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At least 739 records · Page 41

Combustion chemistry in the twenty-first century: Developing theory-informed chemical kinetics models

Over the past 20 to 25 years theoretical chemistry (particularly theoretical chemical kinetics) has played an increasingly important role in developing chemical kinetics models for combustion. Theoretical methods of obtaining rate parameters are now competitive in accuracy with experiment, particularly for small molecules. Moreover, theoretical methods can deal with conditions that experiments frequently cannot. In addition to increased accuracy, theory has rejuvenated methods and discovered phenomena that were completely unappreciated, or at least underappreciated, in the 20th century. Our primary interest here is in molecular-level issues, i.e. in calculating rate and transport parameters. However, dealing with kinetics models that involve thousands of reactions and hundreds of species is important for practical applications and is relatively new to the 21st century. Theory, in a general sense, and theoretical methods development have a role to play here too. We discuss in this review all these topics in some detail with an emphasis on issues and methods that have emerged in the last 20 years or so. Even so, our review is selective, rather than comprehensive, out of necessity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the effective theory of neutrino-electron and neutrino-quark interactions

We determine the four Fermi effective theory of neutrino interactions within the Standard Model including one-loop electroweak radiative corrections, in combination with the measured muon lifetime and precision electroweak data. Including two-loop matching and three-loop running corrections, we determine lepton coefficients accounting for all large logarithms through relative order $\cal{O}(\alpha \alpha_s)$ and quark coefficients accounting for all large logarithms through ${\cal{O}}(\alpha)$. We present four-fermion coefficients valid in $n_f=3$ and $n_f=4$ flavor quark theories, as well as in the extreme low-energy limit. We relate the coefficients in this limit to neutrino charge radii governing matter effects via forward neutrino scattering on charged particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Entanglement entropy of a color flux tube in (1+1)D Yang–Mills theory

In recent work Amorosso et al. (2024), we computed a novel flux tube entanglement entropy (FTE) of the color flux tube stretched between a heavy quark-antiquark pair on a Euclidean lattice in (2+1)D Yang–Mills theory. Our numerical results suggested that FTE can be partitioned into an internal color entanglement entropy and a vibrational entropy corresponding to the transverse excitations of a QCD string, with the latter described by a thin string model. Since the color flux tube does not have transverse excitations in (1+1)D Yang–Mills theory, we use this simpler framework to perform an exact analytical computation of the contribution of the internal color degrees of freedom to FTE. For the multipartite partitioning of the color flux tube, we find the remarkable result that FTE depends only on the dimension of the color group representation and the number of times the flux tube crosses the boundary between the traced and untraced spatial regions but not on the string length. Our proof is independent of whether the replica and region boundaries on the lattice are placed on vertices or in plaquette centers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Towards a theory of hadron resonances

In this review, we present the current state of the art of our understanding of the spectrum of excited strongly interacting particles and discuss methods that allow for a systematic and model-independent calculation of the hadron spectrum. These are lattice QCD and effective field theories. Synergies between both approaches can be exploited allowing for a deeper understanding of the hadron spectrum. Results based on effective field theories and hadron–hadron scattering in lattice QCD or combinations thereof are presented and discussed. We also show that the often used Breit–Wigner parametrization is at odds with chiral symmetry and should not be used in case of strongly coupled channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Theory of the tertiary instability and the Dimits shift within a scalar model

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge ( J. Plasma Phys. , vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Koopman wavefunctions and Clebsch variables in Vlasov–Maxwell kinetic theory

Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quasilinear theory for inhomogeneous plasma

Here, this paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the H -theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Theory of gradient drift instabilities in low-temperature, partially magnetised plasmas

A fluid dispersion theory in partially magnetised plasmas is analysed to examine the conditions under which large-wavelength modes develop in Penning-type configurations, that is, where an electric field is imposed perpendicular to a homogeneous magnetic field. The fluid dispersion relation assuming a slab geometry shows that two types of low-frequency, gradient drift instabilities occur in the direction of the E×B and diamagnetic drifts. One type of instability, observed when the equilibrium electric field and plasma density gradient are in the same direction, is similar to the classic modified Simon–Hoh instability. A second instability is found for conditions in which (i) the diamagnetic drift is in the direction opposite to the E×B drift and (ii) the magnitude of the diamagnetic drift is sufficiently larger than the electron thermal speed. The present fluid dispersion theory suggests that the rotating spokes driven by such fluid instabilities propagate in the same direction as the diamagnetic drift, which can be in the same direction as or opposite to the E×B drift, depending on the plasma conditions. This finding may account for the observation, in some plasma devices, of the rotation of large-scale structures in both the E×B and -E×B directions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗

Predicting and Understanding Non-Covalent Interactions Using Novel Forms of Symmetry-Adapted Perturbation Theory

Although sometimes derided as “weak” interactions, non-covalent forces play a critical role in ligand binding and crystal packing and in determining the conformational landscape of flexible molecules. Symmetry-adapted perturbation theory (SAPT) provides a framework for accurate ab initio calculation of intermolecular interactions and furnishes a natural decomposition of the interaction energy into physically meaningful components: semiclassical electrostatics (rigorously obtained from monomer charge densities), Pauli or steric repulsion, induction (including both polarization and charge transfer), and dispersion. This decomposition helps to foster deeper understanding of non-covalent interactions and can be used to construct transferable, physics-based force fields. Separability of the SAPT interaction energy also provides the flexibility to construct composite methods, a feature that we exploit to improve the description of dispersion interactions. Furthermore, these are challenging to describe accurately because they arise from nonlocal electron correlation effects that appear for the first time at second order in perturbation theory but are not quantitatively described at that level.

74 ATOMIC AND MOLECULAR PHYSICS↗

Measurement and Theory of Gas-Phase Ion Mobility Shifts Resulting from Isotopomer Mass Distribution Changes

The unanticipated discovery of recent ultra-high-resolution ion mobility spectrometry (IMS) measurements revealing that isotopomers-compounds that differ only in the isotopic substitution sites-can be separated has raised questions as to the physical basis for their separation. A study comparing IMS separations for two isotopomer sets in conjunction with theory and simulations accounting for ion rotational effects provides the first-ever prediction of rotation-mediated shifts. The simulations produce observable mobility shifts due to differences in gas–ion collision frequency and translational-to-rotational energy transfer. These differences can be attributed to distinct changes in the moment of inertia and center of mass between isotopomers. The simulations are in broad agreement with the observed experiments and consistent with relative mobility differences between isotopomers. These results provide a basis for refining IMS theory and a new foundation to obtain additional structural insights through IMS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Applicability of Allen–Heine–Cardona Theory on MO x Metal Oxides and ABO 3 Perovskites: Toward High-Temperature Optoelectronic Applications [plus supplemental information]

We report characterizing the temperature-dependent electronic structures of optoelectronic materials is vital for their application in high-temperature processes. Allen–Heine–Cardona (AHC) theory is an established theory to determine the impact of electron–phonon coupling on the temperature renormalization of the electronic structure. A question of fundamental interest is how applicable this approach can be in a broad range of materials. Herein, we establish the consensus on the temperature dependence of band gaps between AHC predictions and experimental measurements, in a versatile set of nine MO x metal oxides and six ABO 3 perovskites that are utilized as gas sensors. Both calculations and measurements point to the appreciable band gap downshifts within the temperature range relevant to typical high-temperature applications in all examined materials. The correlation between the band gaps and temperatures was quantified at zero- and finite-temperature limits using the analytical parameters of the O’Donnell model. We found fairly comparative agreements between AHC- and experiment-derived parameters, especially for the parameters (S and $\langle\hbar$ω$\rangle$) defining the temperature dependence behavior of band gaps at the finite-temperature regime. Our findings provide important implications for the first-principles modeling of the electronic structures and their temperature dependency, which should be the focus toward high-temperature optoelectronic applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theory-Guided Inelastic Neutron Scattering of Crystalline Alkaline Aluminate Salts Bearing Principal Motifs of Solution-State Species

