Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development

Comparing parameterized and self-consistent approaches to ab initio cavity quantum electrodynamics for electronic strong coupling

Molecules under strong or ultra-strong light-matter coupling present an intriguing route to modify chemical structure, properties, and reactivity. A rigorous theoretical treatment of such systems requires handling matter and photon degrees of freedom on an equal quantum mechanical footing. In the regime of molecular electronic strong or ultra-strong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach referred to as ab initio cavity quantum electrodynamics (ai-QED), where the photon degrees of freedom are treated at the level of cavity QED. We analyze two complementary approaches to ai-QED: (1) a parameterized ai-QED, a two-step approach where the matter degrees of freedom are computed using existing electronic structure theories, enabling the construction of rigorous ai-QED Hamiltonians in a basis of many-electron eigenstates, and (2) self-consistent ai-QED, a one-step approach where electronic structure methods are generalized to include coupling between electronic and photon degrees of freedom. Although these approaches are equivalent in their exact limits, we identify a disparity between the projection of the two-body dipole self-energy operator that appears in the parameterized approach and its exact counterpart in the self-consistent approach. We provide a theoretical argument that this disparity resolves only under the limit of a complete orbital basis and a complete many-electron basis for the projection. We present numerical results highlighting this disparity and its resolution in a particularly simple molecular system of helium hydride cation, where it is possible to approach these two complete basis limits simultaneously. In this same helium hydride system, we examine and compare the practical issue of the computational cost required to converge each approach toward the complete orbital and many-electron bases limit. Finally, we assess the aspect of photonic convergence for polar and charged species, finding comparable behavior between parameterized and self-consistent approaches.

Support effects on conical intersections of Jahn-Teller fluxional metal clusters on the sub-nanoscale

The concept of fluxionality has been invoked to explain the enhanced catalytic properties of atomically precise metal clusters of subnanometer size. Cu3 isolated in the gas phase is a classical case of a fluxional metal cluster where a conical intersection leads to a Jahn-Teller (JT) distortion resulting in a potential energy landscape with close-lying multiminima and, ultimately, fluxional behavior. In spite of the role of conical intersections in the (photo)stability and (photo)catalytic properties of surface-supported atomic metal clusters, they have been largely unexplored. In this work, by applying a high-level multi-reference ab initio method aided with dispersion corrections, we analyze support effects on the conical intersection of Cu3 considering benzene as a model support molecule of carbon-based surfaces. We verify that the region around the conical intersection and the associated Jahn-Teller (JT) distortion is very slightly perturbed by the support when the Cu3 cluster approaches it in a parallel orientation: Two electronic states remain degenerate for a structure with C3 symmetry consistent with the D3h symmetry of unsupported Cu3 at the conical intersection. It extends over a one-dimensional seam that characterizes a physisorption minimum of the Cu3-benzene complex. The fluxionality of the Cu3 cluster, reflected in large fluctuations of relaxed Cu-Cu distances as a function of the active JT mode, is kept unperturbed upon complexation with benzene as well. In stark contrast, for the energetically favored perpendicular orientation of the Cu3 plane to the benzene ring plane, the conical intersection (CI) is located 12 100 cm-1 (∼1.5 eV) above the chemisorption minimum, with the fluxionality being kept at the CI's nearby and lost at the chemisorption well. The first excited state at the perpendicular orientation has a deep well (>4000 cm-1), being energetically closer to the CI. The transition dipole moment between ground and excited states has a significant magnitude, suggesting that the excited state can be observed through direct photo-excitation from the ground state. Besides demonstrating that the identity of an isolated Jahn-Teller metal cluster can be preserved against support effects at a physisorption state and lifted out at a chemisorption state, our results indicate that a correlation exists between conical intersection topography and fluxionality in the metal cluster's Cu-Cu motifs.

A Critical Evaluation of the Hybrid KS DFT Functionals Based on the KS Exchange-Correlation Potentials

We have developed a critical methodology for the evaluation of the quality of hybrid exchange-correlation (XC) density functional approximations (DFAs) based on very fundamental quantities, i.e., Kohn-Sham (KS) XC potentials, self-consistent electron densities, first ionization potentials (IPs), and total energies. Since the XC potentials, the primary objects in the current study, are not directly accessible for the hybrids, we calculate them by inverting the KS electron densities. Utilizing this methodology, we tested 155 hybrid DFAs available in the LIBXC library using FCI and CCSD(T) methods as a reference. We have found that a group of functionals produces very decent XC potentials, mainly those with a large mixture of Hartree-Fock exchange. Moreover, the value of IP strongly depends on the XC potential quality. On the other hand, we show that the XC energy is dominated by functional-driven error, which in some cases leads to substantial errors in electronic densities. The study shows new directions for constructing more accurate XC functionals within the KS-DFT framework.

