On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies

Basis Set Extrapolation from the Vanishing Counterpoise Correction Condition

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters.

Targeting spectroscopic accuracy for dispersion bound systems from ab initio techniques: Translational eigenstates of Ne@C70

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Energetic and Electronic Properties of UO0/± and UF0/±

High-level electronic structure calculations were conducted to examine the bonding and spectroscopic properties of the UO0/± and UF0/± diatomic molecules. The low-lying Ω states were described by using multireference SO-CASPT2 calculations. The adiabatic electronic affinity (AEA), adiabatic ionization energy (IE), and bond dissociation energy (BDE) were calculated at the Feller-Peterson-Dixon (FPD) level. The ground state of UO is predicted to be 5I4, and that of UF is 4I9/2. The calculated AEAs of UO and UF are 1.123 and 0.453 eV, respectively, and the corresponding IEs are 5.976 and 6.278 eV. The BDE of UO (749.5 kJ/mol) is predicted to be considerably higher than that of UF (627.2 kJ/mol), and both are higher than those predicted for UB, UC, and UN. NBO calculations show strong ionic character for the ground states of UO and UF and bond orders that range from 2 to 3 and from 1 to 2, respectively. Comparisons of the calculated properties to those of the series comprising UB, UC, and UN diatomic molecules are given.

Prediction of the pKa's of Hydrated Metal Carbonates and Bicarbonates for Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn Dications

The gas- and aqueous-phase acidities of hydrated metal dication carbonates, bicarbonates, and hydroxide complexes M(CO3)(H2O)n for n = 1 to 3, M(HCO3)2, M(HCO3)2(H2O)2, M(HCO3)(OH), and M(HCO3)(H2O)2(OH) for M = Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn were calculated at the CCSD(T)/aug-cc-pwCVDZ/cc-pwCVDZ level in the gas phase and at the B3LYP/aug-cc-pVTZ/cc-pVTZ(-PP) level with the COSMO self-consistent reaction field (SCRF) method in the aqueous phase. The composite correlated molecular orbital theory G3(MP2) and G3(MP2)B3 methods were used to predict the pKa's of the Mg structures and cis-cis carbonic acid to provide additional benchmarks. Using values scaled to experiment for H2CO3, the pKa's of bicarbonate ligands in group 2 and transition-metal complexes were compared to carbonic acid to gauge the effect of the metal complex on the bicarbonate. The group 2 metal complexes M(HCO3)2 and M(HCO3)(OH) decreased the acidity of the bicarbonate ligands, whereas their dihydrates were even less acidic. The transition-metal di-bicarbonate and bicarbonate hydroxide complexes generally made the bicarbonate more acidic especially when reduction of the metal occurs consistent with electron donation from the ligands; this is accompanied by spin transfer which typically increases in the order Mn < Fe < Co < Ni < Cu. The transition-metal dihydrates were less acidic than carbonic acid. Using values scaled to experiment for hydrated metal dications, the pKa's of water coordinated to group 2 and transition-metal complexes were generally more acidic than the hydrated metal dications, with the exception of Ca bicarbonate dihydrate, Co carbonate, Ni di-bicarbonate dihydrate, and Cu bicarbonate hydroxide di-bicarbonate.

Norcaradiene-Cycloheptatriene Equilibrium: A Heavy-Atom Quantum Tunneling Case

The equilibrium between norcaradiene and cycloheptatriene, which has captivated chemists for more than half a century, is revisited by state-of-the-art quantum chemical calculations. Our theoretical data significantly deviate from the experimental results (J. Am. Chem. Soc., 1981, 26, 7791-7792), especially at low temperatures, where isomerization is dominated by heavy-atom tunneling. This effect results in an extremely short half-life for norcaradiene, rendering it undetectable. This work sheds light on this equilibrium, updating the kinetic and thermodynamic data while also expanding the repertoire of organic reactions controlled by this exotic quantum effect.

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin-orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac-Hartree-Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO-D). Employing additional sets of diffuse and core-valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO-D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.

Ni, Cu, Zn, Pd, Ag and Cd Tetraphenylporphyrin Ab Initio Thermochemistry: Enthalpy of Formation of ZnTPP Revisited

