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Modeling absorption spectra of molecules in solution

The presence of solvent tunes many properties of a molecule, such as its ground and excited state geometry, dipole moment, excitation energy, and absorption spectrum. Because the energy of the system will vary depending on the solvent configuration, explicit solute–solvent interactions are key to understanding solution-phase reactivity and spectroscopy, simulating accurate inhomogeneous broadening, and predicting absorption spectra. In this tutorial review, we give an overview of factors to consider when modeling excited states of molecules interacting with explicit solvent. We provide practical guidelines for sampling solute–solvent configurations, choosing a solvent model, performing the excited state electronic structure calculations, and computing spectral lineshapes. Furthermore, we introduce our recent results combining the vertical excitation energies computed from an ensemble of solute–solvent configurations with the vibronic spectra obtained from a small number of frozen solvent configurations, resulting in improved simulation of absorption spectra for molecules in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Preparation Conditions on the Structure and Magnetic Properties of Metal-Doped Magnesium Ferrites Synthesized From Laterite Leaching Solutions

In this paper, metal-doped magnesium ferrites (MgFe{sub 2}O{sub 4}) were synthesized from laterite leaching solutions using a coprecipitation-calcination method. The as-synthesized samples were characterized by x-ray diffraction (XRD), Fourier transform infrared spectrometer (FTIR), and physical property measurement system (PPMS) to determine the structure and magnetic properties. The effects of preparation conditions including precipitant reagents and metal ion concentrations in the laterite leaching solutions on the as-prepared spinel ferrites were investigated systematically. It is indicated that Ni–Co–Mn-doped MgFe{sub 2}O{sub 4} and Mn–Al–Cr-doped MgFe{sub 2}O{sub 4} could be synthesized from laterite leaching solutions by using sodium hydroxide (NaOH) and ammonia solution (NH{sub 3}⋅H{sub 2}O) as precipitant reagent, respectively. By adjusting the metal ion concentrations in the laterite leaching solutions, Ni–Co–Mn-doped MgFe{sub 2}O{sub 4} with different substitution contents were obtained. With the Ni and Mn substitution content increasing, the lattice constant and average grain size decreased, while x-ray density increased correspondingly. Magnetic property tests indicated that all the as-prepared samples exhibited typical ferrimagnetic behavior at room temperature, and the saturation magnetization (Ms) depended on the Ni, Co, and Mn substitution content. Specifically, the Ms and Hc values of the as-prepared metal-doped MgFe{sub 2}O{sub 4} sample with optimum substitution content of 0.185 could reach 33.22 emu g{sup −1} and 53 Oe, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Solute Redistribution During Aging in a Laser-Based Powder Bed Fusion-Produced Fe-18Ni-9Co-5Mo-Ti Maraging Steel

Solute distribution during the laser-based powder bed fusion of metals process is highly complex because of solidification. This study builds on a previous investigation of how solute heterogeneities across different scales influence phase distribution and aging physical phenomena in a Fe-18Ni-9Co-5Mo-Ti maraging steel (Santana et al. in Addit Manuf 104494, 2024). Previous work using energy-dispersive X-ray spectroscopy revealed heterogeneous Ni and Mo enrichment at intercellular regions. Using X-ray diffraction, 8 ± 3% retained austenite was quantified in as-built samples. Additionally, electron backscatter diffraction analysis exposed the location of retained austenite along cell boundaries. In this work, scanning transmission electron microscopy results revealed the presence of non-enriched retained austenite in the as-built condition. With increased aging temperature, Ni and Mo enrichment in austenite increased, especially at the austenite/martensite boundary. Solute diffusion was simulated in DICTRA Thermo-Calc® software to assess solute redistribution between the matrix and second phases and to comprehend whether elemental diffusion processes are interconnected. Three different scenarios were considered: (1) solute diffusion in the matrix; (2) diffusion with enriched austenite in the intercellular region; (3) diffusion with non-enriched austenite in the intercellular region. Results showed that Ni partitioning controls austenite growth and that boundary regions exhibit higher element enrichment than the core.

