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Coupled cluster theory in the standard formulation is unable to correctly describe conical intersections among states of the same symmetry. This limitation has restricted the practical application of an otherwise highly accurate electronic structure model, particularly in nonadiabatic dynamics. Recently, the intersection problem among the excited states was fully characterized and resolved. However, intersections with the ground state remain an open challenge, and addressing this problem is our objective here. We present a generalized coupled cluster framework that correctly accounts for the geometric phase effect and avoids bifurcations of the solutions to the ground state equations. Several applications are presented that demonstrate the correct description of ground state conical intersections. We also propose how the framework can be used for other electronic-structure methods., Comment: 45 pages, 9 figures

We show that intermediate normalization of the electronic wave function, where a constant component is enforced, will lead to an asymptotic discontinuity at one point along any path that encloses a ground state conical intersection. For some electronic structure methods, this gives rise to severe global artifacts in the ground and excited state potential energy surfaces. We investigate how this affects two electronic structure methods: coupled cluster theory and M{\o}ller-Plesset perturbation theory. The analysis suggests that intermediate normalization is problematic not only in near-degenerate regions, such as in the vicinity of conical intersections. In particular, since problems will occur for any path that encloses a ground state intersection, the affected methods can unexpectedly break down in regions of internal coordinate space that are normally considered within their range of validity., Comment: 21 pages, 4 figures

Minimum energy conical intersections can be used to rationalize photochemical processes. In this Letter, we examine an algorithm to locate these structures that does not require the evaluation of nonadiabatic coupling vectors, showing that it minimizes the energy on hypersurfaces that envelop the intersection seam. By constraining the states to be separated by a small non-zero energy difference, the algorithm ensures that numerical artifacts and convergence problems of coupled cluster theory at conical intersections are not encountered during the optimization. In this way, we demonstrate for various systems that minimum energy conical intersections with the ground state are well described by the coupled cluster singles and doubles model, suggesting that coupled cluster theory may in some cases provide a good description of relaxation to the ground state in nonadiabatic dynamics simulations., Comment: 27 pages, 7 figures

Experiments show that light-matter strong coupling affects chemical properties, though the underlying mechanism remains unclear. We present an ab initio quantum electrodynamics coupled cluster method for the collective strong coupling regime. The model accurately describes electronic and electron-photon correlation within a molecular subsystem, while a simplified description of the collective polaritonic excitations allows for realistic microscopic light-matter couplings. We illustrate the model by investigating the potential energy surfaces of the argon dimer. This provides a prototype for excimers, and we analyze the ground and excited state vibrational levels. In the collective regime (small light-matter coupling, large number of molecules), the ground state potential energy surface and the first vibrational levels of the excited state are not changed significantly. However, collective strong coupling produces an abrupt transition in the vibrational landscape of the excimer, causing higher levels to behave similarly to ground state vibrations. Beyond a critical collective coupling strength, the excimer formation is thus inhibited., Comment: 46 pages and 10 figures

Separation of the two mirror images of a chiral molecule, the enantiomers, is a historically complicated problem of major relevance for biological systems. Since chiral molecules are optically active, it has been speculated that strong coupling to circularly polarized fields may be used as a general procedure to unlock enantiospecific reactions. In this work, we focus on how chiral cavities can be used to drive asymmetry in the photochemistry of chiral molecular systems. We first show that strong coupling to circularly polarized fields leads to enantiospecific Rabi splittings, an effect that displays a collective behavior in line with other strong coupling phenomena. Additionally, entanglement with circularly polarized light generates an asymmetry in the enantiomer population of the polaritons, leading to a condensation of the excitation on a preferred molecular configuration. These results confirm that chiral cavities represent a tantalizing opportunity to drive asymmetric photochemistry in enantiomeric mixtures., Comment: 45 pages and 16 figures

We present a new ab-initio approach to study molecules containing heavy atoms strongly interacting with quantum fields in optical devices. The relativistic quantum electrodynamics (QED) theory has been rewritten with a formalism close to relativistic quantum chemistry. This general framework represents the ideal starting point to extend the main quantum chemistry methods to relativistic polaritonic. The Polaritonic Dirac Hartree Fock (Pol-DHF) approach is the first method we propose based on this theory. Pol-DHF allows for the simulation of field induced effects on the ground and excited state properties of heavy transition metals molecular complexes. The method is able to include not only the effects of the photons but can be easily extended also to include explicit interactions with positrons. Application of Pol-DHF to three metal hydrides revealed the importance of including relativistic effects to the treatment in strong coupling conditions. Due to an accurate description of spin-orbit coupling, the method is able to reproduce polaritonic effects happening at the crossing between singlet and triplet potential energy surfaces., Comment: 18 pages, 8 figures