Groups 10-12 metalloporphyrins have been recognized for their numerous properties essential for the development of new sensing materials. In this work, accurate gas-phase enthalpies of formation, ΔfHm0(g,298.15), are predicted for the series of Ni, Cu, Zn, Pd, Ag, and Cd tetraphenylporphyrins (MTPPs) on the basis of the reaction-based Feller-Peterson-Dixon approach and high-level ab initio DLPNO-CCSD(T) calculations. Our recently developed automatic generator of the balanced chemical reactions was employed to reduce the bias of the theoretical ΔfHm0(g,298.15) toward a particular reaction. Theoretical ΔfHm0(g,298.15) for ZnTPP (227.0 ± 3.4 kcal mol-1) does not support the previously reported experimental value of 132 ± 2 kcal mol-1. The origin of the discrepancy probably lies in the experimental solid-state ΔfHm0(ZnTPP, cr,298.15) as it stems from our theoretical evaluations of the ΔfHm0(cr,298.15) values for the entire set of transition metal TPP complexes. The large discrepancy between experiment and theory also holds when different DFT functionals (ωB97M-V, PBE0-D4, and B3LYP-D4) paired with quadruple-ζ quality basis sets are used for the theoretical calculations. Experimental revisiting of the solid-state enthalpy of formation of ZnTPP and analogue measurements for other transition metal TPPs are needed to resolve the observed discrepancy. Based on the predicted enthalpies of formation of MTPPs, the relative energies of the metal-ligand bonding are evaluated and the trends are compared to those for the complexes of the unsubstituted porphyrin with the same set of metals derived in [Can. J. Chem., 2009, 87, 1063]. According to both studies, Pd complexes exhibit the strongest bonding, while the Cd species are the least stable metallocomplexes within the considered series.

Structural and thermochemical investigation of 1,3-bis(λ4-boraneyl)-1λ4,3λ4-imidazolidine adduct for chemical hydrogen storage

The structure, thermochemical properties and reaction pathways of a cyclic amine diborane complex (1,3-bis(λ4-boraneyl)-1λ4,3λ4-imidazolidine) were investigated using quantum chemical calculations. Structural and thermochemical analysis revealed that the simultaneous and spontaneous elimination of both hydrogen molecules from this complex is predicted to occur under thermoneutral conditions. This observation is further supported by the investigation of the BH3-catalysed dehydrogenation pathway. The calculated thermochemical parameters indicate that the energy requirements for hydrogen release from this complex are minimal, suggesting efficient hydrogen release capability under suitable conditions. Additionally, the activation barriers, ∼75 and ∼20 kJ mol-1 for the first and second dihydrogen release from the catalysed dehydrogenation reactions of this compound exhibit moderate kinetics, confirmed by kinetic studies. These findings and the ability of the system to easily release two molecules of dihydrogen emphasize the potential of 1,3-bis(λ4-boraneyl)-1λ4,3λ4-imidazolidine as a highly effective hydrogen storage material.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

Building a New Platform for Significantly Improving Performance of Hartree-Fock and CCSD(T) Correlation Energy Based on Two-Point Complete Basis Set Extrapolation Schemes

The leading cause of high expense in gold standard coupled cluster theory is that calculations of electronic energies converge exceedingly slowly with an increased basis set size. Extrapolation principally allows for achieving higher-quality outcomes at reduced costs. Numerous extrapolation formulas have been developed, with attempts to predict energies up to the complete basis set limit. Unfortunately, since the intricate shape of the function hinges on the molecular properties with the highest angular momentum of the basis set, the accuracy of the extrapolated energies highly depends on the fitted empirical parameters, which rely on the quality of the data sets for fitting. In this work, to overcome the extrapolation deficiency caused by the very limited data sets and smaller basis sets in the early stages, we constructed a new benchmark platform that includes a broader data set of 183 species (containing open-shell, closed-shell, ionic, and neutral species) and a larger basis set up to aug-cc-pV6Z. The newly optimized parameters can significantly improve the energy-predictive abilities of ten published formulas. Notably, all ten formulas perform quite similarly under the new platform with the reoptimized parameters. Finally, we built an online calculator for researchers to use for these extrapolation schemes. Our work would reignite the interest and applications of the underestimated formulas.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Autobench V1.0: Benchmarking Automation for Electronic Structure Calculations

This work reports on new software for automatic conformer energy benchmarking calculations for flexible molecules. The software workflow consists of four parts: conformational search, preoptimization, optimization, and frequency calculations at a higher level and last calculations using several theoretical levels. The software was written to be user-friendly and versatile to be used by nonexperts in computational chemistry. Any theoretical levels available in either Gaussian 16 or ORCA 5 may be applied in the benchmarking study. The workflow will automatically run conformational search calculations and deal with conformers that converge to the same minimum and those that show a negative frequency. At the end of the workflow, the user will have the mean absolute deviations and the most accurate method/DFT functional and basis set in comparison to the benchmark to be applied for the molecular system of interest. Case examples are given at the end of the paper that may help users to get insight into the software's main features.

