Potential energy surfaces for Rh–CO, Rh–OC, Ir–CO, and Ir–OC interactions

Computational Analysis of Chemical Reactions Using a Variational Quantum Eigensolver Algorithm without Specifying Spin Multiplicity

The analysis of a chemical reaction along the ground-state potential energy surface in conjunction with an unknown spin state is challenging because electronic states must be separately computed several times using different spin multiplicities to find the lowest energy state. However, in principle, the ground state could be obtained with just a single calculation using a quantum computer without specifying the spin multiplicity in advance. In the present work, ground-state potential energy curves for PtCO were calculated as a proof-of-concept using a variational quantum eigensolver (VQE) algorithm. This system exhibits a singlet-triplet crossover as a consequence of the interaction between Pt and CO. VQE calculations using a statevector simulator were found to converge to a singlet state in the bonding region, while a triplet state was obtained at the dissociation limit. Calculations performed using an actual quantum device provided potential energies within ±2 kcal/mol of the simulated energies after error mitigation techniques were adopted. The spin multiplicities in the bonding and dissociation regions could be clearly distinguished even in the case of a small number of shots. The results of this study suggest that quantum computing can be a powerful tool for the analysis of the chemical reactions of systems for which the spin multiplicity of the ground state and variations in this parameter are not known in advance.

THEORETICAL STUDY OF NITROGEN MONOXIDE ADSORPTION ON RHODIUM CLUSTERS AT DIFFERENT SITES

The adsorption of nitrogen monoxide NO with charged and neutral [Formula: see text] clusters at atop, bridge, and threefold hollow sites had been investigated by density functional theory calculations. The results showed that rhodium clusters had strong orbital interactions with NO and formed the complex [ Rh n NO ]-/0/+. The stretching vibrational frequencies of the N–O bonds changed with the different adsorption sites and clusters sizes. The interactions between rhodium clusters and NO molecular could be described through the donation and back-donation of their frontier orbitals. The more back donation from Rh to NO , the weaker the N–O bonds, exhibiting that the lengthening of the N–O bond length and the lowering of its vibrational frequency. In general, the donation and back-donation interactions followed the tendencies: anionic > neutral > cationic, big size > small size, threefold hollow site > bridge site > atop site.

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.