Orion MPCV Nonlinear Dynamic Correlation and Model Updating using Quasi-Static Modal Analysis
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Matt Griebel↗
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Correlated atomic dynamics in liquid seen in real space and time
In liquids, the timescales for structure, diffusion, and phonon are all similar, of the order of a pico-second. This not only makes characterization of liquid dynamics difficult but also renders it highly questionable to describe liquids in these terms. In particular, the current definition of the structure of liquids by the instantaneous structure may need to be expanded because the liquid structure is inherently dynamic. Here, we advocate describing the liquid structure through the distinct-part of the Van Hove function, which can be determined by inelastic neutron and x-ray scattering measurements as well as by simulation. It depicts the dynamic correlation between atoms in space and time, starting with the instantaneous correlation function at t = 0. The observed Van Hove functions show that the atomic dynamics is strongly correlated in some liquids, such as water. The effect of atomic correlation on various transport properties of fluid, including viscosity and diffusivity, is discussed.
74 ATOMIC AND MOLECULAR PHYSICS↗
Role of dynamic pairing correlations in fission dynamics
We study the role of dynamic pairing correlations in fission dynamics by considering intrinsic Hartree-Fock-Bogoliubov wave functions that are obtained by minimizing the particle number projected energy. For the restricted variational space, the set of self-consistent wave functions with different values of proton and neutron number particle fluctuations are considered. The particle number projected energy is used to define the potential energy surface for fission whereas collective inertias are computed within the traditional formulas for the intrinsic states. Here, the results show that the effect of the restricted variation after particle number projection in the potential energy surface is small while collective inertias substantially decrease. On the other hand, we show that this quenching is strongly mitigated when Coulomb antipairing is considered and therefore the final outcome of the complete calculation is close to the plain mean field result without Coulomb antipairing. In the light of these beyond-mean-field calculations, the validity of traditional fission calculations is discussed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Data for "Observation of Real-Space Dynamic Electron Correlation in Beryllium"
We studied the electron dynamic correlation using inelastic X-ray scattering measurements. The data files contain a 2D array of numeric data that is used to produce the figures in the paper, "Observation of Real-space Dynamic Electron Correlation in Beryllium."
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Evaluation of a Singular Value Decomposition Approach for Impact Dynamic Data Correlation
Impact dynamic tests are used in the automobile and aircraft industries to assess survivability of occupants during crash, to assert adequacy of the design, and to gain federal certification. Although there is no substitute for experimental tests, analytical models are often developed and used to study alternate test conditions, to conduct trade-off studies, and to improve designs. To validate results from analytical predictions, test and analysis results must be compared to determine the model adequacy. The mathematical approach evaluated in this paper decomposes observed time responses into dominant deformation shapes and their corresponding contribution to the measured response. To correlate results, orthogonality of test and analysis shapes is used as a criterion. Data from an impact test of a composite fuselage is used and compared to finite element predictions. In this example, the impact response was decomposed into multiple shapes but only two dominant shapes explained over 85% of the measured response
Horta, Lucas G.↗
237 Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes
A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. Furthermore, a rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The AFDD International Dynamic Stall Workshop on Correlation of Dynamic Stall Models with 3-D Dynamic Stall Data
A variety of empirical and computational fluid dynamics two-dimensional (2-D) dynamic stall models were compared to recently obtained three-dimensional (3-D) dynamic stall data in a workshop on modeling of 3-D dynamic stall of an unswept, rectangular wing, of aspect ratio 10. Dynamic stall test data both below and above the static stall angle-of-attack were supplied to the participants, along with a 'blind' case where only the test conditions were supplied in advance, with results being compared to experimental data at the workshop itself. Detailed graphical comparisons are presented in the report, which also includes discussion of the methods and the results. The primary conclusion of the workshop was that the 3-D effects of dynamic stall on the oscillating wing studied in the workshop can be reasonably reproduced by existing semi-empirical models once 2-D dynamic stall data have been obtained. The participants also emphasized the need for improved quantification of 2-D dynamic stall.
Tan, C. M.↗
Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B–F)
Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants ($R$ e , $ω$ e , $D$ e ), and potential energy curves, Δ$E$($R$), of the covalently bound AH and AF molecules, A = B–F. The changes in the spectroscopic constants (Δ$R$ e , Δ$ω$ e , Δ$D$ e ) caused by dynamical correlation are erratic and, at times, even surprising. These changes can be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ$E$ DEC ($R$). At large $R$, the magnitude of Δ$E$ DEC ($R$) increases nearly exponentially with decreasing $R$, but this increase slows as $R$ continues to decrease and, in many cases, even reverses at very short $R$. The changes in Δ$E$ DEC ($R$) in the region around $R$ e were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ$E$ DEC ($R$) for the most polar molecules. The variations in Δ$E$ DEC ($R$) for $R$ ≲ $R$ e are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the spin-coupled generalized valence bond wave function. In conclusion, the results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Dynamical electron correlation and the chemical bond. II. Recoupled pair bonds in the $a$ 4 Σ - states of CH and CF
We extended our studies of the effect of dynamical electron correlation on the covalent bonds in the AH and AF series (A = B–F) to the recoupled pair bonds in the excited $a$ 4 Σ - states of the CH and CF molecules. Dynamical correlation is energetically less important in the $a$ 4 Σ - states than in the corresponding X 2 Π states for both molecules, which is reflected in smaller changes in bond energies ($D$ e ). Changes in the equilibrium bond distance ($R$ e ) and vibrational frequency ($ω$ e ), on the other hand, are influenced by the changes in the slope and curvature of the dynamical electron correlation energy as a function of the internuclear distance $R$, $E$ DEC ($R$). In the CH($a$ 4 Σ - ) state, these changes are much smaller than in the CH(X 2 Π) state, but in the CF($a$ 4 Σ - ) state, they are larger, reflecting a significant difference in the shapes of $E$ DEC ($R$) curves. At large $R$, the shape of $E$ DEC ($R$) curves for covalent and recoupled pair bonds is similar although different in magnitude. For the CH($a$ 4 Σ - ) state, $E$ DEC ($R$) has a minimum at $R$ = $R$ e + 0.72 Å as the orbitals associated with the formation of the recoupled pair bond switch places. $E$ DEC (R) for the CF($a$ 4 Σ - ) state decreases continuously throughout the bound region of the potential energy curve because the dynamical correlation energy associated with the electrons in the lone pair orbitals is increasing. In conclusion, these results support our earlier conclusion that we still have much to learn about the nature of dynamical electron correlation in molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
CONTIN XPCS : software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics
X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, called CONTIN XPCS , is an extension of traditional CONTIN analysis and accommodates the various dynamics encountered in equilibrium XPCS measurements.
36 MATERIALS SCIENCE↗
Dynamic electronic correlation effects in NbO 2 as compared to VO 2
In this study we present a comparative investigation of the electronic structures of NbO 2 and VO 2 obtained within a combination of density functional theory and cluster-dynamical mean-field theory calculations. We investigate the role of dynamic electronic correlations on the electronic structure of the metallic and insulating phases of NbO 2 and VO 2 , with a focus on the mechanism responsible for the gap opening in the insulating phases. For the rutile metallic phases of both oxides, we obtain that electronic correlations lead to a strong renormalization of the t 2g subbands, as well as the emergence of incoherent Hubbard subbands, signaling that electronic correlations are also important in the metallic phase of NbO 2 . Interestingly, we find that nonlocal dynamic correlations do play a role in the gap formation of the [body-centered-tetragonal (bct)] insulating phase of NbO 2 , by a similar physical mechanism as that recently proposed by us in the case of the monoclinic (M 1 ) dimerized phase of VO 2 . Finally, although the effect of nonlocal dynamic correlations in the gap opening of bct phase is less important than in the (M 1 and M 2 ) monoclinic phases of VO 2 , their presence indicates that the former is not a purely Peierls-type insulator, as it was recently proposed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
On the role of dynamic electron correlation in non-orthogonal configuration interaction with fragments
Two different approaches have been implemented to include the effect of dynamic electron correlation in the Non-Orthogonal Configuration Interaction for Fragments (NOCI-F) method. The first is based on shifting the diagonal matrix elements of the NOCI matrix, while the second incorporates the dynamic correlation explicitly in the fragment wave functions used to construct the many-electron basis functions of the NOCI. The two approaches are illustrated for the calculation of the electronic coupling relevant in singlet fission and the coupling of spin moments in organic radicals. Comparison of the calculated diabatic couplings, the NOCI energies and wave functions shows that dynamic electron correlation is not only efficiently but also effectively incorporated by the shifting approach and can largely affect the coupling between electronic states. Additionally, it brings the NOCI coupling of the spin moments in close agreement with benchmark calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Dynamic structural correlation via nonlinear programming techniques
A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.