A practical post-Hartree-Fock approach describing open-shell metal cluster-support interactions. Application to Cu3 adsorption on benzene/coronene

Current advances in synthesizing and characterizing atomically precise monodisperse metal clusters (AMCs) at the subnanometer scale have opened up fascinating possibilities in designing new heterogeneous (photo)catalysts as well as functional interfaces between AMCs and biologically relevant molecules. Understanding the nature of AMC-support interactions at molecular-level is essential for optimizing (photo)catalysts performance and designing novel ones with improved properties. Møller-Plesset second-order perturbation theory (MP2) is one of the most cost-efficient single-reference post-Hartree-Fock wave-function-based theories that can be applied to AMC-support interactions considering adequate molecular models of the support, and thus complementing state-of-the-art dispersion-corrected density functional theory. However, the resulting AMC-support interaction is typically overestimated with the MP2 method and must be corrected. The coupled MP2 (MP2C) scheme replacing the uncoupled Hartree-Fock dispersion energy by a coupled dispersion contribution, has been proven to describe accurately van-der-Waals (vdW)-dominated interactions between closed-shell AMCs and carbon-based supports. In this work, the accuracy of a MP2C-based scheme is evaluated in modelling open-shell AMC-cluster interactions that imply charge transfer or other strong attractive energy contributions beyond vdW forces. For this purpose, we consider the interaction of Cu3 with molecular models of graphene of increasing size (benzene and coronene). In this way, it is shown that subchemical precision (within 0.1 kcal mol-1) is achieved with the modified MP2C scheme, using the explicitly correlated coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)-F12] as a benchmark method. It is also revealed that the energy difference between uncoupled and coupled dispersion terms closely follows benchmark values of the repulsive intramonomer correlation contribution. The proposed open-shell MP2C-based approach is expected to be of general applicability to open-shell atomic or molecular species interacting with coronene for regions of the potential landscape where single-reference electronic structure descriptions suffice.

Range Separation of the Interaction Potential in Intermolecular and Intramolecular Symmetry-Adapted Perturbation Theory

Symmetry-adapted perturbation theory (SAPT) is a popular and versatile tool to compute and decompose noncovalent interaction energies between molecules. The intramolecular SAPT (ISAPT) variant provides a similar energy decomposition between two nonbonded fragments of the same molecule, covalently connected by a third fragment. In this work, we explore an alternative approach where the noncovalent interaction is singled out by a range separation of the Coulomb potential. We investigate two common splittings of the 1/r potential into long-range and short-range parts based on the Gaussian and error functions, and approximate either the entire intermolecular/interfragment interaction or only its attractive terms by the long-range contribution. These range separation schemes are tested for a number of intermolecular and intramolecular complexes. We find that the energy corrections from range-separated SAPT or ISAPT are in reasonable agreement with complete SAPT/ISAPT data. This result should be contrasted with the inability of the long-range multipole expansion to describe crucial short-range charge penetration and exchange effects; it shows that the long-range interaction potential does not just recover the asymptotic interaction energy but also provides a useful account of short-range terms. The best consistency is attained for the error-function separation applied to all interaction terms, both attractive and repulsive. This study is the first step toward a fragmentation-free decomposition of intramolecular nonbonded energy.

Forte: A suite of advanced multireference quantum chemistry methods

Forte is an open-source library specialized in multireference electronic structure theories for molecular systems and the rapid prototyping of new methods. This paper gives an overview of the capabilities of Forte, its software architecture, and examples of applications enabled by the methods it implements.

Do Molecular Geometries Change Under Vibrational Strong Coupling?

As pioneering experiments have shown, strong coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current theoretical description is limited and far from complete. To explore the origin of this exciting observation, we investigate how the molecular structure changes under strong light-matter coupling using an ab initio method based on the cavity Born-Oppenheimer Hartree-Fock ansatz. By optimizing H2O and H2O2 resonantly coupled to cavity modes, we study the importance of reorientation and geometric relaxation. In addition, we show that the inclusion of one or two cavity modes can change the observed results. On the basis of our findings, we derive a simple concept to estimate the effect of the cavity interaction on the molecular geometry using the molecular polarizability and the dipole moments.

PyDFT-QMMM: A modular, extensible software framework for DFT-based QM/MM molecular dynamics

PyDFT-QMMM is a Python-based package for performing hybrid quantum mechanics/molecular mechanics (QM/MM) simulations at the density functional level of theory. The program is designed to treat short-range and long-range interactions through user-specified combinations of electrostatic and mechanical embedding procedures within periodic simulation domains, providing necessary interfaces to external quantum chemistry and molecular dynamics software. To enable direct embedding of long-range electrostatics in periodic systems, we have derived and implemented force terms for our previously described QM/MM/PME approach [Pederson and McDaniel, J. Chem. Phys. 156, 174105 (2022)]. Communication with external software packages Psi4 and OpenMM is facilitated through Python application programming interfaces (APIs). The core library contains basic utilities for running QM/MM molecular dynamics simulations, and plug-in entry-points are provided for users to implement custom energy/force calculation and integration routines, within an extensible architecture. The user interacts with PyDFT-QMMM primarily through its Python API, allowing for complex workflow development with Python scripting, for example, interfacing with PLUMED for free energy simulations. We provide benchmarks of forces and energy conservation for the QM/MM/PME and alternative QM/MM electrostatic embedding approaches. We further demonstrate a simple example use case for water solute in a water solvent system, for which radial distribution functions are computed from 100 ps QM/MM simulations; in this example, we highlight how the solvation structure is sensitive to different basis-set choices due to under- or over-polarization of the QM water molecule's electron density.

