High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Titanium Oxides and Their Cations (TiOn/TiOn+, n = 1 and 2)

A larger basis set describes atomization energy core-valence correction better than a higher-order coupled-cluster method

The accuracy of coupled-cluster methods for the computation of core-valence correction to atomization energy was assessed. Truncation levels up to CCSDTQP were considered together with (aug-)cc-pwCVnZ (n = D, T, Q, 5) basis sets and three different extrapolation techniques (canonical and flexible Helgaker formula and Riemann zeta function extrapolation). With the exception of CCSD, a more accurate correction can be obtained from a larger basis set using a lower-level coupled-cluster method, and not vice versa. For the CCSD(T) level, it also implies faster computations with modern codes. We also discussed the importance of moving to higher-order or all-electron methods for geometry optimizations. The present study provides the general knowledge needed for the most accurate state-of-the-art computations.

Ferrocene/ferrocenium, cobaltocene/cobaltocenium and nickelocene/nickelocenium: from gas phase ionization energy to one-electron reduction potential in solvated medium

We propose a theoretical procedure for accurate determination of reduction potentials for three metallocene couples, Cp₂M⁺/Cp₂M, where M = Fe, Co and Ni. This procedure first computes the gas phase ionization energy (IE) using the explicitly correlated CCSD(T)-F12 method and includes the zero-point energy correction, core-valence electronic correlation, and relativistic and spin-orbit coupling effects. By means of Born-Haber thermochemical cycle, the one-electron reduction potential is obtained as the sum of the gas phase IE and the corresponding Gibbs free energies of solvation (ΔG_solv) for both the neutral and cationic species. Among the three solvent models (PCM, SMD and uESE) investigated here, it turns out that only the SMD model (computed at the DFT level) gives the best estimation of the value for "ΔG_solv(cation) - ΔG_solv(neutral)" and thus, combining with the accurate IE values, the theoretical protocol is capable of yielding reliable values (in V) for , and . These predictions compare favorably with the available experimental data (in V): , , and . We show that our theoretical procedure is reliable for accurate reduction potential predictions of Cp₂Fe⁺/Cp₂Fe, Cp₂Co⁺/Cp₂Co and Cp₂Ni⁺/Cp₂Ni redox couples in aqueous and non-aqueous media; the maximum absolute deviation is as small as ≈120 mV, which outperforms those of the existing theoretical methods.

Near-thermo-neutral electron recombination of titanium oxide ions

While the dissociative recombination (DR) of ground-state molecular ions with low-energy free electrons is generally known to be exothermic, it has been predicted to be endothermic for a class of transition-metal oxide ions. To understand this unusual case, the electron recombination of titanium oxide ions (TiO⁺) with electrons has been experimentally investigated using the Cryogenic Storage Ring. In its low radiation field, the TiO⁺ ions relax internally to low rotational excitation (≲100 K). Under controlled collision energies down to ∼2 meV within the merged electron and ion beam configuration, fragment imaging has been applied to determine the kinetic energy released to Ti and O neutral reaction products. Detailed analysis of the fragment imaging data considering the reactant and product excitation channels reveals an endothermicity for the TiO⁺ dissociative electron recombination of (+4 ± 10) meV. This result improves the accuracy of the energy balance by a factor of 7 compared to that found indirectly from hitherto known molecular properties. Conversely, the present endothermicity yields improved dissociation energy values for D₀(TiO) = (6.824 ± 0.010) eV and D₀(TiO⁺) = (6.832 ± 0.010) eV. All thermochemistry values were compared to new coupled-cluster calculations and found to be in good agreement. Moreover, absolute rate coefficients for the electron recombination of rotationally relaxed ions have been measured, yielding an upper limit of 1 × 10^-7 cm³ s^-1 for typical conditions of cold astrophysical media. Strong variation of the DR rate with the TiO⁺ internal excitation is predicted. Furthermore, potential energy curves for TiO⁺ and TiO have been calculated using a multi-reference configuration interaction method to constrain quantum-dynamical paths driving the observed TiO⁺ electron recombination.

