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In this paper, we investigate the role of electron correlation in predicting the S1–S0 and T1–S0 excitation energies and, hence, the singlet–triplet gap (ΔEST) in a set of cyclazines, which act as templates for potential candidates for fifth generation organic light emitting diode materials. This issue has recently garnered much interest with the focus being on the inversion of the ΔEST, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar [J. Am. Chem. Soc. 102, 6068 (1980), J. Am. Chem. Soc. 108, 17(1986)]. We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections, including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cost-effective theories, which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally, we would like to point out that the use of domain-based local pair natural orbital-similarity transformed EOM-coupled cluster singles and doubles as the benchmark for ΔEST [as used in J. Phys. Chem. A 126(8), 1378 (2022), Chem. Phys. Lett. 779, 138827 (2021)] is not a suitable benchmark for these classes of molecules. [ABSTRACT FROM AUTHOR]

Several of the limitations of approximate exchange–correlation functionals within Kohn–Sham density functional theory can be eliminated by extending the single-determinant reference system to a multi-determinant one. Here, we employ the correlation factor ansatz to combine multi-configurational, self-consistent field (MCSCF) with approximate density functionals. In the proposed correlation factor approach, the exchange–correlation hole ρXC(r, u), a function of the reference point r and the electron–electron separation u, is written as a product of the correlation factor fC(r, u) and an exchange plus static-correlation hole ρXS(r, u), i.e., ρ XC CFXS (r, u) = fC(r, u)ρXS(r, u). ρXS(r, u) is constructed to reproduce the exchange–correlation energy of an MCSCF reference wave function. The correlation factor fC(r, u) is designed to account for dynamic correlation effects that are absent in ρXS(r, u). The resulting approximation to the exchange–correlation energy, which we refer to as CFXStatic, is free of empirical parameters, and it combines the qualitatively correct description of the electronic structure obtainable with MCSCF with the advantages of approximate density functionals in accounting for dynamic correlation. [ABSTRACT FROM AUTHOR]

A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play. [ABSTRACT FROM AUTHOR]

The I 3 − molecule is known to undergo substantial structural reorganization upon solvation by a protic solvent, e.g., water. However, the details of this process are still controversially discussed in the literature. In the present study, we combined experimental and theoretical efforts to disentangle this controversy. The valence (5p), N 4 , 5 (4d), and M 4 , 5 (3d) edge photoelectron spectra were measured in an aqueous solution and computed using high-level multi-reference methods. Our previous publication mainly focused on obtaining reliable experimental evidence, whereas in the present article, we focused primarily on theoretical aspects. The complex electronic structure of I 3 − requires the inclusion of both static and dynamic correlation, e.g., via the multi-configurational perturbation theory treatment. However, the resulting photoelectron spectra appear to be very sensitive to problems with variational stability and intruder states. We attempted to obtain artifact-free spectra, allowing for a more reliable interpretation of experiments. Finally, we concluded that the 3d Photoelectron Spectrum (PES) is particularly informative, evidencing an almost linear structure with a smaller degree of bond asymmetry than previously reported. [ABSTRACT FROM AUTHOR]

This recent paper uses multiconfiguration self-consistent field (MCSCF) wave functions to study the structure of Si(001). The results are at odds with density functional theory predictions and experiment. This comment shows that dynamic correlation, which is neglected in MCSCF calculations, is essential for reliable predictions of the geometry of Si(001). © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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The three lowest spin states (S = 0,1,2) of 12 representative Na13+ isomers have been estudied using both, KS‐DFT via three hybrid density functionals, and benchmark multireference CASSCF and CASPT2 methods with a couple of Dunning's correlation consistent basis sets. CASSCF(12,12) geometry optimizations were carried out. Since 12 electrons in 12 active orbitals span the chemically‐significant complete valence space, the results of the present study provide benchmarks for Na13+. The CASPT2(12,12)/cc‐pVTZ* lowest energy structures are three nearly degenerate singlets (S = 0): an isomer formed from two pentagonal bipyramids fused together (PBPb), a capped centered‐squared antiprism [CSAP‐(1,3)] and an optimum tetrahedral OPTET(II) structure, the last two lying 0.88 and 1.63 kcal/mol above the first, respectively. The lowest triplet (S = 1) and quintet (S = 2) states lie 4.33 and 3.77 kcal/mol above the singlet global minimum, respectively. The latter is a deformed icosahedron while the former is a CSAP‐(1,3). The flatness of the potential energy surface of this cluster suggests a rather strong dynamical character at finite temperature. Prediction of the lowest energy structures and electronic properties is crucially sensitive both to non‐dynamical and dynamical electron correlation treatment. The CASPT2 vertical ionization energy is 3.66 eV, in excellent agreement with the 3.6 ± 0.1 eV experimental figure. All the isomers are found to have a strong multireference character, thus making KS density functional theory fundamentally inappropriate for these systems. Only large multiconfigurational CASSCF wavefunctions provide a reliable zeroth‐order description; then the dynamic correlation effects must be properly taken into account for a truly accurate account of the structural and energetic features of alkali‐metal clusters. [ABSTRACT FROM AUTHOR]