Probing Antioxidant-Related Properties for Phenolic Compounds

In this work, properties related to antioxidant-potential mechanisms (such as the bond dissociation enthalpy, BDE, for the homolytic cleavage of the O-H bond and ionization energies, IEs) were determined for phenol, pyrocatechol, and gallic acid (GA). Both the protonated and deprotonated forms of GA were investigated. The Feller-Peterson-Dixon (FPD) composite method was employed with a variety of computational approaches, i.e., density functional theory, Möller-Plesset perturbation theory, and coupled-cluster-based methods, in combination with large correlation consistent basis sets with extrapolation to the complete basis set limit and consideration of core electron correlation effects. FPD results were compared to experimental and computational data available in the literature, presenting good agreement. For example, the FPD BDE (298 K) obtained for phenol, which was based on valence-correlated MP2/CBS calculations with contributions from correlating all electrons, was determined to be 87.56 kcal/mol, a value that is 0.42 kcal/mol lower than the result obtained in the most recent experiments, 87.98 ± 0.62. Calibration against coupled-cluster calculations was also carried out for phenol. We expect that the outcomes gathered here may help in establishing a general protocol for computational chemists that are interested in determining antioxidant-related properties for phenolic compounds with considerable accuracy as well as to motivate future IE measurements (particularly for GA) to be accomplished in the near future.

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

Translational eigenstates of He@C60 from four-dimensional ab initio potential energy surfaces interpolated using Gaussian process regression

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two ab initio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

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.

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Prediction of Aqueous Reduction Potentials of X•, ChH•, and XO• Radicals with X = Halogen and Ch = Chalcogen

The aqueous electron affinity and aqueous reduction potentials for F•, Cl•, Br•, I•, OH•, SH•, SeH•, TeH•, ClO•, BrO•, and IO• were calculated using electronic structure methods for explicit cluster models coupled with a self-consistent reaction field (SMD) to treat the aqueous solvent. Calculations were conducted using MP2 and correlated molecular orbital theory up to the CCSD(T)-F12b level for water tetramer clusters and MP2 for octamer cluster. Inclusion of explicit waters was found to be important for accurately predicting the redox potentials in a number of cases. The calculated reduction potentials for X• and ChH• were predicted to within ∼0.1 V of the reported literature values. Fluorine is anomalous due to abstraction of a hydrogen from one of the surrounding water molecules to form a hydroxyl radical and hydrogen fluoride, so its redox potential was calculated using only an implicit model. Larger deviations from experiment were predicted for ClO• and BrO•. These deviations are due to the free energy of solvation of the anion being too negative, as found in the pKa calculations, and that for the neutral being too positive with the current approach.

Benchmark computational investigations for the basic model of the salt-water complex: NaCl(H2O) and its anion NaCl(H2O). Phys Chem Chem Phys 2023;25:27215-27229. [PMID: 37791409 DOI: 10.1039/d3cp03421f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The microsolvation of salts in water is a fundamental physicochemical process. In this work, the aqueous salt complex NaCl(H2O) and its anion NaCl(H2O)- were investigated using comprehensive calculations, including the costly and accurate CCSD(T)-F12a and focal point analysis (FPA) methods. For the neutral NaCl(H2O), three isomers exist, two of which are mirror-symmetric with almost identical structures and their corresponding anions are also mirror-symmetric. For the NaCl(H2O)- anion, there are four isomers. Several transition states are found for the first time. The structural rearrangements of neutral NaCl(H2O) and NaCl(H2O)- anions are mainly caused by breaking and forming of the hydrogen bonds and the enhancement and weakening of interactions between Na and O atoms. The distributions of the anion complexes from 15-300 K are computed and compared to recent experimental results. The analysis of the intermolecular weak interactions shows the weak van der Waals interactions between Na and O atoms, as well as hydrogen bonding between H and Cl. Moreover, the theoretically predicted anion photoelectron spectra are assigned and analyzed in detail, and they agree with experimental spectra satisfactorily. The Na-Cl stretching vibrational mode dominates the vibrational structure in both anion spectra with some minor contributions from the intermolecular motions between H2O and NaCl.

Coupled Cluster Study of the Heats of Formation of UF6 and the Uranium Oxyhalides, UO2X2 (X = F, Cl, Br, I, and At)

The atomization enthalpies of the U(VI) species UF6 and the uranium oxyhalides UO2X2 (X = F, Cl, Br, I, and At) were calculated using a composite relativistic Feller-Peterson-Dixon (FPD) approach based on scalar relativistic DKH3-CCSD(T) with extrapolations to the CBS limit. The inherent multideterminant nature of the U atom was mitigated by utilizing the singly charged atomic cation in all calculations with correction back to the neutral asymptote via the accurate ionization energy of the U atom. The effects of SO coupling were recovered using full 4-component CCSD(T) with contributions due to the Gaunt Hamiltonian calculated using Dirac-Hartree-Fock. The final atomization enthalpy for UF6 (752.2 kcal/mol) was within 2.5 kcal/mol of the experimental value, but unfortunately the latter carries a ±2.4 kcal/mol uncertainty that is predominantly due to the experimental uncertainty in the formation enthalpy of the U atom. The analogous value for UO2F2 (607.6 kcal/mol) was in nearly exact agreement with the experiment, but the latter has a stated experimental uncertainty of ±4.3 kcal/mol. The FPD atomization enthalpy for UO2Cl2 (540.4 kcal/mol) was within the experimental error limit of ±5.5 kcal/mol. FPD atomization energies for the non-U-containing molecules (used for reaction enthalpies) H2O and HX (X = F, Cl, Br, I, and At) were within at most 0.3 kcal/mol of their experimental values where available. The FPD atomization enthalpies, together with FPD reaction enthalpies for two different reactions, were used to determine heats of formation for all species of this work, with estimated uncertainties of ±4 kcal/mol. The calculated heat of formation for UF6 (-511.0 kcal/mol) is within 2.5 kcal/mol of the accurately known (±0.45 kcal/mol) experimental value.

