Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer.

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

The contribution of Compton ionization to ultrafast x-ray scattering.

We investigate the role of Compton ionization in ultrafast non-resonant x-ray scattering using a molecular model system, which includes the ionization continuum via an orthonormalized plane wave ansatz. Elastic and inelastic components of the scattering signal, as well as coherent-mixed scattering that arises from electron dynamics, are calculated. By virtue of a near-quantitative distinction between scattering related to electronic transitions into bound and continuum states, we demonstrate how Compton ionization contributes to the coherent-mixed component. Analogous to inelastic scattering, the contribution to the coherent-mixed signal is significant and particularly manifests at intermediate and high-momentum transfers. Strikingly, for molecules with inversion symmetry, the exclusion of bound or continuum transitions may lead to the prediction of spurious coherent-mixed signals. We conclude that qualitative and quantitative accuracies of predicted scattering signals on detectors without energy resolution require that elements of the two-electron density operator are used. This approach inherently accounts for all accessible electronic transitions, including ionization.

Nuclear-Electron Correlation Effects and Their Photoelectron Imprint in Molecular XUV Ionisation.

The ionisation of molecules by attosecond XUV pulses is accompanied by complex correlated dynamics, such as the creation of coherent electron wave packets in the parent ion, their interplay with nuclear wave packets, and a correlated photoelectron moving in a multi-centred potential. Additionally, these processes are influenced by the dynamics prior to and during the ionisation. To fully understand and subsequently control the ionisation process on different time scales, a profound understanding of electron and nuclear correlation is needed. Here, we investigate the effect of nuclear-electron correlation in a correlated two-electron and one-nucleus quantum model system. Solving the time-dependent Schrödinger equation allows to monitor the correlation impact pre, during, and post-XUV ionisation. We show how an initial nuclear wave packet displaced from equilibrium influences the post-ionisation dynamics by means of momentum conservation between the target and parent ion, whilst the attosecond electron population remains largely unaffected. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate how the coupled electron-nuclear dynamics are imprinted on top of electron-electron correlation on the photoelectron properties. Finally, our findings give guidelines towards when correlation resulting effects have to be incorporated and in which instances the exact correlation treatment can be neglected.

Post-Ionization Dynamics of the Polar Molecule OCS in Asymmetric Laser Fields.

We have investigated the dissociation mechanisms of the prototypical heavy polar molecule OCS into the two break-up channels of the dication, OCS2+ → O+ + CS+ and OC+ + S+, in phase-locked two-color intense laser fields. The branching ratio of the breaking of the C-O and C-S bonds followed a pronounced 2π-oscillation with a modulation depth of 11%, depending on the relative phase of the two-color laser fields. The fragment ejection direction of both break-up channels reflects the anisotropy of the tunneling ionization rate, following a 2π-periodicity, as well. The two dissociation pathways in the C-S bond breaking channel show different phase dependencies of the fragment ejection direction, which are assigned to post-ionization dynamics. These observations, resulting from the excitation with asymmetric two-color intense laser fields, supported by state-of-the-art theoretical simulations, reveal the importance of post-ionization population dynamics in addition to tunneling ionization in the molecular fragmentation processes, even for heavy polar molecules.

Novel [FeFe]-Hydrogenase Mimics: Unexpected Course of the Reaction of Ferrocenyl α-Thienyl Thioketone with Fe3(CO)12.

The influence of the substitution pattern in ferrocenyl α-thienyl thioketone used as a proligand in complexation reactions with Fe3(CO)12 was investigated. As a result, two new sulfur-iron complexes, considered [FeFe]-hydrogenase mimics, were obtained and characterized by spectroscopic techniques (1H, 13C{1H} NMR, IR, MS), as well as by elemental analysis and X-ray single crystal diffraction methods. The electrochemical properties of both complexes were studied and compared using cyclic voltammetry in the absence and in presence of acetic acid as a proton source. The performed measurements demonstrated that both complexes can catalyze the reduction of protons to molecular hydrogen H2. Moreover, the obtained results showed that the presence of the ferrocene moiety at the backbone of the linker of both complexes improved the stability of the reduced species.

Unraveling the Light-Activated Reaction Mechanism in a Catalytically Competent Key Intermediate of a Multifunctional Molecular Catalyst for Artificial Photosynthesis.

Understanding photodriven multielectron reaction pathways requires the identification and spectroscopic characterization of intermediates and their excited-state dynamics, which is very challenging due to their short lifetimes. To the best of our knowledge, this manuscript reports for the first time on in situ spectroelectrochemistry as an alternative approach to study the excited-state properties of reactive intermediates of photocatalytic cycles. UV/Vis, resonance-Raman, and transient-absorption spectroscopy have been employed to characterize the catalytically competent intermediate [(tbbpy)2 RuII (tpphz)RhI Cp*] of [(tbbpy)2 Ru(tpphz)Rh(Cp*)Cl]Cl(PF6 )2 (Ru(tpphz)RhCp*), a photocatalyst for the hydrogenation of nicotinamide (NAD-analogue) and proton reduction, generated by electrochemical and chemical reduction. Electronic transitions shifting electron density from the activated catalytic center to the bridging tpphz ligand significantly reduce the catalytic activity upon visible-light irradiation.