The Dynamic Ligand Field of a Molecular Qubit: Decoherence Through Spin–Phonon Coupling

Quantum coherence of S = 1/2 transition metal-based quantum bits (qubits) is strongly influenced by the magnitude of spin–phonon coupling. While this coupling is recognized as deriving from dynamic distortions about the first coordination sphere of the metal, a general model for understanding and quantifying ligand field contributions has not been established. Here we derive a general ligand field theory model to describe and quantify the nature of spin–phonon coupling terms in S = 1/2 transition metal complexes. We show that the coupling term for a given vibrational mode is governed by: 1) the magnitude of the metal-based spin–orbit coupling constant, 2) the magnitude and gradient in the ligand field excited state energy, and 3) dynamic relativistic nephelauxetic contributions reflecting the magnitude and gradient in the covalency of the ligand–metal bonds. From an extensive series of density functional theory (DFT) and time-dependent DFT (TDDFT) calculations calibrated to a range of experimental data, spin–phonon coupling terms describing minimalistic D_(4h)/D_(2d) [CuCl₄]²⁻ and C_(4v) [VOCl²⁻ complexes translate to and correlate with experimental quantum coherence properties observed for Cu(II)- and V(IV)-based molecular qubits with different ligand sets, geometries, and coordination numbers. While providing a fundamental framework and means to benchmark current qubits, the model and methodology described herein can be used to screen any S = 1/2 molecular qubit candidate and guide the discovery of room temperature coherent materials for quantum information processing

Interpretation of the UV-vis spectra of the meso(ferrocenyl)-containing porphyrins using a TDDFT approach: is Gouterman's classic four-orbital model still in play?

The vertical excitation energies of H_2TPP [TPP = 5,10,15,20-tetraphenylporphyrin(2-)], H_2FcPh_3P [FcPh_3P = 5-ferrocenyl-10,15,20-triphenylporphyrin(2-)], cis-H_2Fc_2Ph_2P [cis-Fc_2Ph_2P = 5,10-bisferrocenyl-15,20-diphenylporphyrin (2-)], trans-H_2Fc_2Ph_2P [trans-Fc_2Ph_2P = 5,15-bisferrocenyl-10,20-diphenylporphyrin(2-)], H_2Fc_3PhP [H_2Fc_3PhP = 5,10,15-trisferrocenyl-20-phenylporphyrin(2-)], and H_2TFcP [TFcP = 5,10,15,20-tetraferrocenylporphyrin(2-)] were investigated using a time-dependent density functional theory (DFT) approach and compared to their experimental UV-vis spectra in the 10,000-30,000 cm^(-1) region. It was shown that the lowest energy transitions in meso(ferrocenyl)-containing porphyrins have predominantly ferrocene-to-porphyrin charge transfer character, while the porphyrin-centered π-π* transitions predicted by the Gouterman's classic four-orbital model still have the largest intensities in the UV-vis region. The number of predominantly ferrocene-to-porphyrin charge transfer transitions increases with the number of ferrocene substituents and becomes dominant in H_2TFcP

Influence of Hartree-Fock exchange on the calculated Mössbauer isomer shifts and quadrupole splittings in ferrocene derivatives using density functional theory

Influence of molecular geometry, type of exchange-correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of ^(57)Fe Mössbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter's full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange-correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange-correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange-correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree-Fock exchange involved in the applied exchange-correlation functional and the calculated HOMO-LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange-correlation functionals has been suggested for accurate prediction of Mössbauer spectra parameters in ferrocenes

Exploring the ground and excited state potential energy landscapes of the mixed-valence biferrocenium complex