A comprehensive theoretical understanding of electron-photon correlation is essential for describing the reshaping of molecular orbitals in quantum electrodynamics (QED) environments. The strong coupling QED Hartree-Fock (SC-QED-HF) theory tackles these aspects by providing consistent molecular orbitals in the strong coupling regime. The previous implementation, however, has significant convergence issues that limit the applicability. In this work we introduce two second-order algorithms that significantly reduce the computational requirements, thereby enhancing the modeling of large molecular systems in QED environments. Furthermore, the implementation will enable the development of correlated methods based on a reliable molecular orbital framework., Comment: 29 pages and 6 figures

Analytical gradients of potential energy surfaces play a central role in quantum chemistry, allowing for molecular geometry optimizations and molecular dynamics simulations. In strong coupling conditions, potential energy surfaces can account for strong interactions between matter and the quantized electromagnetic field. In this paper, we derive expressions for the ground state analytical gradients in quantum electrodynamics coupled cluster theory. We also present a Cholesky-based implementation for the coupled cluster singles and doubles model. We report timings to show the performance of the implementation and present optimized geometries to highlight cavity-induced molecular orientation effects in strong coupling conditions., Comment: 45 pages and 3 figures

We analyze the real-time electron-photon dynamics in long-range polariton-mediated energy transfer using a real-time quantum electrodynamics coupled cluster (RT-QED-CC) model, which allows for spatial and temporal visualization of transport processes. We compute the time evolution of photonic and molecular observables, such as the dipole moment and the photon coordinate, following the excitation of the system induced by short laser pulses. Our simulation highlights the different time scales of electrons and photons under light-matter strong coupling, the role of dark states, and the differences with the electronic (F\"orster and Dexter) energy exchange mechanisms. The developed method can simulate multiple high-intensity laser pulses while explicitly retaining electronic and electron-photon correlation and is thus suited for nonlinear optics and transient absorption spectroscopies of molecular polaritons., Comment: 19 pages and 9 figures

The fate of thymine upon excitation by ultraviolet radiation has been the subject of intense debate over the past three decades. Today, it is widely believed that its ultrafast excited state decay stems from a radiationless transition from the bright ${\pi}{\pi}^*$ state to a dark $n{\pi}^*$ state. However, conflicting theoretical predictions have made the experimental data difficult to interpret. Here we simulate the ultrafast dynamics in thymine at the highest level of theory to date, performing wavepacket dynamics with a new coupled cluster method. Our simulation confirms an ultrafast ${\pi}{\pi}^*$ to $n{\pi}^*$ transition (${\tau} = 41 \pm 14$ fs). Furthermore, the predicted oxygen-edge X-ray absorption spectra agree quantitatively with the experimental results. Our simulation also predicts an as-yet uncharacterized photochemical pathway: a ${\pi}{\sigma}^*$ channel that leads to hydrogen dissociation at one of the two N-H bonds in thymine. Similar behavior has been identified in other heteroaromatic compounds, including adenine, and several authors have speculated that a similar pathway may exist in thymine. However, this was never confirmed theoretically or experimentally. This prediction calls for renewed efforts to experimentally identify or exclude the presence of this channel., Comment: 42 pages, 23 figures

Coupled cluster theory is one of the most accurate electronic structure methods for predicting ground and excited state chemistry. However, the presence of numerical artifacts at electronic degeneracies, such as complex energies, has made it difficult to apply it in nonadiabatic dynamics simulations. While it has already been shown that such numerical artifacts can be fully removed by using similarity constrained coupled cluster (SCC) theory [J. Phys. Chem. Lett. 2017, 8, 19, 4801-4807], simulating dynamics requires efficient implementations of gradients and nonadiabatic couplings. Here, we present an implementation of nuclear gradients and nonadiabatic derivative couplings at the similarity constrained coupled cluster singles and doubles (SCCSD) level of theory, thereby making possible nonadiabatic dynamics simulations using a coupled cluster theory that provides a correct description of conical intersections between excited states. We present a few numerical examples that show good agreement with literature values and discuss some limitations of the method., Comment: 40 pages, 3 figures, 2 tables

