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

Triple Electron Attachments with a New Intermediate-Hamiltonian Fock-Space Coupled-Cluster Method

The implementation of a new intermediate-Hamiltonian Fock-space coupled-cluster (IHFSCC) scheme for the (3,0) sector of the Fock space is reported. In this IHFSCC approach, the three-body contributions in the cluster operator S(3,0) corresponding to the (3,0) sector of the Fock space are considered, while S(1,0) and S(2,0) at the (1,0) and (2,0) level only include one- and two-body operators. By introducing a suitable partition of the wave operator, the intermediate Hamiltonian, which only depends on the two-body operator of S(1,0), is obtained. S(2,0) and S(3,0) are not required within this new IHFSCC scheme, and a large reference space can be possibly employed. The performance of this (3,0) IHFSCC method in calculating triple ionization potentials and excitation energies for atoms and cations with a ground p3 configuration as well as adiabatic excitation energies for some molecules is investigated. The effect of the number of active virtual orbitals and three different types of orbitals, i.e., reference orbitals, restricted open-shell Hartree-Fock orbitals (ROHF) of the target systems, and canonicalized ROHF orbitals, on IHFSCC results, is also studied. Our calculations indicate that reasonable results can be achieved with this (3,0) IHFSCC method when a minimal reference space is employed. Further increasing the number of active orbitals does not necessarily improve the results. In addition, the IHFSCC results using canonicalized ROHF orbitals generally agree well with reference values, and they are not very sensitive to the number of active orbitals compared with results using the reference orbitals. The new (3,0) IHFSCC method can be applied to open-shell systems with three unpaired electrons with reasonable accuracy at a relatively low computational cost.

Fourth-Order Algebraic Diagrammatic Construction for Electron Detachment and Attachment: The IP- and EA-ADC(4) Methods

We present a non-Dyson fourth-order algebraic diagrammatic construction formulation of the electron propagator, featuring the distinct IP- and EA-ADC(4) schemes for the treatment of ionization and electron attachment processes. The algebraic expressions have been derived automatically using the intermediate state representation approach and implemented in the Q-Chem quantum-chemical program package. The performance of the novel methods is assessed with respect to high-level reference data for ionization potentials and electron affinities of closed- and open-shell systems. While only minor improvements over the corresponding third-order methods are observed for one-hole ionization and one-particle electron attachment processes from closed-shell systems (MAEIP-ADC(4) = 0.27 eV and MAEEA-ADC(4) = 0.05 eV), a significantly enhanced performance is found in case of open-shell reference states (MAEIP-ADC(4) = 0.11 eV and MAEEA-ADC(4) = 0.02 eV). A particularly appealing feature of the novel methods is their accurate treatment of satellite transitions. For closed-shell reference states, we obtain accuracies of MAEIP-ADC(4) = 0.81 eV and MAEEA-ADC(4) = 0.27 eV, while in case of open-shell reference states, mean absolute errors of MAEIP-ADC(4) = 0.15 eV and MAEEA-ADC(4) = 0.27 eV are found.

A unique approach to address avoided crossings in the charge stabilization curve for LUMO identification

In quantum chemistry, Lowest Unoccupied Molecular Orbital (LUMO) is important for studying various chemical processes, including photochemical reactions, electron attached states, and electron excites states. Recently, an effective method has been introduced that involves the use of the Parametric Equation of Motion (PEM) in conjunction with the nuclear charge stabilization method for precise identification of true LUMO. However, the inclusion of extra diffuse functions in the basis set, which is necessary for describing electron-attached and electron-excited states, can cause issues due to the presence of the same symmetry states, leading to avoided crossing. Identifying the true LUMO among these avoided crossings is challenging due to the mixing of states and the exchange of their orbital character. This article introduces a modification of the PEM to identify the true LUMO by preventing the stabilization of specific states involved in avoided crossings. The present method is highly effective and requires minimal computational cost.

Multireference Averaged Quadratic Coupled Cluster (MR-AQCC) Study of the Geometries and Energies for ortho-, meta- and para-Benzyne

The diradical benzyne isomers are excellent prototypes for evaluating the ability of an electronic structure method to describe static and dynamic correlation. The benzyne isomers are also interesting molecules with which to study the fundamentals of through-space and through-bond diradical coupling that is important in so many electronic device applications. In the current study, we utilize the multireference methods MC-SCF, MR-CISD, MR-CISD+Q, and MR-AQCC with an (8,8) complete active space that includes the σ, σ*, π and π* orbitals, to characterize the electronic structure of ortho-, meta- and para-benzyne. We also determine the adiabatic and vertical singlet-triplet splittings for these isomers. MR-AQCC and MR-CISD+Q produced energy gaps in good agreement with previously obtained experimental values. Geometries, orbital energies and unpaired electron densities show significant through-space coupling in the o- and m-benzynes, while p-benzyne shows through-bond coupling, explaining the dramatically different singlet-triplet gaps between the three isomers.

Equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation

Orbital-optimized coupled-cluster methods are very helpful for theoretical predictions of the molecular properties of challenging chemical systems, such as excited states. In this research, an efficient implementation of the equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting (DF) approach, denoted by DF-EOM-OCCD, is presented. The computational cost of the DF-EOM-OCCD method for excitation energies is compared with that of the conventional EOM-OCCD method. Our results demonstrate that DF-EOM-OCCD excitation energies are dramatically accelerated compared to EOM-OCCD. There are almost 17-fold reductions for theC 5 H 12 $$ {\mathrm{C}}_5{\mathrm{H}}_{12} $$ molecule in an aug-cc-pVTZ basis set with the RHF reference. This dramatic performance improvement comes from the reduced cost of integral transformation with the DF approach and the efficient evaluation of the particle-particle ladder (PPL) term, which is the most expensive term to evaluate. Further, our results show that the DF-EOM-OCCD approach is very helpful for the computation of excitation energies in open-shell molecular systems. Overall, we conclude that our new DF-EOM-OCCD implementation is very promising for the study of excited states in large-sized challenging chemical systems.

