Taming the low-lying electronic states of FeH

Fulminic acid: a quasibent spectacle

Fulminic acid (HCNO) played a critical role in the early development of organic chemistry, and chemists have sought to discern the structure and characteristics of this molecule and its isomers for over 200 years. The mercurial nature of the extremely flat H-C-N bending potential of fulminic acid, with a nearly vanishing harmonic vibrational frequency at linearity, remains enigmatic and refractory to electronic structure theory, as dramatic variation with both orbital basis set and electron correlation method is witnessed. To solve this problem using rigorous electronic wavefunction methods, we have employed focal point analyses (FPA) to ascertain the ab initio limit of optimized linear and bent geometries, corresponding vibrational frequencies, and the HCN + O(3P) → HCNO reaction energy. Electron correlation treatments as extensive as CCSDT(Q), CCSDTQ(P), and even CCSDTQP(H) were employed, and complete basis set (CBS) extrapolations were performed using the cc-pCVXZ (X = 4-6) basis sets. Core electron correlation, scalar relativistic effects (MVD1), and diagonal Born-Oppenheimer corrections (DBOC) were all included and found to contribute significantly in determining whether vibrationless HCNO is linear or bent. At the all-electron (AE) CCSD(T)/CBS level, HCNO is a linear molecule with ω5(H-C-N bend) = 120 cm-1. However, composite AE-CCSDT(Q)/CBS computations give an imaginary frequency (51i cm-1) at the linear optimized geometry, leading to an equilibrium structure with an H-C-N angle of 173.9°. Finally, at the AE-CCSDTQ(P)/CBS level, HCNO is once again linear with ω5 = 45 cm-1, and inclusion of both MVD1 and DBOC effects yields ω5 = 32 cm-1. A host of other topics has also been investigated for fulminic acid, including the dependence of re and ωi predictions on a variety of CBS extrapolation formulas, the question of multireference character, the N-O bond energy and enthalpy of formation, and issues that give rise to the quasibent appellation.

A route to high-accuracy ab initio description of electronic excited states in high-spin lanthanide-containing species: A case study of GdO

Accurate description of electronic excited states of high-spin molecular species is a yet unsolved problem in modern electronic structure theory. A composite computational scheme developed in the present work contributes to solving this task for a challenging case of lanthanide-containing molecules. In the scheme, the highest-spin states whose wavefunctions are dominated by a single Slater determinant are described at the single-reference (SR) CCSD(T) level, whereas the lower-spin states, being inherently multiconfigurational in their nature, are treated with multireference (MR) methods, MRCI and/or CASPT2. An original technique which scales MR results against SR CCSD(T) ones to improve the accuracy in the former is proposed and examined, taking the example of 12 electronic states of gadolinium monoxide, X9Σ-, Y7Σ-, A'9Δ, A1'7Δ, A9Π, A17Π, B9Σ-, B17Σ-, C9Π, C17Π, D9Σ-, and D17Σ-, up to 35 000 cm-1. A multitude of the corresponding Ω (spin-coupled) states was then studied within the state-interacting approach employing the full Breit-Pauli spin-orbit coupling operator with CASSCF-generated ΛS states as a basis. For all ΛS and Ω states, the Gd-O bond lengths, spectroscopic constants ωe, ωexe, αe, and adiabatic excitation energies are obtained. The theoretical predictions are in good agreement with the experimental data, with deviations in excitation energies not exceeding 350 cm-1 (1 kcal/mol). The spectroscopic properties of the yet unobserved electronic states, A'9Δ, A1'7Δ, C9Π, C17Π, D9Σ-, and D17Σ-, are evaluated for the first time.