Sub 20 cm-1 computational prediction of the CH bond energy - a case of systematic error in computational thermochemistry

The bond dissociation energy of methylidyne, D0(CH), is studied using an improved version of the High-Accuracy Extrapolated ab initio Thermochemistry (HEAT) approach as well as the Feller-Peterson-Dixon (FPD) model chemistry. These calculations, which include basis sets up to nonuple (aug-cc-pCV9Z) quality, are expected to be capable of providing results substantially more accurate than the ca. 1 kJ mol-1 level that is characteristic of standard high-accuracy protocols for computational thermochemistry. The calculated 0 K CH bond energy (27 954 ± 15 cm-1 for HEAT and 27 956 ± 15 cm-1 for FPD), along with equivalent treatments of the CH ionization energy and the CH+ dissociation energy (85 829 ± 15 cm-1 and 32 946 ± 15 cm-1, respectively), were compared to the existing benchmarks from Active Thermochemical Tables (ATcT), uncovering an unexpected difference for D0(CH). This has prompted a detailed reexamination of the provenance of the corresponding ATcT benchmark, allowing the discovery and subsequent correction of a systematic error present in several published high-level calculations, ultimately yielding an amended ATcT benchmark for D0(CH). Finally, the current theoretical results were added to the ATcT Thermochemical Network, producing refined ATcT estimates of 27 957.3 ± 6.0 cm-1 for D0(CH), 32 946.7 ± 0.6 cm-1 for D0(CH+), and 85 831.0 ± 6.0 cm-1 for IE(CH).

Classical and quantum trial wave functions in auxiliary-field quantum Monte Carlo applied to oxygen allotropes and a CuBr2 model system

In this work, we test a recently developed method to enhance classical auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers against examples from chemistry and material science, representative of classes of industry-relevant systems. As molecular test cases, we calculate the energy curve of H4 and the relative energies of ozone and singlet molecular oxygen with respect to triplet molecular oxygen, which is industrially relevant in organic oxidation reactions. We find that trial wave functions beyond single Slater determinants improve the performance of AFQMC and allow it to generate energies close to chemical accuracy compared to full configuration interaction or experimental results. In the field of material science, we study the electronic structure properties of cuprates through the quasi-1D Fermi-Hubbard model derived from CuBr2, where we find that trial wave functions with both significantly larger fidelities and lower energies over a mean-field solution do not necessarily lead to AFQMC results closer to the exact ground state energy.

Mechanisms and Thermochemistry of Reactions of SiO and Si2O2 with OH and H2O

This paper reports on computational studies of gas-phase reactions of SiO and Si₂O₂. The oxidation of SiO can initiate efficient formation of silica or silicate dust particles in a wide range of environments. Both OH radicals and H₂O molecules are often present in these environments, and their reactions with SiO and the smallest SiO cluster, Si₂O₂, affect the efficiency of eventual dust formation. Density functional theory calculations on these reactions, benchmarked against accurate coupled cluster calculations, indicate that the Si₂O₂ + OH reaction should be faster than SiO + OH. The reaction SiO + H₂O → SiO₂ + H₂ is both endothermic and has high activation energies to reaction. Instead, the formation of molecular complexes is efficient. The reaction of Si₂O₂ with H₂O, which has been suggested as efficient for producing Si₂O₃, might not be as efficient as previously thought. If the H₂O molecules dissociate to form OH radicals, oxidation of SiO and Si₂O₂ could be accelerated instead.

Prediction of the structures and heats of formation of MO2, MO3, and M2O5 for M = V, Nb, Ta, Pa