High-Level Theoretical Study of the C1Π States of GaCl, GaBr, InCl, and InBr

For the first singlet excited states C¹Π of IIIA group monohalides GaCl, GaBr, InCl, and InBr, a very shallow potential well may exist in the flat potential energy curve, which poses a challenge to the theoretical accuracy. In this study, high-level theoretical calculations have been performed through the Feller-Peterson-Dixon composite approach to study the C¹Π states, and the obtained spectroscopic constants agree well with the known experimental ones. It is found that the C¹Π states are sensitive to the size of basis functions, spin-orbit coupling, and strong correlations mainly due to triple excitations. The final results show that the C¹Π states of GaCl and InCl are quasi-bound with one (v' = 0) and four (v' = 0-3) vibrational levels, respectively, being consistent with the experimental findings, whereas the C¹Π states of GaBr and InBr are repulsive. Our conclusions deny the existence of higher vibrational levels v' = 1 for GaCl, v' > 3 for InCl, and v' ≥ 0 for InBr in previous experimental and theoretical studies of C¹Π.

A Novel Hybrid Point Defect of Oxygen Vacancy and Phosphorus Doping in TiO2 Anode for High-Performance Sodium Ion Capacitor

Although sodium ion capacitors (SICs) are considered as one of the most promising electrochemical energy storage devices (organic electrolyte batteries, aqueous batteries and supercapacitor, etc.) due to the combined merits of battery and capacitor, the slow reaction kinetics and low specific capacity of anode materials are the main challenges. Point defects including vacancies and heteroatoms doping have been widely used to improve the kinetics behavior and capacity of anode materials. However, the interaction between vacancies and heteroatoms doping have been seldomly investigated. In this study, a hybrid point defects (HPD) engineering has been proposed to synthesize TiO₂ with both oxygen vacancies (OVs) and P-dopants (TiO₂/C-HPD). In comparison with sole OVs or P-doping treatments, the synergistic effects of HPD on its electrical conductivity and sodium storage performance have been clarified through the density functional theory calculation and sodium storage characterization. As expected, the kinetics and electronic conductivity of TiO₂/C-HPD3 are significantly improved, resulting in excellent rate performance and outstanding cycle stability. Moreover, the SICs assembled from TiO₂/C-HPD3 anode and nitrogen-doped porous carbon cathode show outstanding power/energy density, ultra-long life with good capacity retention. This work provides a novel point defect engineering perspective for the development of high-performance SICs electrode materials.

Ionization Energies and Cationic Bond Dissociation Energies of RuB, RhB, OsB, IrB, and PtB

Two-photon ionization thresholds of RuB, RhB, OsB, IrB, and PtB have been measured using resonant two-photon ionization spectroscopy in a jet-cooled molecular beam and have been used to derive the adiabatic ionization energies of these molecules. From the measured two-photon ionization thresholds, IE(RuB) = 7.879(9) eV, IE(RhB) = 8.234(10) eV, IE(OsB) = 7.955(9) eV, IE(IrB) = 8.301(15) eV, and IE(PtB) = 8.524(10) eV have been assigned. By employing a thermochemical cycle, cationic bond dissociation energies of these molecules have also been derived, giving D0(Ru+-B) = 4.297(9) eV, D0(Rh+-B) = 4.477(10) eV, D0(Os-B+) = 4.721(9) eV, D0(Ir-B+) = 4.925(18) eV, and D0(Pt-B+) = 5.009(10) eV. The electronic structure of the resulting cationic transition metal monoborides (MB+) have been elucidated using quantum chemical calculations. Periodic trends of the MB+ molecules and comparisons to their neutral counterparts are discussed. The possibility of quadruple chemical bonds in all of these cationic transition metal monoborides is also discussed.