The photodissociation of thioanisole is very interesting because the experiments of Lim and Kim provide evidence for mode-specific effects on the product distribution. They showed that, with a specific S-CH3 stretching mode being excited as the reagent is excited to the S1 electronic state, there is a sharp increase in the proportion of the ground-state product to the excited-state product. In the present work, we report 78 011 full-dimensional semiclassical multi-state trajectories of the photodissociation process using the coherent switching with decay of mixing dynamics method. The potential surfaces and couplings are based on electronic structure calculations that include dynamic correlation through second order perturbation theory. We report results for four sets of initial conditions, one corresponding roughly to 0-0 excitation and three corresponding to exciting one vibrational mode, to look for modespecific effects. The simulations show no significant mode-specific effect on the product energy distributions, but they do showan effect on the distribution of minimum-energy gaps in the trajectories and on the lifetime for dissociation. In particular, excitation of the S-CH3 stretching mode leads to trajectories passing closer to the S1-S2 conical intersection and to shorter lifetimes. This provides a possible explanation of why experimental results are different for excitation of this vibration. [ABSTRACT FROM AUTHOR]

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations. [ABSTRACT FROM AUTHOR]

Analytic potential energy surfaces (PESs) and state couplings of the ground and two lowest singlet excited states of thioanisole (C6H5SCH3) are constructed in a diabatic representation based on electronic structure calculations including dynamic correlation. They cover all 42 internal degrees of freedom and a wide range of geometries including the Franck-Condon region and the reaction valley along the breaking S-CH3 bond with the full ranges of the torsion angles. The parameters in the PESs and couplings are fitted to the results of smooth diabatic electronic structure calculations including dynamic electron correlation by the extended multi-configurational quasi-degenerate perturbation theory method for the adiabatic state energies followed by diabatization by the fourfold way. The fit is accomplished by the anchor points reactive potential method with two reactive coordinates and 40 nonreactive degrees of freedom, where the anchor-point force fields are obtained with a locally modified version of the QuickFF package. The PESs and couplings are suitable for study of the topography of the trilayer potential energy landscape and for electronically nonadiabatic molecular dynamics simulations of the photodissociation of the S-CH3 bond. [ABSTRACT FROM AUTHOR]

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime. [ABSTRACT FROM AUTHOR]

In this review we outline the theory and recent progress of the restricted active space configuration interaction (RASCI) methodology within the hole and particle approximation. The RASCI is a single reference approach based on the splitting of the orbital space in different subsets, in which the target CI space is expressed by the concomitant number of electrons and empty orbitals in each subspace. Initially, the method was born as a spin complete version of the spin‐flip ansatz able to deal with any number of unpaired electrons. Since then, the method has experienced several improvements related to its theoretical foundations, its efficient implementation, in the characterization of RASCI wave functions, and in the calculation of molecular properties. It has shown to be especially suitable for the characterization of medium to large molecular diradicals and polyradicals, and to the study of photophysical processes involving open‐shell species and/or multiexcitonic states, like in the singlet fission reaction. But, despite this success, several limitations emerge from the sever truncation of the excitation operator, which might translate into inaccurate relative energies between different regions of the potential energy surface, and overestimated (or underestimated) excitation energies. These errors are associated with the lack of dynamic correlation, which has motivated the development and implementation of various improvements based on multi‐reference perturbation theory and to blend the RASCI wave function with density functional theory through range separation of electron–electron interactions. Finally, we discuss some of the properties available from RASCI wave functions and give potential future developments. This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure MethodsSoftware > Quantum ChemistryQuantum Computing > Theory Development [ABSTRACT FROM AUTHOR]