Introducing SpectraFit: An Open-Source Tool for Interactive Spectral Analysis

In chemistry, analyzing spectra through peak fitting is a crucial task that helps scientists extract useful quantitative information about a sample's chemical composition or electronic structure. To make this process more efficient, we have developed a new open-source software tool called SpectraFit. This tool allows users to perform quick data fitting using expressions of distribution and linear functions through the command line interface (CLI) or Jupyter Notebook, which can run on Linux, Windows, and MacOS, as well as in a Docker container. As part of our commitment to good scientific practice, we have introduced an output file-locking system to ensure the accuracy and consistency of information. This system collects input data, results data, and the initial fitting model in a single file, promoting transparency, reproducibility, collaboration, and innovation. To demonstrate SpectraFit's user-friendly interface and the advantages of its output file-locking system, we are focusing on a series of previously published iron-sulfur dimers and their XAS spectra. We will show how to analyze the XAS spectra via CLI and in a Jupyter Notebook by simultaneously fitting multiple data sets using SpectraFit. Additionally, we will demonstrate how SpectraFit can be used as a black box and white box solution, allowing users to apply their own algorithms to engineer the data further. This publication, along with its Supporting Information and the Jupyter Notebook, serves as a tutorial to guide users through each step of the process. SpectraFit will streamline the peak fitting process and provide a convenient, standardized platform for users to share fitting models, which we hope will improve transparency and reproducibility in the field of spectroscopy.

Demonstration of the Effectiveness of the Cascaded Variational Quantum Eigensolver Using the Jastrow Ansatz for Molecular Calculations

We demonstrate how the cascaded variational quantum eigensolver (CVQE) can be applied to study molecular systems for the family of Jastrow ansatzes. Specifically, we applied CVQE to the water molecule. We find that CVQE has a number of advantages. In particular, our results show that CVQE requires 2 to 3 orders of magnitude fewer quantum computing (QC) executions than VQE for the water molecule. Furthermore, our results indicate that CVQE might provide some robustness against two-qubit gate errors given that the number of CNOT gates used in our calculation was ∼300 and the errors in the QC calculations are still comparable to those obtained by VQE.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

Evaluating the Impact of the Tamm-Dancoff Approximation on X-ray Spectrum Calculations

The impact of the Tamm-Dancoff approximation (TDA) for time-dependent density functional theory (TDDFT) calculations of X-ray absorption and X-ray emission spectra (XAS and XES) is investigated, showing small discrepancies in the excitation energies and intensities. Through explicit diagonalization of the TDDFT Hessian, XES was considered by using full TDDFT with a core-hole reference state. This has previously not been possible with most TDDFT implementations as a result of the presence of negative eigenvalues. Furthermore, a core-valence separation (CVS) scheme for XES is presented, in which only elements including the core-hole are considered, resulting in a small Hessian with the dimension of the number of remaining occupied orbitals of the same spin as the core-hole (CH). The resulting spectra are in surprisingly good agreement with the full-space counterpart, illustrating the weak coupling between the valence-valence and valence-CH transitions. Complications resulting from contributions from the discretized continuum are discussed, which can occur for TDDFT calculations of XAS and XES and for TDA calculations of XAS. In conclusion, we recommend that TDA be used when calculating X-ray emission spectra, and either CVS-TDA or CVS-TDDFT can be used for X-ray absorption spectra.

Exploration of the Two-Electron Excitation Space with Data-Driven Coupled Cluster

Computational cost limits the applicability of post-Hartree-Fock methods such as coupled-cluster on larger molecular systems. The data-driven coupled-cluster (DDCC) method applies machine learning to predict the coupled-cluster two-electron amplitudes (t2) using data from second-order perturbation theory (MP2). One major limitation of the DDCC models is the size of training sets that increases exponentially with the system size. Effective sampling of the amplitude space can resolve this issue. Five different amplitude selection techniques that reduce the amount of data used for training were evaluated, an approach that also prevents model overfitting and increases the portability of data-driven coupled-cluster singles and doubles to more complex molecules or larger basis sets. In combination with a localized orbital formalism to predict the CCSD t2 amplitudes, we have achieved a 10-fold error reduction for energy calculations.

Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction Theory

Polariton chemistry has attracted great attention as a potential route to modify chemical structure, properties, and reactivity through strong interactions among molecular electronic, vibrational, or rovibrational degrees of freedom. A rigorous theoretical treatment of molecular polaritons requires the treatment of matter and photon degrees of freedom on equal quantum mechanical footing. In the limit of molecular electronic strong or ultrastrong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach we refer to as ab initio cavity quantum electrodynamics, where the photon degrees of freedom are treated at the level of cavity quantum electrodynamics. Here, we present an approach called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction theory to provide ground- and excited-state polaritonic surfaces with a balanced description of strong correlation effects among electronic and photonic degrees of freedom. This method provides a platform for ab initio cavity quantum electrodynamics when both strong electron correlation and strong light-matter coupling are important and is an important step toward computational approaches that yield multiple polaritonic potential energy surfaces and couplings that can be leveraged for ab initio molecular dynamics simulations of polariton chemistry.

Accelerating Pythonic Coupled-Cluster Implementations: A Comparison Between CPUs and GPUs

In this work, we benchmark several Python routines for time and memory requirements to identify the optimal choice of the tensor contraction operations available. We scrutinize how to accelerate the bottleneck tensor operations of Pythonic coupled-cluster implementations in the Cholesky linear algebra domain, utilizing a NVIDIA Tesla V100S PCIe 32GB (rev 1a) graphics processing unit (GPU). The NVIDIA compute unified device architecture API interacts with CuPy, an open-source library for Python, designed as a NumPy drop-in replacement for GPUs. Due to the limitations of video memory, the GPU calculations must be performed batch-wise. Timing results of some contractions containing large tensors are presented. The CuPy implementation leads to a factor of 10-16 speed-up of the bottleneck tensor contractions compared to computations on 36 central processing unit (CPU) cores. Finally, we compare example CCSD and pCCD-LCCSD calculations performed solely on CPUs to their CPU-GPU hybrid implementation, which leads to a speed-up of a factor of 3-4 compared to the CPU-only variant.