Structures for the mono-, di-, and tri-bridge isomers of M₂O₅ as well as those for the MO₂ and MO₃ fragments for M = V, Nb, Ta, and Pa were optimized at the density functional theory (DFT) level. Single point CCSD(T) calculations extrapolated to the complete basis set (CBS) limit at the DFT geometries were used to predict the energetics. The lowest energy dimer isomer was the di-bridge for M = V and Nb and the tri-bridge for M = Ta and Pa. The di-bridge isomers were predicted to be composed of MO₂⁺ and MO₃^- fragments, whereas the mono- and tri-bridge are two MO₂⁺ fragments linked by an O^2-. The heats of formation of M₂O₅ dimers, as well as MO₂ and MO₃ neutral and ionic species were predicted using the Feller-Peterson-Dixon (FPD) approach. The heats of formation of the MF₅ species were calculated to provide additional benchmarks. Dimerization energies to form the M₂O₅ dimers are predicted to become more negative going down group 5 and range from -29 to -45 kcal mol^-1. The ionization energies (IEs) for VO₂ and TaO₂ are essentially the same at 8.75 eV whereas the IEs for NbO₂ and PaO₂ are 8.10 and 6.25 eV, respectively. The predicted adiabatic electron affinities (AEAs) range from 3.75 eV to 4.45 eV for the MO₃ species and vertical detachment energies from 4.21 to 4.59 eV for MO₃^-. The calculated MO bond dissociation energies increase from 143 kcal mol^-1 for M = V to ∼170 kcal mol^-1 for M = Nb and Ta to ∼200 kcal mol^-1 for M = Pa. The M-O bond dissociation energies are all similar ranging from 97 to 107 kcal mol^-1. Natural bond analysis provided insights into the types of chemical bonds in terms of their ionic character. Pa₂O₅ is predicted to behave like an actinyl species dominated by the interactions of approximately linear PaO₂⁺ groups.

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.

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted-core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller-Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol^-1 relative to the experiment. The two-point QZ/5Z and TZ/QZ CBS 1 / l max 3 extrapolation schemes are inferior to their inverse power counterpart ( 1 / l max + 1 / 2 4 ) by 1.3 and 4.3 kJ mol^-1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol^-1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double-ζ/triple-ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

Gas-phase reactions driven by polarized metal-metal bonding in atomic clusters

Multimetallic catalysts exhibit great potential in the activation and catalytic transformation of small molecules. The polarized metal-metal bonds have been gradually recognized to account for the reactivity of multimetallic catalysts due to the synergistic effect of different metal centers. Gas-phase reactions on atomic clusters that compositionally resemble the active sites on related condensed-phase catalysts provide a widely accepted strategy to clarify the nature of polarized metal-metal bonds and the mechanistic details of elementary steps involved in the catalysis driven by this unique chemical bonding. This perspective review concerns the progress in the fundamental understanding of industrially and environmentally important reactions that are closely related to the polarized metal-metal bonds in clusters at a strictly molecular level. The following topics have been summarized and discussed: (1) catalytic CO oxidation with O₂, H₂O, and NO as oxidants (2) and the activation of other inert molecules (e.g., CH₄, CO₂, and N₂) mediated with clusters featuring polarized metal-metal bonding. It turns out that the findings in the gas phase parallel the catalytic behaviors of condensed-phase catalysts and the knowledge can prove to be essential in inspiring future design of promising catalysts.

Physical and numerical aspects of sodium ion solvation free energies via the cluster-continuum model

Sodium cation solvation Gibbs free energies (ΔG_solv(Na⁺)) have been obtained in water, dimethylformamide, dimethyl sulfoxide, ethanol, acetone, acetonitrile, and methanol through the "monomer cycle" cluster-continuum approach where a solvent reference state is described by infinitely separated molecules. The following steps are vital for obtaining reliable ΔG_solv(Na⁺) values: (a) a meticulous conformational search involving dispersion corrected density functional theory (DFT-D) and the continuum solvation model (CSM); (b) gas-phase DFT-D geometry optimization followed by single-point (SP) domain-based local pair natural orbital coupled clusters including single, double, and partly triple excitation (DLPNO-CCSD(T)) calculations in conjunction with the complete basis set extrapolation; (c) advanced statistical thermodynamic treatment of the low harmonic frequencies (<100 cm^-1) to obtain the robust gas-phase Gibbs free energy correction; (d) gas-phase and dielectric continuum SP with non-electrostatic contributions included in the CSM; (e) an evaluation of the relative thermodynamic stability of the Na⁺(S)_n clusters to identify the number of explicit solvent molecules n to be considered. Our refined computational protocol is promising with a Pearson correlation coefficient between the predicted and experimental data, ρ, of 0.82, and the mean signed and mean unsigned errors of 0.3 and 1.4 kcal mol^-1, respectively.

Geometries, interaction energies and bonding in [Po(H2O)n]4+ and [PoCln]4-n complexes

Polonium (Z = 84) is one of the rarest elements on Earth. More than a century after its discovery, its chemistry remains poorly known and even basic questions have not yet been satisfactorily addressed. In this work, we perform a systematic study of the geometries, interactions energies and bonding in basic polonium(IV) species, namely the hydrated [Po(H₂O)_n]⁴⁺ and chlorinated [PoCl_n]^4-n complexes by means of gas-phase electronic structure calculations. We show that while up to nine water molecules can fit in the first coordination sphere of the polonium(IV) ion, its coordination sphere can already be filled with eight chloride ligands. Capitalising on previous theoretical studies, a focused methodological study based on interaction energies and bond distances allows us to validate the MP2/def2-TZVP level of theory for future ground-state studies. After discussing the similarities and differences between complexes with the same number of ligands, we perform topological analyses of the MP2 electron densities in the quantum theory of atoms in molecules (QTAIM) fashion. While the water complexes display typical signatures of closed-shell interactions, we reveal large Po-Cl delocalisation indices, especially in the hypothetical [PoCl]³⁺ complex. This "enhanced" covalency opens the way for a significant spin-orbit coupling (SOC) effect on the corresponding bond distance, which has been studied using two independent approaches (i.e. one a priori and one a posteriori). We finally conclude by stressing that while the SOC may not affect much the geometries of high-coordinated polonium(IV) complexes, it should definitely not be neglected in the case of low-coordinated ones.

