Spin-orbit coupling of electrons on separate lanthanide atoms of Pr2O2 and its singly charged cation.

Although it plays a critical role in the photophysics and catalysis of lanthanides, spin-orbit coupling of electrons on individual lanthanide atoms in small clusters is not well understood. The major objective of this work is to probe such coupling of the praseodymium (Pr) 4f and 6s electrons in Pr2O2 and Pr2O2+. The approach combines mass-analyzed threshold ionization spectroscopy and spin-orbit multiconfiguration second-order quasi-degenerate perturbation theory. The energies of six ionization transitions are precisely measured; the adiabatic ionization energy of the neutral cluster is 38 045 (5) cm-1. Most of the electronic states involved in these transitions are identified as spin-orbit coupled states consisting of two or more electron spins. The electron configurations of these states are 4f46s2 for the neutral cluster and 4f46s for the singly charged cation, both in planar rhombus-type structures. The spin-orbit splitting due to the coupling of the electrons on the separate Pr atoms is on the order of hundreds of wavenumbers.

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures.

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

Electronic states and transitions of PrO and PrO+ probed by threshold ionization spectroscopy and spin-orbit multiconfiguration perturbation theory.

The precise ionization energy of praseodymium oxide (PrO) seeded in supersonic molecular beams is measured with mass-analyzed threshold ionization (MATI) spectroscopy. A total of 33 spin-orbit (SO) states of PrO and 23 SO states of PrO+ are predicted by second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Electronic transitions from four low-energy SO levels of the neutral molecule to the ground state of the singly charged cation are identified by combining the MATI spectroscopic measurements with the MCQDPT2 calculations. The precise ionization energy is used to reassess the ionization energies and the reaction enthalpies of the Pr + O → PrO+ + e- chemi-ionization reaction reported in the literature. An empirical formula that uses atomic electronic parameters is proposed to predict the ionization energies of lanthanide monoxides, and the empirical calculations match well with available precise experimental measurements.

Relativistic Segmented Correlation Consistent Basis Sets for the 5p and 6p Elements.

The relativistic all-electron triple-ζ (TZ) and quadruple-ζ (QZ) correlation-consistent basis sets for the 5p and 6p elements were reoptimized to have a segmented contraction scheme. Properties computed with the segmented basis sets using the coupled-cluster level of theory with single, double, and perturbative triple excitations closely match the results obtained using the generally contracted analogues. Deviations in the ionization potentials and electron affinities computed using the segmented basis sets compared with those computed with the generally contracted basis sets are within 1 kcal mol-1. The relative deviation in the computed bond lengths for a selection of diatomic molecules is within 0.02 Å, and the computed harmonic vibrational frequencies differ by less than 3%. The mean absolute deviations (MADs) in the computed bond dissociation energies are 1.01 and 1.31 kcal mol-1 for the TZ and QZ basis sets, respectively, when only the valence electrons are correlated and 0.14 and 0.10 kcal mol-1 for the TZ and QZ basis sets, respectively, when the valence and outer-core electrons are correlated. The segmented basis sets also retain the systematically convergent behavior intrinsic to the correlation-consistent family of basis sets while affording speedups for the average time required to form the Fock matrix from 32.8 to 82.9× compared to the time required with the generally contracted versions when used with integral algorithms employed by many computational chemistry software packages.

Excited states of lutetium oxide and its singly charged cation.

Vibronic spectra of lutetium oxide (LuO) seeded in supersonic molecule beams are investigated with mass-analyzed threshold ionization (MATI) spectroscopy and second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Six states of LuO and four states of LuO+ are located by the MCQDPT2 calculations, and an a3Π(LuO+) ← C2Σ+ (LuΟ) transition is observed by the MATI measurement. The vibronic spectra show abnormal vibrational intervals for both the neural and cation excited states, and the abnormality is attributed to vibrational perturbations induced by interactions with neighboring states.

Segmented correlation consistent basis sets for the 4d and 5d transition metals.

The cc-pVnZ-PP and cc-pwCVnZ-PP (n = D, T, Q, 5) pseudopotential-based correlation consistent basis sets for the 4d and 5d transition metals were reoptimized to have segmented contraction schemes. Computed ionization potentials and dns2 → dn+1s1 excitation energies computed at the coupled cluster level of theory with single, double, and perturbative triple excitations using the segmented basis sets approximate the result obtained with the generally contracted basis sets with mean absolute deviations (MADs) within 0.75 kcal mol-1 for the ionization energies and 2 kcal mol-1 for the excitation energies with respect to the results obtained with the generally contracted basis. The segmented basis sets also retain the systematically convergent behavior of the correlation consistent basis sets with MADs within 0.61 kcal mol-1 with respect to the generally contracted basis for properties extrapolated to the complete basis set limit. The segmented nature of the seg-cc-pVnZ-PP and seg-cc-pwCVnZ-PP basis sets enables significant performance improvements when using algorithms with an a priori treatment of the contraction coefficients with average speedups in the time required to form the Fock matrix ranging from 6.1× for the seg-cc-pVDZ-PP basis sets to 53.8× for the seg-cc-pV5Z-PP basis sets.

