Probing Molecular Chirality of Ground and Electronically Excited States in the UV-vis and X-ray Regimes: An EOM-CCSD Study

ATR-far-ultraviolet spectroscopy: a challenge to new σ chemistry

This review reports the recent progress on ATR-far ultraviolet (FUV) spectroscopy in the condensed phase. ATR-FUV spectroscopy for liquids and solids enables one to explore various topics in physical chemistry, analytical chemistry, nanoscience and technology, materials science, electrochemistry, and organic chemistry. In this review, we put particular emphasis on the three major topics: (1) studies on electronic transitions and structures of various molecules, which one cannot investigate via ordinary UV spectroscopy. The combined use of ATR-FUV spectroscopy and quantum chemical calculations allows for the investigation of various electronic transitions, including σ, n-Rydberg transitions. ATR-FUV spectroscopy may open a new avenue for σ-chemistry. (2) ATR-FUV spectroscopy enables one to measure the first electronic transition of water at approximately 160 nm without peak saturation. Using this band, one can study the electronic structure of water, aqueous solutions, and adsorbed water. (3) ATR-FUV spectroscopy has its own advantages of the ATR method as a surface analysis method. ATR-FUV spectroscopy is a powerful technique for exploring a variety of top surface phenomena (∼50 nm) in adsorbed water, polymers, graphene, organic materials, ionic liquids, and so on. This review briefly describes the principles, characteristics, and instrumentation of ATR-FUV spectroscopy. Next, a detailed description about quantum chemical calculation methods for FUV and UV regions is given. The recent application of ATR-FUV-UV spectroscopy studies on electronic transitions from σ orbitals in various saturated molecules is introduced first, followed by a discussion on the applications of ATR-FUV spectroscopy to studies on water, aqueous solutions, and adsorbed water. Applications of ATR-FUV spectroscopy in the analysis of other materials such as polymers, ionic liquids, inorganic semiconductors, graphene, and carbon nanocomposites are elucidated. In addition, ATR-FUV-UV-vis spectroscopy focusing on electrochemical interfaces is outlined. Finally, FUV-UV-surface plasmon resonance studies are discussed.

Identification of the interchromophore interaction in the electronic absorption and circular dichroism spectra of bis-phenanthrenes

We characterize the low-lying excited electronic states of a series of bis-phenanthrenes using our newly developed diabatic scheme called the fragment particle-hole density (FPHD) method and calculate both the electronic absorption and circular dichroism (ECD) spectra using the time-dependent density functional theory (TDDFT) and the FPHD-based exciton model which couples intrachromophore local excitations (LEs) and the interchromophore charge-transfer excitations (CTEs). TDDFT treats each bis-phenanthrene as a single molecule while the mixed LE-CTE exciton model partitions the molecule into two phenanthrene-based aromatic moieties, and then applies the electronic coupling between the various quasi-diabatic states to cover the interactions. It is found that TDDFT and the mixed LE-CTE model reproduce all experimentally observed trends in the spectral profiles, and the hybridization between LE and CTE states is displayed differently in absorption and ECD spectral intensities, as it usually decreases the absorption maxima and affects the positive/negative extrema of the ECD irregularly. By comparing the results yielded by the LE-CTE model with and without the LE-CTE coupling, we identify the contribution of CTE on the main dipole-allowed transitions.

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures

We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. Two bottlenecks of large scale MC-CPP calculations, namely, the memory footprint and computational time, are addressed. The former is addressed by limiting the size of the subspace of trial vectors by using singular value decomposition (SVD) on either orbital or CI subspaces. The latter is addressed using an efficient parallel implementation as well as the strategy of dynamically adding linear response equations at near-convergence to neighboring roots. Furthermore, a novel methodology for decomposing MC-CPP spectra in terms of intuitive orbital excitations in an approximate fashion is presented. The performance of the code is illustrated with several numerical examples, including the X-ray spectrum of a molecule with nearly one hundred atoms. Additionally, for X-ray spectroscopy, the effect of including or excluding the core orbital in the active space on small covalent metal complexes is discussed.