Theoretical Rotational and Vibrational Spectral Data for the Hypermagnesium Oxide Species Mg2O and Mg2O. Chemphyschem 2024;25:e202400479. [PMID: 38801234 DOI: 10.1002/cphc.202400479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

While magnesium is astronomically observed in small molecules, it largely serves as a contributor to silicate grains, though how these grains form is not well-understood. The smallest hypermagnesium oxide compounds (Mg2 ${{}_{2}}$ O/Mg2 ${{}_{2}}$ O+ ${{}^{+}}$ ) may play a role in silicate formation, but little vibrational reference data exist. As such, anharmonic spectroscopic data are computed forX ˜ 1 Σ g + ${{{\tilde{\rm {X}}}}^1 {\rm{\Sigma }}_g^+ }$ Mg2 ${{}_{2}}$ O,a ˜ 1 Σ u + ${{{\tilde{\rm {a}}}}^1 {\rm{\Sigma }}_u^+ }$ Mg2 ${{}_{2}}$ O, andX ˜ 2 Σ g + ${{{\tilde{\rm {X}}}}^2 {\rm{\Sigma }}_g^+ }$ Mg2 ${{}_{2}}$ O+ ${{}^{+}}$ using quartic force fields (QFFs). Explicitly-correlated coupled-cluster QFFs for the neutral species perform well, implying that full multireference treatment may not be necessary for such systems if enough electron correlation is included. Equation-of-motion ionization potential (EOMIP) methods forX ˜ 2 Σ g + ${{{\tilde{\rm {X}}}}^2 {\rm{\Sigma }}_g^+ }$ Mg2 ${{}_{2}}$ O+ ${{}^{+}}$ QFFs circumvent previous symmetry breaking issues even in explicitly-correlated coupled-cluster results, motivating the need for EOMIP treatments at minimum for such systems. All three species are found to have high-intensity vibrational frequencies. Even so, the highly intense frequency (X ˜ 1 Σ g + ${{{\tilde{\rm {X}}}}^1 {\rm{\Sigma }}_g^+ }$ Mg2 ${{}_{2}}$ O: 894.7 cm-1/11.18 μm;a ˜ 1 Σ u + ${{{\tilde{\rm {a}}}}^1 {\rm{\Sigma }}_u^+ }$ Mg2 ${{}_{2}}$ O: 915.0 cm-1/10.91 μm) for either neutral state may be astronomically obscured by the polycyclic aromatic hydrocarbon 11.2 μm band. Mg2 ${{}_{2}}$ O+ ${{}^{+}}$ may be less susceptible to such obfuscation, and itsν 1 ${{\nu }_{1}}$ intensity is computed to be a massive 4793 km mol-1.

Analytic Gradients for Equation-of-Motion Coupled Cluster with Single, Double, and Perturbative Triple Excitations

Understanding the process of molecular photoexcitation is crucial in various fields, including drug development, materials science, photovoltaics, and more. The electronic vertical excitation energy is a critical property, for example in determining the singlet-triplet gap of chromophores. However, a full understanding of excited-state processes requires additional explorations of the excited-state potential energy surface and electronic properties, which is greatly aided by the availability of analytic energy gradients. Owing to its robust high accuracy over a wide range of chemical problems, equation-of-motion coupled cluster with single and double excitations (EOM-CCSD) is a powerful method for predicting excited-state properties, and the implementation of analytic gradients of many EOM-CCSD variants (excitation energies, ionization potentials, electron attachment energies, etc.) along with numerous successful applications highlights the flexibility of the method. In specific cases where a higher level of accuracy is needed or in more complex electronic structures, the inclusion of triple excitations becomes essential, for example, in the EOM-CCSD* approach of Saeh and Stanton. In this work, we derive and implement for the first time the analytic gradients of EOMEE-CCSD*, which also provides a template for analytic gradients of related excited-state methods with perturbative triple excitations. The capabilities of analytic EOMEE-CCSD* gradients are illustrated by several representative examples.

Time-Resolved Circular Dichroism in Molecules: Experimental and Theoretical Advances

Following changes in chirality can give access to relevant information on the function or reactivity of molecular systems. Time-resolved circular dichroism (TRCD) spectroscopy proves to be a valid tool to achieve this goal. Depending on the class of molecules, different temporal ranges, spanning from seconds to femtoseconds, need to be investigated to observe such chiroptical changes. Therefore, over the years, several approaches have been adopted to cover the timescale of interest, especially based on pump-probe schemes. Moreover, various theoretical approaches have been proposed to simulate and explain TRCD spectra, including linear and non-linear response methods as well as non-adiabatic molecular dynamics. In this review, an overview on both experimental and theoretical advances in the TRCD field is provided, together with selected applications. A discussion on future theoretical developments for TRCD is also given.

Fock Space Coupled-Cluster Method for the Ground and Excited States of the NaMg+ Molecular Cation

This study presents a theoretical investigation of the potential energy curves (PECs) and spectroscopic constants of the NaMg+ molecular cation using the intermediate Hamiltonian Fock space coupled-cluster method with singles and doubles within the (2,0) sector [IH-FS-CCSD(2,0)]. The NaMg+ cation has gained scientific interest due to its potential applications in ultracold chemistry, yet it remains experimentally unexplored. We computed 20 lowest-lying PECs and assigned them to 10 dissociation limits. Our results demonstrated high accuracy, and computed curves are smooth and continuous over the entire range of interatomic distances. The study validates the effectiveness of the IH-FS-CCSD(2,0) method in describing PECs of diatomic molecular cations composed of alkali and alkaline earth metals and provides a solid theoretical foundation for further studies of NaMg+ and similar systems.