Second quantization-based symmetry-adapted perturbation theory: Generalizing exchange beyond single electron pair approximation

This paper presents a general second-quantized form of a permutation operator interchanging n pairs of electrons between interacting subsystems in the framework of the symmetry-adapted perturbation theory (SAPT). We detail the procedure for constructing this operator through the consecutive multiplication of single-pair permutation operators. This generalized form of the permutation operator has enabled the derivation of universal formulas for S2n approximations of the exchange energies in the first and second order of the interaction operator. We present expressions for corrections of S4 approximations and assess its efficacy on a selection of systems anticipated to exhibit a slowly converging overlap expansion. Additionally, we outline a method to sum the overlap expansion series to infinity in second-quantization, up to the second order in V. This new approach offers an alternative to the existing formalism based on density-matrix formulations. When combined with a symbolic algebra program for automated derivations, it paves the way for advancements in SAPT theory, particularly for intricate wavefunction theories.

All-Purpose Measure of Electron Correlation for Multireference Diagnostics

We present an analytical relationship between two natural orbital occupancy-based indices, I N D ¯ and INDmax, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0, and the D2 diagnostic. Numerical validation revealed that I N D ¯ and INDmax can effectively substitute for c0 and D2, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for INDmax, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.

Ab Initio Vibro-Polaritonic Spectra in Strongly Coupled Cavity-Molecule Systems

Recent experiments have revealed the profound effect of strong light-matter interactions in optical cavities on the electronic ground state of molecular systems. This phenomenon, known as vibrational strong coupling, can modify reaction rates and induce the formation of molecular vibrational polaritons, hybrid states involving both photon modes, and vibrational modes of molecules. We present an ab initio methodology based on the cavity Born-Oppenheimer Hartree-Fock ansatz, which is specifically powerful for ensembles of molecules, to calculate vibro-polaritonic IR spectra. This method allows for a comprehensive analysis of these hybrid states. Our semiclassical approach, validated against full quantum simulations, reproduces key features of the vibro-polaritonic spectra. The underlying analytic gradients also allow for optimization of cavity-coupled molecular systems and performing semiclassical dynamics simulations.

Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Double Centrosymmetric Si···π Tetrel Bonds as New Synthons─Evidence from Crystal Structures and DFT Calculations

The crystal structure of bis((μ2-ethynylsilyloxo)-dichloro-aluminum), BEDCA, and a few related structures are characterized by the occurrence of tetrel bonds that link molecules. Particularly, centosymmetric dimers in such structures occur that are connected by two equivalent Si···π tetrel bonds. The dimer of BEDCA and dimers of other model species that similarly are linked by two equivalent Si···π tetrel bonds are analyzed theoretically. Some of the complexes calculated here are also characterized by the occurrence of triel bonds. Thus, ωB97XD/aug-cc-pVTZ calculations are performed and these DFT results are further supported by calculations with the use of other theoretical approaches: the quantum theory of atoms in molecules, QTAIM; the natural bond orbital, NBO; the energy decomposition analysis, EDA; and the noncovalent interactions method, NCI. The results show that the tetrel bonds analyzed here are rather weak, and they are not detected by the QTAIM approach; however, they are detected by other approaches, like NBO, for example. On the other hand, the triel bonds that occur in a few complexes discussed here are very strong and possess characteristics of covalent bonds.

Assign_v2: a novel bonded-force field parameterization software for square planar palladium molecular dynamics simulations

In the present study, a requisite bonded force field for conducting molecular dynamics simulations of palladium compounds was derived utilizing a novel technique termed the "numbering system," implemented through a program named assign.py. A significant challenge in deriving a bonded force field for square-planar palladium compounds emanates from their cis-trans characteristics, whereby the bond angles of identical atoms diverge across different compounds due to the presence of cis and trans isomers. To navigate this challenge, atoms surrounding the palladium were assigned numerical identifiers; consecutively numbered neighboring atoms were designated as "cis," while atoms alternately numbered were regarded as "trans" relative to each other. Through the employment of the newly developed assign.py program, atoms common to GAFF were automatically assigned, facilitating the seamless integration of GAFF with the newly derived force field for cis and trans configurations. The tested innovative force field demonstrated results in close proximity to experimental findings. This research introduced two novel elements: firstly, a comparatively extensive force field was derived for palladium compounds, enabling the simulation of the previously non-simulable square planar geometry of palladium. Secondly, new software, assign.py, was developed, capable of amalgamating "numbering system atom types" with GAFF atom types into a unified force field. Conclusive tests within the study affirmed that the innovative bonded force field and technique utilizing the assign.py program was successful, simulating the square-planar geometry of palladium in a manner highly congruent with the experimental geometry. The program, licensed under Apache2, can be accessed via the following link: https://github.com/bkurt00/palladiumFF2/blob/main/assign_v2/assign_v2.pyCommunicated by Ramaswamy H. Sarma.

A step toward density benchmarking-The energy-relevant "mean field error"

Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that are precise enough to be predictive in many instances, as validated by large- and small-scale benchmarking efforts. However, assessing the quality of densities has been the subject of far less attention, in part because reliable error measures are difficult to define. To this end, this work introduces the mean-field error, which directly assesses the quality of densities from approximations. The mean-field error is contextualized within existing frameworks of density functional error analysis and understanding and shown to be part of the density-driven error. It is demonstrated in several illustrative examples. Its potential use in future benchmarking protocols is discussed, and some conclusions are drawn.

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.

Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles

Experimental studies indicate that optical cavities can affect chemical reactions through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models that take into account intermolecular interactions to describe ensembles are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a nonperturbative, self-consistent description of strongly coupled molecular ensembles, taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated intermolecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.

