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GronOR: Scalable and Accelerated Nonorthogonal Configuration Interaction for Molecular Fragment Wave Functions

GronOR is a program package for nonorthogonal configuration interaction calculations. Electronic wave functions are constructed in terms of antisymmetrized products of multiconfiguration molecular fragment wave functions. The computational complexity of the nonorthogonal methodologies implemented in GronOR applied to large molecular assemblies requires a design that takes full advantage of massively parallel supercomputer architectures and accelerator technologies. This work describes the implementation strategy and resulting performance characteristics. In addition to parallelization and acceleration, the software development strategy includes aspects of fault resiliency and heterogeneous computing. The program was designed for large-scale supercomputers but also runs effectively on small clusters and workstations for small molecular systems. GronOR is available as open source to the scientific community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic Structure of the [Cu 3 (μ-O) 3 ] 2+ Cluster in Mordenite Zeolite and Its Effects on the Methane to Methanol Oxidation

Identifying Cu-exchanged zeolites able to activate C–H bonds and selectively convert methane to methanol is a challenge in the field of biomimetic heterogeneous catalysis. Recent experiments point to the importance of trinuclear [Cu 3 (μ-O) 3 ] 2+ complexes inside the micropores of mordenite (MOR) zeolite for selective oxo-functionalization of methane. The electronic structures of these species, namely, the oxidation state of Cu ions and the reactive character of the oxygen centers, are not yet fully understood. In this study, we performed a detailed analysis of the electronic structure of the [Cu 3 (μ-O) 3 ] 2+ site using multiconfigurational wave-function-based methods and density functional theory. The calculations reveal that all Cu sites in the cluster are predominantly present in the Cu(II) formal oxidation state with a minor contribution from Cu(III), whereas two out of three oxygen anions possess a radical character. These electronic properties, along with the high accessibility of the out-of-plane oxygen center, make this oxygen the preferred site for the homolytic C–H activation of methane by [Cu 3 (μ-O) 3 ] 2+ . These new insights aid in the construction of a theoretical framework for the design of novel catalysts for oxyfunctionalization of natural gas and suggest further spectroscopic examination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The overlapping fragment approach for non-orthogonal configuration interaction with fragments

The non-orthogonal configuration interaction with fragments (NOCI-F) approach is extended opening the possibility to study intramolecular processes and materials with covalent or ionic lattices. So far, NOCI-F has been applied to study intermolecular energy and electron transfer employing ensembles of fragments that do not have atoms or bonds in common. The here presented approach divides the target system into two overlapping fragments that share one or more atoms and/or one or more bonds. After the construction of a collection of (multiconfigurational) fragment wave functions in a state specific optimization procedure, the fragment wave functions are combined to form many-electron basis functions for the non-orthogonal configuration interaction of the whole system. The orbitals in the overlapping fragment are defined by a corresponding orbital transformation of the fragment orbitals through a singular value decomposition. The overlapping fragments approach is first illustrated for a model system and then used to highlight some possible applications of NOCI with overlapping fragments. In conclusion, the results of excited state diffusion in transition metal oxide, intramolecular singlet fission and magnetic interactions in organic biradicals and ionic compounds are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Collision strengths for the intercombination lines of S III

The collision strengths of intercombination lines of S III ions observed in the Io torus are calculated on the basis of data gathered by Voyager instruments, the IUE and the Faint Object Telescope. The doubly ionized ions are excited by electron impacts and move from the 3P2P(3) ground state to excited 3s3P3(1)PO, (1)DO, 3p3d(1)PO, and 3p4s(1)PO states. Excitational cross sections are calculated with a two-state close-coupling approximation for the energy range up to 1,000,000 K, with target states being represented by multiconfiguration interaction wave functions. The close-coupling approximation regarded as an accurate technique because of the dominance of the Coulomb factor in the ionized state. The wave function calculations are estimated to yield values accurate to within 30 percent. Further work is need to quantify the magnitude of error introduced by resonance contributions to the collision strengths.

