts with the substrate but emerges apparently unchanged at the end of the cycle. High‐level quantum chemical calculations confirmed that the multi‐step process to form ScO⁺ and SO is exoergic and that all intermediates and transition states in between are located energetically below the entrance level. The reaction starts from the triplet surface; although three spin‐crossing points with minimal energy have been identified by computational means, there is no evidence that a two‐state scenario is involved in the course of the reaction, by which the reactants could switch from the triplet to the singlet surface and back. Pivotal to the oxygen exchange reaction of ScO⁺ with SO₂ is the occurrence of a highly symmetric four‐membered cyclic intermediate by which two oxygen atoms become equivalent.

Quantum chemistry calculations of the growth patterns, simulated photoelectron spectra, and electronic properties of LaASil (A = Sc, Y, La; l ≤ 10) compounds and their anions

The growth patterns, simulated photoelectron spectra, and electronic properties of LaASi_l (A = Sc, Y, and La; l ≤ 10) compounds and their anions were studied via quantum chemistry calculations using the Perdew-Burke-Ernzerhof (PBE) method and unprejudiced structural searching software ABCluster. The results revealed that the growth patterns of the most stable structures of neutral and anionic LaASi_l showed an adsorptive mode. The lowest-energy structures (LESs) of the LaASi_l (l ≤ 7) clusters were similar, except for those of anionic LaYSi₄^- and LaYSi₅^- and neutral LaScSi₇. Additionally, we investigated and calculated the photoelectron spectra, vertical detachment energies, adiabatic electron affinities, relative stability, charge transfer, magnetic moment, and chemical bond analysis of the LaASi_l ground-state structures. The La₂Si_l clusters exhibited higher stability than the LaYSi_l and LaScSi_l systems owing to their higher dissociation energies (DEs). The DEs of the LESs in the LaASi₃ molecule are higher than those of other clusters. Thus, the LaASi₃ cluster shows potential as a building framework for Si-based cluster materials with good stability. The natural population analysis data and chemical bond analysis results showed that the spd hybridization of the orbitals of the metal atoms in the LaASi_l system occurred. Except for the LaScSi₉ and LaScSi₁₀ clusters, the neutral LaASi_l compounds transform into the corresponding anions when an extra electron is accepted by the Si clusters.

Bonding, Thermodynamics, and Dissociation Dynamics of NiO+ and NiS+ Determined by Photofragment Imaging and Theory

We use photofragment ion imaging and ab initio calculations to determine the bond strength and photodissociation dynamics of the nickel oxide (NiO⁺) and nickel sulfide (NiS⁺) cations. NiO⁺ photodissociates broadly from 20350 to 32000 cm^-1, forming ground state products Ni⁺(²D) + O(³P) below ∼29000 cm^-1. Above this energy, Ni⁺(⁴F) + O(³P) products become accessible and dominate over the ground state channel. In certain images, product spin-orbit levels are resolved, and spin-orbit propensities are determined. Image anisotropy and the results of MRCI calculations suggest NiO⁺ photodissociates via a 3 ⁴Σ^- ← X ⁴Σ^- transition above the Ni⁺(⁴F) threshold and via 3 ⁴Σ^-, 2 ⁴Σ^-, and/or 2 ⁴Π and 3 ⁴Π excited states below the ⁴F threshold. The photodissociation spectrum of NiS⁺ from 19900 to 23200 cm^-1 is highly structured, with ∼12 distinct vibronic peaks, each containing underlying substructure. Above 21600 cm^-1, the Ni⁺(²D_5/2) + S(³P) and Ni⁺(²D_3/2) + S(³P) product spin-orbit channels compete, with a branching ratio of ∼2:1. At lower energy, Ni⁺(²D_5/2) is formed exclusively, and S(³P₂) and S(³P₁) spin-orbit channels are resolved. MRCI calculations predict the ground state of NiS⁺ to be one of two nearly degenerate states, the 1 ⁴Σ^- and 1 ⁴Δ. Based on images and spectra, the ground state of NiS⁺ is assigned as ⁴Δ_7/2, with the 1 ⁴Σ_3/2^- and 1 ⁴Σ_1/2^- states 81 ± 30 and 166 ± 50 cm^-1 higher in energy, respectively. The majority of the photodissociation spectrum is assigned to transitions from the 1 ⁴Δ state to two overlapping, predissociative excited ⁴Δ states. Our D₀ measurements for NiO⁺ (D₀ = 244.6 ± 2.4 kJ/mol) and NiS⁺ (D₀ = 240.3 ± 1.4 kJ/mol) are more precise and closer to each other than previously reported values. Finally, using a recent measurement of D₀(NiS), we derive a more precise value for IE (NiS): 8.80 ± 0.02 eV (849 ± 1.7 kJ/mol).