Exploiting the Correlation between the 1s, 2s, and 2p Energies for the Prediction of Core-Level Binding Energies of Si, P, S, and Cl species

The binding energies (BEs) of the 1s, 2s, and 2p core electrons of third-period elements (Si, P, S, Cl) were calculated using Hartree-Fock (HF) and B3LYP, BH&HLYP, and LC-BOP ΔSCF, and the shifted KS ΔSCF methods. Linear relationships between two BEs were derived and compared with the Auger parameter. The derived lines are essentially parallel, with only the intercepts differing. The difference in intercepts is due to the lack of electron correlation effects in HF and the self-interaction errors (SIEs) of the functional. The slope is the slope of the linear relationship between the chemical shifts. The straight lines between the 2s and 2p BEs also coincided with the Auger parameter lines, which have a slope of 1 by definition and an intercept being the difference between the 2s and 2p BEs. The shifted KS ΔSCF scheme compensates for SIEs, yielding equations that are approximately invariant. The calculated average gaps for the 2s and 2p BEs are 51.21 eV for Si, 57.48 eV for P, 63.85 eV for S, and 70.48 eV for Cl. The straight lines representing the relationships between the BEs of the 1s and 2s and 1s and 2p electrons are also parallel to each other in ΔSCF and converge into a single line in the shifted ΔSCF scheme. However, these lines are steeper than the Auger parameter line. The derived relationships can be used to predict unknown BEs, which we have applied to many molecules. The results are highly accurate, with mean absolute errors (MAEs) of less than 0.2 eV compared to experimental values.

Perspective on Theoretical and Experimental Advances in Atmospheric Photochemistry

Research that explores the chemistry of Earth's atmosphere is central to the current understanding of global challenges such as climate change, stratospheric ozone depletion, and poor air quality in urban areas. This research is a synergistic combination of three established domains: earth observation, for example, using satellites, and in situ field measurements; computer modeling of the atmosphere and its chemistry; and laboratory measurements of the properties and reactivity of gas-phase molecules and aerosol particles. The complexity of the interconnected chemical and photochemical reactions which determine the composition of the atmosphere challenges the capacity of laboratory studies to provide the spectroscopic, photochemical, and kinetic data required for computer models. Here, we consider whether predictions from computational chemistry using modern electronic structure theory and nonadiabatic dynamics simulations are becoming sufficiently accurate to supplement quantitative laboratory data for wavelength-dependent absorption cross-sections, photochemical quantum yields, and reaction rate coefficients. Drawing on presentations and discussions from the CECAM workshop on Theoretical and Experimental Advances in Atmospheric Photochemistry held in March 2024, we describe key concepts in the theory of photochemistry, survey the state-of-the-art in computational photochemistry methods, and compare their capabilities with modern experimental laboratory techniques. From such considerations, we offer a perspective on the scope of computational (photo)chemistry methods based on rigorous electronic structure theory to become a fourth core domain of research in atmospheric chemistry.

Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations

Intermolecular charge-transfer is a highly important process in biology and energy-conversion applications where generated charges need to be transported over several moieties. However, its theoretical description is challenging since the high accuracy required to describe these excited states must be accessible for calculations on large molecular systems. In this benchmark study, we identify reliable low-scaling computational methods for this task. Our reference results were obtained from highly accurate wavefunction calculations that restrict the size of the benchmark systems. However, the density-functional theory based methods that we identify as accurate can be applied to much larger systems. Since targeting charge-transfer states requires the unambiguous classification of an excited state, we first analyze several charge-transfer descriptors for their reliability concerning intermolecular charge-transfer and single out the charge-transfer distance calculated based on the variation of electron density upon excitation (DCT) as an optimal choice for our purposes. In general, best results are obtained for orbital-optimized methods and among those, the maximum overlap method proved to be the most numerically stable variant when using the initial MOs as reference orbitals. Favorable error cancellation with optimally-tuned range-separated hybrid functionals and a rather small basis set can provide an economical yet reasonable wavefunction when using time-dependent density functional theory, which provides relevant information about the excited-state character to be used in the orbital-optimized methods. The qualitative agreement makes these fast calculations attractive for high-throughput screening applications.

Absorption Intensities of Organic Molecules from Electronic Structure Calculations versus Experiments: the Effect of Solvation, Method, Basis Set, and Transition Moment Gauge

Recently, we derived experimental oscillator strengths (OSs) from well-defined UV-visible absorption spectral peaks of 100 molecules in solution. Here, we focus on a subset of transitions with the highest reliability to further benchmark the OSs from several wave function methods and density functionals. We consider multiple basis sets, transition moment gauges (length, velocity, and mixed), and solvent corrections. Most transitions in the comparison set come from conjugated molecules and have π → π* character. We use an automated algorithm to assign computed transitions to experimental bands. OSs computed using the Tamm-Dancoff approximation (TDA), CIS, or EOM-CCSD exhibited a strong gauge dependence, which is diminished in linear response theories (TD-DFT, TD-HF, and to a smaller degree LR-CCSD). OSs calculated from TD-DFT with PCM solvent models are systematically larger than apparent OSs derived from experimental spectra. For example, fcomp from hybrid functionals and PCM have mean absolute errors that are ∼10% of n·fexp, where n is a solvent refractive index factor that arises from the energy flux of the radiation field in a dielectric (solvent). Theoretical cavity field corrections considering spherical cavities do not improve the agreement between computed and experimental data. Corrections that account for the molecular shape and the direction of transition dipole moments, or that explicitly account for the effect of solvent molecules on the local field, should be more appropriate.

Machine Learning Approach to Vertical Energy Gap in Redox Processes

A straightforward approach to calculating the free energy change (ΔG) and reorganization energy of a redox process is linear response approximation (LRA). However, accurate prediction of redox properties is still challenging due to difficulties in conformational sampling and vertical energy-gap sampling. Expensive hybrid quantum mechanical/molecular mechanical (QM/MM) calculations are typically employed in sampling energy gaps using conformations from simulations. To alleviate the computational cost associated with the expensive QM method in the QM/MM calculation, we propose machine learning (ML) methods to predict the vertical energy gaps (VEGs). We tested several ML models to predict the VEGs and observed that simple models like linear regression show excellent performance (mean absolute error ∼0.1 eV) in predicting VEGs in all test systems, even when using features extracted from cheaper semiempirical methods. Our best ML model (extra trees regressor) shows a mean absolute error of around 0.1 eV while using features from the cheapest QM method. We anticipate our approach can be generalized to larger macromolecular systems with more complex redox centers.

Electronic Structure Methods for Simulating Flavin's Spectroscopy and Photophysics: Comparison of Multi-reference, TD-DFT, and Single-Reference Wave Function Methods

The use of flavins and flavoproteins in photocatalytic, sensing, and biotechnological applications has led to a growing interest in computationally modeling the excited-state electronic structure and photophysics of flavin. However, there is limited consensus regarding which computational methods are appropriate for modeling flavin's photophysics. We compare the energies of low-lying excited states of flavin computed with time-dependent density functional theory (TD-DFT), equation-of-motion coupled cluster (EOM-EE-CCSD), scaled opposite-spin configuration interaction [SOS-CIS(D)], multiconfiguration pair-density functional theory (MC-PDFT), and several multireference perturbation theory (MR-PT2) methods. In the first part, we focus on excitation energies of the first singlet excited state (S1) of five different redox and protonation states of flavin, with the goal of finding a suitable active space for MR-PT2 calculations. In the second part, we construct two sets of one-dimensional potential energy surfaces connecting the S0 and S1 equilibrium geometries (S0-S1 path) and the S1 (π,π*) and S2 (n,π*) equilibrium geometries (S1-S2 path). The first path therefore follows a Franck-Condon active mode of flavin while the second path maps crossings points between low-lying singlet and triplet states in flavin. We discuss the similarities and differences in the TD-DFT, EOM-EE-CCSD, SOS-CIS(D), MC-PDFT and MR-PT2 energy profiles along these paths. We find that (TD-)DFT methods are suitable for applications such as simulating the spectra of flavins but are inconsistent with several other methods when used for some geometry optimizations and when describing the energetics of dark (n,π*) states. MR-PT2 methods show promise for the simulation of flavin's low-lying excited states, but the selection of orbitals for the active space and the number of roots used for state averaging must be done carefully to avoid artifacts. Some properties, such as the intersystem crossing geometry and energy between the S1 (π,π*) and T2 (n,π*) states, may require additional benchmarking before they can be determined quantitatively.

Spin-flip equation-of-motion coupled cluster method with singles, doubles and (full) triples: computational implementation and some pilot applications

We present our computational implementation of the spin-flip (SF) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and (full) triples (SDT) within Q-CHEM. The inclusion of triples not only enhances the quantitative accuracy of the SF-EOM-CCSD method but also provides correct qualitative trends in the energy gaps between strongly degenerate states. To assess the accuracy, we compare our SF-EOM-CCSDT results with full configuration interaction (FCI) and complete-active-space self-consistent field second-order (CASSCF-SO) CI benchmarks to study the adiabatic energy gaps in CH2 and NH2+ diradicals, vertical excitation energies in CH radicals and the bond dissociation of the HF molecule. We have implemented SF-EOM-CCSDT using both the conventional double precision (DP) and the single precision (SP) algorithms. The use of SP does not introduce any significant errors in energies and energy gaps, and, due to low cost (relative to DP), turns out to be a promising approach to widen the applicability of EOM-CCSDT to bigger molecules.

Efficient State-Specific Natural Orbital Based Equation of Motion Coupled Cluster Method for Core-Ionization Energies: Theory, Implementation, and Benchmark

We have implemented a reduced-cost partial triples correction scheme to the equation of motion coupled cluster method for core-ionization energy based on state-specific natural orbitals. The second-order Algebraic Diagrammatic Construction (ADC) method is used to generate the state-specific natural orbital, which provides quicker convergence of the core-IP value with respect to the size of the virtual space than that observed in standard MP2-based natural orbitals. The error due to truncation of the virtual orbital can be reduced by using a perturbative correction. The accuracy of the method can be controlled by a single threshold, and there is a black box to use. The inclusion of the partial triples correction in the natural orbital based EOM-CCSD method greatly improves the agreement of the results with the experiment. The efficiency of the present implementation is demonstrated by calculating the core-ionization energy of a molecule containing 60 atoms and more than 2000 basis functions.

Liquid-jet photoemission spectroscopy as a structural tool: site-specific acid-base chemistry of vitamin C

Liquid-jet photoemission spectroscopy (LJ-PES) directly probes the electronic structure of solutes and solvents. It also emerges as a novel tool to explore chemical structure in aqueous solutions, yet the scope of the approach has to be examined. Here, we present a pH-dependent liquid-jet photoelectron spectroscopic investigation of ascorbic acid (vitamin C). We combine core-level photoelectron spectroscopy and ab initio calculations, allowing us to site-specifically explore the acid-base chemistry of the biomolecule. For the first time, we demonstrate the capability of the method to simultaneously assign two deprotonation sites within the molecule. We show that a large change in chemical shift appears even for atoms distant several bonds from the chemically modified group. Furthermore, we present a highly efficient and accurate computational protocol based on a single structure using the maximum-overlap method for modeling core-level photoelectron spectra in aqueous environments. This work poses a broader question: to what extent can LJ-PES complement established structural techniques such as nuclear magnetic resonance? Answering this question is highly relevant in view of the large number of incorrect molecular structures published.

An Innovative Approach for Precise Identification of the Lowest Unoccupied Molecular Orbital Using the Parametric Equation of Motion

The lowest unoccupied molecular orbital (LUMO) plays a crucial role in quantum chemistry, but current quantum chemistry calculations fail to provide useful virtual orbitals, making it challenging to explore various processes such as photochemical reactions, electron attachment, reduction, or excitation processes. The LUMO obtained from the self-consistent field (SCF) solution can not be relied upon and needs to be identified as they are often present among the continuum states having almost similar energies. The nuclear charge stabilization method has been proven useful in identifying LUMO. Herein, we have proposed the application of parametric equations of motion (PEM) in conjunction with nuclear charge stabilization method to identify the LUMO obtained from the SCF solution exhibiting stability with different basis sets including diffuse functions.

Computed Gyration Tensors of Knotted Chiral and Achiral Topological Stereoisomers of C60 Cyclocarbons

The electronic origins of the computed optical rotations of the simplest chiral and achiral chemical knots with comparatively simple compositions and large, anticipated magnetoelectric polarizabilities are provided. Linear response theory (LRT) is used to calculate the gyration at 1064 nm of two knotted polyyne chains, topological stereoisomers of cyclo[60]carbon. One isomer is analogous to the trefoil knot with approximate D3 symmetry and the other to the figure eight knot with approximate S4 symmetry. The response in each case can be attributed largely to the magnetic dipole term that arises in a near degenerate E-like excited state. An oriented achiral figure eight knot is as optically active in some directions as the chiral knot in any direction, and its absolute eigenvalues are larger.

Investigation of the exact spin channels in laser-induced spin dynamics in two mononuclear Cu(II) complexes

In the quest to harness the potential of nanospintronic applications, we analyze and investigate the spin channels for the ultrafast spin dynamics in mononuclear Cu2+(tdp)Cl2 (Cutdp) and Cu2+(tdp)Cl2·MeCN (Cutdp·MeCN) using a high-level ab initio many-body theory. In that spirit, we select two slightly different polymerizations arising from one parent complex. We establish the difference in magnetic behavior between the two complexes which arises solely from the geometrical differences. We calculate the static magnetic properties, such as the magnetic anisotropy of the complexes, which is analyzed by means of the magnetic moment of the ground state. The asymmetry of the core Cu-Cl-Cu-Cl axial plane unit is also reflected in the ground state absorption spectra of the two complexes. Comparisons with the experimental data are in good agreement with the exception of one peak in the theoretical calculations for each of the complexes, confirming the reliability of theoretical methods employed. A major finding in this work is the distinction between classical and coherent superpositions of Λ processes. We employ the selective blocking and retention (SBR) technique to find the unique path or paths for spin dynamic scenarios like spin flip and spin transfer. Additionally, we also present two different scenarios in which intermediate states are involved in spin dynamic processes, (i) classical superposition of Λ processes (i.e., there are many unique paths for transition, even with just one intermediate state the transition completes successfully), and (ii) collective coherent superposition of Λ processes (i.e., there is only one path for the transition, which requires more than one intermediate state to be in a specific coherent superposition). As a consequence, we gain insight into the type of correlations (static or dynamic) involved in a particular spin dynamic scenario.

Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment

Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

Evolution of the ionisation energy with the stepwise growth of chiral clusters of [4]helicene

Polycyclic aromatic hydrocarbons (PAHs) are widely established as ubiquitous in the interstellar medium (ISM), but considering their prevalence in harsh vacuum environments, the role of ionisation in the formation of PAH clusters is poorly understood, particularly if a chirality-dependent aggregation route is considered. Here we report on photoelectron spectroscopy experiments on [4]helicene clusters performed with a vacuum ultraviolet synchrotron beamline. Aggregates (up to the heptamer) of [4]helicene, the smallest PAH with helical chirality, were produced and investigated with a combined experimental and theoretical approach using several state-of-the-art quantum-chemical methodologies. The ionisation onsets are extracted for each cluster size from the mass-selected photoelectron spectra and compared with calculations of vertical ionisation energies. We explore the complex aggregation topologies emerging from the multitude of isomers formed through clustering of P and M, the two enantiomers of [4]helicene. The very satisfactory benchmarking between experimental ionisation onsets vs. predicted ionisation energies allows the identification of theoretically predicted potential aggregation motifs and corresponding energetic ordering of chiral clusters. Our structural models suggest that a homochiral aggregation route is energetically favoured over heterochiral arrangements with increasing cluster size, hinting at potential symmetry breaking in PAH cluster formation at the scale of small grains.

Core Binding Energy Calculations: A Scalable Approach with the Quantum Embedding-Based Equation-of-Motion Coupled-Cluster Method

We investigated the use of density matrix embedding theory to facilitate the computation of core ionization energies (IPs) of large molecules at the equation-of-motion coupled-cluster singles doubles with perturbative triples (EOM-CCSD*) level in combination with the core-valence separation (CVS) approximation. The unembedded IP-CVS-EOM-CCSD* method with a triple-ζ basis set produced ionization energies within 1 eV of experiment with a standard deviation of ∼0.2 eV for the core65 data set. The embedded variant contributed very little systematic error relative to the unembedded method, with a mean unsigned error of 0.07 eV and a standard deviation of ∼0.1 eV, in exchange for accelerating the calculations by many orders of magnitude. By employing embedded EOM-CC methods, we computed the core ionization energies of the uracil hexamer, doped fullerene, and chlorophyll molecule, utilizing up to ∼4000 basis functions within 1 eV from experimental values. Such calculations are not currently possible with the unembedded EOM-CC method.

Using single and double laser pulses on the molecular Ni4@C48H36 system to design integrated nanospintronic units

The accomplishment of long-distance spin transfer scenarios between several magnetic centers is a big challenge for building and supporting spin-logic units for developing future all-optical magnetic unit operations. Using high-level quantum chemistry theory CCSD and EOM-CCSD, we systematically study the ultrafast laser-induced spin-dynamics process on a carbon-based material, to which four magnetic centers are attached. We show that the CCSD method with the 6-31G basis set calculation is sensitive to the C-Ni bond length. The spin density distribution, which is computed using EOM-CCSD with LanL2DZ+ECP calculations, Mulliken population analysis, including spin-orbit-coupling (SOC) and a magnetic field, fulfills the requirements for achieving spin dynamics processes. Different local spin-flip and spin-transfer processes are accomplished within the subpicosecond regime. The impact of the propagation direction of the laser pulse by switching their polar and the azimuthal angles in spherical coordinates on the spin dynamics processes is analyzed. Double laser pulses with time delay δt ≥ 200 × FWHM yield in a realistic magnetic field gradient selectively a lateral resolution, which corresponds to distances smaller than the CMOS scale (2 nm in 2024) while our system size is comparable to the CMOS scale. Here Λ and V processes with two quasi-degenerate intermediate levels are used. We propose a model of an integrated spin-logic processor created from an array of individual spin-logic blocks, which are realized by four magnetic centers Ni. The findings of this study demonstrate the enormous potential of using laser-induced spin dynamics as the fundamental mechanism for future molecular magnetic technology.

Dual Optical Cycling Centers Mounted on an Organic Scaffold: New Insights from Quantum Chemistry Calculations and Symmetry Analysis

Molecules cooled to ultracold temperatures are desirable for applications in fundamental physics and quantum information science. However, cooling polyatomic molecules with more than six atoms has not yet been achieved. Building on the idea of an optical cycling center (OCC), a moiety supporting a set of localized and isolated electronic states within a polyatomic molecule, molecules with two OCCs (bi-OCCs) may afford better cooling efficiency by doubling the photon scattering rate. By using quantum chemistry calculations, we assess the extent of the coupling of the two OCCs with each other and the molecular scaffold. We show that promising coolable bi-OCC molecules can be proposed by following chemical design principles.

Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.

Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

An Intruder-Free Fock Space Coupled-Cluster Study of the Potential Energy Curves of LiMg+ within the (2,0) Sector

The potential energy curves (PECs) and spectroscopic constants of the ground and excited states of a LiMg+ molecular cation were investigated. We obtained accurate results for the fifteen lowest-lying states of the LiMg+ cation using the Intermediate Hamiltonian Fock Space Multireference Coupled Cluster (IH-FS-CC) method applied to the (2,0) sector. Relativistic corrections were accounted for using the third-order Douglas-Kroll method. In each instance, smooth PECs were successfully computed across the entire range of interatomic distances from equilibrium to the dissociation limit. The results are in good accordance with previous studies of this molecular cation. Notably, this study marks the first application of IH-FS-CC in investigating a mixed alkali and alkaline earth molecular cation, proving its usability in determining accurate PECs of such diatomics and their spectroscopic constants.

Beyond Explored Functionals: A Computational Journey of Two-Photon Absorption

We present a thorough investigation into the efficacy of 19 density functional theory (DFT) functionals, relative to RI-CC2 results, for computing two-photon absorption (2PA) cross sections (σ2PA) and key dipole moments (|μ00|, |μ11|, |Δμ|, |μ01|) for a series of coumarin dyes in the gas-phase. The functionals include different categories, including local density approximation (LDA), generalized gradient approximation (GGA), hybrid-GGA (H-GGA), range-separated hybrid-GGA (RSH-GGA), meta-GGA (M-GGA), and hybrid M-GGA (HM-GGA), with 14 of them being subjected to analysis for the first time with respect to predicting σ2PA values. Analysis reveals that functionals integrating both short-range (SR) and long-range (LR) corrections, particularly those within the RSH-GGA and HM-GGA classes, outperform the others. Furthermore, the range-separation approach was found more impactful compared to the varying percentages of Hartree-Fock exchange (HF Ex) within different functionals. The functionals traditionally recommended for 2PA do not appear among the top 9 in our study, which is particularly interesting, as these top-performing functionals have not been previously investigated in this context. This list is dominated by M11, QTP variants, ωB97X, ωB97X-V, and M06-2X, surpassing the performance of other functionals, including the commonly used CAM-B3LYP.

Two- and one-photon absorption spectra of aqueous thiocyanate anion highlight the role of symmetry in the condensed phase

We present the two-photon absorption (2PA) spectrum of aqueous thiocyanate calculated using high-level quantum-chemistry methods. The 2PA spectrum is compared to the one-photon absorption (1PA) spectrum computed using the same computational protocol. Although the two spectra probe the same set of electronic states, the intensity patterns are different, leading to an apparent red-shift of the 2PA spectrum relative to the 1PA spectrum. The presented analysis explains the intensity patterns and attributes the differences between the 1PA and 2PA spectra to the native symmetry of isolated SCN  - , which influences the spectra in the low-symmetry solvated environment. The native symmetry also manifests itself in variations of the polarization ratio (e.g., parallel vs. perpendicular cross sections) across the spectrum. The presented results highlight the potential of 2PA spectroscopy and high-level quantum-chemistry methods in studies of condensed-phase phenomena.

Environmentally Driven Symmetry Breaking Quenches Dual Fluorescence in Proflavine

Nonadiabatic couplings between several electronic excited states are ubiquitous in many organic chromophores and can significantly influence optical properties. A recent experimental study demonstrated that the proflavine molecule exhibits surprising dual fluorescence in the gas phase, which is suppressed in polar solvent environments. Here, we uncover the origin of this phenomenon by parametrizing a linear-vibronic coupling Hamiltonian from spectral densities of system-bath coupling constructed along molecular dynamics trajectories, fully accounting for interactions with the condensed-phase environment. The finite-temperature absorption, steady-state emission, and time-resolved emission spectra are then computed using powerful, numerically exact tensor network approaches. We find that the dual fluorescence in vacuum is driven by a single well-defined coupling mode but is quenched in solution due to dynamic solvent-driven symmetry breaking that mixes the two low-lying electronic states. We expect the computational framework developed here to be widely applicable to the study of non-Condon effects in complex condensed-phase environments.

Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory

We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.

Comparing Self-Consistent GW and Vertex-Corrected G0W0 (G0W0Γ) Accuracy for Molecular Ionization Potentials

We test the performance of self-consistent GW and several representative implementations of vertex-corrected G0W0 (G0W0Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state-of-the-art wave function techniques, our results show that full self-consistency in the GW scheme either systematically outperforms vertex-corrected G0W0 or gives results of at least comparative quality. Moreover, G0W0Γ results in additional computational cost when compared to G0W0 or self-consistent GW. The dependency of G0W0Γ on the starting mean-field solution is frequently more dominant than the magnitude of the vertex correction itself. Consequently, for molecular systems, self-consistent GW performed on the imaginary axis (and then followed by modern analytical continuation techniques) offers a more reliable approach to make predictions of ionization potentials.

Reasons Why Most Single-Reference Coupled Cluster Methods Fail to Provide the Correct Adiabatic Potentials of a Diatomic Carbon Molecule: UCCSDecCCSD Potential Study

Many single-reference coupled cluster (CC) methods offer adiabatically incorrect potentials when calculating the diatomic carbon molecule, so this problem has been studied extensively. Analysis of the full configuration interaction (FCI) wave function indicates that the main cause of the adiabatic collapse of potentials calculated by the CC method with singles, doubles, and triples (CCSDT) is the strongly increasing bonding character of the T4FCI cluster contribution. In turn, comparative analysis of the CCSDTQ adiabats X1Σg+ and B'1Σg+ demonstrates that the gap between them near the avoided crossing geometry is significantly reduced by quantitatively differentiating the character of the T4 and T 4 B ' 1 Σ g + cluster contributions. These observations clearly indicate the need to take into account the T4 cluster contribution in the standard CC wave function to obtain the correct adiabatic potential. Further analysis of this issue shows that the T4 contribution must be additionally bonding to ensure the adiabatic correctness of the potential. What also seems very interesting is that when the UCCSDecCCSD method [Toboła, Chem. Phys. Lett. 2014, 614, 82-88] is used for the potential calculation, the shape of the potential is entirely determined by a subset of unrestricted Hartree-Fock (UHF) configurations, which are structurally identical to the ground-state configuration in the UHF-based CCSD wave function.

Reverse intersystem crossing mechanisms in doped triangulenes

Thermally activated delayed fluorescence (TADF) has emerged as one of the most promising strategies in the quest for organic light emitting diodes with optimal performance. This computational study dissects the mechanistic intricacies of the central photophysical step, reverse intersystem crossing (rISC) in N and B doped triangulenes as potential multi-resonance TADF compounds. Optimal molecular patterns conducive to efficient rISC, encompassing dopant atom size, number, and distribution, are identified. Additionally, we assess various electronic structure methods for characterizing TADF-relevant molecular systems. The findings identify the distinct role of the direct and mediated mechanisms in rISC, and provide insights into the design of advanced TADF chromophores for next-generation OLED technology.

Aufbau Suppressed Coupled Cluster Theory for Electronically Excited States

We introduce an approach to improve single-reference coupled cluster theory in settings where the Aufbau determinant is absent from or plays only a small role in the true wave function. Using a de-excitation operator that can be efficiently hidden within a similarity transform, we create a coupled cluster wave function in which de-excitations work to suppress the Aufbau determinant and produce wave functions dominated by other determinants. Thanks to an invertible and fully exponential form, the approach is systematically improvable, size consistent, size extensive, and, interestingly, size intensive in a granular way that should make the adoption of some ground state techniques, such as local correlation, relatively straightforward. In this initial study, we apply the general formalism to create a state-specific method for orbital-relaxed, singly excited states. We find that this approach matches the accuracy of similar-cost equation-of-motion methods in valence excitations while offering improved accuracy for charge transfer states. We also find the approach to be more accurate than excited-state-specific perturbation theory in both types of states.

Revisiting the benzene excimer using [2,2] paracyclophane model system: Experiment and theory

We report high-level calculations of the excited states of [2,2]-paracyclophane (PCP), which was recently investigated experimentally by ultrafast pump-probe experiments on oriented single crystals [Haggag et al., ChemPhotoChem 6 e202200181 (2022)]. PCP, in which the orientation of the two benzene rings and their range of motion are constrained, serves as a model for studying benzene excimer formation. The character of the excimer state and the state responsible for the brightest transition are similar to those of the benzene dimer. The constrained structure of PCP allows one to focus on the most important degree of freedom, the inter-ring distance. The calculations explain the main features of the transient absorption spectral evolution. This brightest transition of the excimer is polarized along the inter-fragment axis. The absorption of the light polarized in the plane of the rings reveals the presence of other absorbing states of Rydberg character, with much weaker intensities. We also report new transient absorption data obtained by a broadband 8 fs pump, which time-resolve strong modulations of the excimer absorption. The combination of theory and experiment provides a detailed picture of the evolution of the electronic structure of the PCP excimer in the course of a single molecular vibration.

Performance of Density Functionals for Excited-State Properties of Isolated Chromophores and Exciplexes: Emission Spectra, Solvatochromic Shifts, and Charge-Transfer Character

This study assesses the performance of various meta-generalized gradient approximation (meta-GGA), global hybrid, and range-separated hybrid (RSH) density functionals in capturing the excited-state properties of organic chromophores and their excited-state complexes (exciplexes). Motivated by their uses in solar energy harvesting and photoredox CO2 reduction, we use oligo-(p-phenylenes) and their excited-state complexes with triethylamine as model systems. We focus on the fluorescence properties of these systems, specifically emission energies. We also consider solvatochromic shifts and wave function characteristics. The latter is described by using reduced quantities such as natural transition orbitals (NTOs) and exciton descriptors. The functionals are benchmarked against the experimental fluorescence spectra and the equation-of-motion coupled-cluster method with single and double excitations. Both in isolated chromophores and in exciplexes, meta-GGA functionals drastically underestimate the emission energies and exhibit significant exciton delocalization and anticorrelation between electron and hole motion. The performance of global hybrid functionals is strongly dependent on the percentage of exact exchange. Our study identifies RSH GGAs as the best-performing functionals, with ωPBE demonstrating the best agreement with experimental results. RSH meta-GGAs often overestimate emission energies in exciplexes and yield larger hole NTOs. Their performance can be improved by optimally tuning the range-separation parameter.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene)

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the A ~ 1 A ″ states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of A ~ 1 A ″ HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for A ~ 1 A 2 :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

del Campo J. Excited States by Coupling Piris Natural Orbital Functionals with the Extended Random-Phase Approximation

In this work, we explore the use of Piris natural orbital functionals (PNOFs) to calculate excited-state energies by coupling their reconstructed second-order reduced density matrix with the extended random-phase approximation (ERPA). We have named the general method PNOF-ERPA, and specific approaches are referred to as PNOF-ERPA0, PNOF-ERPA1, and PNOF-ERPA2, according to the way the excitation operator is built. The implementation has been tested in the first excited states of H2, HeH+, LiH, Li2, and N2 showing good results compared to the configuration interaction (CI) method. As expected, an increase in accuracy is observed on going from ERPA0 to ERPA1 and ERPA2. We also studied the effect of electron correlation included by PNOF5, PNOF7, and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where GNOF achieves better results. Overall, the extension of PNOF to excited states has been successful, making it a promising method for further applications.

Photodissociation Dynamics of the Highly Stable ortho-Nitroaniline Cation

0rtho-Nitroaniline (ONA) is a model for the insensitive high explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) that shares strong hydrogen bonding character between adjacent nitro and amino groups. This work reports femtosecond time-resolved mass spectrometry (FTRMS) measurements and theoretical calculations that explain the high stability of the ONA cation compared with related nitroaromatic molecules. Ab initio calculations found that the lowest-lying electronic excited state of the ONA cation, D1, lies more than 2 eV above the ground state, and the energetic barriers to rearrangement and dissociation reactions exceed this D1 energy. These theoretical results were confirmed by FTRMS pump-probe measurements showing that (1) fragment ions represented less than 30% of the total ion yield when a 1014 W cm-2, 1300 nm, 20 fs pump pulse was used to ionize ONA; and (2) 3.1 eV (400 nm) photons were required to induce dissociation of the ONA cation. Stronger coupling between the ground D0 and excited D4 states of the ONA cation at the geometry of neutral ONA resulted in a transient enhancement of fragment ion yields at <300 fs pump-probe delay times, prior to relaxation of the ONA cation to its optimal geometry.

Artificial design of organic emitters via a genetic algorithm enhanced by a deep neural network

The design of molecules requires multi-objective optimizations in high-dimensional chemical space with often conflicting target properties. To navigate this space, classical workflows rely on the domain knowledge and creativity of human experts, which can be the bottleneck in high-throughput approaches. Herein, we present an artificial molecular design workflow relying on a genetic algorithm and a deep neural network to find a new family of organic emitters with inverted singlet-triplet gaps and appreciable fluorescence rates. We combine high-throughput virtual screening and inverse design infused with domain knowledge and artificial intelligence to accelerate molecular generation significantly. This enabled us to explore more than 800 000 potential emitter molecules and find more than 10 000 candidates estimated to have inverted singlet-triplet gaps (INVEST) and appreciable fluorescence rates, many of which likely emit blue light. This class of molecules has the potential to realize a new generation of organic light-emitting diodes.

The Role of Bond Functions in Describing Intermolecular Electron Correlation for Van der Waals Dimers: A Study of (CH4)2 and Ne2

We present a study of the intermolecular interactions in van der Waals complexes of methane and neon dimers within the framework of the CCSD method. This approach was implemented and applied to calculate and examine the behavior of the contracted two-particle reduced density matrix (2-RDM). It was demonstrated that the region near the minimum of the two-particle density matrix correlation part, corresponding to the primary bulk of the Coulomb hole contribution, exerts a significant influence on the dispersion interaction energetics of the studied systems. As a result, the bond functions approach was applied to improve the convergence performance for the intermolecular correlation energy results with respect to the size of the atomic basis. For this, substantial acceleration was achieved by introducing an auxiliary basis of bond functions centered on the minima of the 2-RDM. For both methane and neon dimers, this general conclusion was confirmed with a series of CCSD calculations for the 2-RDM and the correlation energies.

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.