Laser-based spectroscopy of FeD: Excitations to the g 6Φ electronic state

Bands of the g ⁶Φ-X ⁴Δ, g ⁶Φ-A ⁴Π, g ⁶Φ-a ⁶Δ, and g ⁶Φ-b ⁶Π electronic transitions of iron monodeuteride (FeD) have been measured in laser excitation and in dispersed fluorescence. The molecules were produced both in a cold supersonic molecular jet source and in a chemical reaction between iron pentacarbonyl [Fe(CO₅)] and a microwave discharge of argon and hydrogen gases. Dispersed fluorescence from the latter source was detected at high resolution with a Fourier transform spectrometer, yielding a large number of the transitions observed. The data reveal that FeD experiences strong interstate couplings that compromise fitting of the data with traditional Hamiltonians but that the problem is less severe than in corresponding spectra of FeH. This work greatly expands the available data on FeD, which were previously characterized only through the F ⁴Δ-X ⁴Δ spectrum and pure rotational data in the ground state.

Route to Chemical Accuracy for Computational Uranium Thermochemistry

Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO₂) and for the bond dissociation energies of UO and UO₂ are reported. The accuracy of these calculations in the treatments of relativistic, electron-correlation, and basis-set effects is analyzed. The intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).

Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair-density functional theory (MC-PDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. The analysis of a dataset consisting of 18 first-row transition-metal diatomics and 6 main-group polyatomic molecules with a multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2-0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated-participating-orbitals scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMC-PDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.

Exploring the excited states of the GeH+ radical cation including spin-orbit interaction: A revisited study

In this paper, we have carried out high-level ab initio calculations on the electronic states of GeH⁺ with the configuration interaction method. The spin-orbit coupling (SOC), core-valence correlation (CV), scalar relativistic effects and Davidson correction (+Q) are included. The potential energy curves (PECs) of 13 Λ-S correlated with the four lowest dissociation limits and 32 Ω electronic states generated from those Λ-S states are obtained. Our results indicate that the first ³Σ^- and second ³Π states are adiabatically correlated with the dissociation limit Ge(³P_g) + H⁺(¹S), which is different from the previously reported Ge⁺(⁴P_g) + H(²S_g). From the computed PECs, the spectroscopic constants of the Λ-S and Ω states are determined, which are in good agreement with previous experiments. The dipole moments (DMs) for Λ-S electronic states are also investigated. With the help of spin-orbit coupling matrix involving the 1³Σ^- and 2³Π states, the intricate couplings related with the crossing states are revealed, and the weak predissociation for ν' ≥0 vibrational levels of 1³Σ^- and the perturbations for vibrational levels of 2¹Σ⁺ (ν' ≥1) and 1¹Δ (ν' ≥0) states are analyzed. Finally, the transition properties of five transitions are predicted, including the Franck-Condon Factors (FCFs), transition dipole moments (TDMs), and the spontaneous radiative lifetimes of lower vibrational states. This study will improve our comprehension on the detailed electronic structure and spectroscopy of GeH⁺ radical cation.

Rovibrational Quantum Chemical Treatment of Inorganic and Organometallic Astrochemicals

ConspectusOur two groups have both independently and collaboratively been pushing quantum-chemical techniques to produce highly accurate predictions of anharmonic vibrational frequencies and spectroscopic constants for molecules containing atoms outside of the typical upper p block. Methodologies employ composite approaches, relying on various levels of coupled cluster theory-most often at the singles, doubles, and perturbative triples level-and quartic force field constructions of the potential portion of the intramolecular Watson Hamiltonian. Such methods are known to perform well for organic species, and we have extended this to molecules containing atoms outside of this realm.One notable atom that has received much attention in this application is magnesium. Mg is the second-most-abundant element in the Earth's mantle, and while molecules containing this element are among the confirmed astrochemicals, its further atomic abundance in the galaxy implies that many more molecules (both purely inorganic and organometallic) containing element 12 exist in astrophysical regions in chemical sizes between those of atoms and dust-sized nanocrystals. Our approach discussed herein is producing quality benchmarks and predicting novel data for magnesium-bearing molecules.The story is similar for Al and Si, which are also notably abundant in both rocky bodies and the universe at large. While Na, Sc, and Cu may not be as abundant as Mg, Al, and Si, molecules containing Na and transition metals have also previously been reported to be detected beyond the Earth. Consequently, the need to produce spectral reference data for molecules containing such atoms is growing. While several experimental groups (including, notably, the groups in Arizona, Boston, and France/Spain) have clearly led the way in detection of inorganic/organometallic molecules in space, computational support and even rational design can provide novel avenues for the detection of molecules containing atoms not typically studied in most laboratories. The application of quantum chemistry to other elements beyond carbon and its cronies at the top right of the periodic table promises a better understanding of the observable universe. It will also provide novel and fundamental chemical insights pushing the "central science" into new molecular territory.

