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33 records · Page 2

Perspective on Kramers symmetry breaking and restoration in relativistic electronic structure methods for open-shell systems

Without rigorous symmetry constraints, solutions to approximate electronic structure methods may artificially break symmetry. In the case of the relativistic electronic structure, if time-reversal symmetry is not enforced in calculations of molecules not subject to a magnetic field, it is possible to artificially break Kramers degeneracy in open shell systems. This leads to a description of excited states that may be qualitatively incorrect. Despite this, different electronic structure methods to incorporate correlation and excited states can partially restore Kramers degeneracy from a broken symmetry solution. For single-reference techniques, the inclusion of double and possibly triple excitations in the ground state provides much of the needed correction. Formally, however, this imbalanced treatment of the Kramers-paired spaces is a multi-reference problem, and so methods such as complete-active-space methods perform much better at recovering much of the correct symmetry by state averaging. Using multi-reference configuration interaction, any additional corrections can be obtained as the solution approaches the full configuration interaction limit. A recently proposed “Kramers contamination” value is also used to assess the magnitude of symmetry breaking.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fundamental chemical physics revealed by scattering reactive open-shell atoms from surfaces

The dynamics of reactive atoms at surfaces are centrally important to areas such as heterogeneous catalysis, corrosion, materials degradation in extreme environments, and plasma etching. Remarkably detailed understanding of dynamical processes at surfaces has been extracted from scattering molecules and inert atoms under well-defined conditions. However, traditional techniques for generating beams of reactive atoms often result in impure mixtures, broad energy distributions, and poorly defined contributions of metastable electronically excited atoms. In this perspective article, we review the state-of-the-art in reactive atom surface scattering with a focus on experiments performed under controlled conditions on well-defined surfaces. We highlight a new technique for controlled state-to-state scattering of polyelectronic atoms from surfaces, based on vacuum ultraviolet photolysis and state-selective ion imaging. The new capabilities provide an avenue for research into the underexplored area of excited state and spin selective chemical dynamics at surfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of Non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of “how difficult the problem is” (like the well-known T 1 diagnostic), but its variation with the level of theory also gives information about “how well this particular method works”, irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be 2 ). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Long-Range Interaction between Molecules with Electronic Degeneracy: Beyond the Born–Oppenheimer Approximation

Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.

ab initio calculations↗

Zero-Field Splitting Calculations by Multiconfiguration Pair-Density Functional Theory

Zero-field splitting (ZFS) is a fundamental molecular property that is especially relevant for single-molecule magnets (SMMs), electron paramagnetic resonance spectra, and quantum computing. Developing a method that can accurately predict ZFS parameters can be very powerful for designing new SMMs. One of the challenges is to include external correlation in an inherently multiconfigurational open-shell species for the accurate prediction of magnetic properties. Previously available methods depend on expensive multireference perturbation theory calculations to include external correlation. In this paper, we present spin-orbit-inclusive multiconfiguration and multistate pair-density functional theory (MC-PDFT) calculations of ZFSs; these calculations have a cost comparable to complete-active-space self-consistent field (CASSCF) theory, but they include correlation external to the active space. We found that combining a multistate formulation of MC-PDFT, namely, compressed-state multistate pair-density functional theory, with orbitals optimized by weighted-state-averaged CASSCF, yields reasonably accurate ZFS results

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reexamining the variational two-particle reduced density matrix for nuclear systems

We report that in most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spectroscopy of Rydberg states in erbium using electromagnetically induced transparency

We present a study of the Rydberg spectrum in 166 Er for series connected to the 4 f 12 ( 3 H 6 )6s, J c = 13/2 and J c = 11/2 ionic core states using an all-optical detection based on electromagnetically induced transparency in an effusive atomic beam. Identifying approximately 550 individual states, we find good agreement with a multi-channel quantum defect theory (MQDT) which allows assignment of most states to ns or nd Rydberg series. We provide an improved accuracy for the lowest two ionization thresholds to E IP, J c =13/2 = 49260:750(1) cm -1 and E IP, J c =11/2 = 49701:184(1) cm -1 as well as the corresponding quantum defects for all observed series. We identify Rydberg states in five different isotopes, and states between the two lowest ionization thresholds. Our results open the way for future applications of Rydberg states for quantum simulation using erbium and exploiting its special open-shell structure.