Electronic Properties of UN and UN- from Photoelectron Spectroscopy and Correlated Molecular Orbital Theory

The results of calculations of the properties of the anion UN^- including electron detachment are described, which further expand our knowledge of this diatomic molecule. High-level electronic structure calculations were conducted for the UN and UN^- diatomic molecules and compared to photoelectron spectroscopy measurements. The low-lying Ω states were obtained using multireference CASPT2 including spin-orbit effects up to ∼20,000 cm^-1. At the Feller-Peterson-Dixon (FPD) level, the adiabatic electron affinity (AEA) of UN is estimated to be 1.402 eV and the vertical detachment energy (VDE) is 1.423 eV. The assignment of the UN excited states shows good agreement with the experimental results with a VDE of 1.424 eV. An Ω = 4 ground state was obtained for UN^- which is mainly associated with the ³H ΛS state. Thermochemical calculations estimate a bond dissociation energy (BDE) for UN^- (U^- + N) of 665.9 kJ/mol, ∼15% larger than that of UN and UN⁺. The NBO analysis reveals U-N triple bonds for the UN, UN^-, and UN⁺ species.

Thermodynamics of the Metal Carbonates and Bicarbonates of Mn, Co, Ni, Cu, and Zn Relevant to Mineral Energetics

The gas phase heats of formation of ground-state MCO₃, M(HCO₃)₂, and M(HCO₃)(OH), where M = Mn, Co, Ni, Cu, and Zn, have been predicted using the correlated molecular orbital theory at the CCSD(T) level extrapolated to the complete basis set limit using the Feller-Peterson-Dixon (FPD) approach. Cohesive energies of the carbonates were predicted based on the calculated gas phase and experimental solid heats of formation. Coulombic dissociation energies (CDEs) between metal cations and anions show a near-linear correlation with Shannon metal cation atomic radii, yet no correlation is found with the hardness of these cations. The total reaction dissociation energies (TRDEs) of transition metals are higher than their CDEs for the di-bicarbonates, in contrast to those for Mg and Ca based on our prior work. In addition to differences in the energies needed to prepare the transition metal dications, electron donation from the ligands to the 3d orbitals of open-shell transition metal dications from lone pairs of adjacent O atoms also plays a role. No electron donation from the ligands to the fully occupied 3d orbitals of Zn and Cd was found. Decomposition energies for generating MO, CO₂, and/or H₂O were calculated. Gas phase metal exchange energies only partially correlate with the electrochemical series for M(s) → M²⁺(aq). The FPD heats of formation were used to benchmark a range of density functional theory exchange-correlation functionals, including those commonly used in solid-state mineral calculations. None of the functionals provided chemical accuracy agreement (±1 kcal/mol) with the FPD results. The best agreement with the FPD results is predicted for the τ-HCTH functional with an average unsigned error of 8.3 kcal/mol.

Automatic generation of complementary auxiliary basis sets for explicitly correlated methods

Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: Coulomb-exchange fitting (JK), resolution of the identity MP2 (RI-MP2), and complementary auxiliary basis set (CABS). If unavailable for the orbital basis set and chemical elements of interest, the first two can be auto-generated on the fly using existing algorithms, but not the third. In this paper, we present a quite simple algorithm named autoCABS; a Python implementation under a free software license is offered at Github. For the cc-pVnZ-F12 (n = D,T,Q,5), the W4-08 thermochemical benchmark, and the HFREQ2014 set of harmonic frequencies, we demonstrate that autoCABS-generated CABS basis sets are comparable in quality to purpose-optimized OptRI basis sets from the literature, and that the quality difference becomes entirely negligible as n increases.

Water-Gas Shift Catalyzed by Iridium-Vanadium Oxide Clusters IrVO2- with Iridium in a Rare Oxidation State of -II

The discovery of compounds containing transition metals with an unusual and well-established oxidation state is vital to enrich our horizon on formal oxidation state. Herein, benefiting from the study of the water-gas shift reaction (CO + H₂O → CO₂ + H₂) mediated with the iridium-vanadium oxide cluster IrVO₂^-, the missing -II oxidation state of iridium was identified. The reactions were performed by using our newly developed double ion trap reactors that can spatially separate the addition of reactants and are characterized by mass spectrometry and quantum-chemical calculations. This finding makes an important step that all the proposed 13 oxidation states of iridium (+IX to -III) have been known. The iridium atom in the IrVO₂^- cluster features the Ir═V double bond and resembles chemically the coordinated oxygen atom. A reactivity study demonstrated that the flexible role switch of iridium between an oxygen-atom like (Ir^-IIVO₂^-) and a transition-metal-atom like behavior (Ir^+IIVO₃^-) in different species can drive the water-gas shift reaction in the gas phase under ambient conditions. This result parallels and well rationalizes the extraordinary reactivity of oxide-supported iridium single-atom catalysts in related condensed-phase reactions.