Low-Lying Electronic States of the Nickel Dimer

The generalized Van Vleck second order multireference perturbation theory (GVVPT2) method was used to investigate the low-lying electronic states of Ni₂. Because the nickel atom has an excitation energy of only 0.025 eV to its first excited state (the least in the first row of transition elements), Ni₂ has a particularly large number of low-lying states. Full potential energy curves (PECs) of more than a dozen low-lying electronic states of Ni₂, resulting from the atomic combinations ³F₄ + ³F₄ and ³D₃ + ³D₃, were computed. In agreement with previous theoretical studies, we found the lowest lying states of Ni₂ to correlate with the ³D₃ + ³D₃ dissociation limit, and the holes in the d-subshells were in the subspace of delta orbitals (i.e., the so-dubbed δδ-states). In particular, the ground state was determined as X ¹Γ_g and had spectroscopic constants: bond length (R_e) = 2.26 Å, harmonic frequency (ω_e) = 276.0 cm⁻¹, and binding energy (D_e) = 1.75 eV; whereas the 1 ¹Σ_g⁺ excited state (with spectroscopic constants: R_e = 2.26 Å, ω_e = 276.8 cm⁻¹, and D_e = 1.75) of the ³D₃ + ³D₃ dissociation channel lay at only 16.4 cm⁻¹ (0.002 eV) above the ground state at the equilibrium geometry. Inclusion of scalar relativistic effects through the spin-free exact two component (sf-X2C) method reduced the bond lengths of both of these two states to 2.20 Å, and increased their binding energies to 1.95 eV and harmonic frequencies to 296.0 cm⁻¹ for X ¹Γ_g and 297.0 cm⁻¹ for 1 ¹Σ_g⁺. These values are in good agreement with experimental values of R_e = 2.1545 ± 0.0004 Å, ω_e = 280 ± 20 cm⁻¹, and D₀ = 2.042 ± 0.002 eV for the ground state. All states considered within the ³F₄ + ³F₄ dissociation channel proved to be energetically high-lying and van der Waals-like in nature. In contrast to most previous theoretical studies of Ni₂, full PECs of all considered electronic states of the molecule were produced.

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.

A combined photoelectron-imaging spectroscopic and theoretical investigation on the electronic structure of the VO2H anion

The electronic structure and vibrational spectrum of the VO2H anion are explored by combining photoelectron imaging spectroscopy and density functional theoretical (DFT) calculations. The electron affinity (EA) of VO2H is determined to be 1.304 ± 0.030 eV from the vibrationally resolved photoelectron spectrum acquired at 1.52 eV (814 nm). The anisotropy parameter (β) for the EA defined peak is measured to be 1.63 ± 0.10, indicating that it is the 17a' (4s orbital of the vanadium atom) electron attachment leading to the formation of the ground state of the VO2H anion. The vibrational fundamentals ν 1, ν 3, ν 4 and ν 5 are obtained for the neutral ground state. Experimental assignments are confirmed by energies from electronic structure calculations and Franck-Condon (FC) spectral simulations. These simulations support assigning the anion ground state as the results obtained from the B3LYP method. In addition, the molecular orbitals and bonding involved in the anionic VO2H cluster are also examined based on the present theoretical calculations.

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.

A full configuration interaction quantum Monte Carlo study of ScO, TiO, and VO molecules

Accurate ab initio calculations of 3d transition metal monoxide molecules have attracted extensive attention because of their relevance in physical and chemical science as well as theoretical challenges in treating strong electron correlation. Meanwhile, recent years have witnessed the rapid development of the full configuration interaction quantum Monte Carlo (FCIQMC) method to tackle electron correlation. In this study, we carry out FCIQMC simulations to ScO, TiO, and VO molecules and obtain accurate descriptions of 13 low-lying electronic states (ScO ²Σ⁺, ²Δ, ²Π; TiO ³Δ, ¹Δ, ¹Σ⁺, ³Π, ³Φ; VO ⁴Σ^-, ⁴Φ, ⁴Π, ²Γ, ²Δ), including states that have significant multi-configurational character. The FCIQMC results are used to assess the performance of several other wave function theory and density functional theory methods. Our study highlights the challenging nature of the electronic structure of transition metal oxides and demonstrates FCIQMC as a promising technique going forward to treat more complex transition metal oxide molecules and materials.

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.