Multiple Bonding in Rhodium Monoboride. Quasi-atomic Analyses of the Ground and Low-Lying Excited States.

The bonding structures of the ground state and the lowest five excited states of rhodium monoboride are identified by determining the quasi-atomic orbitals in full valence space MCSCF wave functions and the interactions between these orbitals. A quadruple bond, namely two π-bonds and two σ-bonds, is identified and characterized for the X1Σ+ ground state, in agreement with a previous report (Cheung J. Phys. Chem. Lett. 2020, 11, 659-663). However, in all excited states, the bonding is predicted to be weaker because, in these states, one of the σ-bonding interactions has a small magnitude. In the a3Δ and A1Δ states, the bond order is between a triple and quadruple bond. In the b3Σ+ state, the Rh-B linkage is a triple bond. In the c3Π and B1Π states, the atoms are linked by a double bond due to an additional weakening of the two π-bonds. The decreases in the predicted bond strengths are reflected in the decreases of the predicted binding energies and in the increases of the predicted bond lengths from the X1Σ+ ground state to the c3Π and the B1Π excited states. Notably, the 5pσ orbital of rhodium, which is vacant in the ground state of the atom, plays a significant role in the molecule.

Quasi-Atomic Bond Analyses in the Sixth Period: I. Relativistic Accurate Atomic Minimal Basis Sets for the Elements Cesium to Radon.

Full-valence relativistic accurate atomic minimal basis set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic basis sets are developed and subsequently used to form the AAMBS orbitals. By virtue of the use of a saturated basis, properties computed based on the AAMBS orbitals are basis set independent. In molecules, the AAMBS orbitals can be used to construct valence virtual orbitals (VVOs) that provide chemically meaningful ab initio lowest unoccupied molecular orbitals (LUMOs) with basis set independent orbital energies. The optimized occupied molecular orbitals complemented with the VVOs form a set of full-valence molecular orbitals. They can be transformed into a set of oriented quasi-atomic orbitals (QUAOs) that provide information on intramolecular bonding via an intrinsic density analysis. In the present work, the development of the AAMBS for the sixth row is presented.

Quasi-Atomic Bond Analyses in the Sixth Period: II. Bond Analyses of Cerium Oxides.

The role of the 4f orbitals in bonding is examined for the molecules cerium monoxide and cerium dioxide that have cerium formally in the +2 and +4 oxidation states, respectively. It is shown that the 4f orbitals are used primarily for polarization of the 5d orbitals when cerium is in the lower oxidation state, while the 4f orbitals play a significant role in chemical bonding via 5d/4f hybridization when cerium is in the +4 oxidation state.

Efficacy of Density Functionals and Relativistic Effective Core Potentials for Lanthanide-Containing Species: The Ln54 Molecule Set.

The utility of 22 density functionals paired with relativistic effective core potentials (RECPs) for the prediction of thermodynamic properties was investigated for the Ln54 set of lanthanide-containing molecules. The Ln54 set includes lanthanide oxides, fluorides, and chlorides with the lanthanide formally in the +1, + 2, or +3 oxidation state. The density functionals were chosen to span the gamut of complexity from the local density approximation to double hybrids. Computed enthalpies of formation and bond dissociation energies were compared to experimental data and to previous calculations performed with all electron basis sets. The performance of the functionals was then assessed for each class of molecules in the Ln54 set. Overall, SVWN was found to be the best-performing functional having the lowest MAD of 22.1 kcal mol-1 and the most systematic deviation in comparison to the other functionals.

Relativistic ab Initio Accurate Atomic Minimal Basis Sets: Quantitative LUMOs and Oriented Quasi-Atomic Orbitals for the Elements Li-Xe.

Valence virtual orbitals (VVOs) are a quantitative and basis set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored ab initio accurate atomic minimal basis sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a minimal basis set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment. In the present work, relativistic AAMBS are developed that span the full valence orbital space. The impact of using full valence AAMBS for the formation of the VVOs and OQUAOs and the resulting bonding analysis is demonstrated with applications to the cuprous chloride, scandium monofluoride, and nickel silicide diatomic molecules.

Gauging the Performance of Density Functionals for Lanthanide-Containing Molecules.