74 ATOMIC AND MOLECULAR PHYSICS↗

Navigating Transition-Metal Chemical Space: Artificial Intelligence for First-Principles Design

Conspectus The variability of chemical bonding in open-shell transition-metal complexes not only motivates their study as functional materials and catalysts but also challenges conventional computational modeling tools. Here, tailoring ligand chemistry can alter preferred spin or oxidation states as well as electronic structure properties and reactivity, creating vast regions of chemical space to explore when designing new materials atom by atom. Although first-principles density functional theory (DFT) remains the workhorse of computational chemistry in mechanism deduction and property prediction, it is of limited use here. DFT is both far too computationally costly for widespread exploration of transition-metal chemical space and also prone to inaccuracies that limit its predictive performance for localized d electrons in transition-metal complexes. These challenges starkly contrast with the well-trodden regions of small-organic-molecule chemical space, where the analytical forms of molecular mechanics force fields and semiempirical theories have for decades accelerated the discovery of new molecules, accurate DFT functional performance has been demonstrated, and gold-standard methods from correlated wavefunction theory can predict experimental results to chemical accuracy. The combined promise of transition-metal chemical space exploration and lack of established tools has mandated a distinct approach. In this Account, we outline the path we charted in exploration of transition-metal chemical space starting from the first machine learning (ML) models (i.e., artificial neural network and kernel ridge regression) and representations for the prediction of open-shell transition-metal complex properties. The distinct importance of the immediate coordination environment of the metal center as well as the lack of low-level methods to accurately predict structural properties in this coordination environment first motivated and then benefited from these ML models and representations. Once developed, the recipe for prediction of geometric, spin state, and redox potential properties was straightforwardly extended to a diverse range of other properties, including in catalysis, computational “feasibility”, and the gas separation properties of periodic metal–organic frameworks. Interpretation of selected features most important for model prediction revealed new ways to encapsulate design rules and confirmed that models were robustly mapping essential structure–property relationships. Encountering the special challenge of ensuring that good model performance could generalize to new discovery targets motivated investigation of how to best carry out model uncertainty quantification. Distance-based approaches, whether in model latent space or in carefully engineered feature space, provided intuitive measures of the domain of applicability. With all of these pieces together, ML can be harnessed as an engine to tackle the large-scale exploration of transition-metal chemical space needed to satisfy multiple objectives using efficient global optimization methods. In practical terms, bringing these artificial intelligence tools to bear on the problems of transition-metal chemical space exploration has resulted in ML-model assessments of large, multimillion compound spaces in minutes and validated new design leads in weeks instead of decades.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Teaching a neural network to attach and detach electrons from molecules

Abstract Interatomic potentials derived with Machine Learning algorithms such as Deep-Neural Networks (DNNs), achieve the accuracy of high-fidelity quantum mechanical (QM) methods in areas traditionally dominated by empirical force fields and allow performing massive simulations. Most DNN potentials were parametrized for neutral molecules or closed-shell ions due to architectural limitations. In this work, we propose an improved machine learning framework for simulating open-shell anions and cations. We introduce the AIMNet-NSE (Neural Spin Equilibration) architecture, which can predict molecular energies for an arbitrary combination of molecular charge and spin multiplicity with errors of about 2–3 kcal/mol and spin-charges with error errors ~0.01e for small and medium-sized organic molecules, compared to the reference QM simulations. The AIMNet-NSE model allows to fully bypass QM calculations and derive the ionization potential, electron affinity, and conceptual Density Functional Theory quantities like electronegativity, hardness, and condensed Fukui functions. We show that these descriptors, along with learned atomic representations, could be used to model chemical reactivity through an example of regioselectivity in electrophilic aromatic substitution reactions.

36 MATERIALS SCIENCE↗

Route to Chemical Accuracy for Computational Uranium Thermochemistry

Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO 2 ) and for the bond dissociation energies of UO and UO 2 are reported. The accuracy of these calculations in the treatments of relativistic, electron correlation, and basis-set effects is analyzed. Furthermore, the intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stress-Alteration Enhancement of the Reactivity of Aluminum Nanoparticles in the Catalytic Decomposition of exo -Tetrahydrodicyclopentadiene (JP-10)