Ho, Y. K.↗

Ab initio study of the RbSr electronic structure: Potential energy curves, transition dipole moments, and permanent electric dipole moments

Excited states and the ground state of the diatomic molecule RbSr were calculated by post Hartree-Fock molecular orbital theory up to 22 000 cm{sup −1}. We applied a multireference configuration interaction calculation based on multiconfigurational self-consistent field wave functions. Both methods made use of effective core potentials and core polarization potentials. Potential energy curves, transition dipole moments, and permanent electric dipole moments were determined for RbSr and could be compared with other recent calculations. We found a good agreement with experimental spectra, which have been obtained recently by helium nanodroplet isolation spectroscopy. For the lowest two asymptotes (Rb (5s {sup 2}S) + Sr (5s4d {sup 3}P°) and Rb (5p {sup 2}P°) + Sr (5s{sup 2} {sup 1}S)), which exhibit a significant spin-orbit coupling, we included relativistic effects by two approaches, one applying the Breit-Pauli Hamiltonian to the multireference configuration interaction wave functions, the other combining a spin-orbit Hamiltonian and multireference configuration interaction potential energy curves. Using the results for the relativistic potential energy curves that correspond to the Rb (5s {sup 2}S) + Sr (5s4d {sup 3}P°) asymptote, we have simulated dispersed fluorescence spectra as they were recently measured in our lab. The comparison with experimental data allows to benchmark both methods and demonstrate that spin-orbit coupling has to be included for the lowest states of RbSr.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quadrupole moment of CO, N2, and NO/+/

Evaluation of quadrupole moments obtained for CO, N2, and NO(+) with multiconfiguration self-consistent-field wave functions chosen by the optimized valence configuration (OVC) approach of Wahl and Das (1972). The quadrupole moments thus obtained are compared with both experimental and Hartree-Fock values. The Hartree-Fock results are found to be not very accurate for N2, especially if vibrational averages over vibrational levels greater than 1 or 2 are to be taken. The agreement between the OVC quadrupole moment and the experimental values is found to be best for CO.

Billingsley, F. P., II↗

Systematic theoretical investigation of the zero-field splitting in Gd(III) complexes: Wave function and density functional approaches

The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H{sub 2}O){sup −}, Gd(III)DTPA(H{sub 2}O){sup 2−}, and Gd(III)(H{sub 2}O){sub 8}{sup 3+} in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spin–Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods

The spin–orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ n d] q ( q = 1–4 and 6–9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin–orbit couplings (SOC) using one-electron Breit–Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations—relativistic elimination of small components (RESC), third-order Douglas–Kroll–Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction—were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ n d] 5 , the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d]q configuration ( q = 2–4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d]q configuration ( q = 6–8), the energy lowering of all 4 F 7/2 , 5 D 1 , and 5 D 3 states due to the SOC effects is smaller than those of the other SM states. Furthermore this difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

74 ATOMIC AND MOLECULAR PHYSICS↗

Dipole moments and transition probabilities of the a 3Sigma(+)g - b 3Sigma(+)u system of molecular hydrogen

Multiconfiguration variational calculations of the electronic wave functions of the a 3Sigma(+)g and b 3Sigma(+)u states of molecular hydrogen are presented, and the electric dipole transition moment between them (of interest in connection with stellar atmospheres and the UV spectrum of the Jovian planets) is obtained. The dipole moment is used to calculate the probabilities of radiative transitions from the discrete vibrational levels of the a 3Sigma(+)g state to the vibrational continuum of the repulsive b 3Sigma(+)u state as functions of the wavelength of the emitted photons. The total transition probabilities and radiative lifetimes of the levels v prime = 0-20 are presented.

Guberman, S.↗

Seniority number description of potential energy surfaces: Symmetric dissociation of water, N{sub 2}, C{sub 2}, and Be{sub 2}

The present study further explores the concept of the seniority number (Ω) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of Ω in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of Ω in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G), N{sub 2} (6-31G), C{sub 2} (6-31G), and Be{sub 2} (cc-pVTZ). We find that the potential energy profile for H{sub 2}O dissociation can be reasonably well described using only the Ω = 0 sector of the CI wave function. For the Be{sub 2} case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either Ω-based (including configurations having up to Ω = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valence-reference function. Finally, in dissociation cases of N{sub 2} and C{sub 2}, we shall also consider novel hybrid wave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ab Initio Unimolecular Reaction Kinetics of CH 2 C(=)OCH 3 and CH 3 C(=O)OCH 2 Radicals