In this work, we present ab initio cavity QED methods which include interactions with a static magnetic field and nuclear spin degrees of freedom using different treatments of the quantum electromagnetic field. We derive explicit expressions for QED-HF magnetizability, nuclear shielding, and spin-spin coupling tensors. We apply this theory to explore the influence of the cavity field on the magnetizability of saturated, unsaturated, and aromatic hydrocarbons, showing the effects of different polarization orientations and coupling strengths. We also examine how the cavity affects aromaticity descriptors, such as the nucleus-independent chemical shift and magnetizability exaltation. We employ these descriptors to study the trimerization reaction of acetylene to benzene. We show how the optical cavity induces modifications in the aromatic character of the transition state leading to variations in the activation energy of the reaction. Our findings shed light on the effects induced by the cavity on magnetic properties, especially in the context of aromatic molecules, providing valuable insights into understanding the interplay between the quantum electromagnetic field and molecules., Comment: 62 pages and 10 figures

The X-ray absorption (XA) spectra of aqueous ammonia and ammonium are computed using a combination of coupled cluster singles and doubles (CCSD) with different quantum mechanical and molecular mechanical embedding schemes. Specifically, we compare frozen Hartree--Fock (HF) density embedding, polarizable embedding (PE), and polarizable density embedding (PDE). Integrating CCSD with frozen HF density embedding is possible within the CC-in-HF framework, which circumvents the conventional system-size limitations of standard coupled cluster methods. We reveal similarities between PDE and frozen HF density descriptions, while PE spectra differ significantly. By including approximate triple excitations, we also investigate the effect of improving the electronic structure theory. The spectra computed using this approach show an improved intensity ratio compared to CCSD-in-HF. Charge transfer analysis of the excitations shows the local character of the pre-edge and main-edge, while the post-edge is formed by excitations delocalized over the first solvation shell and beyond., Comment: 35 pages, 12 figures

Intermolecular interactions are pivotal for aggregation, solvation, and crystallization. We demonstrate that the collective strong coupling of several molecules to a single optical mode results in notable changes in the molecular excitations around an impurity, e.g., in the first aggregation or solvation shell. A competition between short-range Coulombic and long-range photonic correlation inverts the local transition density in a polaritonic state, suggesting notable changes in the polarizability of the solvation shell. Our results provide an alternative perspective on recent work in polaritonic chemistry and pave the way for the rigorous treatment of cooperative effects in aggregation, solvation, and crystallization.

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schr\"odinger equation into different degrees of freedom as in the Born-Oppenheimer approximation. In this paper, we analyze the electron-photon Hamiltonian within the cavity Born-Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. Specifically, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron-photon correlation and the accuracy of CBOA., Comment: 9 pages, 8 figures

We present the first successful application of the coupled cluster approach to simulate the X-ray absorption (XA) spectrum of liquid water. The system size limitations of standard coupled cluster theory are overcome by employing a newly developed coupled cluster method for large molecular systems. This method combines coupled cluster singles, doubles, and perturbative triples in a multilevel framework (MLCC3-in-HF) and is able to describe the delicate nature of intermolecular interactions in liquid water. Using molecular geometries from state-of-the-art path-integral molecular dynamics, we obtain excellent agreement with experimental spectra. Additionally, we show that an accurate description of the electronic structure within the first solvation shell is sufficient to model the XA spectrum of liquid water. Furthermore, we present a rigorous charge transfer analysis with unprecedented reliability, achieved through MLCC3-in-HF. This analysis aligns with previous studies regarding the character of the prominent features of the spectrum., Comment: 32 pages, 4+12 figures

The development of new methodologies for the selective synthesis of individual enantiomers is still one of the major challenges in synthetic chemistry. Many biomolecules, and therefore many pharmaceutical compounds, are indeed chiral. While the use of chiral reactants or catalysts has led to significant progress in the field of asymmetric synthesis, a systematic approach applicable to general reactions has still not been proposed. In this work, we show that strong coupling to circularly polarized fields represents a promising alternative for reaching highly selective asymmetric synthesis in a non-invasive fashion. We demonstrate that the field induces stereoselectivity in the early stages of the chemical reaction, by selecting an energetically preferred direction of approach for the reagents., Comment: 15 pages, 5 figures

