Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: the Hitchhiker's guide to Fock space

On the multiphoton ionisation photoelectron spectra of phenol

The phenol molecule is a prototype for non-adiabatic dynamics and the excited-state photochemistry of biomolecules. In this article, we report a joint theoretical and experimental investigation on the resonance enhanced multiphoton ionisation photoelectron (REMPI) spectra of the two lowest ionisation bands of phenol. The focus is on the theoretical interpretation of the measured spectra using quantum dynamics simulations. These were performed by numerically solving the time-dependent Schrödinger equation using the multi-layer variant of the multiconfiguration time-dependent Hartree algorithm together with a vibronic coupling Hamiltonian model. The ionising laser pulse is modelled explicitly within the ionisation continuum model to simulate experimental femtosecond 1+1 REMPI photoelectron spectra. These measured spectra are sensitive to very short lived electronically excited states, providing a rigorous benchmark for our theoretical methods. The match between experiment and theory allows for an interpretation of the features of the spectra at different wavelengths and shows that there are features due to both 'direct' and 'indirect' ionisation, resulting from non-resonant and resonant excitation by the pump pulse.

Generalization of One-Center Nonorthogonal Configuration Interaction Singles to Open-Shell Singlet Reference States: Theory and Application to Valence-Core Pump-Probe States in Acetylacetone

We formulate a one-center nonorthogonal configuration interaction singles (1C-NOCIS) theory for the computation of core excited states of an initial singlet state with two unpaired electrons. This model, which we refer to as 1C-NOCIS two-electron open-shell (2eOS), is appropriate for computing the K-edge near-edge X-ray absorption spectra (NEXAS) of the valence excited states of closed-shell molecules relevant to pump-probe time-resolved (TR) NEXAS experiments. With the inclusion of core-hole relaxation effects and explicit spin adaptation, 1C-NOCIS 2eOS requires mild shifts to match experiment, is free of artifacts due to spin contamination, and can capture the high-energy region of the spectrum beyond the transitions into the singly occupied molecular orbitals (SOMOs). Calculations on water and thymine illustrate the different key features of excited-state NEXAS, namely, the core-to-SOMO transitions as well as shifts and spin-splittings in the transitions analogous to those of the ground state. Simulations of the TR-NEXAS of acetylacetone after excitation to its π → π* singlet excited state at the carbon K-edge, an experiment carried out recently, showcase the ability of 1C-NOCIS 2eOS to efficiently simulate NEXAS based on nonadiabatic molecular dynamics simulations.

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.

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].

An environmental impact statement for molecular anions

A molecular anion's (MA's) chemical reactivity and physical behavior can be quite different when it is surrounded by other molecules than when it exists in isolation. This sensitivity to the surrounding environment is especially high for anions because their outermost valence electrons are typically loosely bound and exist in rather spatially diffuse orbitals, allowing even weak intermolecular interactions arising from the environment to have strong effects. This Perspective offers illustrations of such sensitivity for a variety of cases including (i) the effect of solvation on electron binding energies, (ii) how some "well known" anions need to have solvent molecules around to even exist as stable species, (iii) how internal Coulomb repulsions within a multiply charged MA can provide temporary stability toward electron loss, (iv) how MAs arrange themselves spatially near liquid/vapor interfaces in manners that can produce unusual reactivity, (v) how nearby cationic sites can facilitate electron attachment to form a MA site elsewhere, (vi) how internal vibrational or rotational energy can make a MA detach an electron.

Core-ionization spectrum of liquid water

We present state-of-the-art calculations of the core-ionization spectrum of water. Despite significant progress in procedures developed to mitigate various experimental complications and uncertainties, the experimental determination of ionization energies of solvated species involves several non-trivial steps such as assessing the effect of the surface potential, electrolytes, and finite escape depths of photoelectrons. This provides a motivation to obtain robust theoretical values of the intrinsic bulk ionization energy and the corresponding solvent-induced shift. Here we develop theoretical protocols based on coupled-cluster theory and electrostatic embedding. Our value of the intrinsic solvent-induced shift of the 1sO ionization energy of water is -1.79 eV. The computed absolute position and the width of the 1sO peak in photoelectron spectrum of water are 538.47 eV and 1.44 eV, respectively, agreeing well with the best experimental values.

Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method

A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.

Photophysical Outcomes of Water-Solvated Heterocycles: Single-Conformation Ultraviolet and Infrared Spectroscopy of Microsolvated 2-Phenylpyrrole

The molecular chromophores within brown carbon (BrC) aerosols absorb solar radiation at visible and near-ultraviolet wavelengths. This contributes to the overall warming of the troposphere and the photochemical aging of aerosols. In this investigation, we combine a suite of experimental and theoretical methods to reveal the conformation-specific ultraviolet and infrared spectroscopy of 2-phenylpyrrole (2PhPy)─an extended π-conjugated pyrrole derivative and a model BrC chromophore─along with its water microsolvated molecular complexes (2PhPy:nH2O, n = 1-3). Using resonant two-photon ionization and double-resonance holeburning techniques alongside MP3 (ground state) and ADC(3) (excited state) torsional potential energy surfaces and discrete variable representation simulations, we characterized the ultraviolet spectra of 2PhPy and 2PhPy:1H2O. This analysis revealed evidence for Herzberg-Teller vibronic coupling along the CH wagging and NH stretching coordinates of the aromatic rings. Conformation-specific infrared spectroscopy revealed extended hydrogen-bonding networks of the 2PhPy:nH2O complexes. Upon stepwise addition of H2O solvation, the nearest H2O acceptor forms a strong, noncovalent interaction with the pyrrole NH donor, while the second and third H2O partners interface with the phenyl and pyrrole aromatic rings through growing van der Waals π/H atom stabilization. A local-mode Hamiltonian approach was employed for comparison with the experimental spectra, thus identifying the vibrational spectral signatures to specific 2PhPy:nH2O oscillators.

Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2

Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Shape resonance induced electron attachment to cytosine: The effect of aqueous media

We have investigated the impact of microsolvation on shape-type resonance states of nucleobases, taking cytosine as a case study. To characterize the resonance position and decay width of the metastable states, we employed the newly developed DLPNO-based EA-EOM-CCSD method in conjunction with the resonance via Padé (RVP) method. Our calculations show that the presence of water molecules causes a redshift in the resonance position and an increase in the lifetime for the three lowest-lying resonance states of cytosine. Furthermore, there are some indications that the lowest resonance state in isolated cytosine may get converted to a bound state in the presence of an aqueous environment. The obtained results are extremely sensitive to the basis set used for the calculations.

Computing Decay Widths of Autoionizing Rydberg States with Complex-Variable Coupled-Cluster Theory

We compute autoionization widths of various Rydberg states of neon and N2 by equation-of-motion coupled-cluster theory combined with complex scaling and complex basis functions. This represents the first time that complex-variable methods are applied to Rydberg states represented in Gaussian basis sets. A new computational protocol based on Kaufmann basis functions is designed to make these methods applicable to atomic and molecular Rydberg states. As a first step, we apply our protocol to the neon atom and compute widths of the 3s, 3p, 4p and 3d Rydberg states. We then proceed to compute the widths of the 3sσg, 3dσg, and 3dπg Rydberg states of N2, which belong to the Hopfield series. Our results demonstrate a decrease in the decay width for increasing angular momentum and principal quantum number within both Rydberg series.

Magnetic optical rotation from real-time simulations in finite magnetic fields

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.

Benchmark Study of the Electronic States of the LiRb Molecule: Ab Initio Calculations with the Fock Space Coupled Cluster Approach

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants.

Direct Calculation of Electron Transfer Rates with the Binless Dynamic Histogram Analysis Method

Umbrella sampling molecular dynamics simulations are widely used to enhance sampling along the reaction coordinates of chemical reactions. The effect of the artificial bias can be removed using methods such as the dynamic weighted histogram analysis method (DHAM), which in addition to the global free energy profile also provides kinetic information about barrier-crossing rates directly from the Markov matrix. Here we present a binless formulation of DHAM that extends DHAM to high-dimensional and Hamiltonian-based biasing to allow the study of electron transfer (ET) processes, for which enhanced sampling is usually not possible based on simple geometric grounds. We show the capabilities of binless DHAM on examples such as aqueous ferrous-ferric ET and intramolecular ET in the radical anion of benzoquinone-tetrathiafulvalene-benzoquinone (Q-TTF-Q)-. From classical Hamiltonian-based umbrella sampling simulations and electronic coupling values from quantum chemistry calculations, binless DHAM provides ET rates for adiabatic and nonadiabatic ET reactions alike in excellent agreement with experimental results.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.