Computational chemistry provides a powerful route to determine thermochemical properties. For transition metal thermochemistry, typically, high-level quantum methodologies are required. Ab initio composite methods – which aim to replicate the predictions possible from a high-level method/advanced basis set with predictions from a series of lower-level methods/basis sets to reduce computational cost – have proven to be effective for transition metal species, with better than chemical accuracy for transition metal energetics (<12 kJ mol−1), on average. While useful, to provide a more robust computational approach, Super ccCA (s-ccCA) is introduced herein and varies from its predecessor, ccCA, by utilising higher-level coupled-cluster corrections along with a spin–orbit contribution from a Breit-Pauli Hamiltonian. In this work, s-ccCA has been utilised for the prediction of dissociation energies of 3d and 4d molecules. A set of borides, sulphides and carbides in conjunction with three early first-row transition metals (Sc, Ti, V) and three second-row transition metals (Y, Zr, Nb) were studied with this new composite method. The energies calculated herein were compared with the experiment and shown to be in excellent agreement. The energetic predictions show that for cases where a balance of static and dynamic correlation is of paramount importance, s-ccCA offers an effective approach. [ABSTRACT FROM AUTHOR]

We present a technique for using quantum Monte Carlo (QMC) to obtain high quality energy differences. We use generalized valence bond (GVB) wave functions, for an intuitive approach to capturing the important sources of static correlation, without needing to optimize the orbitals with QMC. Using our modifications to Walker branching and Jastrows, we can then reliably use diffusion quantum Monte Carlo to add in all the dynamic correlation. This simple approach is easily accurate to within a few tenths of a kcal/mol for a variety of problems, which we demonstrate for the adiabatic singlet-triplet splitting in methylene, the vertical and adiabatic singlet-triplet splitting in ethylene, 2+2 cycloaddition, and Be2 bond breaking. [ABSTRACT FROM AUTHOR]

The geometries, electronic structures, and vibrational frequencies of two isoelectronic compounds PuO22+ and PuN2 have been studied in detail at the density functional theory (DFT) and multiconfigurational ab initio levels of theory. Dynamic correlation was taken into account using second-order perturbation theory (CASPT2) and the variational difference-dedicated configuration interaction method for comparison with the results of the DFT study. Spin-orbit effects were included within the framework of an effective uncontracted spin-orbit configuration-interaction method which considers electron correlation effects and spin-orbit coupling on equal footing. The twelve lowest f-f electronic transitions are reported. The electronic ground state of both systems is found to be the Ω=4 component of 3Hg. We thus disagree with an earlier assignment of the ground state of PuN2 [E. F. Archibong and A. K. Ray, J. Mol. Struct: THEOCHEM 530, 165 (2000)]. Spin-orbit effects are small on both the geometry and vibrational frequencies of the ground states of PuO22+ and PuN2, but they completely change the distribution of electronically excited states. A comparison of results obtained with the two classes of methods allows us to demonstrate that an unambiguous assignment of the electronic ground state and electronic spectra requires the use of multireference methods including spin-orbit coupling. Single-reference methods such as DFT provide a reasonable description of the electronic properties of ground states of these open-shell systems, and therefore also of their structural and vibrational properties. The experimental antisymmetric stretching frequency of matrix-isolated PuN2 is reproduced well by both CASPT2 and DFT calculations; generalized gradient approximation formulations of DFT are more successful than hybrid versions in this respect. Ground-state properties of UO22+, UN2, UO2, PuO22+, and PuN2 are compared and discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications. [ABSTRACT FROM AUTHOR]

Fully relativistic all-electron self-consistent field calculations based on the Dirac–Coulomb Hamiltonian have been performed on the three lowest lying states of the PtH molecule. The resulting four-component Dirac–Hartree–Fock (DHF) molecular spinors are subsequently used in relativistic configuration interaction (CI) calculations on the five lower states of PtH. Spectroscopic properties are obtained by fitting the potential curve to a Morse function and show good agreement with experimental data. The effect of relativistic corrections to the Coulomb electron–electron interaction is investigated at the DHF level and is found to be insignificant for the molecular spectroscopic properties investigated by us. The CI wave functions are found to have only one dominant configuration, indicating a lack of static correlation. Dynamic correlation in the d shell is, however, important for the spectroscopic properties of PtH. The results conform with a bonding scheme in which the three lower and two upper states of PtH are assigned 5d3/245d5/25σ1/22 and 5d3/235d5/26σ1/22 electronic configurations, respectively. The configurations are only approximate and are perturbed by 5d participation in bonding. The stability of the Pt–H bond is explained in terms of the relativistic stabilization of the 6s orbital in analogy with the electron affinity of the platinum atom. [ABSTRACT FROM AUTHOR]

Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree–Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated. [ABSTRACT FROM AUTHOR]