42 ENGINEERING↗

Least-squares solutions of generalized inverse eigenvalue problem over Hermitian–Hamiltonian matrices with a submatrix constraint

In this paper, a gradient-based iterative algorithm is proposed for finding the least-squares solutions of the following constrained generalized inverse eigenvalue problem: given X∈C{sup n×m}, Λ=diag(λ{sub 1},λ{sub 2},…,λ{sub m})∈C{sup m×m}, find A{sup ∗},B{sup ∗}∈C{sup n×n}, such that ∥AX−BXΛ∥ is minimized, where A{sup ∗},B{sup ∗} are Hermitian–Hamiltonian except for a special submatrix. For any initial constrained matrices, a solution pair (A{sup ∗},B{sup ∗}) can be obtained in finite iteration steps by this iterative algorithm in the absence of roundoff errors. The least-norm solution can be obtained by choosing a special kind of initial matrix pencil. In addition, the unique optimal approximation solution to a given matrix pencil in the solution set of the above problem can also be obtained. A numerical example is given to show the efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

A Bi-Level Formulation And Solution Method For The Integration Of Process Design And Scheduling

Design and operation decisions of manufacturing plants can often be expressed within a hierarchical structure, where optimal decisions at lower operating level provide constraints for the decision raking at a higher decision level. In this work, we are addressing the case of a hierarchical design and scheduling optimization problem. The integration of design and scheduling decisions can play a big role in designing economically profitable plants and improving their operational performance. This problem can be expressed as a bi-level problem, where design related decisions occur at the upper level and operational scheduling decisions at the lower level. Since discrete decisions are involved in both optimization levels, the resulting formulation typically corresponds to bi-level mixed-integer programming problems (B-MIP). The solution of B-MIP problems is very challenging, and typically requires the use of global optimization techniques, with many algorithms not able to guarantee feasibility. To overcome the challenges in solving this class of problems we propose the use of a multi-parametric based algorithm for the solution of bi-level mixed-integer linear and quadratic programming problems, capable of providing the exact and global solution. The main idea of this approach is to treat the lower scheduling problem as a multi-parametric programming problem in which the design decisions are considered as parameters. Here, the resulting parametric solutions can then be substituted into the upper level design problem, which can be solved as a set of single-level deterministic programming problems. Through the developed formulation and algorithm we are able to supply the decision makers with the exact solution of the integrated design and scheduling problem.

42 ENGINEERING↗

Combining solution-, precipitation- and load-transfer strengthening in a cast Al-Ce-Mn- Sc -Zr alloy

Here, a cast Al-9Ce-0.75Mn-0.18Sc-0.12Zr (wt%) alloy is designed to combine three strengthening phases: (i) micron-scale Al 11 Ce 3 platelets formed during eutectic solidification, (ii) nano-scale L1 2 -Al 3 (Sc,Zr) precipitates formed during aging, and (iii) Mn in solid solution in the α-Al matrix. Microstructural analyses by SEM, TEM, and atom-probe tomography reveal that Mn remains in solid solution in the as-cast alloy, providing solution strengthening with no influence on the eutectic Al-Al 11 Ce 3 microstructure, which provides precipitation- and load-transfer strengthening. During long-term over-aging at 400 °C, Mn-rich precipitates grow at the Al-Al 11 Ce 3 interface, with no effect on the microhardness. However, after short aging at 350 °C, a high number density of fine L1 2 -Al 3 (Sc,Zr) nanoprecipitates form in the Al matrix (with a coarser size at the Al-Al 11 Ce 3 interface), providing precipitation strengthening. The synergistic combination of the three strengthening mechanisms (solution, precipitation, and load transfer) in our Al-Ce-Mn-Sc-Zr alloy results in higher microhardness after aging at 350 and 400 °C, and higher creep resistance at 300 °C, as compared to alloys with two strengthening mechanisms: an Al-10Ce-0.93Mn control alloy (without precipitation strengthening from Sc and Zr), Al-Ce-Sc-Zr (without solution strengthening from Mn), and Al-Mn-Zr-Er (without load-transfer strengthening from Ce). Furthermore, these dual-strengthened alloys are more creep resistant than alloys with a single strengthening mechanism (Al-Ce, Al-Mn, and Al-Sc-Zr), confirming that the three mechanisms can be combined in pairs or all together.