Aluminate salts precipitated from caustic alkaline solutions exhibit a correlation between the anionic speciation and the identity of the alkali cation in the precipitate, with the aluminate ions occurring either in monomeric (Al(OH) 4 – ) or dimeric (Al 2 O(OH) 6 2– ) forms. The origin of this correlation is poorly understood as are the roles that oligomeric aluminate species play in determining the solution structure, prenucleation clusters, and precipitation pathways. Characterization of aluminate solution speciation with vibrational spectroscopy results in spectra that are difficult to interpret because the ions access a diverse and dynamic configurational space. To investigate the Al(OH) 4 – and Al 2 O(OH) 6 2– anions within a well-defined crystal lattice, inelastic neutron scattering (INS) and Raman spectroscopic data were collected and simulated by density functional theory for K 2 [Al 2 O(OH) 6 ], Rb 2 [Al 2 O(OH) 6 ], and Cs[Al(OH) 4 ]·2H 2 O. These structures capture archetypal solution aluminate species: the first two salts contain dimeric Al 2 O(OH) 6 2– anions, while the third contains the monomeric Al(OH) 4 – anion. Here, comparisons were made to the INS and Raman spectra of sodium aluminate solutions frozen in a glassy state. In contrast to solution systems, the crystal lattice of the salts results in well-defined vibrations and associated resolved bands in the INS spectra. The use of a theory-guided analysis of the INS of this solid alkaline aluminate series revealed that differences were related to the nature of the hydrogen-bonding network and showed that INS is a sensitive probe of the degree of completeness and strength of the bond network in hydrogen-bonded materials. Results suggest that the ionic size may explain cation-specific differences in crystallization pathways in alkaline aluminate salts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting Mössbauer Parameters of Nonheme Diiron Complexes with Density Functional Theory

Mössbauer spectroscopy provides significant insights into the electronic structure and environment of the metal centers. In this work, we investigate the electronic structures of a set of nonheme diiron complexes by evaluating two key parameters pertaining to Mössbauer spectroscopy, namely, the isomer shift (δ) and quadrupole splitting (|ΔE Q |), using different levels of density functional theory (DFT). The diiron systems investigated here span diverse oxidation states, bridging motifs, and spin coupling patterns, which present a challenging case for theoretical predictions. We demonstrate that the combination of B97-D3/def2-TZVP is an efficient approach in modeling both the δ and |ΔEQ| values with high accuracy for the representative nonheme diiron complexes. We also show that δ is accurately predicted irrespective of the choice of approximate density functional while the |ΔE Q | is sensitive to the level of theory employed. Further investigation shows that the present methodology assessed using synthetic nonheme diiron complexes could be extended to nonheme diiron enzyme active sites, featuring both ferromagnetic and antiferromagnetic coupling between the iron centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atom Equivalent Energies for the Rapid Estimation of the Heat of Formation of Explosive Molecules from Density Functional Tight Binding Theory

Atom equivalent energies have been derived from which the gas-phase heat of formation of explosive molecules can be estimated from fast, semiempirical density functional tight binding total energy calculations. The root-mean-square deviation and maximum deviation of the heats of formation from the experimental values for the set of 45 energetic molecules compiled by Byrd and Rice [ J. Phys. Chem. A, 2006, 110, 1005–1013] are 10.4 and 25.5 kcal/mol, respectively, using 4 atom equivalent energies and 7.4 and 15.0 kcal/mol, respectively, using 7 atom equivalent energies. These errors are around a factor of 2–3 larger than those obtained from density functional theory calculations but are smaller than those obtained from other semiempirical electronic structure methods. Heats of formation calculated with density functional tight binding theory using the 4 and 7 atom equivalent energies, the Byrd and Rice scheme, and the atom pair contribution method for a new set of 531 energetic molecules that contain only carbon, hydrogen, nitrogen, and oxygen are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Geometric Measure Theory Approach to Identify Complex Structural Features on Soft Matter Surfaces

The structural features that protrude above or below a soft matter interface are well-known to be related to interfacially mediated chemical reactivity and transport processes. It is a challenge to develop a robust algorithm for identifying these organized surface structures, as the morphology can be highly varied and they may exist on top of an interface containing significant interfacial roughness. A new algorithm that employs concepts from geometric measure theory, algebraic topology, and optimization is developed to identify candidate structures at a soft matter surface, and then, using a probabilistic approach, to rank their likelihood of being a complex structural feature. The algorithm is tested for a surfactant laden water/oil interface, where it is robust to identifying protrusions responsible for water transport against a set identified by visual inspection. To our knowledge, this is the first example of applying geometric measure theory to analyze the properties of a chemical/materials science system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unmasking Static Correlation Error in Hybrid Kohn–Sham Density Functional Theory

To uncover the way Hartree–Fock exchange brings static correlation error into hybrid Kohn–Sham density functional theory, we compare the potential energy curves of four diatomic molecules, namely, H 2 , F 2 , HF, and NaF, using both restricted and unrestricted Kohn–Sham theory. Here, we find that increasing the percentage of Hartree–Fock exchange significantly increases the static correlation error because Hartree–Fock exchange replaces the ability of local exchange in density functionals to account for the localization effects associated with static correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