Density functional theory (DFT) and time-dependent DFT (TDDFT) have been used to explore the potential energy landscapes in the class II (in Robin and Day classification) mixed-valence biferrocenium mono-cation (BF^+) in an effort to evaluate factors affecting optical and thermal intramolecular electron transfer rates. Both energy- and spectroscopy-based benchmarks were used to explore the adiabatic potential energy surfaces (PESs) of the mixed-valence BF^+ cation along with the optimization of appropriate ground-, excited-, and transition-state geometries. The calculation of Mossbauer isomer shifts and quadrupole splittings, UV-vis excitation energies, and the electronic coupling matrix element, H_(ab), corroborate the PES analyses. The adiabatic electron transfer pathway is also analyzed with respect to several possible vibronic coordinates. The degree of the electronic coupling between iron sites, the value of H_(ab), and the nature of the electron transfer pathway correlate with the amount of Hartree-Fock exchange involved in the DFT calculation with hybrid (approximately 20% of Hartree-Fock exchange) methods providing the best agreement between theory and experiment. DFT (B3LYP) predicted values of H_(ab) (839, 1085, and 1265 cm^(-1)) depend on the computational method and are in good agreement with experimental data

Controlling Singlet Fission with Coordination Chemistry-Induced Assembly of Dipyridyl Pyrrole Bipentacenes

Singlet fission has the potential to surpass current efficiency limits in next-generation photovoltaics and to find use in quantum information science. Despite the demonstration of singlet fission in various materials, there is still a great need for fundamental design principles that allow for tuning of photophysical parameters, including the rate of fission and triplet lifetimes. Here, we describe the synthesis and photophysical characterization of a novel bipentacene dipyridyl pyrrole (HDPP-Pent) and its Li- and K-coordinated derivatives. HDPP-Pent undergoes singlet fission at roughly 50% efficiency (τ_(SF) = 730 ps), whereas coordination in the Li complex induces significant structural changes to generate a dimer, resulting in a 7-fold rate increase (τ_(SF) = 100 ps) and more efficient singlet fission with virtually no sacrifice in triplet lifetime. We thus illustrate novel design principles to produce favorable singlet fission properties, wherein through-space control can be achieved via coordination chemistry-induced multipentacene assembly

Controlling Singlet Fission with Coordination Chemistry-Induced Assembly of Dipyridyl Pyrrole Bipentacenes

Singlet fission has the potential to surpass current efficiency limits in next-generation photovoltaics and to find use in quantum information science. Despite the demonstration of singlet fission in various materials, there is still a great need for fundamental design principles that allow for tuning of photophysical parameters, including the rate of fission and triplet lifetimes. Here, we describe the synthesis and photophysical characterization of a novel bipentacene dipyridyl pyrrole (HDPP-Pent) and its Li- and K-coordinated derivatives. HDPP-Pent undergoes singlet fission at roughly 50% efficiency (τ_(SF) = 730 ps), whereas coordination in the Li complex induces significant structural changes to generate a dimer, resulting in a 7-fold rate increase (τ_(SF) = 100 ps) and more efficient singlet fission with virtually no sacrifice in triplet lifetime. We thus illustrate novel design principles to produce favorable singlet fission properties, wherein through-space control can be achieved via coordination chemistry-induced multipentacene assembly

Comparative calculation of EPR spectral parameters in [Mo^VOX_4]^-, [Mo^VOX_5]^(2-), and [Mo^VOX_4(H_2O)]^- complexes

The EPR spectral parameters, i.e. g-tensors and molybdenum hyperfine couplings, for several d^1 systems of the general formula [Mo^VEX_4]^(n-), [Mo^VOX_5]^(2-), and [Mo^VOX_4(H_2O)]^- (E = O, N; X = F, Cl, Br; n = 1 or 2) were calculated using Density Functional Theory. The influence of basis sets, their contraction scheme, the type of exchange-correlation functional, the amount of Hartree-Fock exchange, molecular geometry, and relativistic effects on the calculated EPR spectra parameters have been discussed. The g-tensors and molybdenum hyperfine coupling parameters were calculated using a relativistic Hamiltonian coupled with several LDA, GGA, and 'hybrid' exchange-correlation functionals and uncontracted full-electron DGauss DZVP basis sets. The calculated EPR parameters are found to be sensitive to the Mo=E distance and E=Mo-Cl angle, and thus the choice of starting molecular geometry should be considered as an important factor in predicting the g-tensors and hyperfine coupling constants in oxo-molybdenum compounds. In the present case, the GGA exchange-correlation functionals provide a better agreement between the theory and the experiment