36 MATERIALS SCIENCE↗

Study of static wormhole solutions in F(T,T{sub G}) gravity

In this paper, we investigate static spherically symmetric wormhole solutions in the background of F(T,T{sub G}) gravity (T is the torsion scalar and T{sub G} represents teleparallel equivalent of the Gauss–Bonnet term). We study the wormhole solutions by assuming four different matter contents, a specific redshift function and a particular F(T,T{sub G}) model. The behavior of null/weak energy conditions for these fluids is analyzed graphically. It turns out that wormhole solutions can be obtained in the absence of exotic matter for some particular regions of spacetime. We also explore stability of wormhole solutions through equilibrium condition. It is concluded that there exist physically acceptable wormhole solutions for anisotropic, isotropic and traceless fluids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

New solutions of coupled nonlocal NLS and coupled nonlocal mKdV equations

In this study, we provide several novel solutions of the coupled Ablowitz–Musslimani (AM) version of the nonlocal nonlinear Schrödinger (NLS) equation and the coupled nonlocal modified Korteweg–de Vries (mKdV) equation. In each case we compare and contrast the corresponding solutions of the relevant coupled local equations. Further, we provide new solutions of the coupled local NLS and coupled local mKdV equations which are not the solutions of the corresponding nonlocal equations. We also show that the nonlocal coupled (as well as uncoupled) mKdV equations have hidden Galilean invariance and admit novel solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

CO 2 solubility in aqueous solutions containing Na + , Ca 2+ , Cl - , SO 4 2- and HCO 3 - : The effects of electrostricted water and ion hydration thermodynamics

Dissolution of CO 2 into deep subsurface brines for carbon sequestration is regarded as one of the few viable means of reducing the amount of CO 2 entering the atmosphere. Ions in solution partially control the amount of CO 2 that dissolves, but the mechanisms of the ion's influence are not clearly understood and thus CO 2 solubility is difficult to predict. Here in this study, CO 2 solubility was experimentally determined in water, NaCl, CaCl 2 , Na 2 SO 4 , and NaHCO 3 solutions and a mixed brine similar to the Bravo Dome natural CO 2 reservoir; ionic strengths ranged up to 3.4 molal, temperatures to 140 °C, and CO 2 pressures to 35.5 MPa. Increasing ionic strength decreased CO 2 solubility for all solutions when the salt type remained unchanged, but ionic strength was a poor predictor of CO 2 solubility in solutions with different salts. A new equation was developed to use ion hydration number to calculate the concentration of electrostricted water molecules in solution. Dissolved CO 2 was strongly correlated (R 2 = 0.96) to electrostricted water concentration. Strong correlations were also identified between CO 2 solubility and hydration enthalpy and hydration entropy. These linear correlation equations predicted CO 2 solubility within 1% of the Bravo Dome brine and within 10% of two mixed brines from literature (a 10 wt % NaCl + KCl + CaCl 2 brine and a natural Na + , Ca 2+ , Cl - type brine with minor amounts of Mg 2+ , K + , Sr 2+ and Br - ).

58 GEOSCIENCES↗

Application of spectroscopic evidence to diffuse layer model (DLM) parameter estimation for cation adsorption onto ferrihydrite in single- and bi-solute systems