A high level theory investigation on the lowest-lying ionization potentials of glycine (NH2CH2COOH)

In this work, an investigation on the ionization potentials (IPs) of the glycine molecule (NH₂CH₂COOH) is presented. IPs ranging up to ∼20 eV were probed for each of the six conformations considered, with the referred threshold being chosen based on both: (i) the observations by recent photoelectron-photoion coincidence (PEPICO) experiments and (ii) the energy range of relevance to the modeling of other photo-induced processes (e.g., photoionization). For computing the IPs, the equation-of-motion ionization potential coupled-cluster with single and double excitations method (EOMIP-CCSD) was employed with large correlation consistent aug-cc-pVXZ and aug-cc-pCVXZ (X = D, T, and Q) basis sets. Extrapolation to the complete basis set limit and consideration of core electron correlation effects were also taken into account. Subsequently, the Feller-Peterson-Dixon (FPD) approach was used for considering all the contributions and to obtain accurate IPs. In addition, coupled-cluster with single and double excitations as well as perturbative triples, CCSD(T), was also used with the aug-cc-pVTZ basis set. When compared to each other, results obtained through the use of these approaches yielded excellent agreement. In general, the outcomes from the present work provide additional information to the insights gathered from the recent PEPICO experiments as well as accurate IPs for all 6 conformations of glycine using an approach based on high levels of theory. Hence, it is expected that other investigations focusing on photo-induced processes originating from NH₂CH₂COOH (for instance, the computational modeling of its photoionization) will be motivated for study in the future.

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.

"In Vitro" and "In Vivo" Diagnostic Check for the Thermochemistry of Metal-Organic Compounds

Volatile metal β-diketonates are of interest from both practical and theoretical perspectives (manufacturing of film materials, catalysis, and the nature of metal-ligand bonding). Knowledge of their reliable thermochemical properties is essential for effective applications. However, there is an unacceptable scattering of the available data on the enthalpies of formation. In this work, we proposed "in vitro" and "in vivo" diagnostic tools to verify the available enthalpies of formation in both the crystalline and gaseous states for metal tris-β-diketonates. The "in vitro" procedure involved high-level quantum-chemical calculations and was applied to define a consistent data set on the enthalpies of formation for iron(III) β-diketonates. This data set has provided the basis for "in vivo" structure-property-based diagnostics to evaluate the robustness of the thermochemical data for β-diketonate tris-complexes with metals other than iron.

Reverse water-gas shift reaction catalyzed by diatomic rhodium anions

The reverse water-gas shift (RWGS, CO₂ + H₂ → CO + H₂O, ΔH₂₉₈ = +0.44 eV) reaction mediated by the diatomic anion Rh₂^- was successfully constructed. The generation of a gas-phase H₂O molecule and ion product [Rh₂(CO)_ads]^- was identified unambiguously at room temperature and the only elementary step that requires extra energy to complete the catalysis is the desorption of CO from [Rh₂(CO)_ads]^-. This experimentally identified Rh₂^- anion represents the first gas-phase species that can drive the RWGS reaction because it is challenging to design effective routes to yield H₂O from CO₂ and H₂. The reactions were performed by using our newly developed double ion trap reactors and characterized by mass spectrometry, photoelectron spectroscopy, and high-level quantum-chemical calculations. We found that the order that the reactants (CO₂ or D₂) were fed into the reactor did not have a pronounced impact on the reactivity and the final product distribution (D₂O and Rh₂CO^-). The atomically precise insights into the key steps to guide the reaction toward the RWGS direction were provided.

Explicitly Correlated Electronic Structure Calculations with Transcorrelated Matrix Product Operators

In this work, we present the first implementation of the transcorrelated electronic Hamiltonian in an optimization procedure for matrix product states by the density matrix renormalization group (DMRG) algorithm. In the transcorrelation ansatz, the electronic Hamiltonian is similarity-transformed with a Jastrow factor to describe the cusp in the wave function at electron-electron coalescence. As a result, the wave function is easier to approximate accurately with the conventional expansion in terms of one-particle basis functions and Slater determinants. The transcorrelated Hamiltonian in first quantization comprises up to three-body interactions, which we deal with in the standard way by applying robust density fitting to two- and three-body integrals entering the second-quantized representation of this Hamiltonian. The lack of hermiticity of the transcorrelated Hamiltonian is taken care of along the lines of the first work on transcorrelated DMRG [ J. Chem. Phys. 2020, 153, 164115] by encoding it as a matrix product operator and optimizing the corresponding ground state wave function with imaginary-time time-dependent DMRG. We demonstrate our quantum chemical transcorrelated DMRG approach at the example of several atoms and first-row diatomic molecules. We show that transcorrelation improves the convergence rate to the complete basis set limit in comparison to conventional DMRG. Moreover, we study extensions of our approach that aim at reducing the cost of handling the matrix product operator representation of the transcorrelated Hamiltonian.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

