The electronic structure of vanadium monochloride cation (VCl+): Tackling the complexities of transition metal species

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.

The structure of ScC2 (X̃2A1): A combined Fourier transform microwave/millimeter-wave spectroscopic and computational study

Pure rotational spectra of Sc¹³C₂ (X̃²A₁) and Sc¹²C¹³C (X̃²A') have been measured using Fourier transform microwave/millimeter-wave methods. These molecules were synthesized in a DC discharge from the reaction of scandium vapor, produced via laser ablation, with ¹³CH₄ or ¹³CH₄/¹²CH₄, diluted in argon. The N_Ka,Kc = 1_0,1 → 0_0,0, 2_0,2 → 1_0,1, 3_0,3 → 2_0,2, and 4_0,4 → 3_0,3 transitions in the frequency range of 14 GHz-61 GHz were observed for both species, each exhibiting hyperfine splittings due to the nuclear spins of ¹³C (I = 1/2) and/or Sc (I = 7/2). These data have been analyzed with an asymmetric top Hamiltonian, and rotational, spin-rotation, and hyperfine parameters have been determined for Sc¹³C₂ and Sc¹²C¹³C. In addition, a quartic force field was calculated for ScC₂ and its isotopologues using a highly accurate coupled cluster-based composite method, incorporating complete basis set extrapolation, scalar relativistic corrections, outer core and inner core electron correlation, and higher-order valence correlation effects. The agreement between experimental and computed rotational constants, including the effective constant (B + C), is ∼0.5% for all three isotopologues. This remarkable agreement suggests promise in predicting rotational spectra of new transition metal-carbon bearing molecules. In combination with previous work on Sc¹²C₂, an accurate structure for ScC₂ has been established using combined experimental (B, C) and theoretical (A) rotational constants. The radical is cyclic (or T-shaped) with r_(Sc-C) = 2.048(2) Å, r_(C-C) = 1.272(2) Å, and ∠_(C-Sc-C) = 36.2(1)°. The experimental and theoretical results also suggest that ScC₂ contains a C₂ ^- moiety and is largely ionic.

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.

Theoretical study of the low-lying electronic states of iron hydride cation

Both FeH and FeH⁺ are predicted to be abundant in cool stellar atmospheres and proposed to be molecular components of the gas phase interstellar medium (ISM). However, experimental and simulated data for both species are lacking, which have hindered astronomical detection. There are no published laboratory data for the spectroscopy of FeH⁺ in any frequency regime. It is also not established if FeH⁺ possesses salient multireference character, which would pose significant challenges for ab initio modeling of geometric and spectroscopic properties. With a set of high-level coupled cluster and multireference configuration interaction computations, a study of the electronic structure of the ground state and seven excited states of FeH⁺ was carried out. An X⁵Δ_i electronic ground state of FeH⁺ is found, in agreement with previous theoretical studies. Including corrections for spin-orbit coupling and anharmonic vibrational effects, the Ω = 3, ν = 0 spin ladder of the A⁵Π_i electronic state lies 872 cm^-1 higher in energy than the Ω = 4, ν = 0 spin ladder of the ground state. Combined with previous work in our laboratory, the ionization energy of FeH is computed to be 7.4851 eV. With modern multireference configuration interaction and coupled cluster methods, spectroscopic constants (r_e, B_e, ω_e, ω_ex_e, α_e, and D¯_e) for several bound excited states (A⁵Π_i, B ⁵Σ_i ⁺, a ³Σ_r ^-, b³Φ_i, c³Π_i, d³Δ_r, and ⁷Σ⁺) were characterized. This study will lead efforts to identify FeH⁺ in the ISM and help solve important remaining questions in quantifying metal-hydride bonding.

Spin-Adapted Formulation and Implementation of Density Cumulant Functional Theory with Density-Fitting Approximation: Application to Transition Metal Compounds

Density cumulant functional theory (DCT) has recently emerged as an attractive ab initio approach for the treatment of electron correlation. In its orbital-optimized formulation (ODC-12) [J. Chem. Phys. 139, 204110 (2013)], DCT has been shown to provide reliable results for a variety of challenging chemical systems. Among the attractive properties of DCT are its size-consistency and size-extensivity, as well as the efficient computation of the molecular properties and analytic gradients. In this work, we present a new formulation and implementation of DCT that takes advantage of spin adaptation and the density-fitting approximation (DF-ODC-12). Our new spin-adapted DF-ODC-12 implementation is more efficient than the previous ODC-12 implementation with up to a ∼12-fold speed-up. We demonstrate the capabilities of DF-ODC-12 with a study of transition metal compounds, which require high levels of electron correlation treatment. For transition metal carbonyl complexes [Fe(CO)₅, Cr(CO)₆] and the ferrocene molecule [Fe(Cp)₂], the DF-ODC-12 equilibrium parameters and bond dissociation energies extrapolated to the complete basis set limit are in very good agreement with reference data derived from experiment.