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At least 1,621 records · Page 90

Exclusive meson photo- and electro-production, a window on the structure of hadronic matter

At high energy, exclusive meson photo- and electro-production give access to the structure of hadronic matter. At low momentum transfers, the exchange of a few Regge trajectories leads to a comprehensive account of the cross-sections. Among these trajectories, which are related to the mass spectrum of families of mesons, the Pomeron plays an interesting role as it is related to glue-ball excitations. At high momentum transfers, the exchange of these collective excitations is expected to reduce to the exchange of their simplest (quark or gluon) components. However, contributions from unitarity rescattering cuts are relevant even at high energies. In the JLab energy range, the asymptotic regime, where the players in the game are current quarks and massless gluons has not been reached yet. One has to rely on more effective degrees of freedom adapted to the scale of the probe. A consistent picture, the Partonic Non-Perturbative Regime, is emerging. The properties of its various components (dressed propagators, effective coupling constants, quark wave functions, shape of the Regge trajectories, etc) provide us with various links to hadron properties. I will review the status of the field, will put in perspective the current achievements at JLab, SLAC and Hermes, and will assess future developments that are made possible by continuous electron beams at higher energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron Scattering and Ab-initio Studies of Zero-Field Splittings

Zero-field splitting (ZFS) parameters of nondeuterated metalloporphyrins [Fe(TPP)X] (X = F, Br, I; H 2 TPP = tetraphenylporphyrin) are determined by inelastic neutron scattering (INS). The ZFS values are D = 4.49(9) cm –1 for tetragonal polycrystalline [Fe(TPP)F], and D = 8.8(2) cm –1 , E = 0.1(2) cm –1 and D = 13.4(6) cm –1 , E = 0.3(6) cm –1 for monoclinic polycrystalline [Fe(TPP)Br] and [Fe(TPP)I], respectively. Along with our recent report of the ZFS value of D = 6.33(8) cm –1 for tetragonal polycrystalline [Fe(TPP)Cl], these data provide a rare, complete determination of ZFS parameters in a metalloporphyrin halide series. The electronic structure of [Fe(TPP)X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring the origin of the large and positive zero-field splitting D of the 6 A 1 ground state. D was calculated from wave functions of the electronic multiplets spanned by the d 5 configuration of Fe(III) along with spin–orbit coupling accounted for by quasi degenerate perturbation theory. Results reproduce trends of D from inelastic neutron scattering data increasing in the order from F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the S = 3/2 excited states on ligand field theory was used to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab initio calculations on CrX 6 3- complexes and also with the spectrochemical series showing a decrease of the ligand field in the same directions. A correlation is found between the increase of D and decrease of the π- and σ-antibonding energies e λ X (λ = σ, π) in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular overlap parameters rationalizes the experimentally deduced trend. Furthermore, D parameters from CASSCF and NEVPT2 results have been calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative agreement between ab initio calculated and experimental D and spectroscopic transitions for high-spin Fe(III) complexes are proposed.

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Molecular and electronic structure of Re 2 Br 4 (PMe 3 ) 4

The dinuclear rhenium(II) complex Re 2 Br 4 (PMe 3 ) 4 was prepared from the reduction of [Re 2 Br 8 ] 2– with ( n -Bu 4 N)BH 4 in the presence of PMe 3 in propanol. The complex was characterized by single-crystal X-ray diffraction (SCXRD) and UV–visible spectroscopy. It crystallizes in the monoclinic C2/c space group and is isostructural with its molybdenum and technetium analogues. The Re–Re distance (2.2521(3) Å) is slightly longer than the one in Re 2 Cl 4 (PMe 3 ) 4 (2.247(1) Å). The molecular and electronic structure of Re 2 X 4 (PMe 3 ) 4 (X = Cl, Br) were studied by multiconfigurational quantum chemical methods. The computed ground-state geometry is in excellent agreement with the experimental structure determined by SCXRD. The calculated total bond order (2.75) is consistent with the presence of an electron-rich triple bond and is similar to the one found for Re 2 Cl 4 (PMe 3 ) 4 . The electronic absorption spectrum of Re 2 Br 4 (PMe 3 ) 4 was recorded in benzene and shows a series of low-intensity bands in the range 10 000–26 000 cm –1 . The absorption bands were assigned based on calculations of the excitation energies with the multireference wave functions followed by second-order perturbation theory using the CASSCF/CASPT2 method. As a result, calculations predict that the lowest energy band corresponds to the δ* → σ* transition, while the next higher energy bands were attributed to the δ* → π*, δ → σ*, and δ → π* transitions.