Several density functional approaches have been considered for their ability to predict enthalpies of formation and bond dissociation energies for lanthanide-containing molecules. To enable comparison with experiment, the Ln54 set, introduced here, is compiled to include lanthanides both in the common 3+ oxidation state as well as in more exotic oxidation states. Due to the magnitude of the experimental uncertainties a "lanthanide chemical accuracy" of 5.0 kcal mol(-1) is proposed. The density functionals considered span the full range of complexity from LDA through double hybrids. The performance of the density functionals is assessed for each class of lanthanide-containing molecules and for the Ln54 molecule set overall. In general, hybrid functionals perform worse than functionals without exact exchange, and TPSS performs the best overall for the Ln54 set with a MAD of 19.2 kcal mol(-1) and MSD of -1.9 kcal mol(-1).

A Computational Study on the Ground and Excited States of Nickel Silicide.

Nickel silicide has been studied with a range of computational methods to determine the nature of the Ni-Si bond. Additionally, the physical effects that need to be addressed within calculations to predict the equilibrium bond length and bond dissociation energy within experimental error have been determined. The ground state is predicted to be a (1)Σ(+) state with a bond order of 2.41 corresponding to a triple bond with weak π bonds. It is shown that calculation of the ground state equilibrium geometry requires a polarized basis set and treatment of dynamic correlation including up to triple excitations with CR-CCSD(T)L resulting in an equilibrium bond length of only 0.012 Å shorter than the experimental bond length. Previous calculations of the bond dissociation energy resulted in energies that were only 34.8% to 76.5% of the experimental bond dissociation energy. It is shown here that use of polarized basis sets, treatment of triple excitations, correlation of the valence and subvalence electrons, and a Λ coupled cluster approach is required to obtain a bond dissociation energy that deviates as little as 1% from experiment.

Ground and excited electronic state analysis of PrF²âº and PmF²âº.

The ground state and excited state manifolds are computed for PrF(2+) and PmF(2+) at the CASSCF (n,8) level of theory where the active space spans the Ln 4f orbitals as well as the F 2pz orbital. Dynamical correlation is included using second-order multireference quasidegenerate perturbation theory (MCQDPT2). The spin-orbit multiplets for each of the excited states are resolved, and spin-orbit coupling constants are computed using the Breit-Pauli spin-orbit operator. Equilibrium geometries for each of the ground and excited states are computed, and the nature of the Ln-F bond is examined. Potential energy curves for the lowest four triplet states and lowest two quintet states are computed for PrF(2+), which split into 14 levels upon application of the spin-orbit Hamiltonian. Likewise, the lowest six quintet states are computed for PmF(2+) as well as the lowest triplet state and the lowest two septet states. These nine states split into 43 terms upon application of the spin-orbit Hamiltonian.

Low valency in lanthanides: a theoretical study of NdF and LuF.

The ground and low-lying excited state potential energy curves of neodymium monofluoride were calculated using multireference (CASSCF) and single reference (EOM-CR-CCSD(T)) methods. Optimized bond lengths were obtained and accurate bond dissociation energies were computed. The EOM-CR-CCSD(T) method was used to determine the bond dissociation energy of lutetium monofluoride, and it is shown that core correlation is required to produce bond dissociation energies in agreement with experiment.

A neoteric neodymium model: ground and excited electronic state analysis of NdF2+.

Neodymium monofluoride dication was studied as a model of the Nd-F bond in NdFx. Multiconfigurational self-consistent field (MCSCF) and second order multireference quasi-degenerate perturbation theory (MCQDPT2) methods were used with a variety of active spaces to elucidate the roles of the Nd 4f, 5d, and 6s orbitals. Spin-orbit coupling calculations were performed at the SO-MCQDPT2 level, and potential energy curves were obtained for the four lowest energy quartet states as well as for the four lowest doublet states and the lowest sextet state. Inclusion of spin-orbit coupling splits these states into 30 levels. Equilibrium bond lengths, dissociation energies, transition energies, and crossing points were determined.

Highly enantioselective zirconium-catalyzed cyclization of aminoalkenes.