Spin-Flip Unitary Coupled Cluster Method: Toward Accurate Description of Strong Electron Correlation on Quantum Computers

Quantum computers have emerged as a promising platform to simulate strong electron correlation that is crucial to catalysis and photochemistry. However, owing to the choice of a trial wave function employed in the variational quantum eigensolver (VQE) algorithm, accurate simulation is restricted to certain classes of correlated phenomena. Herein, we combine the spin-flip (SF) formalism with the unitary coupled cluster with singles and doubles (UCCSD) method via the quantum equation-of-motion (qEOM) approach to allow for an efficient simulation of a large family of strongly correlated problems. We show that the developed qEOM-SF-UCCSD/VQE method outperforms its UCCSD/VQE counterpart for simulation of the cis-trans isomerization of ethylene, and the automerization of cyclobutadiene and the predicted qEOM-SF-UCCSD/VQE barrier heights are in a good agreement with the experimentally determined values. The developments presented herein will further stimulate the investigation of this approach for simulations of other types of correlated/entangled phenomena on quantum computers.

Computational study on the catalytic control of endo/exo Diels-Alder reactions by cavity quantum vacuum fluctuations

Achieving control over chemical reaction's rate and stereoselectivity realizes one of the Holy Grails in chemistry that can revolutionize chemical and pharmaceutical industries. Strong light-matter interaction in optical or nanoplasmonic cavities might provide the knob to reach such control. In this work, we demonstrate the catalytic and selectivity control of an optical cavity for two selected Diels-Alder cycloaddition reactions using the quantum electrodynamics coupled cluster (QED-CC) method. Herein, we find that by changing the molecular orientation with respect to the polarization of the cavity mode the reactions can be significantly inhibited or selectively enhanced to produce major endo or exo products on demand. This work highlights the potential of utilizing quantum vacuum fluctuations of an optical cavity to modulate the rate of Diels-Alder cycloaddition reactions and to achieve stereoselectivity in a practical and non-intrusive way. We expect that the present findings will be applicable to a larger set of relevant reactions, including the click chemical reactions.

Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers

Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer.

Local Potentials Reconstructed within Linearly Independent Product Basis Sets of Increasing Size

Given a matrix representation of a local potential v(r) within a one-electron basis set of functions that form linearly independent products (LIP), it is possible to construct a well-defined local potential v ~ ( r ) that is equivalent to v(r) within that basis set and has the form of an expansion in basis function products. Recently, we showed that for exchange-correlation potentials vXC(r) defined on the infinite-dimensional Hilbert space, the potentials v ~ XC ( r ) reconstructed from matrices of vXC(r) within minimal LIP basis sets of occupied Kohn-Sham orbitals bear only qualitative resemblance to the originals. Here, we show that if the LIP basis set is enlarged by including low-lying virtual Kohn-Sham orbitals, the agreement between v ~ XC ( r ) and vXC(r) improves to the extent that the basis function products are appropriate as a basis for vXC(r). These findings validate the LIP technology as a rigorous potential reconstruction method.

Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry

Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to convert the mathematical formulation of a new wavefunction ansätze to a working implementation. Fanpy is designed based on our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI) framework, where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system's Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly explore new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for various operating systems. In addition, it adheres to principles of modern software development, including comprehensive documentation, extensive testing, quality assurance, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library.

Toward routine Kohn-Sham inversion using the "Lieb-response" approach

Kohn-Sham (KS) inversion, in which the effective KS mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, especially in finite basis sets. The present work presents a KS inversion method, dubbed the "Lieb-response" approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potential. It thus enables the routine inversion of even difficult KS systems, as illustrated in a variety of problems within this work, and provides outputs that can be used for embedding schemes or machine learning of density functional approximations. The effect of finite basis sets on KS inversion is also analyzed and investigated.

Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding

The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.

Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory

Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B covalently connected via a linker C. However, the existing ISAPT algorithm displays several issues for many fragmentation patterns (that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive electrostatic energy (even when the fragments are hydrogen-bonded) and very large and mutually cancelling induction and exchange-induction terms. We attribute those issues to the presence of artificial dipole moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing electrons on one of their hybrid orbitals. Therefore, we propose several new partitioning algorithms which reassign one electron, on a singly occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals are added to fragment density matrices, the computation of ISAPT electrostatic, induction, and dispersion energies proceeds exactly as normal, and the exchange energy expressions need only minor modifications. Among the link partitioning algorithms introduced, the so-called ISAPT(SIAO1) approach (in which the link orbital is obtained by a projection onto the intrinsic atomic orbitals (IAOs) of a given fragment followed by orthogonalization to this fragment's occupied space) leads to reasonable values of all ISAPT corrections for all fragmentation patterns, and exhibits a fast and systematic basis set convergence. This improvement is made possible by a significant reduction in magnitude (even though not a complete elimination) of the unphysical dipole moments at the interfragment boundaries. We demonstrate the utility of the improved ISAPT partitioning by examining intramolecular interactions in several pentanediol isomers, examples of linear and branched alkanes, and the open and closed conformations of a family of N-arylimide molecular torsion balances.

ipie: A Python-Based Auxiliary-Field Quantum Monte Carlo Program with Flexibility and Efficiency on CPUs and GPUs