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High-Pressure Studies of Cesium Uranyl Chloride

Here, the pressure behavior of crystalline Cs 2 UO 2 Cl 4 has been explored using a diamond anvil cell. The uranyl fluorescence intensity decreases dramatically with increasing pressure. Using the O–U–O symmetric stretching frequency, an apparent linear decrease in bond length with increasing pressure was observed. A linear decrease in fluorescence intensity with increasing pressure was attributed to a large growth in the nonradiative relaxation, likely attributed to increased relaxation through phonon modes. Quantum theory of atoms in molecules calculations and ab initio wave function methods (CASSCF) support the U≡O bond in UO 2 2+ being highly sensitive to the bond distance, but negligibly affected by the U–Cl bond length.

anions↗

Molecular and Electronic Structure, and Hydrolytic Reactivity of a Samarium(II) Crown Ether Complex

The reaction of SmI 2 with dibenzo-30-crown-10 (DB30C10), followed by metathesis with [Bu 4 N][BPh 4 ], allows for the isolation of [Sm II (DB30C10)][BPh 4 ] 2 as bright-red crystals in good yield. Moreover, exposure of [Sm(DB30C10)] 2+ to solvents containing trace water results in the conversion to the dinuclear Sm III complex, Sm 2 (DB30C10)(OH) 2 I 4 . Structural analysis of both complexes shows substantial rearrangement of the crown ether from a folded, Pac-Man form with Sm II to a twisted conformation with Sm III . The optical properties of [Sm II (DB30C10)][BPh 4 ] 2 exhibit a strong temperature dependence and change from broad-band absorption features indicative of domination by 5d states to fine features characteristic of 4f → 4f transitions at low temperatures. Here, exploration of the electronic structure of these complexes via ab initio wave function calculations (SO-CASSCF) reflects that the ground state of Sm II in [Sm II (DB30C10)] 2+ is a 4f 6 state with low-lying 4f 5 5d 1 states, where the latter states have been lowered in energy by ~12 000 cm –1 with respect to the free ion. The decacoordination of the Sm II cation by the crown ether is responsible for this alteration in the energies of the excited state and demonstrates the ability to tune the electronic structure of Sm II .

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Teaching Nonradiative Transitions with MATLAB and Python

Nonradiative transitions are changes in energy states of atoms, ions, or molecules that do not involve the emission or absorption of photons. Despite their importance in understanding luminescent properties and photochemical reaction mechanisms, nonradiative transitions are rarely given more than a qualitative overview in undergraduate and even graduate physical chemistry curricula. To supplement the coverage of nonradiative transition topics, we provide here a set of active learning exercises to help students develop an intuitive understanding of the factors that determine the rate of nonradiative transitions. Here, we start by outlining the theoretical background through the formulations of the Franck–Condon factor and its relation to the rate of nonradiative transition. We then introduce three teaching modules, with associated MATLAB and Python codes, to explore how (1) the excited state nuclear displacement, (2) the electronic energy gap between excited and ground state and (3) the excited/ground state vibrational mode frequencies affect the magnitude of the Franck–Condon factor and thereby the rate of nonradiative transitions. The wave function overlap plots that accompany all teaching modules provide direct visualization of the effect of input parameters on the magnitude of Franck–Condon overlap integral.

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Spin–Orbit Matrix Elements for a Combined Spin-Flip and IP/EA approach

We introduce a practical approach for computing the Breit–Pauli spin–orbit matrix elements of multiconfigurational systems with both spin and spatial degeneracies based on our recently developed RAS-nSF-IP/EA method (Houck, S. E.; et al. J. Chem. Theory Comput. 2019, 15, 2278). The spin–orbit matrix elements over all the multiplet components are computed using a single one-particle reduced density matrix as a result of the Wigner–Eckart theorem. A mean field spin–orbit approximation was used to account for the two-electron contributions. Basis set dependence as well as the effect of including additional excitations is presented. The effect of correlating the core and semicore orbitals is also examined. Surprisingly accurate results are obtained for spin–orbit coupling constants, despite the fact that the efficient wave function approximations we research neglect the bulk of dynamical correlation.

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N 5 -Scaling Excited-State-Specific Perturbation Theory

In this paper, we show that by working in a basis similar to that of the natural transition orbitals and using a modified zeroth-order Hamiltonian, the cost of a recently introduced perturbative correction to excited-state mean field theory can be reduced from seventh to fifth order in the system size. The (occupied) 2 (virtual) 3 asymptotic scaling matches that of ground-state second-order Møller-Plesset theory but with a significantly higher prefactor because the bottleneck is iterative: it appears in the Krylov-subspace-based solution of the linear equation that yields the first-order wave function. Here, we discuss the details of the modified zeroth-order Hamiltonian we use to reduce the cost and the automatic code generation process we used to derive and verify the cost scaling of the different terms. Overall, we find that our modifications have little impact on the method's accuracy, which remains competitive with singles and doubles equation-of-motion coupled cluster.