Molecular Properties of Thorium Hydrides: Electron Affinities and Thermochemistry

High-level electronic structure calculations of the ground and low-lying energy electronic states for ThH_x and ThH_x^- for x = 2-5 are reported and compared to available anion photoelectron detachment experiments. The adiabatic electron affinities (EAs) are predicted to be 0.82, 0.88, 0.51, and 2.36 eV for x = 2 to 5, respectively, at the Feller-Peterson-Dixon (FPD) level. The vertical detachment energies (VDEs) are predicted to be 0.84, 0.88, 0.81, and 4.38 eV for x = 2-5, respectively. The corresponding experimental VDEs are 0.871 eV for x = 2, 0.88 eV for x = 3, and 4.09 eV for x = 5. As for ThH, there is a significant spin-orbit (SO) correction for the EA of ThH₂, and this correction decreases substantially for x > 2. The observed ThH₂^- photoelectron spectrum has many transitions as predicted at the CASPT2-SO level. The FPD bond dissociation energies (BDEs) increase from 67 to 75 kcal/mol for x = 2 to x = 4 at the FPD level. The BDE for ThH₅ is much lower as it is a complex of H₂ with ThH₃. The hydride affinities for x = 2 to 4 are all comparable and near 70 kcal/mol. A natural bond orbital analysis is consistent with a significant Th⁺-H^- ionic contribution to the Th-H bonds. There is very little participation of the 5f orbitals in the bonding and the valence electrons on the Th are dominated by 7s and 6d for the neutrals and anions except for ThH₂^- where there is a significant contribution from the 7p.

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.

Electronically Excited Complex Formation in Magnesium Cluster-Halogen Atom Reactions

A near ultraviolet transition of Mg₂F has been observed in emission from the reaction between magnesium clusters, most likely Mg₃, and fluorine atoms. Because there is little evidence for upper-state internal excitation, the spectrum is assigned assuming that the upper state is quenched to its lowest vibrational levels. Two of possibly three ground-state vibrational frequencies, υ₁ = 516 ± 10 cm^-1 and υ₂ = 104 ± 10 cm^-1, have been established. Dispersed laser-induced fluorescence studies extrapolating on the observed chemiluminescence indicate an excited-state symmetric stretch frequency of order 370 ± 30 cm^-1. Electronic structure calculations at the CCSD(T)/CBS level predict that the ground state of Mg₂F has C_2v symmetry and can be described as an Mg₂⁺F^- ion pair with two Mg-F bonds. Like the MgF A-X transition that is largely a transition between Mg orbitals, the observed transition in Mg₂F is largely between orbitals on the magnesium dimer ion. The asymmetric C_∞v Mg₂⁺F^- complex is also a minimum and is predicted to be 6.7 kcal/mol higher in energy. Calculated structures for the Mg₂Cl isomers are also presented and used to further interpret the experimental results for the reaction of Mg clusters with Cl atoms. In contrast to Mg₂F, the ground state of Mg₂Cl is a linear C_∞v MgMgCl structure with the C_2v and D_∞h isomers of the MgClMg structure slightly higher in energy.

Correlation-Consistent Gaussian Basis Sets for Solids Made Simple

The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. We find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-ζ correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of 19 semiconductors and insulators.

The effect of midbond functions on interaction energies computed using MP2 and CCSD(T)

In this article we use MP2 and CCSD(T) calculations for the A24 and S66 data sets to explore how midbond functions can be used to generate cost effective counterpoise corrected supramolecular interaction energies of noncovalent complexes. We use the A24 data set to show that the primary role of midbond functions is not to approach the complete basis set limit, but rather to ensure a balanced description of the molecules and the interaction region (unrelated to the basis set superposition error). The need for balance is a consequence of using atom centered basis sets. In the complete basis set limit, the error will disappear, but reaching the complete basis set limit is not feasible beyond small systems. For S66 we investigate the need for increasing the number of midbond centers. Results show that adding a second midbond center increases the accuracy, but the effect is secondary to changing the atom centered basis set. Further, by comparing calculations using the 3s3p2d1f1g midbond set with using aug-cc-pVDZ and aug-cc-pVTZ as midbond sets, we see that the requirements for the midbond set to be effective, is not just that it contains diffuse functions, but also that high angular momentum functions are included. By comparing two approaches for placing midbond centers we show that results are not particularly sensitive to placement as long as the placement is reasonable.