The diffuse layer model (DLM) is one of the most frequently used surface complexation models (SCM) for predicting cation adsorption onto ferrihydrite. However, the DLM with its existing database sometimes fails to predict cation adsorption, especially in multi-solute systems. Notably, the failure is often attributed to inaccurate selection of the surface complexes and/or underestimation of the site density for DLM formulation. DLM simulations of batch adsorption data conducted with cadmium, copper, lead, and zinc on ferrihydrite in CO2 free systems demonstrates the ability of the DLM to fit single-solute data reasonably well but highlights its limitations with respect to predicting bi-solute data. Modifications to the DLM were made in two steps. First, spectroscopic evidence was used to guide cation complexation reactions at the ferrihydrite surface. Second, surface characteristics (reactive site density, specific surface area, and acidity constants) of ferrihydrite were updated according to recent literature. The results from this study suggest that when spectroscopic verification is employed and surface site density is increased, a simple two-site DLM can predict cation adsorption on ferrihydrite in single-solute systems for pH data above 3.5 and in most of the bi-solute systems tested.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modelling nanofiltration of electrolyte solutions

This review critically examines current models for nanofiltration (NF) of electrolyte solutions. We start from linear irreversible thermodynamics, we derive a basic equation set for ion transfer in terms of gradients of ion electrochemical potentials and transmembrane volume flux. These equations are extended to the case of significant differences of thermodynamic forces across the membrane (continuous version of irreversible thermodynamics) and solved in quadratures for single salts and trace ions added to single salts in the case of macroscopically-homogeneous membranes. These solutions reduce to (quasi)analytical expressions in the popular Spiegler-Kedem approximation (composition independent phenomenological coefficients), which we extend to the case of trace ions. This enables us to identify membrane properties (e.g. ion permeances, ion reflection coefficients, electrokinetic charge density) that control its performance in NF of multi-ion solutions. Further, we specify the phenomenological coefficients of irreversible thermodynamics in terms of ion partitioning, hindrance and diffusion coefficients for the model of straight cylindrical capillaries. The corresponding expressions enable assessment of the applicability of the popular nanopore model of NF. This model (based on the use of macroscopic approaches at nanoscale) leads to a number of trends that have never been observed experimentally. We also show that the use of the Born formula (frequently employed for the description of dielectric exclusion) hardly leads to meaningful values of solvent dielectric constant in membrane pores because this formula disregards the very solvent structure whose changes are supposed to bring about the reduction of dielectric permittivity in nanopores. We conclude that the effect should better be quantified in terms of ion excess solvation energies in the membrane phase. As an alternative to the nanopore description of NF, we review recent work on the development of an advanced engineering model for NF of multi ion solutions in terms of a solution-diffusionelectromigration mechanism. This model (taking into account spontaneously arising transmembrane electric fields) captures several trends observed experimentally, and the use of trace ions can provide model parameters (ion permeances in the membrane) from experiment. We also consider a recent model (ultrathin barrier layers with deviations from local electroneutrality) that may reproduce observed feed-salt concentration dependences of membrane performance in terms of concentration independent properties like excess ion solvation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Understanding Gas Absorption in Multivalent Ionic Liquids via Solute-Solvent Interaction Analyses

Solute-solvent interactions are often evaluated to understand and explain gas solubilities. This information is regularly used to interpret gas solubility and separation within ionic liquids (ILs). Here, we use several different quantum chemical and previous molecular dynamics simulation results to show that strong solute-solvent interactions neither lead to high solubility nor to high selectivity, with respect to other solutes. Instead, the solute-solvent interaction strength with different isolated IL ions is affected by the electrostatic extremes. Also, the solute-solvent interaction with different IL molecules is strongly correlated to the molecular volumes or polarizabilities (within a series of same-anion based ILs).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparison of vapour pressure osmometry, freezing point osmometry and direct membrane osmometry for determining the osmotic pressure of concentrated solutions

Osmometry is the analytical method of measuring osmotic pressure ($π$) and related colligative properties. Accurately measuring $π$ is essential for applications that use osmosis, including drug delivery systems and water filtration methods such as forward osmosis. The three most common forms of directly or indirectly measuring $π$ are vapour pressure osmometry (VPO), freezing point osmometry (FPO), and direct membrane osmometry (DMO). In this report, the performance of VPO, FPO, and DMO are compared for various aqueous solutions, including small molecule and polymer solutes, and potentially more difficult samples such as concentrated, carbonated, or viscous solutions. Furthermore, potential problems with each of the three methods are examined. Good practices can avoid inaccuracies in DMO due to external concentration polarization and solute diffusion through the membrane. Similarly, it is important to be aware of and avoid weaknesses in VPO and FPO in order to obtain reliable results. Even with care, however, the three methods still give different values of $π$ for concentrated aqueous solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A step-wise ion hydration model of aqueous electrolyte solution: The 2:2, 2:1 and 1:2 punches