Correlation vs. exchange competition drives the singlet-triplet excited-state inversion in non-alternant hydrocarbons

In this work, we focus on the understanding of the driving force behind the S1-T1 excited-state energy inversion (which would thus violate Hund's rule, making the S1 state lower in energy than the T1 state) of two non-benzenoid non-alternant hydrocarbons, composed of odd-membered rings. The molecules considered here have identical chemical composition but different atomic configuration in space. The delicate interplay between structural and electronic factors that might induce inversion and its energy extension, only by a few meV, is systematically investigated here by state-of-the-art calculations. Qualitative and quantitative accurate predictions are obtained employing post-HF methods, thanks to the balanced and careful inclusion of electron correlation effects. The obtained results might guide and rationalize new searches for molecules violating Hund's rule, concomitantly demonstrating the importance of key contributions from the theoretical method of choice.

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.

Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation

Parity non-conservation (PNC) due to the weak interaction is predicted to give rise to enantiomer dependent vibrational constants in chiral molecules, but the phenomenon has so far eluded experimental observation. The enhanced sensitivity of molecules to physics beyond the Standard Model (BSM) has led to substantial advances in molecular precision spectroscopy, and these may be applied to PNC searches as well. Specifically, trapped molecular ion experiments leverage the universality of trapping charged particles to optimize the molecular ion species studied toward BSM searches, but in searches for PNC, only a few chiral molecular ion candidates have been proposed so far. Importantly, viable candidates need to be internally cold, and their internal state populations should be detectable with high quantum efficiency. To this end, we focus on molecular ions that can be created by near threshold resonant two-photon ionization and detected via state-selective photo-dissociation. Such candidates need to be stable in both charged and neutral chiral versions to be amenable to these methods. Here, we present a collection of suitable chiral molecular ion candidates we have found, including CHDBrI+ and CHCaBrI+, that fulfill these conditions according to our ab initio calculations. We find that organo-metallic species have low ionization energy as neutrals and relatively high dissociation thresholds. Finally, we compute the magnitude of the PNC values for vibrational transitions for some of these candidates. An experimental demonstration of state preparation and readout for these candidates will be an important milestone toward measuring PNC in chiral molecules for the first time.

Laser-induced ultrafast spin-transfer processes in non-linear zigzag carbon chain systems

We combine the high-level quantum chemistry theory CCSD and EOM-CCSD together with local and global Λ processes to investigate the details of the laser-induced ultrafast spin manipulation scenarios in non-linear zigzag carbon chain systems Ni2@C32H32 and Ni2@C36H36. The spin density distribution, which is calculated on each many-body state using a Mulliken population analysis, fulfills the requirements to accomplish the spin dynamics processes. Various spin-flip and spin-transfer scenarios are accomplished. All the spin-dynamics processes can be achieved within subpicosecond times. Under the influence of a magnetic field, we find that the spin-transfer scenarios are preserved, while the local spin-flip scenario on a Ni atom can be significantly inhibited depending on the strength of the magnetic field. The impact of the propagation direction of the laser pulse on the spin dynamics processes by varying their polar and azimuthal angles in spherical coordinates is investigated. Additionally, we find that double laser pulses successfully induce the spin-transfer processes. Our outcomes underline the significant potential of carbon chain systems as building blocks for developing future all-optical integrated logic processing units.

Analytic Evaluation of Nonadiabatic Couplings within the Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method

We present the theory for the evaluation of nonadiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motion can facilitate transitions between different resonances and between resonances and bound states. These nonadiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the NAC between bound states and pseudocontinuum states, between bound states and resonances, and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate, whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.