An accurate assessment of how quantum computers can be used for chemical simulation, especially their potential computational advantages, provides important context on how to deploy these future devices. To perform this assessment reliably, quantum resource estimates must be coupled with classical computations attempting to answer relevant chemical questions and to define the classical algorithms simulation frontier. Herein, we explore the quantum computation and classical computation resources required to assess the electronic structure of cytochrome P450 enzymes (CYPs) and thus define a classical-quantum advantage boundary. This is accomplished by analyzing the convergence of density matrix renormalization group plus n-electron valence state perturbation theory (DMRG+NEVPT2) and coupled-cluster singles doubles with noniterative triples [CCSD(T)] calculations for spin gaps in models of the CYP catalytic cycle that indicate multireference character. The quantum resources required to perform phase estimation using qubitized quantum walks are calculated for the same systems. Compilation into the surface code provides runtime estimates to compare directly to DMRG runtimes and to evaluate potential quantum advantage. Both classical and quantum resource estimates suggest that simulation of CYP models at scales large enough to balance dynamic and multiconfigurational electron correlation has the potential to be a quantum advantage problem and emphasizes the important interplay between classical computations and quantum algorithms development for chemical simulation. [ABSTRACT FROM AUTHOR]

Electronic structure calculations have the potential to predict key matter transformations for applications of strategic technological importance, from drug discovery to material science and catalysis. However, a predictive physicochemical characterization of these processes often requires accurate quantum chemical modeling of complex molecular systems with hundreds to thousands of atoms. Due to the computationally demanding nature of electronic structure calculations and the complexity of modern high-performance computing hardware, quantum chemistry software has historically failed to operate at such large molecular scales with accuracy and speed that are useful in practice. In this paper, novel algorithms and software are presented that enable extreme-scale quantum chemistry capabilities with particular emphasis on exascale calculations. This includes the development and application of the multi-Graphics Processing Unit (GPU) library LibCChem 2.0 as part of the General Atomic and Molecular Electronic Structure System package and of the standalone Extreme-scale Electronic Structure System (EXESS), designed from the ground up for scaling on thousands of GPUs to perform high-performance accurate quantum chemistry calculations at unprecedented speed and molecular scales. Among various results, we report that the EXESS implementation enables Hartree–Fock/cc-pVDZ plus RI-MP2/cc-pVDZ/cc-pVDZ-RIFIT calculations on an ionic liquid system with 623 016 electrons and 146 592 atoms in less than 45 min using 27 600 GPUs on the Summit supercomputer with a 94.6% parallel efficiency. [ABSTRACT FROM AUTHOR]

In our recent work, we revisited C–H and C–C bond activation in rhodium (I) complexes of pincer ligands PCP, PCN, PCO, POCOP, and SCS. Our findings indicated that an η3-Csp2Csp3H agostic intermediate acts as a common precursor to both C–C and C–H bond activation in these systems. We explore the electronic structure and bonding nature of these precleavage complexes using electron density and molecular orbital analyses. Using NBO, IBO, and ESI-3D methods, the bonding in the η3-CCH agostic moiety is depicted by two three-center agostic bonds: Rh–Csp2–Csp3 and Rh–Csp3–H, with all three atoms datively bound to Rh(I). IBO analysis specifically highlights the involvement of three orbitals (CC→Rh and CH→Rh σ donation, plus Rh→CCH π backdonation) in both C–C and C–H bond cleavages. NCIPLOT and QTAIM analyses highlight anagostic (Rh–H) or β-agostic (Rh–Csp2–H) interactions and the absence of Rh–Csp3 interactions. QTAIM molecular graphs suggest bond path instability under dynamic conditions due to the nearness of line and ring critical points. Several low-frequency and low-force vibrational modes interconvert various bonding patterns, reinforcing the dynamic η3-CCH agostic nature. The kinetic preference for C–H bond breaking is attributed to the smaller reduced mass of C–H vibrations compared to C–C vibrations. [ABSTRACT FROM AUTHOR]

Quantum chemical calculations on atomistic systems have evolved into a standard approach to studying molecular matter. These calculations often involve a significant amount of manual input and expertise, although most of this effort could be automated, which would alleviate the need for expertise in software and hardware accessibility. Here, we present the AutoRXN workflow, an automated workflow for exploratory high-throughput electronic structure calculations of molecular systems, in which (i) density functional theory methods are exploited to deliver minimum and transition-state structures and corresponding energies and properties, (ii) coupled cluster calculations are then launched for optimized structures to provide more accurate energy and property estimates, and (iii) multi-reference diagnostics are evaluated to back check the coupled cluster results and subject them to automated multi-configurational calculations for potential multi-configurational cases. All calculations are carried out in a cloud environment and support massive computational campaigns. Key features of all components of the AutoRXN workflow are autonomy, stability, and minimum operator interference. We highlight the AutoRXN workflow with the example of an autonomous reaction mechanism exploration of the mode of action of a homogeneous catalyst for the asymmetric reduction of ketones. [ABSTRACT FROM AUTHOR]

