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The compound-tunable embedding potential (CTEP) method is applied to study actinide substitutions in the niobate crystals YNbTiO$_6$ and CaNb$_2$O$_6$. Two one-center clusters centered on Ca and Y are built and 20 substitutions of Ca and Y with U, Np, Pu, Am, and Cm in four different oxidation states were made for each cluster. Geometry relaxation is performed for each resulting structure, and electronic properties are analyzed by evaluating the spin density distribution and X-ray emission spectra chemical shifts. Though the studied embedded clusters with actinides having the same oxidation state are found in general to yield similar local structure distortions, for Am and Cm in high "starting" oxidation states the electron transfer from the environment was found, resulting in decrease of their oxidation states, while for "starting" U$^{\rm III}$ state the electron transfer goes in the opposite direction, resulting in increase of its oxidation state to U$^{\rm IV}$. The U substitutions are additionally studied with the use of multi-center models, which can provide both more structural and electronic relaxation and also include charge-compensating vacancies. For "starting" U$^{\rm VI}$ case, the decrease in oxidation state similar to that of Am$^{\rm VI}$ and Cm$^{\rm VI}$ in one-center clusters is observed in our calculations but in a different way. Since the really synthesized YNbTiO$_6$ structures can not be considered as perfect (periodic) crystals because the Nb and Ti atoms are statistically distributed within them occupying the same Wyckoff positions, different Ti $\leftrightarrow$ Nb substitutions are studied and corresponding structural changes are estimated.

A method to simulate local properties and processes in crystals with impurities via constructing cluster models within the frame of the compound-tunable embedding potential (CTEP) and highly-accurate {\it ab initio} relativistic molecular-type electronic structure calculations is developed and applied to the Ce and Th-doped yttrium orthophosphate crystals, YPO$_4$, having xenotime structure. Two embedded cluster models are considered, the "minimal" one, YO$_8$@CTEP$_{\rm min}$, consisting of the central Y$^{3+}$ cation and its first coordination sphere of eight O$^{2-}$ anions (i.~e.\ with broken P--O bonds), and its extended counterpart, Y(PO$_4$)$_6$@CTEP$_{\rm ext}$, implying the full treatment of all atoms of the PO$_4^{3-}$ anions nearest to the central Y$^{3+}$ cation. CTEP$_{\rm min,ext}$ denote here the corresponding cluster environment described within the CTEP method. The relativistic Fock-space coupled cluster (FS RCC) theory is applied to the minimal cluster model to study electronic excitations localized on Ce$^{3+}$ and Th$^{3+}$ impurity ions. Calculated transition energies for the cerium-doped xenotime are in a good agreement with the available experimental data (mean absolute deviation of ca.0.3 eV for $4f{\to}5d$ type transitions). For the thorium-doped crystal the picture of electronic states is predicted to be quite complicated, the ground state is expected to be of the $6d$ character. The uncertainty for the excitation energies of thorium-doped xenotime is estimated to be within 0.35 eV. Radiative lifetimes of excited states are calculated at the FS RCC level for both doped crystals. The calculated lifetime of the lowest $5d$ state of Ce$^{3+}$ differs from the experimentally measured one by no more than twice.

The $^{229}$Th nucleus has a long-lived isomeric state $A^*$ at 8.338(24) eV [Kraemer et al, Nature, \textbf{617}, 706 (2023)]. This state is connected to the ground state by an M1 transition. For a hydrogenlike Th ion in the $1s$ state the hyperfine structure splitting is about 0.7 eV. This means that the hyperfine interaction can mix the nuclear ground state with the isomeric state with a mixing coefficient $\beta$ about 0.03. If the electron is suddenly removed from this system, the nucleus will be left in the mixed state. The probability to find the nucleus in the isomeric state $A^*$ is equal to $\beta^2\sim 10^{-3}$. For the $2s$ state the effect is roughly two orders of magnitude smaller. An atom with a hole in the $1s$ or $2s$ shell is similar to the hydrogenlike atom, only the hole has a short lifetime $\tau$. After the hole is filled, there is a non-zero probability to find the nucleus in the $A^*$ state. Estimates of this probability are presented along with a discussion of possible experiments on Th-doped xenotime-type orthophosphate crystals and other broad band gap materials., Comment: 6 pages, 1 figure. V.2: Sec. IV and references added

