Pseudopotential-Based Correlation Consistent Composite Approach (rp-ccCA) for First- and Second-Row Transition Metal Thermochemistry

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T₀) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T₀) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T₀). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium-Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D_e and bond length r_e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15-0.19. For the single-reference methods, Kohn-Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D_e and r_e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core-valence terms; this results in highly accurate dissociation energies and good bond lengths. Averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

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.

Predissociation Measurements of Bond Dissociation Energies

A fundamental need in chemistry is understanding the chemical bond, for which the most quantitative measure is the bond dissociation energy (BDE). While BDEs of chemical bonds formed from the lighter main group elements are generally well-known and readily calculated by modern computational chemistry, chemical bonds involving the transition metals, lanthanides, and actinides remain computationally extremely challenging. This is due to the simultaneous importance of electron correlation, spin-orbit interaction, and other relativistic effects, coupled with the large numbers of low-lying states that are accessible in systems with open d or f subshells. The development of efficient and accurate computational methods for these species is currently a major focus of the field. An obstacle to this effort has been the scarcity of highly precise benchmarks for the BDEs of M-X bonds. For most of the transition metal, lanthanide, or actinide systems, tabulated BDEs of M-X bonds have been determined by Knudsen effusion mass spectrometric measurements of high-temperature equilibria. The measured ion signals are converted to pressures and activities of the species involved in the equilibrium, and the equilibrium constants are then analyzed using a van't Hoff plot or the third-law method to extract the reaction enthalpy, which is extrapolated to 0 K to obtain the BDE. This procedure introduces errors at every step and ultimately leads to BDEs that are typically uncertain by 2-20 kcal mol^-1 (0.1-1 eV). A second method in common use employs a thermochemical cycle in which the ionization energies of the MX molecule and M atom are combined with the BDE of the M⁺-X bond, obtained via guided ion beam mass spectrometry, to yield the BDE of the neutral, M-X. When accurate values of all three components of the cycle are available, this method yields good results-but only rarely are all three values available. We have recently implemented a new method for the precise measurement of BDEs in molecules with large densities of electronic states that is based on the rapid predissociation of these species as soon as the ground separated atom limit is exceeded. When a sharp predissociation threshold is observed, its value directly provides the BDE of the system. With this method, we are able in favorable cases to determine M-X BDEs to an accuracy of ∼0.1 kcal mol^-1 (0.004 eV). The method is generally applicable to species that have a high density of states at the ground separated atom limit and has been used to measure the BDEs of more than 50 transition metal-main group MX molecules thus far. In addition, a number of metal-metal BDEs have also been measured with this method. There are good prospects for the extension of the method to polyatomic systems and to lanthanide and actinide-containing molecules. These precise BDE measurements provide chemical trends for the BDEs across the transition metal series, as well as crucial benchmarks for the development of efficient and accurate computational methods for the d- and f-block elements.

Bond dissociation energies of FeSi, RuSi, OsSi, CoSi, RhSi, IrSi, NiSi, and PtSi

Resonant two-photon ionization spectroscopy has been used to investigate the spectra of the diatomic late transition metal silicides, MSi, M = Fe, Ru, Os, Co, Rh, Ir, Ni, and Pt, in the vicinity of the bond dissociation energy. In these molecules, the density of vibronic states is so large that the spectra appear quasicontinuous in this energy range. When the excitation energy exceeds the ground separated atom limit, however, a new decay process becomes available-molecular dissociation. This occurs so rapidly that the molecule falls apart before it can absorb another photon and be ionized. The result is a sharp drop to the baseline in the ion signal, which we identify as occurring at the thermochemical 0 K bond dissociation energy, D₀. On this basis, the measured predissociation thresholds provide D₀ = 2.402(3), 4.132(3), 4.516(3), 2.862(3), 4.169(3), 4.952(3), 3.324(3), and 5.325(9) eV for FeSi, RuSi, OsSi, CoSi, RhSi, IrSi, NiSi, and PtSi, respectively. Using thermochemical cycles, the enthalpies of formation of the gaseous MSi molecules are derived as 627(8), 700(10), 799(10), 595(8), 599(8), 636(10), 553(12), and 497(8) kJ/mol for FeSi, RuSi, OsSi, CoSi, RhSi, IrSi, NiSi, and PtSi, respectively. Likewise, combining these results with other data provides the ionization energies of CoSi and NiSi as 7.49(7) and 7.62(7) eV, respectively. Chemical bonding trends among the diatomic transition metal silicides are discussed.

Bond dissociation energies of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi

Predissociation thresholds have been observed in the resonant two-photon ionization spectra of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi. It is argued that because of the high density of electronic states at the ground separated atom limit in these molecules, the predissociation threshold in each case corresponds to the thermochemical bond dissociation energy. The resulting bond dissociation energies are D₀(TiSi) = 2.201(3) eV, D₀(ZrSi) = 2.950(3) eV, D₀(HfSi) = 2.871(3) eV, D₀(VSi) = 2.234(3) eV, D₀(NbSi) = 3.080(3) eV, and D₀(TaSi) = 2.999(3) eV. The enthalpies of formation were also calculated as Δ_f,0KH°(TiSi(g)) = 705(19) kJ mol^-1, Δ_f,0KH°(ZrSi(g)) = 770(12) kJ mol^-1, Δ_f,0KH°(HfSi(g)) = 787(10) kJ mol^-1, Δ_f,0KH°(VSi(g)) = 743(11) kJ mol^-1, Δ_f,0KH°(NbSi(g)) = 879(11) kJ mol^-1, and Δ_f,0KH°(TaSi(g)) = 938(8) kJ mol^-1. Using thermochemical cycles, ionization energies of IE(TiSi) = 6.49(17) eV and IE(VSi) = 6.61(15) eV and bond dissociation energies of the ZrSi^- and NbSi^- anions, D₀(Zr-Si^-) ≤ 3.149(15) eV, D₀(Zr^--Si) ≤ 4.108(20) eV, D₀(Nb-Si^-) ≤ 3.525(31) eV, and D₀(Nb^--Si) ≤ 4.017(39) eV, have also been obtained. Calculations on the possible low-lying electronic states of each species are also reported.

Towards a quantum chemical protocol for the prediction of rovibrational spectroscopic data for transition metal molecules: Exploration of CuCN, CuOH, and CuCCH

High accuracy electronic structure computations for small transition metal-containing molecules have been a long term challenge. Due to coupling between electronic and nuclear wave functions, even experimental/theoretical identification of the ground electronic state requires tremendous efforts. Quartic force fields (QFFs) are effective ab initio tools for obtaining reliable anharmonic spectroscopic properties. However, the method that employs complete basis set limit extrapolation ("C"), consideration of core electron correlation ("cC"), and inclusion of scalar relativity ("R") to produce the energy points on the QFF, the composite CcCR methodology, has not yet been utilized to study inorganic spectroscopy. This work takes the CcCR methodology and adapts it to test whether such an approach is conducive for the closed-shell, copper-containing molecules CuCN, CuOH, and CuCCH. Gas phase rovibrational data are provided for all three species in their ground electronic states. Equilibrium geometries and many higher-order rovibrational properties show good agreement with earlier studies. However, there are notable differences, especially in computation of fundamental vibrational frequencies. Even with further additive corrections for the inner core electron correlation and coupled cluster with full single, double, and triple substitutions (CCSDT), the differences are still larger than expected indicating that more work should follow for predicting rovibrational properties of transition metal molecules.

Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works

It was recently reported ( J. Chem. Theory Comput. 2015 , 11 , 2036 - 2052 ) that the coupled cluster singles and doubles with perturbative triples method, CCSD(T), should not be used as a benchmark tool for the prediction of dissociation energies (heats of formation) for the first row transition metal diatomics based on a comparison with the experimental thermodynamic values for a set of 20 diatomics. In the present work the bond dissociation energies as well as the heats of formation for those diatomics have been calculated by the Feller-Peterson-Dixon approach at the CCSD(T)/complete basis set (CBS) level of theory including scalar relativistic corrections and correlation of the outer shell of core electrons in addition to the valence electrons. Revised experimental values for the hydrides are presented that are based on new heterolytic R-H bond dissociation energies, which are needed for analysis of the mass spectrometry experiments. The agreement between the calculated bond dissociation energies and the revised experimental values of the hydrides is good. Good agreement of the calculated bond dissociation energies/heats of formation is also found for most of the chlorides, oxides, and sulfides given the experimental error bars from experiment and those of the transition metal atoms in the gas phase. Thus, reliable results can be achieved by the CCSD(T) method at the CBS limit. The use of PW91 orbitals for the CCSD(T) calculations improves the predictions for some compounds with large T₁ diagnostics at the HF-CCSD(T) level. The optimized bond distances and calculated vibrational frequencies for the diatomics also agree well with the available experimental values.