Dilute magnetic semiconductors (DMSs) with both charge and spin degrees of freedom have emerged as promising candidates in the spintronic industry. However, the Curie temperature below room temperature and uncertainty about the origin of ferromagnetism hinder the application of DMSs. To address these issues, we explored a better SnO2-based co-doped method (Fe, V + VSn) using ab initio calculations. The calculation results show that the Sn13FeVO32 (Fe, V + VSn) has a high Curie temperature (716 K), good ferromagnetic properties, stronger covalency of bonds, and better optical transparency in the visible light range. In addition, the holes or electrons generated by the complexes in the (Fe, V + VO/VSn) co-doped system cause a spin-polarized double exchange effect in the Fe-3d, V-3d, and O-2p orbitals, which leads to magnetism of the co-doped systems. The static dielectric constant ɛ1(0) of the system increases after doping. Among them, Sn14FeVO31 (Fe, V + VO) has the largest ɛ1(0), indicating that Sn14FeVO31 has the strongest polarization ability and better photocatalytic properties. In Sn14FeVO31, the imaginary part of the dielectric function and the absorption spectrum all have new peaks in the low-energy region, which are caused by the jump of electrons from the guide band of the spin-polarized impurity energy level. This paper proposes a new method for preparing dilute magnetic semiconductors in spin electronic devices with high room temperature ferromagnetic properties and excellent optical properties through the (Fe, V + VO/VSn) co-doped SnO2. [ABSTRACT FROM AUTHOR]

Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication [H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021)], I introduced a generalized extension to the nonorthogonal Wick's theorem that allows matrix elements to be derived between excited configurations from a pair of reference determinants with a singular nonorthogonal orbital overlap matrix. However, that work only provided explicit expressions for one- and two-body matrix elements between singly- or doubly-excited configurations. Here, this framework is extended to compute generalized nonorthogonal matrix elements between higher-order excitations. Pre-computing and storing intermediate values allows one- and two-body matrix elements to be evaluated with an O (1) scaling relative to the system size, and the LIBGNME computational library is introduced to achieve this in practice. These advances make the evaluation of all nonorthogonal matrix elements almost as easy as their orthogonal counterparts, facilitating a new phase of development in nonorthogonal electronic structure theory. [ABSTRACT FROM AUTHOR]

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H 3 + is studied, which is an (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries. [ABSTRACT FROM AUTHOR]

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations. [ABSTRACT FROM AUTHOR]

This work assesses the reliability of the recently proposed [M. Piris, Phys. Rev. Lett. 127, 233001 (2021)] global natural orbital functional (GNOF) in the treatment of the strong electron correlation regime. First, we use an H10 benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 2D ring, a 2D sheet, and a 3D close-packed pyramid. Second, we study two paradigmatic models for strongly correlated Mott insulators, namely, a 1D H50 chain and a 4 × 4 × 4 3D H cube. We show that GNOF, without hybridization to other electronic structure methods and free of tuned parameters, succeeds in treating weak and strong correlation in a more balanced way than the functionals that have preceded it. [ABSTRACT FROM AUTHOR]

A natural range separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations ( h c I ) and the other at short distances ( h c I I ) , is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that h c I , which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how h c I can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how h c I I helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold out the promise to aid in developing new electronic structure methods that efficiently capture electron correlation. [ABSTRACT FROM AUTHOR]

We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree–Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree–Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment's one-electron Hamiltonian. As an application of the embedded fragment approach, we investigate the performance of full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice, we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be rather large. As a test case, we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore, the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies. [ABSTRACT FROM AUTHOR]

Developing global, high-dimensional potential energy surfaces (PESs) is a formidable task. Beside the challenges of PES fitting and fitting set generation, one also has to choose an electronic structure method capable of delivering accurate potential energy values for all geometries in the fitting set, even in regions far from equilibrium. Such regions are often plagued by Hartree–Fock (HF) convergence issues, and even if convergence is achieved, self-consistent field (SCF) procedures that are used to obtain HF solutions offer no guarantee that the solution found is the lowest-energy solution. We present a study of the reactant regions of CH3OH + OH·, C2H6 + F·, and CH3NH2 + Cl·, where the SCF procedure often converges to a higher-energy state or fails to converge, resulting in erratic post-HF energies and regions where no energy is obtained, both of which are major obstacles for PES development. We introduce a pragmatic method for automatically finding better HF solutions (dubbed ManyHF) and present evidence that it may extend the applicability of single-reference methods to some systems previously thought to require multireference methods. [ABSTRACT FROM AUTHOR]