Theoretical Study of the Photochemical Mechanisms of the Electronic Quenching of NO(A2Σ+) with CH4, CH3OH, and CO2

The electronic quenching of NO(A2Σ+) with molecular partners occurs through complex non-adiabatic dynamics that occurs on multiple coupled potential energy surfaces. Moreover, the propensity for NO(A2Σ+) electronic quenching depends heavily on the strength and nature of the intermolecular interactions between NO(A2Σ+) and the molecular partner. In this paper, we explore the electronic quenching mechanisms of three systems: NO(A2Σ+) + CH4, NO(A2Σ+) + CH3OH, and NO(A2Σ+) + CO2. Using EOM-EA-CCSD calculations, we rationalize the very low electronic quenching cross-section of NO(A2Σ+) + CH4 as well as the outcomes observed in previous NO + CH4 photodissociation studies. Our analysis of NO(A2Σ+) + CH3OH suggests that it will undergo facile electronic quenching mediated by reducing the intermolecular distance and significantly stretching the O-H bond of CH3OH. For NO(A2Σ+) + CO2, intermolecular attractions lead to a series of low-energy ON-OCO conformations in which the CO2 is significantly bent. For both the NO(A2Σ+) + CH3OH and NO(A2Σ+) + CO2 systems, we see evidence of the harpoon mechanism and low-energy conical intersections between NO(A2Σ+) + M and NO(X2Π) + M. Overall, this work provides the first detailed theoretical study on the NO(A2Σ+) + M potential energy surface of each of these systems and will inform future velocity map imaging experiments.

Ultrafast control of laser-induced spin-dynamics scenarios on two-dimensional Ni3@C63H54 magnetic system

The concept of building logically functional networks employing spintronics or magnetic heterostructures is becoming more and more popular today. Incorporating logical segments into a circuit needs physical bonds between the magnetic molecules or clusters involved. In this framework, we systematically study ultrafast laser-induced spin-manipulation scenarios on a closed system of three carbon chains to which three Ni atoms are attached. After the inclusion of spin-orbit coupling and an external magnetic field, different ultrafast spin dynamics scenarios involving spin-flip and long-distance spin-transfer processes are achieved by various appropriately well-tailored time-resolved laser pulses within subpicosecond timescales. We additionally study the various effects of an external magnetic field on spin-flip and spin-transfer processes. Moreover, we obtain spin-dynamics processes induced by a double laser pulse, rather than a single one. We suggest enhancing the spatial addressability of spin-flip and spin-transfer processes. The findings presented in this article will improve our knowledge of the magnetic properties of carbon-based magnetic molecular structures. They also support the relevant experimental realization of spin dynamics and their potential applications in future molecular spintronics devices.

State-specific frozen natural orbital for reduced-cost algebraic diagrammatic construction calculations: The application to ionization problem

We have developed a reduced-cost algebraic diagrammatic construction (ADC) method based on state-specific frozen natural orbital and natural auxiliary functions. The newly developed method has been benchmarked on the GW100 test set for the ionization problem. The use of state-specific natural orbitals drastically reduces the size of the virtual space with a systematically controllable accuracy and offers a significant speedup over the standard ionization potential (IP)-ADC(3) method. The accuracy of the method can be controlled by two thresholds and nearly a black box to use. The inclusion of the perturbative correction significantly improves the accuracy of the calculated IP values, and the efficiency of the method has been demonstrated by calculating the IP of a molecule with 60 atoms and more than 2216 basis functions.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

Structural, Thermodynamic, and Spectroscopic Evolution in the Hydration of Copper(II) Ions, Cu2+(H2O)2-8

Gas-phase clusters of the hydrated Cu(II) cation with 2-8 water molecules were investigated using ab initio quantum chemistry. Isomer structures, energies, and vibrational spectra were computed across this size range, yielding a qualitative picture of this ion as an intact Cu2+ hydrate that also partially oxidizes the surrounding water network at equilibrium. At sufficient cluster sizes, these ion hydrates also become thermodynamically preferred over competitive Cu(II) hydroxide hydrates. Competitive coordination environments were found to exist at some cluster sizes, due to both hydrogen-bonding and d-orbital chemical effects, and the dominant coordination number was found in some cases to be temperature-dependent. Clear spectral signatures of the ion's coordination environment were computed to exist at each cluster size, which should make experimental verification of these computational predictions straightforward. Through comparison to recent studies of hydrated CuOH+, the effective charge on the metal center was shown to converge to approximately +1.5 in both cases, despite qualitatively different behavior of their radical spin densities. Therefore, nominally Cu(II) ions exhibit considerable electronic, chemical, and structural flexibility. The electronic origins of this flexibility─including key roles played by the water network itself─are investigated in this work and should provide a conceptual foundation for future studies of copper-based, water-oxidation catalysts.