High energy density aluminum nanoparticles (AlNP) upon thermal annealing followed by super-quenching results in elevated stress levels in the metallic core and reduced surface energy at the core-shell interface. Isomer-selective vacuum ultraviolet based photoionization mass spectrometry coupled to a high temperature chemical microreactor reveals that these stress-altered (SA) AlNPs exhibit distinctive temperature-dependent reactivities towards catalytic decomposition of the hydrocarbon jet fuel exo-tetrahydrodicyclopentadiene (JP-10, C 10 H 16 ) compared to untreated (UN) AlNPs. SA-AlNPs show a delayed initiation of the decomposition for JP-10 by 200 K relative to the UN-AlNPs, however, the full decomposition is achieved at 100 K lower temperature. Furthermore, there is less oxygenated products that are generated from the alumina surface-induced heterogeneous oxidation process, and a larger fraction of closed and open-shell hydrocarbons. Furthermore, chemical insight bridging the reactivity order of SA-AlNPs at low and high temperatures, simultaneously, is obtained via a detailed examination of the product branching ratios obtained in this study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoluminescence, photophysics, and photochemistry of the V B - defect in hexagonal boron nitride

Extensive photochemical and spectroscopic properties of the V B - defect in hexagonal boron nitride are calculated, concluding that the observed photoemission associated with recently observed optically detected magnetic resonance is most likely of (1) 3 E'' → (1) 3 A' 2 origin. Rapid intersystem crossing from the defect's triplet to singlet manifolds explains the observed short excited-state lifetime and very low quantum yield. New experimental results reveal smaller intrinsic spectral bandwidths than previously recognized, interpreted in terms of spectral narrowing and zero-phonon-line shifting induced by the Jahn-Teller effect. Different types of computational methods are applied to map out the complex triplet and singlet defect manifolds, including the doubly ionized formulation of the equation-of-motion coupled-cluster theory that is designed to deal with the open-shell nature of defect states, and mixed quantum-mechanics/molecular-mechanics schemes enabling 5763-atom simulations. Finally, two other energetically feasible spectral assignments from among the singlet and triplet manifolds are considered, but ruled out based on inappropriate photochemical properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

COLUMBUS─An Efficient and General Program Package for Ground and Excited State Computations Including Spin–Orbit Couplings and Dynamics

The COLUMBUS program system provides the tools for performing high-level multireference (MR) computations, including the multireference configuration interaction (MRCI) method and its multireference averaged quadratic coupled cluster (MR-AQCC) extension, allowing computations on a wide range of fascinating atomic and molecular systems, including the treatment of open-shells and complicated excited state phenomena. The inclusion of spin−orbit coupling (SOC) directly within the MRCI step enables the description of systems containing heavy elements, such as lanthanides and actinides, whose properties are strongly influenced by SOC. Analytic energy gradients and nonadiabatic couplings at the correlated MRCI level provide the foundation for a variety of dynamics studies, giving insight into ultrafast photochemistry. New and ongoing method developments in COLUMBUS include the computation of spin densities, improved descriptions of ionic states, enhancements to the AQCC method, and the porting of COLUMBUS to graphical processing units (GPUs). New external interfaces enable an enhanced description of electronic resonances and molecules in strong laser fields. This work highlights these new developments while providing a detailed account of the diverse applications of COLUMBUS in recent years.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Extending Orbital-Optimized Density Functional Theory to L-Edge XPS and Beyond: Spin–Orbit Coupling via Nonorthogonal Quasi-Degenerate Perturbation Theory

Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. Here, to extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computing x-ray absorption spectra from linear-response particles atop optimized holes

State specific orbital optimized density functional theory (OO-DFT) methods, such as restricted open-shell Kohn–Sham (ROKS), can attain semiquantitative accuracy for predicting x-ray absorption spectra of closed-shell molecules. OO-DFT methods, however, require that each state be individually optimized. In this Communication, we present an approach to generate an approximate core-excited state density for use with the ROKS energy ansatz, which is capable of giving reasonable accuracy without requiring state-specific optimization. Herein, this is achieved by fully optimizing the core-hole through the core-ionized state, followed by the use of electron-addition configuration interaction singles to obtain the particle level. This hybrid approach can be viewed as a DFT generalization of the static-exchange (STEX) method and can attain ~0.6 eV rms error for the K-edges of C–F through the use of local functionals, such as PBE and OLYP. This ROKS(STEX) approach can also be used to identify important transitions for full OO ROKS treatment and can thus help reduce the computational cost of obtaining OO-DFT quality spectra. ROKS(STEX), therefore, appears to be a useful technique for the efficient prediction of x-ray absorption spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