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A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the high-throughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree–Fock exchange matrix. Here, we call this new scheme the “approximate pair coefficient” (APC) method and we show that it performs quite well for the test systems presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spin–Orbit Natural Transition Orbitals and Spin-Forbidden Transitions

Natural transition orbitals (NTOs) are in widespread use for visualizing and analyzing electronic transitions. Here, the present work introduces the analysis of formally spin-forbidden transitions with the help of complex-valued spin-orbit (SO) NTOs. The analysis specifically focuses on the components in such transitions that cause their intensity to be non-zero because of SO coupling. Transition properties such as transition dipole moments are partitioned into SO-NTO hole-particle pairs, such that contributions to the intensity from specific occupied and unoccupied orbitals are obtained. The method has been implemented within the restricted active space (RAS) self-consistent field wave function theory framework, with SO coupling treated by RAS state interaction. SO-NTOs have a broad range of potential applications, which is illustrated by the T 2 -S 1 state mixing in pyrazine, spin-forbidden vs. spin-allowed 4f–5d transitions in the Tb 3+ ion, and the phosphorescence of tris(2-phenylpyridine) iridium [Ir(ppy) 3 ].

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An Orbital Basis Set for Double Photoionization of Atoms and Molecules

The ab initio theoretical treatment of one-photon double photoionization processes has been limited to atoms and diatomic molecules by the challenges posed by large grid-based representations of the double ionized continuum wave function. To provide a path for extensions to polyatomics, an energy-adapted orbital basis approach is demonstrated that reduces the dimensions of such representations and simultaneously allows larger time steps in time-dependent computational descriptions of double ionization. Additionally, an algorithm that exploits the diagonal nature of the two-electron integrals in the grid basis and dramatically accelerates the transformation between grid and orbital representations is presented. Excellent agreement between the present results and benchmark theoretical calculations is found for H – and Be atoms, as well as the hydrogen molecule, including for the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the molecular frame.

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Superposition of Fragment Excitations for Excited States of Large Clusters with Application to Helium Clusters

We develop a local excited-state method, based on the configuration interaction singles (CIS) wave function, for large atomic and molecular clusters. This method exploits the properties of absolutely localized molecular orbitals (ALMOs), which strictly limits the total number of excitations, and results in formal scaling with the third power of the system size for computing the full spectrum of ALMO-CIS excited states. Here, the derivation of the equations and design of the algorithm are discussed in detail, with particular emphasis on the computational scaling. Clusters containing ~500 atoms were used in evaluating the scaling, which agrees with the theoretical predictions, and the accuracy of the method is evaluated with respect to standard CIS. Finally, a pioneering application to the size dependence of the helium cluster spectrum is also presented for clusters of 25-231 atoms, the largest of which results in the computation of 2310 excited states per sampled cluster geometry.

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Enabling Multireference Calculations on Multimetallic Systems with Graphic Processing Units

Modeling multimetallic systems efficiently enables faster prediction of desirable chemical properties and the design of new materials. This work describes an initial implementation for performing multireference wave function method localized active-space self-consistent field (LASSCF) calculations through the use of multiple graphics processing units (GPUs) to accelerate time-to-solution. Density fitting is leveraged to reduce memory requirements, and we demonstrate the ability to fully utilize multi-GPU compute nodes. Performance improvements of 5–10x in total application runtime were observed in LASSCF calculations for multimetallic catalyst systems up to 1200 AOs and an active space of (22e,40o) using up to four NVIDIA A100 GPUs. Furthermore, written with performance portability in mind, a comparable performance is also observed in early runs on the Aurora exascale system using Intel Max Series GPUs.

Algorithms↗

A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo

We present a modification to variational Monte Carlo’s linear method optimization scheme that addresses a critical memory bottleneck while maintaining compatibility with both the traditional ground state variational principle and our recently-introduced variational principle for excited states. For wave function ansatzes with tens of thousands of variables, our modification reduces the required memory per parallel process from tens of gigabytes to hundreds of megabytes, making the methodology a much better fit for modern supercomputer architectures in which data communication and per-process memory consumption are primary concerns. We verify the efficacy of the new optimization scheme in small molecule tests involving both the Hilbert space Jastrow antisymmetric geminal power ansatz and real space multi-Slater Jastrow expansions. Satisfied with its performance, we have added the optimizer to the QMCPACK software package, with which we demonstrate on a hydrogen ring a prototype approach for making systematically convergent, non-perturbative predictions of Mott-insulators’ optical band gaps.