Aminoalkenes are catalytically cyclized in the presence of cyclopentadienylbis(oxazolinyl)borato group 4 complexes {PhB(C5H4)(Ox(R))2}M(NMe2)2 (M = Ti, Zr, Hf; Ox(R) = 4,4-dimethyl-2-oxazoline, 4S-isopropyl-5,5-dimethyl-2-oxazoline, 4S-tert-butyl-2-oxazoline) at room temperature and below, affording five-, six-, and seven-membered N-heterocyclic amines with enantiomeric excesses of >90% in many cases and up to 99%. Mechanistic investigations of this highly selective system employed synthetic tests, kinetics, and stereochemistry. Secondary aminopentene cyclizations require a primary amine (1-2 equiv vs catalyst). Aminoalkenes are unchanged in the presence of a zirconium monoamido complex {PhB(C5H4)(Ox(4S-iPr,Me2))2}Zr(NMe2)Cl or a cyclopentadienylmono(oxazolinyl)borato zirconium diamide {Ph2B(C5H4)(Ox(4S-iPr,Me2))}Zr(NMe2)2. Plots of initial rate versus [substrate] show a rate dependence that evolves from first-order at low concentration to zero-order at high concentration, and this is consistent with a reversible substrate-catalyst interaction preceding an irreversible step. Primary kinetic isotope effects from substrate conversion measurements (k'obs((H))/k'obs((D)) = 3.3 ± 0.3) and from initial rate analysis (k2((H))/k2((D)) = 2.3 ± 0.4) indicate that a N-H bond is broken in the turnover-limiting and irreversible step of the catalytic cycle. Asymmetric hydroamination/cyclization of N-deutero-aminoalkenes provides products with higher optical purities than obtained with N-proteo-aminoalkenes. Transition state theory, applied to the rate constant k2 that characterizes the irreversible step, provides activation parameters consistent with a highly organized transition state (ΔS(++) = -43(7) cal·mol(-1) K(-1)) and a remarkably low enthalpic barrier (ΔH(++) = 6.7(2) kcal·mol(-1)). A six-centered, concerted transition state for C-N and C-H bond formation and N-H bond cleavage involving two amidoalkene ligands is proposed as most consistent with the current data.

Spectroscopic properties of Ar(x)-Zn and Ar(x)-Ag(+) (x = 1,2) van der Waals complexes.

Potential energy curves have been constructed using coupled cluster with singles, doubles, and perturbative triple excitations (CCSD(T)) in combination with all-electron and pseudopotential-based multiply augmented correlation consistent basis sets [m-aug-cc-pV(n + d)Z; m = singly, doubly, triply, n = D,T,Q,5]. The effect of basis set superposition error on the spectroscopic properties of Ar-Zn, Ar2-Zn, Ar-Ag(+), and Ar2-Ag(+) van der Waals complexes was examined. The diffuse functions of the doubly and triply augmented basis sets have been constructed using the even-tempered expansion. The a posteriori counterpoise scheme of Boys and Bernardi and its generalized variant by Valiron and Mayer has been utilized to correct for basis set superposition error (BSSE) in the calculated spectroscopic properties for diatomic and triatomic species. It is found that even at the extrapolated complete basis set limit for the energetic properties, the pseudopotential-based calculations still suffer from significant BSSE effects unlike the all-electron basis sets. This indicates that the quality of the approximations used in the design of pseudopotentials could have major impact on a seemingly valence-exclusive effect like BSSE. We confirm the experimentally determined equilibrium internuclear distance (re), binding energy (De), harmonic vibrational frequency (ωe), and C(1)Π â† X(1)Σ transition energy for ArZn and also predict the spectroscopic properties for the low-lying excited states of linear Ar2-Zn (X(1)Σg, (3)Πg, (1)Πg), Ar-Ag(+) (X(1)Σ, (3)Σ, (3)Π, (3)Δ, (1)Σ, (1)Π, (1)Δ), and Ar2-Ag(+) (X(1)Σg, (3)Σg, (3)Πg, (3)Δg, (1)Σg, (1)Πg, (1)Δg) complexes, using the CCSD(T) and MR-CISD + Q methods, to aid in their experimental characterizations.

Roles of acetone and diacetone alcohol in coordination and dissociation reactions of uranyl complexes.

Combined collision-induced dissociation mass spectrometry experiments with DFT and MP2 calculations were employed to elucidate the molecular structures and energetics of dissociation reactions of uranyl species containing acetone and diacetone alcohol ligands. It is shown that solutions containing diacetone alcohol ligands can produce species with more than five oxygen atoms available for coordination. Calculations confirm that complexes with up to four diacetone alcohol ligands can be energetically stable but that the effective number of atoms coordinating with uranium in the equatorial plane does not exceed five. Water elimination reactions of diacetone alcohol ligands are shown to have two coordination-dependent reaction channels, through formation of mesityl oxide ligands or formation of alkoxide and protonated mesityl oxide species. The present results provide an explanation for the implausible observation of "[UO(2)(ACO)(6,7,8)](2+)" in and observed water-elimination reactions from purportedly uranyl-acetone complexes (Rios, D.; Rutkowski, P. X.; Van Stipdonk, M. J.; Gibson, J. K. Inorg. Chem. 2011, 50, 4781).

On the formation of "hypercoordinated" uranyl complexes.

Recent gas-phase experimental studies suggest the presence of hypercoordinated uranyl complexes. Coordination of acetone (Ace) to uranyl to form hypercoordinated species is examined using density functional theory (DFT) with a range of functionals and second-order perturbation theory (MP2). Complexes with up to eight acetones were studied. It is shown that no more than six acetones can bind directly to uranium and that the observed uranyl complexes are not hypercoordinated. In addition, other more exotic species involving proton transfer between acetones and species involving enol tautomers of acetone are high-energy species that are unlikely to form.