The direct variational optimization of the two-electron reduced density matrix (2RDM) can provide a reference-independent description of the electronic structure of many-electron systems that naturally capture strong or nondynamic correlation effects. Such variational 2RDM approaches can often provide a highly accurate description of strong electron correlation, provided that the 2RDMs satisfy at least partial three-particle N-representability conditions (e.g., the T2 condition). However, recent benchmark calculations on hydrogen clusters [N. H. Stair and F. A. Evangelista, J. Chem. Phys. 153, 104108 (2020)] suggest that even the T2 condition leads to unacceptably inaccurate results in the case of two- and three-dimensional clusters. We demonstrate that these failures persist under the application of full three-particle N-representability conditions (3POS). A variety of correlation metrics are explored in order to identify regimes under which 3POS calculations become unreliable, and we find that the relative squared magnitudes of the cumulant three- and two-particle reduced density matrices correlate reasonably well with the energy error in these systems. However, calculations on other molecular systems reveal that this metric is not a universal indicator for the reliability of the reduced-density-matrix theory with 3POS conditions. [ABSTRACT FROM AUTHOR]

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations. [ABSTRACT FROM AUTHOR]

Electronically excited NdO is a possible product of the chemistry associated with the release of Nd into the ionosphere, and emission from these states may contribute to the observations following such experiments. To better characterize the energetics and spectroscopy of NdO, we report a combined experimental and theoretical study using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled NdO− anions (cryo-SEVI) supplemented by wave function-based quantum-chemical calculations. Using cryo-SEVI, we measure the electron affinity of NdO to be 1.0091(7) eV and resolve numerous transitions to low-lying electronic and vibrational states of NdO that are assigned with the aid of the electronic structure calculations. Additionally, temperature-dependent data suggest contributions from the (2)4.5 state of NdO− residing 2350 cm−1 above the ground anion state. Photodetachment to higher-lying excited states of NdO is also reported, which may help to clarify observations from prior release experiments. [ABSTRACT FROM AUTHOR]

Due to their small size and unique properties, single-molecule electronics have long seen research interest from experimentalists and theoreticians alike. From a theoretical standpoint, modeling these systems using electronic structure theory can be difficult due to the importance of electron correlation in the determination of molecular properties, and this electron correlation can be computationally expensive to consider, particularly multiconfigurational correlation energy. In this work, we develop a new approach for the study of single-molecule electronic systems, denoted NEGF-MCPDFT, which combines multiconfiguration pair-density functional theory (MCPDFT) with the non-equilibrium Green's function formalism (NEGF). The use of MCPDFT with NEGF allows for the efficient inclusion of both static and dynamic electron correlations in the description of the junction's electronic structure. Complete active space self-consistent field wave functions are used as references in the MCPDFT calculation, and as with any active space method, effort must be made to determine the proper orbital character to include in the active space. We perform conductance and transmission calculations on a series of alkanes (predominantly single-configurational character) and benzyne (multiconfigurational character), exploring the role that active space selection has on the computed results. For the alkane junctions explored (where dynamic electron correlation dominates), the MCPDFT-NEGF results agree well with the DFT-NEGF results. For the benzyne junction (which has a significant static correlation), we see clear differences in the MCPDFT-NEGF and DFT-NEGF results and evidence that NEGF-MCPDFT is capturing additional electron correlation effects beyond those provided by the Perdew–Burke–Ernzerhof functional. [ABSTRACT FROM AUTHOR]

A method recently proposed by Brown and Truhlar to correct large-scale configuration interaction calculations for incomplete dynamic correlation of electrons is reformulated using the formalism of the double many-body expansion method. Rather than making the assumption that large-basis-set multireference configuration interaction calculations including all single and double excitations from a complete-active space recover an approximately constant fraction of the external correlation, it is suggested that this fraction is approximately constant for the various n-body terms which arise in a cluster expansion of the total molecular energy. A new variant of this method in which the assumption of geometry-independent fraction of the external correlation is relaxed for the diatomics is also examined. Results are reported for the ground electronic states of the H3 and HO2 systems. [ABSTRACT FROM AUTHOR]

Excited state molecular dynamics simulations of the photoexcited phenyl azide have been performed. The semi‐classical surface hopping approximation has enabled an unconstrained analysis of the electronic and nuclear degrees of freedom which contribute to the molecular dissociation of phenyl azide into phenyl nitrene and molecular nitrogen. The significance of the second singlet excited state in leading the photodissociation has been established through electronic structure calculations, based on multi‐configurational schemes, and state population dynamics. The investigations on the structural dynamics have revealed the N−N bond separation to be accompanied by synchronous changes in the azide N−N−N bond angle. The 100 fs simulation results in a nitrene fragment that is electronically excited in the singlet manifold. [ABSTRACT FROM AUTHOR]