In prior work we showed that the current step-wise hydration framework shows promise for modeling the concentration-activity relationship in aqueous solutions of ions representing 1:1 electrolytes, alcohols, and sugars, and accurately predicting the partitioning of the water between the bound (hydrated) pool and an unbound (free) pool. Here, in the current work, we continue developing this framework by applying it to ions representing 2:2, 2:1 and 1:2 electrolyte in aqueous solutions. Properly treating ion hydration as an ideal solution along with employing mean spherical approximation of the long-range electrostatic interactions yields an accurate model for most electrolytes considered. This simple model of aqueous solutions is robust for electrolytes and organic solutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental estimation of the bisulfite isomer quotient as a function of temperature: Implications for sulfur isotope fractionations in aqueous sulfite solutions

Bisulfite (HSO 3 - ) and sulfite (SO 3 2- ) compounds play key roles in numerous geochemical and biochemical processes extending from the atmosphere to the subseafloor biosphere. Despite decades of spectroscopic investigations, the molecular composition of HSO 3 - in solution remains uncertain and, thus, the role of bisulfite in (bio)chemical and isotope fractionation processes is unclear. We report new experimental estimates for the bisulfite isomer quotient (Qi= [(HO)SO 2 - ]/[(HS)O3-]; [] = concentration) as a function of temperature from the interpretation of Raman spectra collected from aqueous NaHSO 3 solutions contained in fused silica capsules. In pure NaHSO 3 solutions (1Na + :1HSO 3 - , stoichiometric) over [NaHSO 3 ] = 0.2–0.4 m (moles/kg H 2 O), the following relationship is obtained: ln(Q i )=[formula omitted]-1.9642(±0.1081),where T = 278–358 K (5–85 °C) (based on 50 determinations; additional significant figures are provided to avoid rounding errors). This relationship suggests that the minor isomer, (HS)O 3 - , may comprise 23–38% (±3%) of the mole fraction of HSO 3 - over 5–85 °C, respectively, which is higher in relative abundance than has generally been understood previously. We additionally provide estimates for Q i in NaHSO 3 solutions containing a total ionic strength of µ = 1.0 m (0.2 m NaHSO 3 + 0.8 m NaCl) and different pH (3.3–4.5), but do not appear to resolve any significant differences in Q i as a function of these additional variables. These new values of Q i are employed to re-assess the bulk sulfur isotope fractionations among bisulfite and other S(IV) compounds as a function of temperature, which appear to be highly dependent on the amount of (HS)O 3 - present. Our new constraints on the bisulfite isomer quotient may allow for a detailed assessment of the molecular composition and isotope mass balance of S(IV) solutions containing HSO 3 - , and may be useful in the further investigation of the mechanisms and isotope fractionations associated with a number of processes that involve bisulfite compounds. Furthermore, these may include the intracellular enzymatic transformations of sulfite and bisulfite compounds that occur as part of dissimilatory sulfate reduction, which is a major and geologically important form of anaerobic respiration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Generalizable Class Solutions for Treatment Planning of Spinal Stereotactic Body Radiation Therapy