The unimolecular dissociation and isomerization kinetics of the methyl ester combustion intermediates methoxycarbonylmethyl (CH 2 C(=O)OCH 3 ) and acetyloxylmethyl (CH 3 C(=O)OCH 2 ) are theoretically investigated using high-level ab initio methods and the Rice–Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) theory. Potential energy surfaces (PESs) are obtained using coupled cluster singles and doubles with perturbative triples correction (CCSD(T)), multireference singles and doubles configuration interaction (MRSDCI) with the Davidson–Silver (DS) correction, and multireference averaged coupled pair functional (MRACPF2) theory. The transition states exhibit high T1 diagnostics in coupled cluster calculations, suggesting the need for a multireference correlated wave function treatment. MRSDCI+DS and MRACPF2 capture their multiconfigurational character well, yielding lower barrier heights than CCSD(T) for these reactions. Additionally, the rate coefficients are computed using the RRKM/ME theory over a 500–2500 K temperature range and at a pressure range of 0.01 atm to the high-pressure limit. The temperature- and pressure-dependent rate coefficients are given in modified Arrhenius expressions. The β-scission of CH 2 C(=O)OCH 3 is predicted to have a much higher barrier than the corresponding isomerization reaction and the β-scission of CH 3 C(=O)OCH 2 . Consequently, the rate coefficients for β-scission of CH 2 C(=O)OCH 3 are the smallest among the three reactions and the isomerization followed by decomposition to CH 3 C(=O) and HCHO is the dominant reaction pathway for CH 2 C(=O)OCH 3 . Furthermore, both radicals CH 2 C(=O)OCH 3 and CH 3 C(=O)OCH 2 are predicted to mainly decompose to CH 3 C(=O) + HCHO rather than to the bimolecular product CH 2 C(=O) + CH 3 O. A newly developed MA combustion mechanism, using our theoretical rate coefficients for the MA-related reactions, predicts combustion properties in good agreement with available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shakeup and shakeoff spectra in the electron capture decay of atomic 7 Be

The most stringent laboratory-based experimental limits on the existence of submegaelectronvolt sterile neutrinos are currently set by decay spectroscopy of radioactive 7 Be embedded into superconducting sensors. The systematic uncertainties are dominated by the modeling of the electron shakeup and shakeoff spectra that are not based on state-of-the-art atomic theory and do not include electron correlations or relativistic effects. We have used the multiconfiguration Dirac-Fock formalism to obtain correlated wave functions ab initio and compute all single and double shake processes in the electron capture decay of atomic 7 Be . The simulations can explain some but not all of the observed spectral features, likely because the wave functions are modified by the Ta sensor material that the 7 Be is embedded into. The new models also show that the 𝐿/𝐾 electron capture ratio of 7 Be in Ta has previously been slightly underestimated revising the previous value of 0.070(7) to a new value of 0.0756(20).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantum Monte Carlo calculation of the binding energy of the beryllium dimer

The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be{sub 2} is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be{sub 2} from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be{sub 2}, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm{sup −1}, only slightly below the 935 cm{sup −1} value derived from experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrogen atom abstraction from aldehydes - OH + H2CO and O + H2CO

The essential features of the potential energy surfaces governing hydrogen abstraction from formaldehyde by oxygen atom and hydroxyl radical have been characterized with ab inito multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) wave functions. The results are consistent with a very small activation energy for the OH + H2CO reaction, and an activation energy of a few kcal/mol for the O + H2CO reaction. In the transition state structure of both systems, the attacking oxygen atom is nearly collinear with the attacked CH bond.

Dupuis, M.↗

Potential surfaces for O atom-polymer reactions

Ab initio quantum chemistry methods are used to study the energetics of interactions of O atoms with organic compounds. Polyethylene (CH2)n has been chosen as the model system to study the interactions of O(3P) and O(1D) atoms with polymers. In particular, H abstraction is investigated and polyethylene is represented by a C3 (propane) oligomeric model. The gradient method, as implemented in the GRADSCF package of programs, is used to determine the geometries and energies of products and reactants. The saddle point, barrier geometry is determined by minimizing the squares of the gradients of the potential with respect to the internal coordinates. To correctly describe the change in bonding during the reaction at least a two configuration MCSCF (multiconfiguration self consistent field) or GVB (generalized valence bond) wave function has to be used. Basis sets include standard Pople and Dunning sets, however, increased with polarization functions and diffuse p functions on both the C and O atoms. The latter is important due to the O(-) character of the wave function at the saddle point and products. Normal modes and vibrational energy levels are given for the reactants, saddle points and products. Finally, quantitative energetics are obtained by implementing a small CAS (complete active space) approach followed by limited configuration interaction (CI) calculations. Comparisons are made with available experimental data.