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.

Riddles of the structure and vibrational dynamics of HO3 resolved near the ab initio limit

The hydridotrioxygen (HO₃) radical has been investigated in many previous theoretical and experimental studies over several decades, originally because of its possible relevance to the tropospheric HO_x cycle but more recently because of its fascinating chemical bonding, geometric structure, and vibrational dynamics. We have executed new, comprehensive research on this vexing molecule via focal point analyses (FPA) to approach the ab initio limit of optimized geometric structures, relative energies, complete quartic force fields, and the entire reaction path for cis-trans isomerization. High-order coupled cluster theory was applied through the CCSDT(Q) and even CCSDTQ(P) levels, and CBS extrapolations were performed using cc-pVXZ (X = 2-6) basis sets. The cis isomer proves to be higher than trans by 0.52 kcal mol^-1, but this energetic ordering is achieved only after the CCSDT(Q) milestone is reached; the barrier for cis → trans isomerization is a minute 0.27 kcal mol^-1. The FPA central r_e(O-O) bond length of trans-HO₃ is astonishingly long (1.670 Å), consistent with the semiexperimental r_e distance we extracted from microwave rotational constants of 10 isotopologues using FPA vibration-rotation interaction constants (α_i). The D₀(HO-O₂) dissociation energy converges to a mere 2.80 ± 0.25 kcal mol^-1. Contrary to expectation for such a weakly bound system, vibrational perturbation theory performs remarkably well with the FPA anharmonic force fields, even for the torsional fundamental near 130 cm^-1. Exact numerical procedures are applied to the potential energy function for the torsional reaction path to obtain energy levels, tunneling rates, and radiative lifetimes. The cis → trans isomerization occurs via tunneling with an inherent half-life of 1.4 × 10^-11 s and 8.6 × 10^-10 s for HO₃ and DO₃, respectively, thus resolving the mystery of why the cis species has not been observed in previous experiments executed in dissipative environments that allow collisional cooling of the trans-HO₃ product. In contrast, the pure ground eigenstate of the cis species in a vacuum is predicted to have a spontaneous radiative lifetime of about 1 h and 5 days for HO₃ and DO₃, respectively.

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.

Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born–Oppenheimer breakdown corrections

Analytical and numerical solutions describing Born–Oppenheimer breakdown in a simple, widely applicable, model depict shortcomings in modern computational methods.

Is near-"spectroscopic accuracy" possible for heavy atoms and coupled cluster theory? An investigation of the first ionization potentials of the atoms Ga-Kr

Recent developments in ab initio coupled cluster (CC) theory and correlation consistent basis sets have ushered in an era of unprecedented accuracy when studying the spectroscopy and thermodynamics of molecules containing main group elements. These same developments have recently seen application to heavier inorganic or transition metal-containing species. The present work benchmarks conventional single reference coupled cluster theory (up to full configuration interaction for valence electron correlation and coupled cluster with up to full pentuple excitations (CCSDTQP) for core-valence correlation) and explicitly correlated coupled cluster methods [CC with single, double, and perturbative triple substitutions (CCSD(T)-F12)] for the atomic ionization potentials of the six 4p elements (Ga-Kr), a property with experimental error bars no greater than a few cm(-1). When second-order spin orbit coupling effects are included, a composite methodology based on CCSD(T) calculations yielded a mean signed error of just -0.039 kcal mol(-1) and a mean unsigned error of 0.043 kcal mol(-1). Inclusion of post-CCSD(T) correlation corrections reduced both of these values to -0.008 kcal mol(-1) and 0.025 kcal mol(-1), respectively, with the latter corresponding to an average error of just 9 cm(-1). The maximum signed error in the latter scheme was just -0.043 kcal mol(-1) (15 cm(-1)).