We report the development of a python-based auxiliary-field quantum Monte Carlo (AFQMC) program, ipie, with preliminary timing benchmarks and new AFQMC results on the isomerization of [Cu₂O₂]²⁺. We demonstrate how implementations for both central and graphical processing units (CPUs and GPUs) are achieved in ipie. We show an interface of ipie with PySCF as well as a straightforward template for adding new estimators to ipie. Our timing benchmarks against other C++ codes, QMCPACK and Dice, suggest that ipie is faster or similarly performing for all chemical systems considered on both CPUs and GPUs. Our results on [Cu₂O₂]²⁺ using selected configuration interaction trials show that it is possible to converge the ph-AFQMC isomerization energy between bis(μ-oxo) and μ-η²:η² peroxo configurations to the exact known results for small basis sets with 10⁵-10⁶ determinants. We also report the isomerization energy with a quadruple-zeta basis set with an estimated error less than a kcal/mol, which involved 52 electrons and 290 orbitals with 10⁶ determinants in the trial wave function. These results highlight the utility of ph-AFQMC and ipie for systems with modest strong correlation and large-scale dynamic correlation.

Competition between ultralong organic phosphorescence and thermally activated delayed fluorescence in dichloro derivatives of 9-benzoylcarbazole

Optoelectronic materials based on metal-free organic molecules represent a promising alternative to traditional inorganic devices. Significant attention has been devoted to the development of the third generation of OLEDs which are based on the temperature-activated delayed fluorescence (TADF) mechanism. In the last few years, several materials displaying ultra-long organic phosphorescence (UOP) have been designed using strategies such as crystal engineering and halogen functionalisation. Both TADF and UOP are controlled by the population of triplet states and the energy gaps between the singlet and triplet manifolds. In this paper, we explore the competition between TADF and UOP in the molecular crystals of three dichloro derivatives of 9H-carbazol-3-yl(phenyl)methanone. We investigate the excited state mechanisms in solution and the crystalline phase and address the effects of exciton transport and temperature on the rates of direct and reverse intersystem crossing under the Marcus-Levich-Jortner model. We also analyse how the presence of isomeric impurities and the stabilisation of charge transfer states affect these processes. Our simulations explain the different mechanisms observed for the three derivatives and highlight the role of intramolecular rotation and crystal packing in determining the energy gaps. This work contributes to a better understanding of the connection between chemical and crystalline structures that will enable the design of efficient materials.

Reconstruction of Exchange-Correlation Potentials from Their Matrix Representations

Within a basis set of one-electron functions that form linearly independent products (LIPs), it is always possible to construct a unique local (multiplicative) real-space potential that is precisely equivalent to an arbitrary given operator. Although standard basis sets of quantum chemistry rarely form LIPs in a numerical sense, occupied and low-lying virtual canonical Kohn-Sham orbitals often do so, at least for small atoms and molecules. Using these principles, we construct atomic and molecular exchange-correlation potentials from their matrix representations in LIP basis sets of occupied canonical Kohn-Sham orbitals. The reconstructions are found to imitate the original potentials in a consistent but exaggerated way. Since the original and reconstructed potentials produce the same ground-state electron density and energy within the associated LIP basis set, the procedure may be regarded as a rigorous solution to the Kohn-Sham inversion problem within the subspace spanned by the occupied Kohn-Sham orbitals.

Amplitude Reordering Accelerates the Adaptive Variational Quantum Eigensolver Algorithms

The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy-intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying ansatz. Therefore, the most important issue is to generate a compact and accurate ansatz, which requires a shallower parametric quantum circuit and can achieve an acceptable accuracy. The newly developed adaptive algorithms (AAs) such as the adaptive derivative-assembled pseudo-Trotter VQE (ADAPT-VQE) can solve this issue via generating compact and accurate ansatzes. However, these AAs show very low computational efficiency because they require a large number of additional measurements. Here we propose an amplitude reordering (AR) strategy to accelerate the promising but expensive AAs by adding operators in a "batched" fashion in a way that their order is still quasi-optimal. We first introduce the AR method into ADAPT-VQE and build the AR-ADAPT-VQE algorithm. We then endow the energy-sorting VQE (ES-VQE) algorithm with the adaptive feature and introduce the AR into AES-VQE to form the AR-AES-VQE algorithm. To demonstrate the performance of these algorithms, we calculate the dissociation curves of three small molecules, LiH, linear BeH₂, and linear H₆, by using (AR-)ADAPT-VQE and (AR-)AES-VQE algorithms. It is found that all of the AR-equipped AAs (AR-AAs) can significantly reduce the number of iterations and subsequently accelerate the calculations with a speedup of up to more than ten times without the obvious loss of accuracy. The final ansatz generated by the AR-AAs not only avoids extra circuit depth but also maintains the computational accuracy; sometimes the AR-AAs even outperforms their original counterparts.

del Campo J. Charge delocalization error in Piris Natural Orbital Functionals

Piris Natural Orbital Functionals (PNOF) have been recognized as a low-scaling alternative to study strong correlated systems. In this work, we address the performance of the fifth functional (PNOF5) and the seventh functional (PNOF7) to deal with another common problem, the charge delocalization error. The effects of this problem can be observed in charged systems of repeated well-separated fragments, where the energy should be the sum of the charged and neutral fragments, regardless of how the charge is distributed. In practice, an energetic overstabilization of fractional charged fragments leads to a preference for having the charge delocalized throughout the system. To establish the performance of PNOF functionals regarding charge delocalization error, charged chains of helium atoms and the W4-17-MR set molecules were used as base fragments and their energy, charge distribution and correlation regime were studied. It was found that PNOF5 prefers localized charge distributions, while PNOF7 improves the treatment of interpair static correlation and tends to the correct energetic limit for several cases, although a preference for delocalized charge distributions may arise in highly strong correlation regimes. Overall, it is concluded that PNOF functionals can simultaneously deal with static correlation and charge delocalization errors, resulting in a promising choice to study charge-related problems.