Ting, T.↗
Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory
Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Correlation of dynamic dielectric measurements with viscosity in polymeric resin systems
Dynamic dielectric analysis has been used to study curing polymer systems and thermoplastics. Measurements have been made over a frequency range of six decades. This wide range of frequencies increases the amount of information which can be obtained. The data are analyzed in terms of the frequency dependence of the specific conductivity sigma and the relaxation time tau, parameters which are characteristic of the cure state of the material and independent of size of the sample. Dynamic dielectric measurements have been correlated with viscosity for the polysulfone thermoplastic UDEL-P1700 and with viscosity and ultrasonic measurements on the DGEBA-type epoxy Epon 828 cured with Agent U. The experimental results suggest that when ionic processes dominate the dielectric response, the intensive property sigma is a good monitor of the resin's viscosity. The results show that the dielectric relaxation time tau can be used to monitor the state of the system and the extent and rate of the reaction.
Kranbuehl, D.↗
Dynamical electron correlation and the chemical bond. III. Covalent bonds in the A 2 molecules (A = C–F)
The behavior of the dynamical electron correlation energy is remarkably complex at short internuclear distances: Δ E DEC (Δ R ) = E DEC (Δ R ) − E DEC ( R = ∞) with Δ R = R − R e .
Dunning, Thom H.↗
A linearized model of helicopter dynamics including correlation with flight test
A linearized model for rotorcraft dynamics has been developed through the use of symbolic automatic equation generation techniques. The dynamic model has been formulated in a unique way such that it can be used to analyze a variety of rotor/body coupling problems including a rotor mounted on a flexible shaft with a number of modes as well as free flight stability and control characteristics. Direct comparison of the time response to longitudinaol, lateral and directional control inputs at various trim conditions shows that the linear model yields good to very good correlation with flight test. In particular it is also shown that a dynamic inflow model is essential to obtain good time response correlation especially for the hover trim condition and also that at translational flight trim conditions the main rotor wake interaction with the tail rotor and fixed tail surfaces is a significant contributor to the response. A relatively simple model for the downwash and sidewash at tail surfaces based on flat vortex wake theory is shown to produce good agreement. Finaly, the influence of rotor flap and lag dynamics on automatic control systems feedback gain limitations is investigated with the model.
Curtiss, H. C.↗
Benchmarking an Embedded Adaptive Sampling Configuration Interaction Method for Surface Reactions: H 2 Desorption from and CH 4 Dissociation on Cu(111)
Embedded (emb-) correlated wavefunction (CW) theory enables accurate assessments of both ground- and excited-state reaction mechanisms involved in heterogeneous catalysis. Embedded multireference second-order perturbation theory (emb-MRPT2) based on reference wavefunctions generated via embedded complete active space self-consistent field (emb-CASSCF) theory is currently state-of-the-art. However, the factorial scaling of CASSCF limits the size of active space and the complexity of systems that can be studied. In this work, we assess the efficacy of an alternative CW method, adaptive sampling configuration interaction (ASCI)–which enables large active spaces to be used–for studying surface reactions. We couple ASCI with density functional embedding theory (DFET) and benchmark its performance for two reactions: H 2 desorption from and CH 4 dissociation on the Cu(111) surface. Unlike embedded complete active space second-order perturbation theory (emb-CASPT2) that accurately reproduces a measured H 2 desorption barrier, embedded ASCI, using a very large active space (though one that still comprises a small portion of the full set of orbitals) fails to do so. Adding an extra correlation term from embedded Møller–Plesset second-order perturbation theory (emb-MP2) improves the desorption barrier and endothermicity predictions. Thus, the inaccuracy of embedded ASCI comes from the missing dynamic correlation from the many other electrons and orbitals not included in the active space. For CH 4 dissociation, again embedded ASCI overestimates the dissociation barrier compared to emb-CASPT2 predictions. Adding dynamic correlation from emb-MP2 helps correct the barrier. However, this composite approach suffers from double counting of correlation within embedded ASCI followed by emb-MP2 calculations. We therefore conclude that the state-of-the-art emb-MRPT2 based on reference wavefunctions generated via emb-CASSCF remains the method of choice for studying surface reactions. emb-ASCI is useful when large active spaces beyond the limit of emb-CASSCF are essential, such as to study complex surface reactions with significant multiconfigurational character (static correlation) but weak dynamic correlation.
08 HYDROGEN↗