What Levels of Coupled Cluster Theory Are Appropriate for Transition Metal Systems? A Study Using Near-Exact Quantum Chemical Values for 3d Transition Metal Binary Compounds

Transition metal compounds are traditionally considered to be challenging for standard quantum chemistry approximations like coupled cluster (CC) theory, which are usually employed to validate lower level methods like density functional theory (DFT). To explore this issue, we present a database of bond dissociation energies (BDEs) for 74 spin states of 69 diatomic species containing a 3d transition metal atom and a main group element, in the moderately sized def2-SVP basis. The presented BDEs appear to have an (estimated) 3σ error less than 1 kJ/mol relative to the exact solutions to the nonrelativistic Born-Oppenheimer Hamiltonian. These benchmark values were used to assess the performance of a wide range of standard single reference CC models, as the results should be beneficial for understanding the limitations of these models for transition metal systems. We find that interactions between metals and monovalent ligands like hydride and fluoride are well described by CCSDT. Similarly, CCSDTQ appears to be adequate for bonds between metals and nominally divalent ligands like oxide and sulfide. However, interactions with polyvalent ligands like nitride and carbide are more challenging, with even CCSDTQ(P)_Λ yielding errors on the scale of a few kJ/mol. We also find that many perturbative and iterative approximations to higher order terms either yield disappointing results or actually worsen the performance relative to the baseline low level CC method, indicating that complexity does not always guarantee accuracy.

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.

Hydrogen Activation by Silica-Supported Metal Ion Catalysts: Catalytic Properties of Metals and Performance of DFT Functionals

Single-site heterogeneous catalysts (SSHC) have received increasing attention due to their well-defined active sites and potentially high specific activity. Detailed computational studies were carried out on a set of potential SSHC's, i.e., silica-supported metal ions, to investigate the reactivity of these catalysts with H₂ as well as to evaluate the performance of density functional theory (DFT) methods in conjunction with triple-ζ quality basis sets (i.e., cc-pVTZ) on reaction energetics. The ions considered include 4d and 5d metals as well as several post-transition metal ions. A representative cluster model of silica is used to calculate reaction free energies of the metal hydride formation that results from the heterolytic cleavage of H₂ on the M-O bond. The hydride formation free energy is previously shown to be strongly correlated with the catalytic activity of such catalysts for alkene hydrogenation. ONIOM calculations (CCSD(T)//MP2) are used to assess the accuracy and reliability of the MP2 results and it is found that MP2 is a suitable level of theory for gauging the performance of DFT functionals. The performance of various DFT functionals is assessed relative to MP2 results and it is found that the wB97xd and PBE0 functionals have the lowest standard deviation (STD) value while the MN12SX and PBE functionals have the lowest mean absolute deviation (MAD) values. The B3LYP functional is shown to have similar MAD and STD values as the top performing functionals. Potential active SSHC's for exergonic hydrogen activation predicted in this study include mostly late and post transition metal ions, i.e., Au³⁺, Pd²⁺, Pt⁴⁺, Pd⁴⁺, Ir⁴⁺, Hg²⁺, Rh³⁺, Pb⁴⁺, Tl³⁺, In³⁺, Ir³⁺, Os⁴⁺, Cd²⁺, Ru²⁺, and Ga³⁺. This study provides important guidance to future computational studies of such catalyst systems.

Spin-Unrestricted Self-Energy Embedding Theory

We present a new theoretical approach, unrestricted self-energy embedding theory (USEET), that is a Green's function embedding theory used to study problems in which an open, embedded system exchanges electrons with the environment. USEET has a high potential to be used in studies of strongly correlated systems with an odd number of electrons and open shell systems such as transition metal complexes important in inorganic chemistry. In this paper, we show that USEET results agree very well with common quantum chemistry methods while avoiding typical bottlenecks present in these methods.

Towards a quantum chemical protocol for the prediction of rovibrational spectroscopic data for transition metal molecules: Exploration of CuCN, CuOH, and CuCCH

High accuracy electronic structure computations for small transition metal-containing molecules have been a long term challenge. Due to coupling between electronic and nuclear wave functions, even experimental/theoretical identification of the ground electronic state requires tremendous efforts. Quartic force fields (QFFs) are effective ab initio tools for obtaining reliable anharmonic spectroscopic properties. However, the method that employs complete basis set limit extrapolation ("C"), consideration of core electron correlation ("cC"), and inclusion of scalar relativity ("R") to produce the energy points on the QFF, the composite CcCR methodology, has not yet been utilized to study inorganic spectroscopy. This work takes the CcCR methodology and adapts it to test whether such an approach is conducive for the closed-shell, copper-containing molecules CuCN, CuOH, and CuCCH. Gas phase rovibrational data are provided for all three species in their ground electronic states. Equilibrium geometries and many higher-order rovibrational properties show good agreement with earlier studies. However, there are notable differences, especially in computation of fundamental vibrational frequencies. Even with further additive corrections for the inner core electron correlation and coupled cluster with full single, double, and triple substitutions (CCSDT), the differences are still larger than expected indicating that more work should follow for predicting rovibrational properties of transition metal molecules.