The current constraint on the electron electric dipole moment ($e$EDM), $|d_e|<4.1\times 10^{-30}$ ${e {\cdotp} {\rm cm}}$ (90\% confidence), was recently established using the trapped $^{180}$Hf$^{19}$F$^+$ molecular ions in the $J=1$ rotational level of its $ ^3\Delta_1$ electronic state [T. S. Roussy, L. Caldwell, T. Wright, et al., arxiv:2212.11841]. The extensive experimental study of the HfF$^+$ cation provides detailed spectroscopy of the $\Omega-$doublet levels in the external rotating electric and magnetic fields. We showed that previously developed theoretical approaches can fully reproduce the latest experimental data. Their justification from the first principles is very important for the examination of both modern molecular theory and possible systematic uncertainties in the interpretation of the experimental data obtained with high accuracy.

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

The method of moments is developed and employed to analyze the equilibrium correlation functions of the magnetization of ferromagnetic nanoparticles in the case of inertial magnetization dynamics. The method is based on the Taylor series expansion of the correlation functions and the estimation of the expansion coefficients. This method significantly reduces the complexity of analysis of equilibrium correlation functions. Analytical expressions are derived for the first three coefficients for the longitudinal and transverse correlation functions for the uniaxial magnetocrystalline anisotropy of ferromagnetic nanoparticles with a longitudinal magnetic field. The limiting cases of very strong and negligibly weak external longitudinal fields are considered. The Gordon sum rule for inertial magnetization dynamics is discussed. In addition, we show that finite analytic series can be used as a simple and satisfactory approximation for the numerical calculation of correlation functions at short times.

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework., Comment: Contribution to Snowmass 2021; updated with community edits and endorsements

The successive ionization potentials (IPs) and electron affinities (EAs) for superheavy elements with $111 \leq Z \leq 114$, namely, Rg, Cn, Nh, and Fl are reexamined using the relativistic Fock-space coupled-cluster method with nonperturbative single (S), double (D), and triple (T) cluster amplitudes (FS-CCSDT). For the most of considered quantities, the triple-amplitude contributions turn out to be important. The Breit and frequency-dependent Breit corrections are evaluated by means of the configuration-interaction method. The quantum-electrodynamics corrections to the IPs and EAs are taken into account within the model-QED-operator approach. The obtained results are within 0.10 eV uncertainty., Comment: 10 pages, 6 tables

Magnetization dynamics and spin waves in ferromagnets are investigated using the inertial Landau-Lifshitz-Gilbert equation. Taking inertial magnetization dynamics into account, dispersion relations describing the propagation of nutation spin waves in an arbitrary direction relative to the applied magnetic field are derived via Maxwell's equations. It is found that the inertia of magnetization causes the hybridization of electromagnetic waves and nutation spin waves in ferromagnets, hybrid nutation spin waves emerge, and the redshift of frequencies of precession spin waves is initiated, which transforms to precession-nutation spin waves. These effects depend sharply on the direction of wave propagation relative to the applied magnetic field. Moreover, the waves propagating parallel to the applied field are circularly polarized, while the waves propagating perpendicular to that field are elliptically polarized. The characteristics of these spin nutation waves are also analyzed.

Relativistic effective atomic configurations of superheavy elements Cn, Nh and Fl and their lighter homologues (Hg, Tl and Pb) in their simple compounds with fluorine and oxygen are determined using the analysis of local properties of molecular Kohn-Sham density matrices in the vicinity of heavy nuclei. The difference in populations of atomic spinors with the same orbital angular momentum and different total angular momenta is demonstrated to be essential for understanding the peculiarities of chemical bonding in superheavy element compounds. The results are fully compatible with those obtained by the relativistic iterative version of conventional projection analysis of global density matrices.