The two‐electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many‐electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave function, by minimizing this energy with respect to variations in the elements of the 2RDM, while also enforcing known N‐representability conditions. In this tutorial review, we provide an overview of the theoretical underpinnings of the v2RDM approach and the N‐representability constraints that are typically applied to the 2RDM. We also discuss the semidefinite programming (SDP) techniques used in v2RDM computations and provide enough Python code to develop a working v2RDM code that interfaces to the libSDP library of SDP solvers. This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure MethodsSoftware > Quantum Chemistry [ABSTRACT FROM AUTHOR]

Nonorthogonal approaches to electronic structure methods have recently received renewed attention, with the hope that new forms of nonorthogonal wavefunction Ansätze may circumvent the computational bottleneck of orthogonal-based methods. The basis in which nonorthogonal configuration interaction is performed defines the compactness of the wavefunction description and hence the efficiency of the method. Within a molecular orbital approach, nonorthogonal configuration interaction is defined by a "different orbitals for different configurations" picture, with different methods being defined by their choice of determinant basis functions. However, identification of a suitable determinant basis is complicated, in practice, by (i) exponential scaling of the determinant space from which a suitable basis must be extracted, (ii) possible linear dependencies in the determinant basis, and (iii) inconsistent behavior in the determinant basis, such as disappearing or coalescing solutions, as a result of external perturbations, such as geometry change. An approach that avoids the aforementioned issues is to allow for basis determinant optimization starting from an arbitrarily constructed initial determinant set. In this work, we derive the equations required for performing such an optimization, extending previous work by accounting for changes in the orthogonality level (defined as the dimension of the orbital overlap kernel between two determinants) as a result of orbital perturbations. The performance of the resulting wavefunction for studying avoided crossings and conical intersections where strong correlation plays an important role is examined. [ABSTRACT FROM AUTHOR]

Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder than their orthogonal counterparts. While several different approaches have been developed, these are predominantly derived from the first-quantized generalized Slater–Condon rules and usually require biorthogonal occupied orbitals to be computed for each matrix element. For coupling terms between nonorthogonal excited configurations, a second-quantized approach such as the nonorthogonal Wick's theorem is more desirable, but this fails when the two reference determinants have a zero many-body overlap. In this contribution, we derive an entirely generalized extension to the nonorthogonal Wick's theorem that is applicable to all pairs of determinants with nonorthogonal orbitals. Our approach creates a universal methodology for evaluating any nonorthogonal matrix element and allows Wick's theorem and the generalized Slater–Condon rules to be unified for the first time. Furthermore, we present a simple well-defined protocol for deriving arbitrary coupling terms between nonorthogonal excited configurations. In the case of overlap and one-body operators, this protocol recovers efficient formulas with reduced scaling, promising significant computational acceleration for methods that rely on such terms. [ABSTRACT FROM AUTHOR]

The accurate description of biradical systems, and in particular the resolution of their singlet–triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schrödinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet–triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature. [ABSTRACT FROM AUTHOR]

We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2p and 3p1h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections. [ABSTRACT FROM AUTHOR]

With this work, we present a protocol for the parameterization of a Linear Vibronic Coupling (LVC) Hamiltonian for quantum dynamics using highly accurate multiconfigurational electronic structure methods such as RASPT2/RASSCF, combined with a maximum-overlap diabatization technique. Our approach is fully portable and can be applied to many medium-size rigid molecules whose excited state dynamics requires a quantum description. We present our model and discuss the details of the electronic structure calculations needed for the parameterization, analyzing critical situations that could arise in the case of strongly interacting excited states. The protocol was applied to the simulation of the excited state dynamics of the pyrene molecule, starting from either the first or the second bright state (S2 or S5). The LVC model was benchmarked against state-of-the-art quantum mechanical calculations with optimizations and energy scans and turned out to be very accurate. The dynamics simulations, performed including all active normal coordinates with the multilayer multiconfigurational time-dependent Hartree method, show good agreement with the available experimental data, endorsing prediction of the excited state mechanism, especially for S5, whose ultrafast deactivation mechanism was not yet clearly understood. [ABSTRACT FROM AUTHOR]