Molecular polaritons arise when molecules interact so strongly with light that they become entangled with each other. This light-matter hybridization alters the chemical and physical properties of the molecular system and allows chemical reactions to be controlled without the use of external fields. We investigate the impact of strong light-matter coupling on the electronic structure using perturbative approaches and demonstrate that Rayleigh-Schr\"odinger perturbation theory can reproduce the ground state energies in optical cavities to comparable accuracy as ab initio cavity quantum electrodynamics methodologies for currently relevant coupling strengths. The method is effective in both low and high cavity frequency regimes and straightforward to implement via response functions. Furthermore, we establish simple relations between cavity-induced intermolecular forces and van der Waals forces. These findings provide valuable insight into the manipulation of ground-state polaritonic energy landscapes, shedding light on the systems and conditions in which modifications can be achieved., Comment: 11 pages, 3 Figures

Time-dependent equation-of-motion coupled cluster (TD-EOM-CC) is used to simulate impulsive stimulated x-ray Raman scattering (ISXRS) of ultrashort laser pulses by neon, carbon monoxide, pyrrole, and p-aminophenol. The TD-EOM-CC equations are expressed in the basis of field-free EOM-CC states, where the calculation of the core-excited states is simplified through the use of the core-valence separation (CVS) approximation. The transfer of electronic population from the ground state to the core- and valence-excited states is calculated for different numbers of included core- and valence-excited states, as well as for electric field pulses with different polarizations and carrier frequencies. The results indicate that Gaussian pulses can transfer significant electronic populations to the valence states through the Raman process. The sensitivity of this population transfer to the model parameters is analyzed. The time-dependent electronic density for p-aminophenol is also showcased, supporting the interpretation that ISXRS involves localized core excitations and can be used to rapidly generate valence wavepackets., Comment: 10 pages, 5 figures

Polaritonic chemistry is an interdisciplinary emerging field that presents several challenges and opportunities in chemistry, physics, and engineering. A systematic review of polaritonic response theory is presented, following a chemical perspective based on molecular response theory. We provide the reader with a general strategy for developing response theory for ab initio cavity quantum electrodynamics (QED) methods and critically emphasize details that still need clarification and require cooperation between the physical and chemistry communities. We show that several well-established results can be applied to strong coupling light-matter systems, leading to novel perspectives on the computation of matter and photonic properties. The application of the Pauli-Fierz Hamiltonian to polaritons is discussed, focusing on the effects of describing operators in different mathematical representations. We thoroughly examine the most common approximations employed in ab initio QED, such as the dipole approximation. We introduce the polaritonic response equations for recently developed ab initio QED Hartree-Fock and QED coupled cluster methods. The discussion focuses on the similarities and differences from standard quantum chemistry methods, providing practical equations for computing the polaritonic properties., Comment: 37 pages, 3 figures

Strong coupling between molecules and quantized fields has emerged as an effective methodology to engineer molecular properties. New hybrid states are formed when molecules interact with quantized fields. Since the properties of these states can be modulated by fine-tuning the field features, an exciting and new side of chemistry can be explored. In particular, significant modifications of the molecular properties can be achieved in plasmonic nanocavities, where the field quantization volume is reduced to sub-nanometric volumes. Intriguing applications of nanoplasmonics include the possibility of coupling the plasmons with a single molecule, instrumental for sensing, high-resolution spectroscopy, and single-molecule imaging. In this work, we focus on phenomena where the simultaneous effects of multiple plasmonic modes are critical. We propose a theoretical methodology to account for many plasmonic modes simultaneously while retaining computational feasibility. Our approach is conceptually simple and allows us to accurately account for the multimode effects and rationalize the nature of the interaction between multiple plasmonic excitations and molecules., Comment: 27 pages, 6 figures

We present an efficient implementation of analytical non-adiabatic derivative coupling elements for the coupled cluster singles and doubles model. The derivative coupling elements are evaluated in a biorthonormal formulation in which the nuclear derivative acts on the right electronic state, where this state is biorthonormal with respect to the set of left states. This stands in contrast to earlier implementations based on normalized states and a gradient formula for the derivative coupling. As an illustration of the implementation, we determine a minimum energy conical intersection between the n{\pi}* and {\pi}{\pi}* states in the nucleobase thymine., Comment: 8 pages, 4 figures