The electron affinity (EA) of superheavy element Og is calculated by the use of the relativistic Fock-space coupled cluster (FSCC) and configuration interaction methods. The FSCC cluster operator expansion included single, double, and triple excitations treated in a non-perturbative manner. The Gaunt and retardation electron-electron interactions are taken into account. Both methods yield the results that are in agreement with each other. The quantum electrodynamics correction to EA is evaluated using the model Lamb-shift operator approach. The electron affinity of Og is obtained to be 0.076(4) eV., Comment: 11 pages, 5 tables, 3 figures

The existence of the fundamental CP-violating interactions inside the nucleus leads to the existence of the nuclear Schiff moment. The Schiff moment potential corresponds to the electric field localized inside the nucleus and directed along its spin. This field can interact with electrons of an atom and induce the permanent electric dipole moment (EDM) of the whole system. The Schiff moment and corresponding electric field are enhanced in the nuclei with the octupole deformation leading to the enhanced atomic EDM. There is also a few-order enhancement of the T,P-violating effects in molecules due to the existence of energetically close levels of opposite parity. We study the Schiff moment enhancement in the class of diatomic molecules with octupole-deformed lanthanide and actinide nuclei: $^{227}$AcF, $^{227}$AcN, $^{227}$AcO$^+$, $^{229}$ThO, $^{153}$EuO$^+$ and $^{153}$EuN. Projecting the existing experimental achievements to measure EDM in diamagnetic molecules with spherical nucleus ($^{205}$TlF) to the considered systems one can expect a very high sensitivity to the quantum chromodynamics parameter ${\bar \theta}$ and other hadronic CP-violation parameters surpassing the current best limits by several orders of magnitude. It can have a dramatic impact on the modern understanding of the nature of CP-violating fundamental interactions.

Compound-tunable embedding potential (CTEP) method developed in previous works to describe electronic structure of fragments in materials is applied to crystals containing periodically arranged lanthanide atoms, which can have open $4f$ shell. We consider YbF$_2$ and YbF$_3$ as examples such that $4f$ shell is excluded from both the crystal and cluster stages of generating the CTEP. Instead, 10 and 11 valence-electron pseudopotentials for Yb, correspondingly, are applied and the latter treats the $4f$-hole implicitly. At the next stage of the two-component embedded cluster studies of the YbF$_{2,3}$ crystals we apply the 42 valence-electron relativistic pseudopotential for Yb and, thus, $4f$ shell is treated explicitly. A remarkable agreement of the electronic density and interatomic distances within the fragment with those of the original periodic crystal calculation is attained., Comment: 5 pages, 2 figures

Relativistic study of xenotime, YPO$_4$, containing atoms thorium and uranium as point defects is performed in the framework of cluster model with using the compound-tunable embedding potential (CTEP) method proposed by us recently. The Y-(PO$_4$)$_6$-Y'$_{22}$-O'$_{104}$ cluster for xenotime is considered, in which central part, [Y-(PO$_4$)$_6$]$^{-15}$, is the main cluster, whereas outermost 22 atoms of yttrium and 104 atoms of oxygen are treated as its environment and compose electron-free CTEP with the total charge of $+15$. The P and O atoms of the orthophosphate groups nearest to the central Y atom are treated at all-electron level. The central Y, its substitutes, Th and U, together with environmental Y atoms are described within different versions of the generalized relativistic pseudopotential method. Correctness of our cluster and CTEP models, constructed in the paper, is justified by comparing the Y-O and P-O bond lengths with corresponding periodic structure values of the \ypo4 crystal, both experimental and theoretical. Using this cluster model, chemical properties of solitary point defects, X = U, Th, in xenotime are analyzed. It has been shown that the oxidation state ${+3}$ is energetically more profitable than ${+4}$ not only for thorium but for uranium as well ($\Delta E \approx 5$ eV) despite the notably higher ionic radius of U$^{+3}$ compared to Y$^{+3}$, whereas ionic radii of U$^{+4}$ and Y$^{+3}$ are close. This leads to notable local deformation of crystal geometry around the U$^{+3}$ impurity in xenotime and contradicts to widespread opinion about favorite oxidation state of uranium in such kind of minerals., Comment: 8 pages, 4 figures, 3 tables. Advanced version of this paper is available at https://doi.org/10.1039/D0CP02277B

The absolute requirement to increase the amount of energy generation from renewable sources e.g. predominantly asynchronously connected wind turbines and photovoltaic installations, may in practice during transient events (where frequency changes are examined) excite oscillatory response of the power output of large grid connected synchronous-generators. The response of such generators must be controlled either by varying the applied torque of a turbine or by altering the electromagnetic torque in the airgap. Choosing the latter, the adequacy of a voltage regulator, particularly that of the embedded Power System Stabilizer (PSS) circuit, is investigated using the IEEE PSS1A model for the automatic voltage regulator of a synchronous generator driven by a gas turbine. The response is obtained via closed form analytic solutions for both small (linear) and large (nonlinear) scale transient events in the energy grid system. In tandem with the analytical study, the behavior simulated with a computer model from MatLab-SimPowerSystems is reviewed., Comment: 8 pages, 7 figures. Published in: IEEE Transactions on Power Systems (Early Access), 17 April 2019

Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation stations. Whereas the Kuramoto model is good for describing high inertia grid systems, the cage one allows both high and low inertia grids to be modelled. This is illustrated by comparing both the synchronization time and relaxation towards synchronization of each model by treating their equations of motion in a common framework rooted in the dynamics of many coupled phase oscillators. A solution of these equations via matrix continued fractions is implemented rendering the characteristic relaxation times of a grid-generator system over a wide range of inertia and damping. Following an abrupt change in the dynamical system, the power output and both generator and grid frequencies all exhibit damped oscillations now depending on the (finite) grid inertia. In practical applications, it appears that for a small inertia system the cage model is preferable., Comment: 8 pages, 7 figures. Published in: IEEE Transactions on Power Systems (Early Access), 31 July 2019

The original perturbative Kramers' method (starting from the phase space coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion equation for Newtonian particles with separable and additive Hamiltonians is generalized to yield the energy-controlled diffusion equation and thus the very low damping (VLD) escape rate including spin-transfer torque for classical giant magnetic spins with two degrees of freedom. These have dynamics governed by the magnetic Langevin and Fokker-Planck equations and thus are generally based on non-separable and non-additive Hamiltonians. The derivation of the VLD escape rate directly from the (magnetic) Fokker-Planck equation for the surface distribution of magnetization orientations in the configuration space of the polar and azimuthal angles $(\vartheta, \varphi)$ is much simpler than those previously used., Comment: 16 pages, 1 figure. Published in: Physica A: Statistical Mechanics and its Applications. Journal reference: Physica A, volume 527, 121195. Date of Publication: 1 August 2019. Publisher: Elsevier

An unknown absorber near the cloud top level of Venus generates a broad absorption feature from the ultraviolet (UV) to visible, peaking around 360 nm, and therefore plays a critical role in the solar energy absorption. We present a quantitative study on the variability of the cloud albedo at 365 nm and its impact on Venus' solar heating rates based on an analysis of Venus Express and Akatsuki's UV images, and Hubble Space Telescope and MESSENGER's UV spectral data; in this analysis the calibration correction factor of the UV images of Venus Express (VMC) is updated relative to the Hubble and MESSENGER albedo measurements. Our results indicate that the 365-nm albedo varied by a factor of 2 from 2006 to 2017 over the entire planet, producing a 25-40% change in the low latitude solar heating rate according to our radiative transfer calculations. Thus, the cloud top level atmosphere should have experienced considerable solar heating variations over this period. Our global circulation model calculations show that this variable solar heating rate may explain the observed variations of zonal wind from 2006 to 2017. Overlaps in the timescale of the long-term UV albedo and the solar activity variations make it plausible that solar extreme UV intensity and cosmic-ray variations influenced the observed albedo trends. The albedo variations might also be linked with temporal variations of the upper cloud SO2 gas abundance, which affects the H2SO4-H2O aerosol formation., Comment: 22 pages, 16 figures, accepted

Compound-tunable embedding potential (CTEP) method is proposed. A fragment of some chemical compound, "main cluster" in the present paper, is limited by boundary anions such that the nearest environmental atoms are cations. The CTEP method is based on constructing the embedding potential as linear combination of short-range "electron-free" spherical "tunable" pseudopotentials for cations from nearest environment of the main cluster, whereas the long-range CTEP part consists of Coulomb potentials from optimized fractional point charges centered on both environmental cations and anions. A pilot application of the CTEP method to the fersmite crystal, CaNb$_2$O$_6$, is performed and a remarkable agreement of the electronic density and interatomic distances within the fragment with those of the original periodic crystal calculation is attained. Characteristics of "atoms-in-compounds" which are of great importance for compound of $f$- and $d$-elements (Nb in fersmite) are considered on examples of chemical shifts of $K_{{\alpha}_{1,2}}\ $ and $K_{{\beta}_{1,2}}\ $ lines of X-ray emission spectra in niobium. A very promising potential of this approach in studying variety of properties of point defects containing $f$- and heavy $d$-elements with relativistic effects, extended basis set and broken crystal symmetry considered is discussed.