Persistence of a Delocalized Radical in Larger Clusters of Hydrated Copper(II) Hydroxide, CuOH+(H2O)3-7

The structures, vibrational spectra, and electronic properties of copper hydroxide hydrates CuOH+(H2O)3-7 were investigated with quantum chemistry computations. As a follow-up to a previous analysis of CuOH+(H2O)0-2, this investigation examined the progression as the square-planar metal coordination environment was filled and as solvation shells expanded. Four-, five-, and six-coordinate structures were found to be low-energy isomers. The delocalized radical character, which was discovered in the small clusters, was found to persist upon continued hydration, although the hydrogen-bonded water network in the larger clusters was found to play a more significant role in accommodating this spin. Partial charges indicated that the electronic structure includes more Cu2+···OH- character than was observed in smaller clusters, but this structure remains decidedly mixed with Cu+···OH· configurations and yields roughly half-oxidation of the water network in the absence of any electrochemical potential. Computed vibrational spectra for n = 3 showed congruence with spectra from recent predissociation spectroscopy experiments, provided that the role of the D2 tag was taken into account. Spectra for n = 4-7 were predicted to exhibit features that are reflective of both the mixed electronic character and proton-/hydrogen-shuttling motifs within the hydrogen-bonded water network.

Two Algorithms for Excited-State Quantum Solvers: Theory and Application to EOM-UCCSD

Near-term quantum devices promise to revolutionize quantum chemistry, but simulations using the current noisy intermediate-scale quantum (NISQ) devices are not practical due to their high susceptibility to errors. This motivated the design of NISQ algorithms leveraging classical and quantum resources. While several developments have shown promising results for ground-state simulations, extending the algorithms to excited states remains challenging. This paper presents two cost-efficient excited-state algorithms inspired by the classical Davidson algorithm. We implemented the Davidson method into the quantum self-consistent equation-of-motion unitary coupled-cluster (q-sc-EOM-UCC) excited-state method adapted for quantum hardware. The circuit strategies for generating desired excited states are discussed, implemented, and tested. We demonstrate the performance and accuracy of the proposed algorithms (q-sc-EOM-UCC/Davidson and its variational variant) by simulations of H2, H4, LiH, and H2O molecules. Similar to the classical Davidson scheme, q-sc-EOM-UCC/Davidson algorithms are capable of targeting a small number of excited states of the desired character.

Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure

Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.

Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems

An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.

Ab Initio Investigation of the Auger Spectra of Methane, Ethane, Ethylene, and Acetylene

We present an ab initio computational study of the Auger spectra of methane, ethane, ethylene, and acetylene. Auger spectroscopy is an established technique to probe the electronic structure of molecules and exploits the Auger-Meitner effect that core-ionized states undergo. We compute partial decay widths using coupled-cluster theory with single and double substitutions (CCSD) and equation-of-motion CCSD theory combined with complex-scaled basis functions and Feshbach-Fano projection. We generate Auger spectra from these partial widths and draw conclusions about the strength of particular decay channels and trends among the four molecules. A connection to experimental results about fragmentation pathways of the electronic states produced by Auger decay is also made.

Resonant Inner-Shell Photofragmentation of Adamantane (C10H16)

Adamantane, the smallest diamondoid molecule with a symmetrical cage, contains two distinct carbon sites, CH and CH2. The ionization/excitation of the molecule leads to the cage opening and strong structural reorganization. While theoretical predictions suggest that the carbon site CH primarily causes the cage opening, the role of the other CH2 site remains unclear. In this study, we used advanced experimental Auger electron-ion coincidence techniques and theoretical calculations to investigate the fragmentation dynamics of adamantane after resonant inner-shell photoexcitation. Our results demonstrate that some fragmentation channels exhibit site-sensitivity of the initial core-hole location, indicating that different carbon site excitations could lead to unique cage opening mechanisms.