Triple electron-electron-proton excitations and second-order approximations in nuclear-electronic orbital coupled cluster methods

The accurate description of nuclear quantum effects, such as zero-point energy, is important for modeling a wide range of chemical and biological processes. Within the nuclear-electronic orbital (NEO) approach, such effects are incorporated in a computationally efficient way by treating electrons and select nuclei, typically protons, quantum mechanically with molecular orbital techniques. Herein, we implement and test a NEO coupled cluster method that explicitly includes the triple electron-proton excitations, where two electrons and one proton are excited simultaneously. Our calculations show that this NEO-CCSD(eep) method provides highly accurate proton densities and proton affinities, outperforming any previously studied NEO method. These examples highlight the importance of the triple electron-electron-proton excitations for an accurate description of nuclear quantum effects. Additionally, we also implement and test the second-order approximate coupled cluster with singles and doubles (NEO-CC2) method, as well as its scaled-opposite-spin (SOS) versions. The NEO-SOS$'$-CC2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electron-electron correlation energy, achieves nearly the same accuracy as the NEO-CCSD(eep) method for the properties studied. Because of its low computational cost, this method will enable a wide range of chemical and photochemical applications for large molecular systems. This work sets the stage for a wide range of developments and applications within the NEO framework.

Wavefunction embedding for molecular polaritons

Polaritonic chemistry relies on the strong light-matter interaction phenomena for altering the chemical reaction rates inside optical cavities. To explain and to understand these processes, the development of reliable theoretical models is essential. While computationally efficient quantum electrodynamics self-consistent field (QED-SCF) methods, such as quantum electrodynamics density functional theory (QEDFT) needs accurate functionals, quantum electrodynamics coupled cluster (QED-CC) methods provide a systematic increase in accuracy but at much greater cost. To overcome this computational bottleneck, herein we introduce and develop the QED-CC-in-QED-SCF projection-based embedding method that inherits all the favorable properties from the two worlds, computational efficiency and accuracy. The performance of the embedding method is assessed by studying some prototypical but relevant reactions, such as methyl transfer reaction, proton transfer reaction, as well as protonation reaction in a complex environment. The results obtained with the new embedding method are in excellent agreement with more expensive QED-CC results. The analysis performed on these reactions indicate that the electron-photon correlation effects are local in nature and that only a small region should be treated at the QED-CC level for capturing important effects due to cavity. This work sets the stage for future developments of polaritonic quantum chemistry methods and it will serve as a guideline for development of other polaritonic embedding models.

Non-Hermitian Cavity Quantum Electrodynamics - Configuration Interaction Singles Approach for Polaritonic Structure with ab initio Molecular Hamiltonians

We combine ab initio molecular electronic Hamiltonians with a cavity quantum electrodynamics model for dissipative photonic modes and apply mean-field theories to the ground- and excited-states of resulting polaritonic systems. In particular, we develop a non-Hermitian configuration interaction singles theory for mean-field ground- and excited-states of the molecular system strongly interacting with a photonic mode, and apply these methods to elucidating the phenomenology of paradigmatic polaritonic systems. We leverage the Psi4Numpy framework to yield open-source and accessible reference implementations of these methods.

Environment Effects on X-Ray Absorption Spectra With Quantum Embedded Real-Time Time-Dependent Density Functional Theory Approaches

In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods' performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@( H 2 O ) 8 - , X = F, Cl). We observe that for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L1 edges, and is capable of reproducing the splitting of the 1s1 (n + 1)p1 final states (n + 1 being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the 1s1 (n + 2)p1 states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent. The BOMME results, on the other hand, provide a faithful qualitative representation of the spectra in all energy regions considered, though its intrinsic approximation of employing a lower-accuracy exchange-correlation functional for the environment induces non-negligible shifts in peak positions for the excitations from the halide to the environment. Our results thus confirm that QM/QM embedding approaches are viable alternatives to standard real-time simulations of X-ray absorption spectra of species in complex or confined environments.

Fermi.jl: A Modern Design for Quantum Chemistry

Approximating molecular wave functions involves heavy numerical effort; therefore, codes for such tasks are written completely or partially in efficient languages such as C, C++, and Fortran. While these tools are dominant throughout quantum chemistry packages, the efficient development of new methods is often hindered by the complexity associated with code development. In order to ameliorate this scenario, some software packages take a dual approach where a simpler, higher-level language, such as Python, substitutes the traditional ones wherever performance is not critical. Julia is a novel, dynamically typed, programming language that aims to solve this two-language problem. It gained attention because of its modern and intuitive design, while still being highly optimized to compete with "low-level" languages. Recently, some chemistry-related projects have emerged exploring the capabilities of Julia. Herein, we introduce the quantum chemistry package Fermi.jl, which contains the first implementations of post-Hartree-Fock methods written in Julia. Its design makes use of many Julia core features, including multiple dispatch, metaprogramming, and interactive usage. Fermi.jl is a modular package, where new methods and implementations can be easily added to the existing code. Furthermore, it is designed to maximize code reusability by relying on general functions with specialized methods for particular cases. The feasibility of the project is explored through evaluating the performance of popular ab initio methods. It is our hope that this project motivates the usage of Julia within the community and brings new contributions into Fermi.jl.