Efficient Protocol for Computing MCD Spectra in a Broad Frequency Range Combining Resonant and Damped CC2 Quadratic Response Theory

Coupled cluster response theory offers a path to high-accuracy calculations of spectroscopic properties, such as magnetic circular dichroism (MCD). However, divergence or slow convergence issues are often encountered for electronic transitions in high-energy regions with a high density of states. This is here addressed for MCD by an implementation of damped quadratic response theory for resolution-of-identity coupled cluster singles-and-approximate-doubles (RI-CC2), along with an implementation of the MCD A term from resonant response theory. Combined, damped and resonant response theory calculations provide an efficient strategy to obtain MCD spectra over a broad frequency range and for systems that include highly symmetric molecules with degenerate excited states. The protocol is illustrated by application to zinc tetrabenzoporphyrin in the energy region of 2-8 eV and comparison to experimental data. Timings are reported for the resonant and damped approaches, showing that a greater part of the calculation time is consumed by the construction of the building blocks for the final MCD ellipticity. A recommendation on how to use the procedure is outlined.

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.

Electronic circular dichroism from real-time propagation in state space

In this paper, we propose to compute the electronic circular dichroism (ECD) spectra of chiral molecules using a real-time propagation of the time-dependent Schrödinger equation (TDSE) in the space of electronic field-free eigenstates, by coupling TDSE with a given treatment of the electronic structure of the target. The time-dependent induced magnetic moment is used to compute the ECD spectrum from an explicit electric perturbation. The full matrix representing the transition magnetic moment in the space of electronic states is generated from that among pairs of molecular orbitals. In the present work, we show the ECD spectra of methyloxirane, of several conformers of L-alanine, and of the Λ-Co(acac)₃ complex, computed from a singly excited ansatz of time-dependent density functional theory eigenstates. The time-domain ECD spectra properly reproduce the frequency-domain ones obtained in the linear-response regime and quantitatively agree with the available experimental data. Moreover, the time-domain approach to ECD allows us to naturally go beyond the ground-state rotationally averaged ECD spectrum, which is the standard outcome of the linear-response theory, e.g., by computing the ECD spectra from electronic excited states.

Theoretical Investigation of the X-ray Stark Effect in Small Molecules

We have studied the Stark effect in the soft x-ray region for various small molecules by calculating the field-dependent x-ray absorption spectra. This effect is explained in terms of the response of molecular orbitals (core and valence), the molecular dipole moment, and the molecular geometry to the applied electric field. A number of consistent trends are observed linking the computed shifts in absorption energies and intensities with specific features of the molecular electronic structure. We find that both the virtual molecular orbitals (valence and/or Rydberg) as well as the core orbitals contribute to observed trends in a complementary fashion. This initial study highlights the potential impact of x-ray Stark spectroscopy as a tool to study electronic structure and environmental perturbations at a submolecular scale.

Molecular Chirality and Its Monitoring by Ultrafast X-ray Pulses

Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Ångström and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are discussed.

Cherry-Picking Resolvents: Recovering the Valence Contribution in X-ray Two-Photon Absorption within the Core-Valence-Separated Equation-of-Motion Coupled-Cluster Response Theory

Calculations of first-order response wave functions in the X-ray regime often diverge within correlated frameworks such as equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), a consequence of the coupling with the valence ionization continuum. Here, we extend our strategy of introducing a hierarchy of approximations to the EOM-EE-CCSD resolvent (or, inversely, the model Hamiltonian) involved in the response equations for the calculation of X-ray two-photon absorption (X2PA) cross sections. We exploit the frozen-core core-valence separation (fc-CVS) scheme to first decouple the core and valence Fock spaces, followed by a separate approximate treatment of the valence resolvent. We demonstrate the robust convergence of X-ray response calculations within this framework and compare X2PA spectra of small benchmark molecules with the previously reported density functional theory results.

Velocity map imaging spectroscopy of C2H- and C2D-: A benchmark study of vibronic coupling interactions

High-resolution velocity-map imaged photoelectron spectra of the ethynyl anions C₂H^- and C₂D^- are measured at photon wavelengths between 355 and 266 nm to investigate the complex interactions between the closely lying X̃²Σ⁺ and Ã²Π electronic states. An indicative kinetic energy resolution of 0.4%, together with the full angular dependence of the fast electrons, provides a detailed description of the vibronically coupled structure. It is demonstrated that a modest quadratic vibronic coupling model, parameterized by the quasidiabatic ansatz, is sufficient to accurately recreate all the observed vibronic interactions. Simulated spectra are shown to be in excellent agreement with the experimental data, verifying the proposed model and providing a framework that may be used to accurately simulate spectra of larger C_2nH monohydride carbon chains. New spectral assignments are supported by experimental electron anisotropy measurements and Dyson orbital calculations.