Benchmarking ionization potentials using the simple pCCD model

The electron-detachment energy is measured by the ionization potential (IP). As a result, it is a fundamental, observable and important molecular electronic signature in photoelectron spectroscopy. A precise theoretical prediction of electron-detachment energies or ionization potentials is essential for organic optoelectronic systems like transistors, solar cells, or light-emitting diodes. In this work, we benchmark the performance of the recently presented IP variant of the equation-of-motion pair coupled cluster doubles (IP-EOM-pCCD) model to determine IPs. Specifically, the predicted ionization energies are compared to experimental results and higher-order coupled cluster theories based on statistically assessing 201 electron-detached states of 41 organic molecules for three different molecular orbital basis sets and two sets of particle-hole operators. While IP-EOM-pCCD features a reasonable spread and skewness of ionization energies, its mean error and standard deviation differ by up to 1.5 eV from reference data. Our study, thus, highlights the importance of dynamical correlation to reliably predict IPs from a pCCD reference function in small organic molecules.

F12+EOM Quartic Force Fields for Rovibrational Predictions of Electronically Excited States

Quartic force fields (QFFs) constructed using a sum of ground-state CCSD(T)-F12b energies with EOM-CCSD excitation energies are proposed for computation of spectroscopic properties of electronically excited states. This is dubbed the F12+EOM approach and is shown to provide similar accuracy to previous methodologies at lower computational cost. Using explicitly correlated F12 approaches instead of canonical CCSD(T), as in the corresponding (T)+EOM approach, allows for 70-fold improvement in computational time. The mean percent difference between the two methods for anharmonic vibrational frequencies is only 0.10%. A similar approach is also developed herein which accounts for core correlation and scalar relativistic effects, named F12cCR+EOM. The F12+EOM and F12cCR+EOM approaches both match to within 2.5% mean absolute error of experimental fundamental frequencies. These new methods should help in clarifying astronomical spectra by assigning features to vibronic and vibrational transitions of small astromolecules when such data are not available experimentally.

Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra

Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.

Simulation of the VUV Absorption Spectra of Oxygenates and Hydrocarbons: A Joint Theoretical-Experimental Study

Vacuum UV absorption spectroscopy is regularly used to provide unambiguous identification of a target species, insight into the electronic structure of molecules, and quantitative species concentrations. As molecules of interest have become more complex, theoretical spectra have been used in tandem with laboratory spectroscopic analysis or as a replacement when experimental data is unavailable. However, it is difficult to determine which theoretical methodologies can best simulate experiment. This study examined the performance of EOM-CCSD and 10 TD-DFT functionals (B3LYP, BH&HLYP, BMK, CAM-B3LYP, HSE, M06-2X, M11, PBE0, ωB97X-D, and X3LYP) to produce reliable vacuum UV absorption spectra for 19 small oxygenates and hydrocarbons using vertical excitation energies. The simulated spectra were analyzed against experiment using both a qualitative analysis and quantitative metrics, including cosine similarity, relative integral change, mean signed error, and mean absolute error. Based on our ranking system, it was determined that M06-2X was consistently the top performing TD-DFT method with BMK, CAM-B3LYP, and ωB97X-D also producing reliable spectra for these small combustion species.

Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory

State-specific electronic structure theory provides a route toward balanced excited-state wave functions by exploiting higher-energy stationary points of the electronic energy. Multiconfigurational wave function approximations can describe both closed- and open-shell excited states and avoid the issues associated with state-averaged approaches. We investigate the existence of higher-energy solutions in complete active space self-consistent field (CASSCF) theory and characterize their topological properties. We demonstrate that state-specific approximations can provide accurate higher-energy excited states in H₂ (6-31G) with more compact active spaces than would be required in a state-averaged formalism. We then elucidate the unphysical stationary points, demonstrating that they arise from redundant orbitals when the active space is too large or symmetry breaking when the active space is too small. Furthermore, we investigate the singlet-triplet crossing in CH₂ (6-31G) and the avoided crossing in LiF (6-31G), revealing the severity of root flipping and demonstrating that state-specific solutions can behave quasi-diabatically or adiabatically. These results elucidate the complexity of the CASSCF energy landscape, highlighting the advantages and challenges of practical state-specific calculations.