Cumulants as the variables of density cumulant theory: A path to Hermitian triples

We study the combination of orbital-optimized density cumulant theory and a new parameterization of reduced density matrices in which the variables are the particle-hole cumulant elements. We call this combination OλDCT. We find that this new Ansatz solves problems identified in the previous unitary coupled cluster Ansatz for density cumulant theory: the theory is now free of near-zero denominators between occupied and virtual blocks, can correctly describe the dissociation of H₂, and is rigorously size-extensive. In addition, the new Ansatz has fewer terms than the previous unitary Ansatz, and the optimal orbitals delivered by the exact theory are the natural orbitals. Numerical studies on systems amenable to full configuration interaction show that the amplitudes from the previous ODC-12 method approximate the exact amplitudes predicted by this Ansatz. Studies on equilibrium properties of diatomic molecules show that even with the new Ansatz, it is necessary to include triples to improve the accuracy of the method compared to orbital-optimized linearized coupled cluster doubles. With a simple iterative triples correction, OλDCT outperforms other orbital-optimized methods truncated at comparable levels in the amplitudes, as well as coupled cluster single and doubles with perturbative triples [CCSD(T)]. By adding four more terms to the cumulant parameterization, OλDCT outperforms CCSDT while having the same O(V⁵O³) scaling.

Hydrogen and Lithium Bonds-Lewis Acid Units Possessing Multi-Center Covalent Bonds

MP2/aug-cc-pVTZ calculations were carried out on complexes wherein the proton or the lithium cation is located between π-electron systems, or between π-electron and σ-electron units. The acetylene or its fluorine and lithium derivatives act as the Lewis base π-electron species similarly to molecular hydrogen, which acts as the electron donor via its σ-electrons. These complexes may be classified as linked by π-H∙∙∙π/σ hydrogen bonds and π-Li∙∙∙π/σ lithium bonds. The properties of these interactions are discussed, and particularly the Lewis acid units are analyzed, because multi-center π-H or π-Li covalent bonds may occur in these systems. Various theoretical approaches were applied here to analyze the above-mentioned interactions—the Quantum Theory of Atoms in Molecules (QTAIM), the Symmetry-Adapted Perturbation Theory (SAPT) and the Non-Covalent Interaction (NCI) method.

Photodissociation dynamics of halogenated aromatic molecules: the case of core-ionized tetrabromothiophene

We studied the gas-phase photodissociation of a fully halogenated aromatic molecule, tetrabromothiophene, upon core-shell ionization by using synchrotron radiation and energy-resolved multiparticle coincidence spectroscopy. Photodynamics was initiated by the selective soft X-ray ionization of three elements - C, S, and Br - leading to the formation of dicationic states by Auger decay. From a detailed study of photodissociation upon Br 3d ionization, we formulate a general fragmentation scheme, where dissociation into neutral fragments and a pair of cations prevails, but dicationic species are also produced. We conclude that dicationic tetrabromothiophene typically undergoes deferred charge separation (with one of the ions being often Br⁺) that may be followed by secondary dissociation steps, depending on the available internal energy of the parent dication. Observations suggest that the ejection of neutral bromine atoms as the first step of deferred charge separation is a prevailing feature in dicationic dissociation, although sometimes in this step the C-Br bonds appear to remain intact and the thiophene ring is broken instead. Ionization-site-specific effects are observed particularly in doubly charged fragments and as large differences in the yields of the intact parent dication. We interpret these effects, using first-principles calculations and molecular dynamics simulations of core-hole states, as likely caused by the geometry changes during the core-hole lifetime.

Polaritonic Unitary Coupled Cluster for Quantum Computations

In the field of polaritonic chemistry, strong light-matter interactions are used to alter chemical reactions inside optical cavities. To understand these processes, the development of reliable theoretical models is essential. While traditional methods have to balance accuracy and system size, new developments in quantum computing offer a path for accurate calculations on currently available quantum devices. Here, we introduce the quantum electrodynamics unitary coupled cluster (QED-UCC) method combined with the Variational Quantum Eigensolver algorithm, as well as the quantum electrodynamics equation-of-motion (QED-EOM) method formulated in the qubit basis that allow accurate calculations of ground-state and excited-state properties of strongly coupled light-matter systems suitable for quantum computers. These methods show excellent agreement with the exact reference results and can outperform their traditional counterparts when strong electronic correlations become significant. This work sets the stage for future developments of polaritonic quantum chemistry methods suitable for both classical and quantum computers.

GQCP: The Ghent Quantum Chemistry Package

The Ghent Quantum Chemistry Package (GQCP) is an open-source electronic structure software package that aims to provide an intuitive and expressive software framework for electronic structure software development. Its high-level interfaces (accessible through C++ and Python) have been specifically designed to correspond to theoretical concepts, while retaining access to lower-level intermediates and allowing structural run-time modifications of quantum chemical solvers. GQCP focuses on providing quantum chemical method developers with the computational "building blocks" that allow them to flexibly develop proof of principle implementations for new methods and applications up to the level of two-component spinor bases.

Inverse Kohn-Sham Density Functional Theory: Progress and Challenges

Inverse Kohn-Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute to the construction of empirical exchange-correlation functionals and to the development of techniques for density-based embedding. Unlike the forward Kohn-Sham problems, numerical iKS problems are ill-posed and can be unstable. We discuss some of the fundamental and practical difficulties of iKS problems with constrained-optimization methods on finite basis sets. Various factors that affect the performance are systematically compared and discussed, both analytically and numerically, with a focus on two of the most practical methods: the Wu-Yang method (WY) and the partial differential equation constrained optimization (PDE-CO). Our analysis of the WY and PDE-CO highlights the limitation of finite basis sets. We introduce new ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions.