Electronic States and Potential Energy Curves of Zirconium and Hafnium Carbon Monoxide

Gas-phase and solid-state electronic structure analysis and DFT benchmarking of HfCO

Ab initio multi-reference configuration interaction (MRCI) and coupled cluster singles doubles and perturbative triples [CCSD(T)] levels of theory were used to study ground and excited electronic states of HfCO. We report potential energy curves, dissociation energies (De), excitation energies, harmonic vibrational frequencies, and chemical bonding patterns of HfCO. The 3Σ- ground state of HfCO has an 1σ22σ21π2 electron configuration and a ∼30 kcal mol-1 dissociation energy with respect to its lowest-energy fragments Hf(3F) + CO(X1Σ+). We further evaluated the De of its isovalent HfCX (X = S, Se, Te, Po) series and observed that they increase linearly from the lighter HfCO to the heavier HfCPo with the dipole moment of the CX ligand. The same linear relationship was observed for TiCX and ZrCX. We utilized the CCSD(T) benchmark values of De, excitation energy, and ionization energy (IE) values to evaluate density functional theory (DFT) errors with 23 exchange-correlation functionals spanning GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, and double-hybrid functional families. The global GGA hybrid B3LYP and range-separated hybrid ωB97X performed well at representing the ground state properties of HfCO (i.e., De and IE). Finally, we extended our DFT analysis to the interaction of a CO molecule with a Hf surface and observed that the surface chemisorption energy and the gas-phase molecular dissociation energy are very similar for some DFAs but not others, suggesting moderate transferability of the benchmarks on these molecules to the solid state.

Spectroscopic and theoretical investigations of vibrational frequencies in binary unsaturated transition-metal carbonyl cations, neutrals, and anions

Figure 18 presents the C-O stretching vibrational frequencies of the first-row transition-metal monocarbonyl cations, neutrals, and anions in solid neon; similar diagrams have been reported for neutral MCO species in solid argon, but three of the early assignments have been changed by recent work and one new assignment added. The laser-ablation method produces mostly neutral atoms with a few percent cations and electrons for capture to make anions; in contrast, thermal evaporation gives only neutral species. Hence, the very recent neon matrix investigations in our laboratory provide carbonyl cations and anions for comparison to neutrals on a level playing field. Several trends are very interesting. First, for all metals, the C-O stretching frequencies follow the order cations > neutrals > anions with large diagnostic 100-200 cm-1 separations, which is consistent with the magnitude of the metal d to CO pi * donation. Second, for a given charge, there is a general increase in C-O stretching vibrational frequencies with increasing metal atomic number, which demonstrates the expected decrease in the metal to CO pi * donation with increasing metal ionization potential. Some of the structure in this plot arises from the extra stability of the filled and half-filled d shell and from the electron pairing that occurs at the middle of the TM row; the plot resembles the "double-humped" graph found for the variation in properties across a row of transition metals. For the anions, the variation with metal atom is the smallest since all of the metals can easily donate charge to the CO ligand. Third, for the early transition-metal Ti, V, and Cr families, the C-O stretching frequencies decrease when going down the family, but the reverse relationship is observed for the late transition-metal Fe, Co, and Ni families. In most of the present discussion, we have referred to neon matrix frequencies; however, the argon matrix frequencies are complementary, and useful information can be obtained from comparison of the two matrix hosts. In most cases, the neon-to-argon red shift for neutral carbonyls is from 11 to 26 cm-1, but a few (CrCO) lie outside of this range. In the case of FeCO and Fe(CO)2, it appears that neon and argon trap different low-lying electronic states. In general, the carbonyl neutrals and anions have similar shifts but carbonyl cations have larger matrix shifts. For example, the FeCO+ fundamental is at 2123.0 cm-1 in neon and 2081.5 cm-1 in argon, a 42.5 cm-1 shift, which is larger than those found for FeCO- (11.7 cm-1) and FeCO (11.7 cm-1). It is unusual for different low-lying electronic states to be trapped in different matrices, but CUO provides another example. The linear singlet state (1047.3, 872.2 cm-1) is trapped in solid neon, and a calculated 1.2 kcal/mol higher triplet state is trapped in solid argon (852.5, 804.3 cm-1) and stabilized by a specific interaction with argon. The bonding trends are well described by theoretical calculations of vibrational frequencies. Table 5 compares the scale factors (observed neon matrix/calculated) for the C-O stretching modes of the monocarbonyl cations, neutrals, and anions of the first-row transition metals observed in a neon matrix using the B3LYP and BP86 density functionals. Most of the calculated carbonyl harmonic stretching frequencies are within 1% of the experimental fundamentals at the BP86 level of theory, while calculations using the B3LYP functional give frequencies that are 3-4% higher as expected for these density functionals and calculations on saturated TM-carbonyls. For second- and third-row carbonyls using the BP86 density functional and the LANL effective core potential in conjunction with the DZ basis set, the agreement between theory and experiment is just as good. For example, the 16 M(CO)1-4 neutral and anion and 2 MCO+ cation (M = Ru, Os) carbonyl frequencies are fit within 1.5%. The 16 species (M = Rh, Ir) are fit within 1%, but the Rh(CO)1-4+ calculations are 2-3% too low and Ir(CO)1-4+ computations are 1-2% too low. In addition to predicting the vibrational frequencies, DFT can be used to calculate different isotopic frequencies, and isotopic frequency ratios can be computed as a measure of the normal vibrational mode in the molecule for an additional diagnostic. For diatomic CO, the 12CO/13CO ratio 1.0225 and C16O/C18O ratio 1.0244 characterize a pure C-O stretching mode. In a series of molecules such as RhCO+, RhCO, and RhCO-, where the metal-CO bonding varies, the Rh-C, C-O vibrational interaction is different and the unique isotopic ratios for the carbonyl vibration are characteristic of that particular molecule. Table 6 summarizes the isotopic ratios observed and calculated for the RhCO+,0,- species. Note that RhCO+ exhibits slightly more carbon-13 and less oxygen-18 involvement in the C-O vibration than CO itself and that this trend increases to RhCO and to RhCO- as the Rh-C bond becomes shorter and stronger. Note also how closely the calculated and observed ratios both follow this trend. In a molecule with two C-O stretching modes, for example, bent Ni(CO)2 exhibits a strong b2 mode at 1978.9 cm-1 and a weak a1 mode at 2089.7 cm-1 in solid neon, and these two modes involve different C and O participations. The symmetric mode shows substantially more C (1.0242) and less O (1.0217) participation than does the antisymmetric mode with C (1.0228) and O (1.0238) involvement, based on the given isotopic frequency ratios, which are nicely matched by DFT calculations (a1 1.0244, 1.0224 and b2 1.0232, 1.0241, respectively). These investigations of vibrational frequencies in unsaturated transition-metal carbonyl cations, neutrals, and anions clearly demonstrate the value of a close working relationship between experiment and theory to identify and characterize new molecular species.