We present a novel approach to spin-adapted coupled cluster theory. This approach is based on the entanglement of an open-shell molecule with electrons in a non-interacting bath; together they form a closed-shell state. For the total system, electron correlation can be added with the standard spin-adapted closed-shell coupled cluster formalism. A projection operator, which enforces conditions on the electrons in the bath, is used to obtain the desired state of the molecular system. This entanglement coupled cluster theory is detailed and proof-of-concept calculations for doublet states are reported. The approach is extendable to open-shell systems with other values of the total spin., Comment: 17 pages, 3 figures and 7 tables

The time-dependent equation-of-motion coupled cluster (TD-EOM-CC) and time-dependent coupled cluster (TDCC) methods are compared by simulating Rabi oscillations for different numbers of non-interacting atoms in a classical electromagnetic field. While the TD-EOM-CC simulations are numerically stable, the oscillating time-dependent energy scales unreasonably with the number of subsystems resonant with the field. The TDCC simulations give the correct scaling of the time-dependent energy in the initial stages of the Rabi cycle, but the numerical solution breaks down when the multi-atom system approaches complete population inversion. We present a general theoretical framework in which the two methods can be described, where the cluster amplitude time derivatives are taken as auxiliary conditions, leading to a shifted time-dependent Hamiltonian matrix. In this framework, TDCC has a shifted Hamiltonian with a block upper triangular structure, explaining the correct scaling properties of the method., Comment: 9 pages and 4 figures

We present a computational study of static and dynamic linear polarizabilities in solution. We use different theoretical approaches to describe solvent effects, ranging from quantum mechanics/molecular mechanics (QM/MM) to quantum embedding approaches. In particular, we consider non-polarizable and polarizable QM/MM methods, the latter based on the fluctuating charge (FQ) force field. In addition, we use a quantum embedding method defined in the context of multilevel Hartree-Fock (MLHF), where the system is divided into active and inactive regions, and combine it with a third layer described by means of the FQ model. The multiscale approaches are then used as reference wave functions for equation-of-motion coupled cluster (EOM-CC) response properties, allowing for the account of electron correlation. The developed models are applied to the calculation of linear response properties of two organic moieties -- namely, para-nitroaniline and benzonitrile -- in non-aqueous solvents -- 1,4-dioxane, acetonitrile, and tetrahydrofuran. The computed polarizabilities are then discussed in terms of the physico-chemical solute-solvent interactions described by each method (electrostatic, polarization and Pauli repulsion), and finally compared with the available experimental references., Comment: 13 pages, 9 figures

Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. However, there are currently very limited approaches to manipulate van der Waals interactions. In this work, we demonstrate that strong light-matter coupling can be used to tune van der Waals interactions, and, thus, control the thermodynamic properties of many-molecule systems. Our analyses reveal orientation dependent single molecule energies and interaction energies for van der Waals molecules (for example, H$_{2}$). For example, we find intermolecular interactions that depend on the distance between the molecules $R$ as $R^{-3}$ and $R^{0}$. Moreover, we employ non-perturbative \textit{ab initio} cavity quantum electrodynamics calculations to develop machine learning-based interaction potentials for molecules inside optical cavities. By simulating systems ranging from $12$ H$_2$ to $144$ H$_2$ molecules, we demonstrate that strong light-matter coupling can tune the structural and thermodynamic properties of molecular fluids. In particular, we observe varying degrees of orientational order as a consequence of cavity-modified interactions, and we explain how quantum nuclear effects, light-matter coupling strengths, number of cavity modes, molecular anisotropies, and system size all impact the extent of orientational order. These simulations and analyses demonstrate both local and collective effects induced by strong light-matter coupling and open new paths for controlling the properties of molecular clusters., Comment: 7 pages and 3 figures in main text - 16 pages and 13 figures supplemental material