High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Vanadium Methylidene, Vanadium Methyl Species, and Their Cations (VCH2/VCH2+, VCH3/VCH3+)

The ionization energies of VCH₂ and VCH₃, the various 0 K bond dissociation energies (D₀s) in their neutrals and cations, and their respective heats of formation at 0 and 298 K are computed by the single-reference, wave function-based CCSDTQ/CBS procedure. The core of the composite method is the approximation to the complete basis set (CBS) limit at the coupled cluster (CC) level which includes up to full quadruple excitations. The zero-point vibrational energy, core-valence correlation, spin-orbit coupling, and scalar relativistic effects have their contributions incorporated in an additive manner. For the species in the current study, this protocol requires geometry optimizations and harmonic frequency calculations practically no higher than the CCSD(T)/aug-cc-pwCVTZ and CCSD(T)/aug-cc-pVTZ levels, respectively. The present calculations successfully predict D₀(V⁺-CH₃) = 2.126 eV and D₀(V⁺-CH₂) = 3.298 eV in remarkable agreement with the data recently measured by a spin-orbit state selected V⁺ + CH₄ collision experiment (Phys. Chem. Chem. Phys. 2021, 23, 273-286). The good accord encourages the use of CCSDTQ/CBS protocol in thermochemical predictions of various feasible product channels identified in methane activation by transition metal species.

Ab Initio Calculations on Sequential Reactions of Nitric Oxide with Titanium Ions in the Gas Phase

Potential energy surfaces of sequential reactions of NO with Ti⁺ ion in the gas phase were investigated for various spin multiplicities using the coupled-cluster and the multireference configuration interaction methods. The mechanisms of Ti⁺ reactions with up to four NO molecules were fully determined, with all transition-state structures being found by relaxed surface scans and confirmed by the intrinsic reaction coordinate (IRC) calculations. The reaction mechanisms are consistent with the products observed in mass spectrometric experiments. In the first reaction, the nitrogen atom and TiO⁺ ion are produced with intersystem crossings for singlet and triplet states. The OTi(NO)⁺ complex is formed in the second reaction, and the third reaction involves N-N bond formation, yielding the N₂O molecule and TiO₂⁺ ion. The fourth NO molecule reacts with the TiO₂⁺ ion in an electron-transfer reaction to produce final products TiO₂ and NO⁺. The coupled-cluster relative energies were used as a reference to evaluate the overall performance of common density functionals for this particular reaction.

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.

Defect-Assisted Selective Surface Phosphorus Doping to Enhance Rate Capability of Titanium Dioxide for Sodium Ion Batteries

Phosphorus doping is an effective strategy to simultaneously improve the electronic conductivity and regulate the ionic diffusion kinetics of TiO₂ being considered as anode materials for sodium ion batteries. However, efficient phosphorus doping at high concentration in well-crystallized TiO₂ nanoparticles is still a big challenge. Herein, we propose a defect-assisted phosphorus doping strategy to selectively engineer the surface structure of TiO₂ nanoparticles. The reduced TiO_2-x shell layer that is rich in oxygen defects and Ti³⁺ species precisely triggered a high concentration of phosphorus doping (∼7.8 at. %), and consequently a TiO₂@TiO_2-x-P core@shell architecture was produced. Comprehensive characterizations and first-principle calculations proved that the surface-functionalized TiO_2-x-P thin layer endowed the TiO₂@TiO_2-x-P with substantially enhanced electronic conductivity and accelerated Na ion transportation, resulting in great rate capability (167 mA h g^-1 at 10 000 mA g^-1) and stable cycling (99% after 5000 cycles at 10 A g^-1). Combining in/ex situ X-ray diffraction with ex situ electron spin resonance clearly demonstrated the high reversibility and robust mechanical behavior of TiO₂@TiO_2-x-P upon long-term cycling. This work provides an interesting and effective strategy for precise heteroatoms doping to improve the electrochemical performance of nanoparticles.

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.