The complete-active-space self-consistent field (CASSCF) method is a canonical electronic structure theory that holds a central place in conceptualizing and practicing first principles simulations. For application to realistic molecules, however, the CASSCF must be approximated to circumvent its exponentially scaling computational costs. Applying the many-body expansion—also known as the method of increments—to CASSCF (iCASSCF) has been shown to produce a polynomially scaling method that retains much of the accuracy of the parent theory and is capable of treating full valence active spaces. Due to an approximation made in the orbital gradient, the orbital parameters of the original iCASSCF formulation could not be variationally optimized, which limited the accuracy of its nuclear gradient. Herein, a variational iCASSCF is introduced and implemented, where all parameters are fully optimized during energy minimization. This method is able to recover electronic correlations from the full valence space in large systems, produce accurate gradients, and optimize stable geometries as well as transition states. Demonstrations on challenging test cases, such as the oxoMn(salen)Cl complex with 84 electrons in 84 orbitals and the automerization of cyclobutadiene, show that the fully variational iCASSCF is a powerful tool for describing challenging molecular chemistries. [ABSTRACT FROM AUTHOR]

The electronic structure parameter (WM) of the nuclear magnetic quadrupole moment (MQM) interaction in numerous open-shell metal monofluorides (viz., MgF, CaF, SrF, BaF, RaF, and PbF) is computed in the fully relativistic coupled-cluster framework. The electron-correlation effects are found to be very important for the precise calculation of WM in the studied molecular systems. The molecular MQM interaction parameter scales nearly as Z2 in the alkaline earth metal monofluorides, where Z is the nuclear charge of metal. Our study identifies 223RaF as a good candidate for the experimental search of the nuclear MQM, which can help unravel the physics beyond the standard model in the hadron sector of matter. [ABSTRACT FROM AUTHOR]

Geometries and electronic structures of germanium trimer clusters doped with titanium TiGe3−/0 were studied making use of the complete active space self-consistent field followed by second-order perturbation theory explicitly correlated coupled cluster singles and doubles method with perturbative triples corrections CCSD(T)-F12 and Tao-Perdew-Staroverov-Scuseria methods. Two electronic states (²A′ and ²A″) of the anion (pyramid shape) were determined to be nearly degenerate and energetically competing for the anionic ground state of TiGe3−. These two anionic states are believed to be concurrently populated in the experiment and induce six observed anion photoelectron bands. Total 14 electronic transitions starting from the ²A′ and ²A″ states were assigned to five out of six visible bands in the experimental anion photoelectron spectrum of TiGe3−. Each band was proven to be caused by multiple one-electron detachments from two populated anionic states. The last experimental band with the highest detachment energy is believed to be the result of various inner one-electron removals. [ABSTRACT FROM AUTHOR]

Charge transfer and multi-exciton states are among the most difficult to characterize using electronic structure theories. Previously, restricted active space-spin flip (RAS-SF) methods have been applied to describe multi-exciton states, but these have not yet been shown to be useful for charge-transfer states. Herein, a variant of RAS-SF is introduced to treat charge-transfer states and electronic couplings. This approach relies on partitioning of the full RAS-SF Hamiltonian into charge-transfer and non-charge-transfer blocks, allowing the different types of diabatic states to be resolved in a straightforward fashion. To demonstrate this approach in practice, model dimer systems, intramolecular charge-transfer dyads, and an intramolecular singlet fission system were examined. Being low-cost and relatively accurate, RAS-SF provides important insight into electron transfer pathways in conventional donor–acceptor systems, as well as characterizations of charge transfer mechanisms involving strongly correlated multi-exciton states. Studies of electron transfer from an intramolecular singlet fission chromophore to an anthraquinone acceptor demonstrate the unique capabilities of the proposed RAS-SF method. [ABSTRACT FROM AUTHOR]

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science. [ABSTRACT FROM AUTHOR]

The properties of molecular oxygen including its condensed phases continue to be of great relevance for the scientific community. The richness and complexity of its associated properties stem from the fact that it is a very stable diradical. Its open-shell nature leads to low-lying multiplets with total electronic spin S = 0, 1, 2 in the case of the dimer, (O2)2, and the accurate calculation of the intermolecular potentials represents a challenge to ab initio electronic structure methods. In this work, we present intermolecular potentials calculated at a very high level, thus competing with the most accurate restricted potentials obtained to date. This is accomplished by drawing on an analogy between the coupled and uncoupled representations of angular momentum and restricted vs unrestricted methodologies. The S = 2 state can be well represented by unrestricted calculations in which the spins of the unpaired electrons are aligned in parallel; however, for the state where they are aligned in antiparallel fashion, it would seem that the total spin is not well defined, i.e., the well-known spin contamination problem. We show that its energy corresponds to that of the S = 1 state and perform unrestricted coupled cluster calculations for these two states. Then, we obtain the S = 0 state through the Heisenberg Hamiltonian and show that this is very reliable in the well region of the potentials. We make extensive comparisons with the best restricted potentials [Bartolomei et al., Phys. Chem. Chem. Phys. 10(35), 5374–5380 (2008)] and with reliable experimental determinations, and a very good agreement is globally found. [ABSTRACT FROM AUTHOR]