The development of efficient techniques to distinguish mirror images of chiral molecules (enantiomers) is very important in both chemistry and physics. Enantiomers share most molecular properties except, for instance, the absorption of circularly polarized light. Enantiomer purification is therefore a challenging task that requires specialized equipment. Strong coupling between quantized fields and matter (e.g. in optical cavities) is a promising technique to modify molecular processes in a non-invasive way. The modulation of molecular properties is achieved by changing the field characteristics. In this work, we investigate whether strong coupling to circularly polarized electromagnetic fields is a viable way to discriminate chiral molecules. To this end, we develop a nonperturbative framework to calculate the behavior of molecules in chiral cavities. We show that in this setting the enantiomers have different energies -- that is, one is more stable than the other. The field-induced energy differences are also shown to give rise to enantiospecific signatures in rotational spectra., Comment: 18 pages and 14 figures

The ionization of molecular systems is important in many chemical processes such as electron transfer and hot electron injection. Strong coupling between molecules and quantized fields (e.g. inside optical cavities) represents a new promising way to modify molecular properties in a non-invasive way. Recently, strong light-matter coupling has shown the potential to significantly improve the rates of hot electron driven processes, for instance in water splitting. In this paper, we demonstrate that inside an optical cavity the residual interaction between an outgoing free electron and the vacuum field is significant. We further show that, since the quantized field is also interacting with the ionized molecule, the free electron and the molecular system are correlated. We develop a theoretical framework to account for the field induced correlation and show that the interaction between the free electron and the field free electron-field interaction has sizeable effects on the ionization potential of typical organic molecules., Comment: 8 pages, 4 figures

We present an efficient implementation of the equation of motion oscillator strengths for the closed-shell multilevel coupled cluster singles and doubles with perturbative triples method (MLCC3) in the electronic structure program eT. The orbital space is split into an active part treated with CC3 and an inactive part computed at the coupled cluster singles and doubles (CCSD) level of theory. Asymptotically, the CC3 contribution scales as $O(n_\text{V} n^3_\text{v} n^3_\text{o})$ floating-point operations (FLOP), where $n_V$ is the total number of virtual orbitals while $n_\text{v}$ and $n_\text{o}$ are the number of active virtual and occupied orbitals, respectively. The CC3 contribution, thus, only scales linearly with the full system size and can become negligible compared to the cost of CCSD. We demonstrate the capabilities of our implementation by calculating the UV-VIS spectrum of azobenzene and a core excited state of betaine 30 with more than 1000 molecular orbitals., Comment: 38 page and 10 pages SI and 6 figures

We present an efficient implementation of ground and excited state CCSD gradients based on Cholesky-decomposed electron repulsion integrals. Cholesky decomposition, like density-fitting, is an inner projection method, and thus similar implementation schemes can be applied for both methods. One well-known advantage of inner projection methods, which we exploit in our implementation, is that one can avoid storing large V3O and V4 arrays by instead considering three-index intermediates. Furthermore, our implementation does not require the formation and storage of Cholesky vector derivatives. The new implementation is shown to perform well, with less than 10% of the time spent calculating the gradients in geometry optimizations. The computational time spent per optimization cycle are furthermore found to be significantly lower compared to other implementations based on an inner projection method. We illustrate the capabilities of the implementation by optimizing the geometry of the retinal molecule (C20H28O) at the CCSD/aug-cc-pVDZ level of theory., Comment: 12 pages, 1 figure

Coupling between molecules and vacuum photon fields inside an optical cavity has proven to be an effective way to engineer molecular properties, in particular reactivity. To ease the rationalization of cavity induced effects we introduce an ab initio method leading to the first fully consistent molecular orbital theory for quantum electrodynamics environments. Our framework is non-perturbative and explains modifications of the electronic structure due to the interaction with the photon field. We show that the newly developed orbital theory can be used to predict cavity induced modifications of molecular reactivity and pinpoint classes of systems with significant cavity effects. We also investigate cavity-induced modifications of molecular reactivity in the vibrational strong coupling regime., Comment: 23 pages, 7 figures

A time-dependent equation of motion coupled cluster singles and doubles (TD-EOM-CCSD) method is implemented, which uses a reduced basis calculated with the asymmetric band Lanczos algorithm. The approach is used to study weak-field processes in small molecules induced by ultrashort valence pump and core probe pulses. We assess the reliability of the procedure by comparing TD-EOM-CCSD absorption spectra to spectra obtained from the time-dependent coupled-cluster singles and doubles (TDCCSD) method and observe that spectral features can be reproduced for several molecules, at much lower computational times. We discuss how multiphoton absorption and symmetry can be handled in the method and general features of the core-valence separation (CVS) projection technique. We also model the transient absorption of an attosecond X-ray probe pulse by the glycine molecule., Comment: 15 pages and 5 figures