Jet-Cooled Phosphorescence Excitation Spectrum of the T1(n,π*) ← S0 Transition of 4H-Pyran-4-one

The 4H-pyran-4-one (4PN) molecule is a cyclic conjugated enone with spectroscopically accessible singlet and triplet (n,π*)excited states. Vibronic spectra of 4PN provide a stringent test of electronic-structure calculations, through comparison of predicted vs measured vibrational frequencies in the excited state. We report here the T1(n,π*) ← S0 phosphorescence excitation spectrum of 4PN, recorded under the cooling conditions of a supersonic free-jet expansion. The jet cooling has eliminated congestion appearing in previous room-temperature measurements of the T1 ← S0 band system and has enabled us to determine precise fundamental frequencies for seven vibrational modes of the molecule in its T1(n,π*) state. We have also analyzed the rotational contour of the 000 band, obtaining experimental values for spin-spin and spin-rotation constants of the T1(n,π*) state. We used the experimental results to test predictions from two commonly used computational methods, equation-of-motion excitation energies with dynamical correlation incorporated at the level of coupled cluster singles doubles (EOM-EE-CCSD) and time-dependent density functional theory (TDDFT). We find that each method predicts harmonic frequencies within a few percent of observed fundamentals, for in-plane vibrational modes. However, for out-of-plane modes, each method has specific liabilities that result in frequency errors on the order of 20-30%. The calculations have helped to identify a perturbation from the T2(π,π*) state that leads to unexpected features observed in the T1(n,π*) ← S0 origin band rotational contour.

Real-Time Equation-of-Motion Coupled-Cluster Cumulant Green's Function Method: Heterogeneous Parallel Implementation Based on the Tensor Algebra for Many-Body Methods Infrastructure

We report the implementation of the real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function method [ J. Chem. Phys. 2020, 152, 174113] within the Tensor Algebra for Many-body Methods (TAMM) infrastructure. TAMM is a massively parallel heterogeneous tensor library designed for utilizing forthcoming exascale computing resources. The two-body electron repulsion matrix elements are Cholesky-decomposed, and we imposed spin-explicit forms of the various operators when evaluating the tensor contractions. Unlike our previous real algebra Tensor Contraction Engine (TCE) implementation, the TAMM implementation supports fully complex algebra. The RT-EOM-CC singles (S) and doubles (D) time-dependent amplitudes are propagated using a first-order Adams-Moulton method. This new implementation shows excellent scalability tested up to 500 GPUs using the Zn-porphyrin molecule with 655 basis functions, with parallel efficiencies above 90% up to 400 GPUs. The TAMM RT-EOM-CCSD was used to study core photoemission spectra in the formaldehyde and ethyl trifluoroacetate (ESCA) molecules. Simulations of the latter involve as many as 71 occupied and 649 virtual orbitals. The relative quasiparticle ionization energies and overall spectral functions agree well with available experimental results.

Secondary Electron Attachment-Induced Radiation Damage to Genetic Materials

Reactions of radiation-produced secondary electrons (SEs) with biomacromolecules (e.g., DNA) are considered one of the primary causes of radiation-induced cell death. In this Review, we summarize the latest developments in the modeling of SE attachment-induced radiation damage. The initial attachment of electrons to genetic materials has traditionally been attributed to the temporary bound or resonance states. Recent studies have, however, indicated an alternative possibility with two steps. First, the dipole-bound states act as a doorway for electron capture. Subsequently, the electron gets transferred to the valence-bound state, in which the electron is localized on the nucleobase. The transfer from the dipole-bound to valence-bound state happens through a mixing of electronic and nuclear degrees of freedom. In the presence of aqueous media, the water-bound states act as the doorway state, which is similar to that of the presolvated electron. Electron transfer from the initial doorway state to the nucleobase-bound state in the presence of bulk aqueous media happens on an ultrafast time scale, and it can account for the decrease in DNA strand breaks in aqueous environments. Analyses of the theoretically obtained results along with experimental data have also been discussed.