Shape and energy consistent pseudopotentials for correlated electron systems

A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy consistent correlated electron pseudopotentials (eCEPPs) are constructed for H, Li-F, Sc-Fe, and Cu. Their accuracy is quantified by comparing the relaxed molecular geometries and dissociation energies which they provide with all electron results, with all quantities evaluated using coupled cluster singles, doubles, and triples calculations. Errors inherent in the pseudopotentials are also compared with those arising from a number of approximations commonly used with pseudopotentials. The eCEPPs provide a significant improvement in optimised geometries and dissociation energies for small molecules, with errors for the latter being an order-of-magnitude smaller than for Hartree-Fock-based pseudopotentials available in the literature. Gaussian basis sets are optimised for use with these pseudopotentials.

Modeling of Manganese Atom and Dimer Isolated in Solid Rare Gases: Structure, Stability, and Effect on Spin Coupling

Structures and energies of the trapping sites of manganese atom and dimer in solid Ar, Kr, and Xe are investigated within the classical model, which balances local distortion and long-range crystal order of the host and provides a means to estimate the relative site stabilities. The model is implemented with the additive pairwise potential field based on the ab initio and best empirical interatomic potential functions. In agreement with experiment, Mn single substitution (SS) and tetrahedral vacancy (TV) occupation are identified as stable for Ar and Kr, whereas the SS site is only found for Xe. Stable trapping sites of the weakly bound Mn₂ dimer are shown to be the mergers of SS and/or TV atomic sites. For Ar, (SS + SS) and (TV + TV) sites are close in energy, whereas (SS + TV) site lies higher. The (SS + SS) accommodation is identified as the only stable site in Kr and Xe at low energies. The results are compared with the resonance Raman, electron spin resonance, and absorption spectroscopy data. Reproducing the numbers of stable sites, the calculations tend to underestimate the matrix effect on the dimer vibrational frequency and spin-spin coupling constant. Nonetheless, the level of agreement is found to be informative for tentative assignments of the complex features seen in Mn₂ matrix isolation spectroscopy.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

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.

Calibrating Reaction Enthalpies: Use of Density Functional Theory and the Correlation Consistent Composite Approach in the Design of Photochromic Materials

Acquisition of highly accurate energetic data for chromium-containing molecules and various chromium carbonyl complexes is a major step toward calibrating bond energies and thermal isomerization energies from mechanisms for Cr-centered photochromic materials being developed in our laboratories. The performance of six density functionals in conjunction with seven basis sets, utilizing Gaussian-type orbitals, has been evaluated for the calculation of gas-phase enthalpies of formation and enthalpies of reaction at 298.15 K on various chromium-containing systems. Nineteen molecules were examined: Cr(CO)₆, Cr(CO)₅, Cr(CO)₅(C₂H₄), Cr(CO)₅(C₂ClH₃), Cr(CO)₅(cis-(C₂Cl₂H₂)), Cr(CO)₅(gem-(C₂Cl₂H₂)), Cr(CO)₅(trans-(C₂Cl₂H₂)), Cr(CO)₅(C₂Cl₃H), Cr(CO)₅(C₂Cl₄), CrO₂, CrF₂, CrCl₂, CrCl₄, CrBr₂, CrBr₄, CrOCl₂, CrO₂Cl₂, CrOF₂, and CrO₂F₂. The performance of 69 density functionals in conjunction with a single basis set utilizing Slater-type orbitals (STO) and a zeroth-order relativistic approximation was also evaluated for the same test set. Values derived from density functional theory were compared to experimental values where available, or values derived from the correlation consistent composite approach (ccCA). When all reactions were considered, the functionals that exhibited the smallest mean absolute deviations (MADs, in kcal mol^-1) from ccCA-derived values were B97-1 (6.9), VS98 (9.0), and KCIS (9.4) in conjunction with quadruple-ζ STO basis sets and B97-1 (9.3) in conjunction with cc-pVTZ basis sets. When considering only the set of gas-phase reaction enthalpies (Δ_rH°_gas), the functional that exhibited the smallest MADs from ccCA-derived values were B97-1 in conjunction with cc-pVTZ basis sets (9.1) and PBEPBE in conjunction with polarized valence triple-ζ basis set/effective core potential combination for Cr and augmented and multiple polarized triple-ζ Pople style basis sets (9.5). Also of interest, certainly because of known cancellation of errors, PBEPBE with the least-computationally expensive basis set combination considered in the present study (valence double-ζ basis set/effective core potential combination for Cr and singly-polarized double-ζ Pople style basis sets) also provided reasonable accuracy (11.1). An increase in basis set size was found to have an improvement in accuracy for the best performing functional (B97-1).