Plasmonic nanocavities enable the confinement of molecules and electromagnetic fields within nano-metric volumes. As a consequence, the molecules experience a remarkably strong interaction with the electromagnetic field, to such an extent that the quantum states of the system become hybrids between light and matter: polaritons. Here we present a non-perturbative method to simulate the emerging properties of such polaritons: it combines a high-level quantum chemical description of the molecule with a quantized description of the localized surface plasmons in the nanocavity. We apply the method to molecules of realistic complexity in a typical plasmonic nanocavity, featuring also a subnanometric asperity (picocavity). Our results disclose the effects of the mutual polarization and correlation of plasmons and molecular excitations, disregarded so far. They also quantify to what extent the molecular charge density can be manipulated by nanocavities, and stand as benchmarks to guide the development of methods for molecular polaritonics., Comment: 13 Pages Main text, 4 Figures and 11 pages Supporting Information

We investigate the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable. In particular, such a coupling is discussed for the multilevel families of methods, in which the system is divided into an active and an inactive orbital spaces. The computational cost of the resulting three layers approaches is reduced by treating the long-range interactions at the classical level.The methods developed are tested against the calculation of the excitation energies of molecular systems in aqueous solution, for which an atomistic description of the environment is crucial to correctly reproduce the specific solute-solvent interactions, such as hydrogen bonding. In particular, we present the results obtained for three different moieties, acrolein, pyridine and para-nitroaniline, showing that an almost perfect agreement with experimental data can be achieved when the relevant physico-chemical interactions are included in the modeling of the condensed phase., Comment: 13 pages and 10 figures

Intermolecular bonds are weak compared to covalent bonds, but they are strong enough to influence the properties of large molecular systems. In this work, we investigate how strong light-matter coupling inside an optical cavity can modify these intermolecular forces. We perform a detailed comparison between currently available ab initio electron-photon methodologies. The electromagnetic field inside the cavity can modulate the ground state properties of weakly bound complexes. Controlling the field polarization, the interactions can be stabilized or destabilized, and electron densities, dipole moments, and polarizabilities can be altered. We demonstrate that electron-photon correlation is fundamental to describe intermolecular interactions in strong light-matter coupling. This work proposes optical cavities as a novel tool to manipulate and control ground state properties, solvent effects, and intermolecular interactions for molecules and materials., Comment: 11 pages and 9 figures

We present the first investigation of excited state dynamics by resonant Auger-Meitner spectroscopy (also known as resonant Auger spectroscopy) using the nucleobase thymine as an example. Thymine is photoexcited in the UV and probed with X-ray photon energies at and below the oxygen K-edge. After initial photoexcitation to a {\pi}{\pi}* excited state, thymine is known to undergo internal conversion to an n{\pi}* excited state with a strong resonance at the oxygen K-edge, red-shifted from the ground state {\pi}* resonances of thymine (see our previous study Wolf et al., Nat. Commun., 2017, 8, 29). We resolve and compare the Auger-Meitner electron spectra associated both with the excited state and ground state resonances, and distinguish participator and spectator decay contributions. Furthermore, we observe simultaneously with the decay of the n{\pi}* state signatures the appearance of additional resonant Auger-Meitner contributions at photon energies between the n{\pi}* state and the ground state resonances. We assign these contributions to population transfer from the n{\pi}* state to a {\pi}{\pi}* triplet state via intersystem crossing on the picosecond timescale based on simulations of the X-ray absorption spectra in the vibrationally hot triplet state. Moreover, we identify signatures from the initially excited {\pi}{\pi}* singlet state which we have not observed in our previous study.

