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.

Long-range electron tunneling

Electrons have so little mass that in less than a second they can tunnel through potential energy barriers that are several electron-volts high and several nanometers wide. Electron tunneling is a critical functional element in a broad spectrum of applications, ranging from semiconductor diodes to the photosynthetic and respiratory charge transport chains. Prior to the 1970s, chemists generally believed that reactants had to collide in order to effect a transformation. Experimental demonstrations that electrons can transfer between reactants separated by several nanometers led to a revision of the chemical reaction paradigm. Experimental investigations of electron exchange between redox partners separated by molecular bridges have elucidated many fundamental properties of these reactions, particularly the variation of rate constants with distance. Theoretical work has provided critical insights into the superexchange mechanism of electronic coupling between distant redox centers. Kinetics measurements have shown that electrons can tunnel about 2.5 nm through proteins on biologically relevant time scales. Longer-distance biological charge flow requires multiple electron tunneling steps through chains of redox cofactors. The range of phenomena that depends on long-range electron tunneling continues to expand, providing new challenges for both theory and experiment.

Outer valence ionic states of Cr(CO)6 and (eta(5)-C5H5)Co(CO)2 observed by two-dimensional penning ionization electron spectroscopy

Outer valence ionic states of Cr(CO)(6) and (eta(5)-C(5)H(5))Co(CO)(2) were investigated by means of Penning ionization electron spectroscopy (PIES) upon collision with metastable He*(2(3)S) excited atoms as well as high-level ab initio molecular orbital calculations taking electron correlation effects into consideration. By the 2D measurement combining the collision-energy-resolved technique of the metastable atomic beam and electron spectroscopy, ionic-state-resolved measurement of collision energy dependence of partial ionization cross sections (CEDPICS) was carried out. Because partial Penning ionization cross sections can be connected to the spatial extent of corresponding molecular orbitals (MOs) outside the boundary surface of colliding He* atoms, different slopes of CEDPICS were related to anisotropic interaction around the MO region. The observed CEDPICS and PIES band intensity were consistent with the order of calculated ionic states.

Stereodynamics and outer valence ionic States of ferrocene in collisional ionization with a He*(2(3)S) metastable atom by two-dimensional penning ionization electron spectroscopy

Outer valence ionic states of ferrocene were investigated by means of Penning ionization electron spectroscopy upon collision with metastable He*(2(3)S) excited atoms. By two-dimensional measurement combining electron spectroscopy and collision-energy-resolved technique of the metastable atomic beam, ionic-state-resolved measurements of collision energy dependence of partial Penning ionization cross sections (CEDPICS) were carried out. Since the partial Penning ionization cross sections can be connected with spatial extension of corresponding molecular orbitals (MOs) outside the boundary surface for the collision with He* atoms, different slope values of CEDPICS were related with stereodynamics in Penning ionization as well as anisotropic interaction around the ionization region: attractive interaction around ligand pi orbitals and repulsive interaction around ligand sigma orbtials and the metal atom. The observed negative collision energy dependence of ionization cross sections for the first ((2)E(2)') and second ((2)A(1)') ionic states was consistent with configuration interactions suggested by ab initio MO calculations [J. Chem. Phys. 2002, 117, 6533], which is due to the strong electron correlation effects beyond the one-electron MO description.

Dipolar Second-Order Nonlinear Optical Chromophores Containing Ferrocene, Octamethylferrocene, and Ruthenocene Donors and Strong π-Acceptors: Crystal Structures and Comparison of π-Donor Strengths

Crystal structures have been determined for six dipolar polyene chromophores with metallocenyl - ferrocenyl (Fc), octamethylferrocenyl (Fc″), or ruthenocenyl (Rc) - donors and strong heterocyclic acceptors based on 1,3-diethyl-2-thiobarbituric acid or 3-dicyanomethylidene-2,3-dihydrobenzothiophene-1,1-dioxide. In each case, crystals were found to belong to centrosymmetric space groups. For one example, polymer-induced heteronucleation revealed the existence of two additional polymorphs, which were inactive in second-harmonic generation, suggesting that they were also centrosymmetric. The bond-length alternations between the formally double and single bonds of the polyene bridges are reduced compared to simple polyenes, indicating significant contribution from charge-separated resonance structures, although the metallocenes are not significantly distorted towards the [(η(6)-fulvene)(η(5)-cyclopentadienyl)metal(II)](+) extreme. DFT geometries are in excellent agreement with those determined crystallographically; while the π-donor strengths of the three metallocenyl groups are insufficiently different to result in detectable differences in the crystallographic bond-length alternations, the DFT geometries, as well as DFT-calculations of partial charges for atoms, suggest that π-donor strength decreases in the order Fc″ ≫ Fc > Rc. NMR, IR and electrochemical evidence also suggests that octamethylferrocenyl is the stronger π-donor, exhibiting similar π-donor strength to a p-(dialkylamino)phenyl group, while ferrocenyl and ruthenocenyl show very similar π-donor strengths to one another in chromophores of this type.

Strong oscillations in molecular valence photoemission intensities

Photoemission from the two outermost ionizations [highest occupied molecular orbitals (HOMO and HOMO-1)] of Mg(eta(5)-C(5)H(5))(2) has been studied with synchrotron radiation in the gas phase. Strong oscillations in the HOMO-1/HOMO ratio, qualitatively similar to those well-known for fullerenes, are found. Excellent agreement with the experimental ratio is provided by accurate cross section calculations both at the density-functional theory and time-dependent density-functional theory level, indicating that a many electron response has a minor role for this effect. A comparison with the calculated values for other metal sandwich compounds indicate that the presence of oscillations is a widespread phenomenon, and a potential source of interesting information on the structural and electronic properties of the target molecule.

Electronic structure of [(CpCr)[(CO)3M]]mu-Cot (M = Cr, Fe): a theoretical study

The electronic structure of two cyclooctatetraene-bridged dinuclear first-row transition metal complexes of the type [(CpM)[(CO)3M']]mu-Cot (M = Cr; M' = Fe (1), Cr (2)) was investigated by complete active space self-consistent field (CASSCF) calculations. In this context the differences in the binding capabilities of the complex fragments CpM and (CO)3M are discussed on the basis of extended Huckel molecular orbital (MO) calculations. The geometries used for the CASSCF calculations for complex 1 were obtained from the crystal structure. For 2 a model structure was established by geometry optimization using density functional methods. The CASSCF results agree well with the experimental findings and provide insight into the binding situation of the two compounds. Complex 1 can be regarded as being composed of a chromocene-like subunit CpCr(eta5-C5H5) and the fragment (CO)3Fe(eta3-C3H3). A direct metal-metal bond is found, involving one initially singly occupied orbital of each fragment, leading to a doublet ground state for 1 with the remaining unpaired electron localized at the chromium center. For 2 no such direct metal-metal bond can be recognized. A very weak direct metal-metal interaction is induced by electron donation from the Cot2- ligand into a formally unoccupied metal-metal binding orbital combination. In the quartet ground state all three unpaired electrons are localized at the chromium center of the formally doubly positive charged CpCr unit, on which complex fragment [(CO)3Cr(eta5-Cot)]2- acts like a cyclopentadienyl ligand. The coordination sphere of the chromium center of the CpCr unit resembles that of a metallocene metal center and its metal 3d occupation scheme corresponds to that of vanadocene.