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Benchmarking the GW Approximation and Bethe–Salpeter Equation for Groups IB and IIB Atoms and Monoxides

Energies from the GW approximation and the Bethe–Salpeter equation (BSE) are benchmarked against the excitation energies of transition-metal (Cu, Zn, Ag, and Cd) single atoms and monoxide anions. We demonstrate that best estimates of GW quasiparticle energies at the complete basis set limit should be obtained via extrapolation or closure relations, while numerically converged GW -BSE eigenvalues can be obtained on a finite basis set. Calculations using real-space wave functions and pseudopotentials are shown to give best-estimate GW energies that agree (up to the extrapolation error) with calculations using all-electron Gaussian basis sets. We benchmark the effects of a vertex approximation (ΓLDA) and the mean-field starting point in GW and the BSE, performing computations using a real-space, transition-space basis and scalar-relativistic pseudopotentials. Here, while no variant of GW improves on perturbative G 0 W 0 at predicting ionization energies, G 0 W 0 Γ LDA -BSE computations give excellent agreement with experimental absorption spectra as long as off-diagonal self-energy terms are included. We also present G 0 W 0 quasiparticle energies for the CuO – , ZnO – , AgO – , and CdO – anions, in comparison to available anion photoelectron spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction

Here, we present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix–vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 10 16 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2–5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Simple Correction for Nonadditive Dispersion within Extended Symmetry-Adapted Perturbation Theory (XSAPT)

Extended symmetry-adapted perturbation theory (XSAPT), in conjunction with empirical “+aiD” potentials fit to ab initio dispersion data, is a low-scaling approach to compute intermolecular interaction energies in noncovalent clusters. One shortcoming is that the aiD atom–atom dispersion potentials are independent of the chemical environment of the atoms in question and therefore neglect nonadditive dispersion effects. These can be significant in large systems, so to account for them we test a simple correction to XSAPT(KS)+aiD, where “KS” indicates the use of Kohn–Sham orbitals. This correction, which can be evaluated at fourth-order cost using double-ζ basis sets, is based on comparing second-order SAPT dispersion with and without a self-consistent charge embedding for the monomer wave functions. The correction amounts to ~1.4 kcal/mol in (H 2 O) 6 but ~5.5 kcal/mol in (H 2 O) 20 . With the nonadditive dispersion correction, XSAPT(KS)+aiD affords errors of ~1 kcal/mol for isomers of F–(H 2 O) 10 and (H 2 O) 20 , where the benchmarks are complete-basis CCSD(T) energies, as well as for ion–water clusters X(H 2 O)n where n ≤ 6 and X = F – , Cl – , SO 4 2– , Li + , Na + , or K + . We also test the MP2 method and a variety of density-functional methods that have been specifically recommended for noncovalent interactions. Among the latter, only ωB97X-V and ωB97M-V can be recommended for ion–water clusters, as mean errors for other popular approaches (including ωB97X-D3 and several Minnesota functionals) exceed 1 kcal/mol. Lastly, we examine clathrate-hydrate host/guest complexes whose mixture of hydrogen bonding and dispersion make them challenging tests for noncovalent quantum chemistry. Although the B97-D2 functional performs best for clathrate hydrates and has been previously recommended in other studies of these inclusion complexes, its performance for other systems examined here is quite poor. We are unable to find a functional whose accuracy is ≲1 kcal/mol accuracy for both clathrate hydrates and ion–water clusters. However, the XSAPT(KS)+aiD method with the nonadditive dispersion correction can achieve this, with a mean error for the clathrate hydrates of 0.3 kcal/mol.

74 ATOMIC AND MOLECULAR PHYSICS↗

Ab Initio Computation of Rotationally-Averaged Pump–Probe X-ray and Electron Diffraction Signals

We develop a new algorithm for the computation of the rotationally averaged elastic molecular diffraction signal for the cases of perpendicular or parallel pump–probe geometries. The algorithm first collocates the charge density from an arbitrary ab initio wave function onto a Becke quadrature grid [A. Becke, J. Chem. Phys. 1988, 88, 2457], providing a high-fidelity multiresolution representation of the charge density. A double sum is then performed over the Becke grid points, and the interaction between points computed using the scattering kernels of Williamson and Zewail [J. C. Williamson and A. H. Zewail, J. Phys. Chem. 1994, 98, 2766]. These kernels analytically average over the molecular orientations with the cos 2 γ selection factor appropriate for one-photon dipole absorption in a perpendicular pump–probe geometry. We demonstrate that the method is converged with small grids containing <500 points/atom. We implement the algorithm on a GPU for increased efficiency and emonstrate the algorithm for molecules with up to a few dozen atoms. We explore the accuracy of the independent atom model (IAM) by comparison with our new and more accurate method. We also investigate the possibility of detecting signatures of electronic transitions in polyatomic pump–probe diffraction experiments.

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