We present a novel energy-based localization procedure able to localize molecular orbitals into specific spatial regions. The method is applied to several cases including both conjugated and non-conjugated systems. The obtained localized molecular orbitals are used in a multiscale framework based on the multilevel Hartree-Fock approach. An almost perfect agreement with reference values is achieved for both ground state properties, such as dipole moments, and local excitation energies calculated at the coupled cluster level. The proposed approach is useful to extend the application range of high level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations., Comment: 29 pages and 7 figures

We introduce a novel density-based multilevel approach in density functional theory. In this multilevel density functional theory (MLDFT), the system is partitioned in an active and an inactive fragment, and all interactions are retained between the two parts. In MLDFT, the Kohn-Sham equations are solved in the MO basis for the active part only, while keeping the inactive density frozen. This results in a reduction of computational cost. We outline the theory and implementation, and discuss applications to aqueous solutions of methyloxirane and glycidol., Comment: 33 pages and 9 figures

In coupled cluster methods, the electronic states are biorthonormal in the sense that the left states are orthonormal to the right states. Here we present an extension of this formalism to a left and right total molecular wave function. Starting from left and right Born-Huang expansions, we derive projected Schr\"odinger equations for the left and right nuclear wave functions. Observables may be extracted from the resulting wave function pair using standard expressions. The formalism is shown to be invariant under electronic basis transformations, such as normalization of the electronic states. Consequently, the nonadiabatic coupling elements can be expressed with biorthonormal wave functions. Calculating normalization factors that scale as full-CI is therefore not necessary, contrary to claims in the literature. For nuclear dynamics, we therefore need expressions for the vector and scalar couplings in the biorthonormal formalism. We derive these expressions using a Lagrangian formalism., Comment: 41 pages, 1 figure

We present an implementation of equation-of-motion oscillator strengths for the multilevel CCSD (MLCCSD) model where CCS is used as the lower level method (CCS/CCSD). In this model, the double excitations of the cluster operator are restricted to an active orbital space, whereas the single excitations are unrestricted. Calculated nitrogen K-edge spectra of adenosine, adenosine triphosphate (ATP), and an ATP-water system are used to demonstrate the performance of the model. Projected atomic orbitals (PAOs) are used to partition the virtual space into active and inactive orbital sets. Cholesky decomposition of the Hartree-Fock density is used to partition the occupied orbitals. This Cholesky-PAO partitioning is cheap, scaling as $\mathcal{O}(N^3)$, and is suitable for the calculation of core excitations which are localized in character. By restricting the single excitations of the cluster operator to the active space, as well as the double excitations, the CCSD-in-HF model is obtained. A comparison of the two models---MLCCSD and CCSD-in-HF---is presented for the core excitation spectra of the adenosine and ATP systems., Comment: 30 pages, 7 figures

We present a new and efficient implementation of the closed shell coupled cluster singles and doubles with perturbative triples method (CC3) in the electronic structure program $e^T$. Asymptotically, a ground state calculation has an iterative cost of $4n_{\text{V}}^{4}n_{\text{O}}^{3}$ floating point operations (FLOP), where $n_{\text{V}}$ and $n_{\text{O}}$ are the number of virtual and occupied orbitals respectively. The Jacobian and transpose Jacobian transformations, required to iteratively solve for excitation energies and transition moments, both require $8n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP. We have also implemented equation of motion (EOM) transition moments for CC3. The EOM transition densities require recalculation of triples amplitudes, as $n_{\text{V}}^{3}n_{\text{O}}^{3}$ tensors are not stored in memory. This results in a noniterative computational cost of $10n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP for the ground state density and $26n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP per state for the transition densities. The code is compared to the CC3 implementations in CFOUR, Dalton and Psi4. We demonstrate the capabilities of our implementation by calculating valence and core excited states of L-proline., Comment: 33 pages, 2 figures and TOC

We present efficient implementations of the multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) models. As the system size increases, MLCC2 and MLCCSD exhibit the scaling of the lower level coupled cluster model. In order to treat large systems, we combine MLCC2 and MLCCSD with a reduced orbital space approach where the multilevel coupled cluster calculation is performed in a significantly truncated molecular orbital basis. The truncation scheme is based on the selection of an active region of the molecular system and the subsequent construction of localized Hartree-Fock orbitals. These orbitals are used in the multilevel coupled cluster calculation. The electron repulsion integrals are Cholesky decomposed using a screening protocol that guarantees accuracy in the truncated molecular orbital basis. The Cholesky factors are constructed directly in the truncated basis, ensuring low storage requirements. Even larger systems can be treated by using a multilevel Hartree-Fock reference. With the reduced space approach, we can handle systems with more than a thousand atoms. This is demonstrated for paranitroaniline in aqueous solution., Comment: 42 pages, 9 figures