Purpose: Spinal stereotactic body radiation therapy (SBRT) continues to emerge as an effective therapeutic approach to spinal metastases; however, treatment planning and delivery remain resource intensive at many centers, which may hamper efficient implementation in clinical practice. We sought to develop a generalizable class solution approach for spinal SBRT treatment planning that would allow confidence that a given plan provides optimal target coverage, reduce integral dose, and maximize planning efficiency. Methods and Materials: We examined 91 patients treated with spinal SBRT at our institution. Treatment plans were categorized by lesion location, clinical target volume (CTV) configuration, and dose fractionation scheme, and then analyzed to determine the technically achievable dose gradient. A radial cord expansion was subtracted from the CTV to yield a planning CTV (pCTV) construct for plan evaluation. We reviewed the treatment plans with respect to target coverage, dose gradient, integral dose, conformality, and maximum cord dose to select the best plans and develop a set of class solutions. Results: The class solution technique generated plans that maintained target coverage and improved conformality (1.2-fold increase in the 95% van't Riet Conformation Number describing the conformality of a reference dose to the target) while reducing normal tissue integral dose (1.3-fold decrease in the volume receiving 4 Gy (V{sub 4Gy}) and machine output (19% monitor unit (MU) reduction). In trials of planning efficiency, the class solution technique reduced treatment planning time by 30% to 60% and MUs required by {approx}20%: an effect independent of prior planning experience. Conclusions: We have developed a set of class solutions for spinal SBRT that incorporate a pCTV metric for plan evaluation while yielding dosimetrically superior treatment plans with increased planning efficiency. Our technique thus allows for efficient, reproducible, and high-quality spinal SBRT treatment planning.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

The strong influence of Ti, Zr, Hf solutes and their oxidation on microstructure and performance of Nb 3 Sn superconductors

The strong influence of Ti, Zr, Hf solutes and their oxidation on microstructure and performance of Nb 3 Sn superconductors Over the last few years a new type of Nb 3 Sn superconducting composite based on the internal oxidation approach has emerged and has demonstrated performance significantly superior to conventional Nb 3 Sn. It requires a supply of O and the use of a Nb alloy – Nb-X, where X is a solute element that can be selectively oxidized to form oxide particles within the Nb 3 Sn. Such oxide particles not only refine Nb 3 Sn grain size, but also have the proper size to act as artificial pinning centers (APC) directly restraining fluxon motion, and thus dramatically improve superconducting properties. In this article we show that the size and volume fraction of the oxide particles determine both the levels of grain refinement and the shift in the peak field of the flux pinning force (F p -B) curve. Additionally, we explore the factors influencing these microstructure and properties, which we find include: selection of the solute element X, solute content, O content, and heat treatment. For the selection of X, we searched the periodic table for all promising candidates but focused down on the group-IVB elements (Ti, Zr, Hf) here as the drawability of Nb 3 Sn wires made from Nb-Ti, Nb-Zr, and Nb-Hf alloys has been demonstrated in the past few decades. We found that while internally oxidizing Nb-1.5at.%Ti led to negligible grain refinement and F p -B peak shift, Nb-Zr alloys led to much more dramatic results, and internally oxidizing Nb-Hf alloys led to the strongest grain refinement and F p -B peak shift. For Hf alloying in particular, we compared our internal oxidation method with another method for grain refinement, which uses Hf alloying itself without oxidation, and found that internal oxidation led to much stronger grain refinement and F p -B peak shift. We also found that higher solute content and lower reaction temperature led to stronger grain refinement and F p -B peak shift. We conclude with a discussion of the possible mechanisms for the influence of these factors.

43 PARTICLE ACCELERATORS↗

Manufactured solutions for the three-dimensional Euler equations with relevance to Inertial Confinement Fusion

We present a set of manufactured solutions for the three-dimensional (3D) Euler equations. The purpose of these solutions is to allow for code verification against true 3D flows with physical relevance, as opposed to 3D simulations of lower-dimensional problems or manufactured solutions that lack physical relevance. Of particular interest are solutions with relevance to Inertial Confinement Fusion (ICF) capsules. While ICF capsules are designed for spherical symmetry, they are hypothesized to become highly 3D at late time due to phenomena such as Rayleigh–Taylor instability, drive asymmetry, and vortex decay. ICF capsules also involve highly nonlinear coupling between the fluid dynamics and other physics, such as radiation transport and thermonuclear fusion. The manufactured solutions we present are specifically designed to test the terms and couplings in the Euler equations that are relevant to these phenomena. Example numerical results generated with a 3D Finite Element hydrodynamics code are presented, including mesh convergence studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