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

A configuration interaction correction on top of pair coupled cluster doubles

Numerous numerical studies have shown that geminal-based methods are a promising direction to model strongly correlated systems with low computational costs. Several strategies have been introduced to capture the missing dynamical correlation effects, which typically exploit a posteriori corrections to account for correlation effects associated with broken-pair states or inter-geminal correlations. In this article, we scrutinize the accuracy of the pair coupled cluster doubles (pCCD) method extended by configuration interaction (CI) theory. Specifically, we benchmark various CI models, including, at most double excitations against selected CC corrections as well as conventional single-reference CC methods. A simple Davidson correction is also tested. The accuracy of the proposed pCCD-CI approaches is assessed for challenging small model systems such as the N₂ and F₂ dimers and various di- and triatomic actinide-containing compounds. In general, the proposed CI methods considerably improve spectroscopic constants compared to the conventional CCSD approach, provided a Davidson correction is included in the theoretical model. At the same time, their accuracy lies between those of the linearized frozen pCCD and frozen pCCD variants.

Jahn-Teller effects in initial and final states: high-resolution X-ray absorption, photoelectron and Auger spectroscopy of allene

Carbon K-edge resonant Auger spectra of gas-phase allene following excitation of the pre-edge 1s → π* transitions are presented and analysed with the support of EOM-CCSD/cc-pVTZ calculations. X-Ray absorption (XAS), X-ray photoelectron (XPS), valence band and non-resonant Auger spectra are also reanalysed with a series of computational approaches. The results presented demonstrate the importance of including nuclear ensemble effects for simulating X-ray observables and as an effective strategy for capturing Jahn-Teller effects in spectra.

Why Is Quantum Chemistry So Complicated?

The myriad tools of quantum chemistry are now widely used by a diverse community of chemists, biologists, physicists, and material scientists. The large number of methods (e.g., Hartree-Fock, density functional theory, configuration interaction, perturbation theory, coupled-clusters, equations of motion, Green's functions, and more) and the multitude of atomic orbital basis sets often give rise to consternation and confusion. In this Perspective, I explain why quantum chemistry has so many different methods and why researchers should understand their relative strengths and weaknesses. I explain how chemistry's use of orbitals and the need for wave functions to be antisymmetric causes computational-effort scaling proportional to the cube or higher power of the number of orbitals. I also illustrate how the fact that the Schrödinger equation's energies are extensive makes it difficult to extract intensive properties such as bond and excitation energies, ionization potentials, and electron affinities.

New Implementation of an Equation-of-Motion Coupled-Cluster Damped-Response Framework with Illustrative Applications to Resonant Inelastic X-ray Scattering

We present an implementation of a damped response framework for calculating resonant inelastic X-ray scattering (RIXS) at the equation-of-motion coupled-cluster singles and doubles (CCSD) and second-order approximate coupled-cluster singles and doubles (CC2) levels of theory in the open-source program e^T. This framework lays the foundation for future extension to higher excitation methods (notably, the coupled-cluster singles and doubles with perturbative triples, CC3) and to multilevel approaches. Our implementation adopts a fully relaxed ground state and different variants of the core-valence separation projection technique to address convergence issues. Illustrative results are compared with those obtained within the frozen-core core-valence separated approach, available in Q-Chem, as well as with experiment. The performance of the CC2 method is evaluated in comparison with that of CCSD. It is found that, while the CC2 method is noticeably inferior to CCSD for X-ray absorption spectra, the quality of the CC2 RIXS spectra is often comparable to that of the CCSD level of theory, when the same valence excited states are probed. Finally, we present preliminary RIXS results for a solvated molecule in aqueous solution.

The Auger spectrum of benzene

We present an ab initio computational study of the Auger electron spectrum of benzene. Auger electron spectroscopy exploits the Auger-Meitner effect, and although it is established as an analytic technique, the theoretical modeling of molecular Auger spectra from first principles remains challenging. Here, we use coupled-cluster theory and equation-of-motion coupled-cluster theory combined with two approaches to describe the decaying nature of core-ionized states: (i) Feshbach-Fano resonance theory and (ii) the method of complex basis functions. The spectra computed with these two approaches are in excellent agreement with each other and also agree well with experimental Auger spectra of benzene. The Auger spectrum of benzene features two well-resolved peaks at Auger electron energies above 260 eV, which correspond to final states with two electrons removed from the 1e_1g and 3e_2g highest occupied molecular orbitals. At lower Auger electron energies, the spectrum is less well resolved, and the peaks comprise multiple final states of the benzene dication. In line with theoretical considerations, singlet decay channels contribute more to the total Auger intensity than the corresponding triplet decay channels.