Laskowski, B. C.↗

Computation of Auger Electron Spectra in Organic Molecules with Multiconfiguration Pair-Density Functional Theory

Efficient and accurate computation of molecular Auger electron spectra for larger systems is limited by the rapid increase in the number of doubly ionized final states as the system size grows. Here, in this work, we benchmark the application of multiconfiguration pair-density functional theory with a restricted active space (RAS) reference wave function for computing the carbon K-edge decay spectra of 20 organic molecules. Decay rates are computed within the one-center approximation. We evaluate the performance of different basis sets and on-top functionals and find that multiconfiguration pair-density functional theory achieves accuracy comparable to RAS followed by second-order perturbation theory, but at significantly lower computational cost.

Fouda, Adam E. A. [Argonne National Laboratory (AN↗

Thermally averaged collision strengths for extreme-ultraviolet line of Fe ix

Collision strengths and thermally averaged collision strengths for a large number of extreme-ultraviolet lines of Fe ix arising by electron impact have been reported. The thermally averaged collision strengths are calculated at electron temperatures in the range 10{sup 4}–10{sup 7} K for the 122,043 forbidden and allowed transitions between the 370 fine-structure levels. The atomic parameters for Fe ix play an important role in modeling of various astrophysical plasmas, including especially the solar corona. The B-spline Breit–Pauli R-matrix method has been used in the calculation of collision strengths. The target wave functions and transition probabilities have been determined by combining the multiconfiguration Hartree–Fock method with the B-spline box-based multichannel expansions. We have included 370 fine-structure levels of Fe ix in the energy region up to 3s{sup 2}3p{sup 5}5s states. The close-coupling expansion includes levels of the 3s{sup 2}3p{sup 6}, 3s{sup 2}3p{sup 5}3d,4l,5s, 3s3p{sup 6}3d,4s,4p, 3s{sup 2}3p{sup 4}3d{sup 2}, 3s3p{sup 5}3d{sup 2} configurations and some low-lying levels of the 3s{sup 2}3p{sup 3}3d{sup 3} configuration in our collision strengths and transition probabilities calculations. There is a good agreement with the previous R-matrix collision strength calculations by Storey et al. and Del Zanna et al. for transitions between the lowest 17 levels of the 3s{sup 2}3p{sup 6}, 3s{sup 2}3p{sup 5}3d, and 3s3p{sup 6}3d configurations, especially for electron temperatures log T(K) ≥ 5.0. The transitions between the first 17 levels are dominated by Rydberg series of resonances converging to the levels of the 3s{sup 2}3p{sup 4}3d{sup 2} configuration. The present results and the calculation of Del Zanna et al. show significant differences for many weaker forbidden and intercombination transitions with thermally averaged collision strengths smaller than 0.01.

79 ASTRONOMY AND ASTROPHYSICS↗

Single-Determinant Ground State in Ce 4+ Imidophosphorane Complexes

X-ray spectroscopy techniques are critical in the electronic structure analysis of high-valent lanthanides. The interpretation of multipeaked features at the lanthanide L 3 -edge has remained a challenging question, as it is observed across a range of material classes. A series of structurally related Ce 4+ complexes were prepared to probe the potential ligand field perturbation of the ground state within the series. The tuning of relative 4f and ligand orbital energies in homoleptic and heteroleptic tetravalent Ce imidophosphorane complexes is achieved through ligand derivatization and is clearly demonstrated by UV−vis spectroscopy and electrochemically measured redox potentials. However, Ce L 3 - edge high-energy resolution fluorescence-detected (HERFD) X-ray absorption near-edge structure (XANES) spectra present features at consistent numbers and energies across the range of complexes. Resonant inelastic X-ray scattering (RIXS) is employed to visualize the observed features in the HERFD-XANES spectra. Large complete active space configuration interaction singles and doubles (CASCISD) calculations demonstrate that the ground-state wave function of all complexes can be described employing a single determinant. As a result, the multielectron feature at the L 3 -edge observed in this study for the Ce 4+ imidophosphorane complexes is described as excited-state multiconfigurational behavior that is independent of ligand variation, in systems where the ground state is described using the simple single determinant wave function.

Lanthanides↗