An exactly solvable quantum-mechanical model of DNA bases is presented. The proposed model is based on the harmonic approximation of the potential energy of the canonical and tautomeric forms for the bases in question. The transition rate of single-proton transfer in the base pairs adenine-thymine and guanine-cytosine is determined within this model using the Fermi Golden Rule. The transition rates derived from the application of the 'bare' Fermi Golden Rule can be approximated by the Fano line curves. In turn, the application of the thermally averaged Fermi Golden Rule leads to an exponential increase in transition rates across the biologically relevant temperature range for the base pairs under consideration. The kinetic isotope effect for the base pairs at room temperature is also estimated. All calculations are consistently carried out in a phase-space representation using the Wigner distribution function.

Photoinduced electron transfer (PET) lies at the heart of energy conversion from light into chemical reactions. It governs a variety of biological processes including DNA damage and repair and biological photosynthesis. Quantifying PET rates and optimizing them is also crucial for selective photoredox catalysis. However, commonly used rate theories break down for PET operating in the strong coupling and nonequilibrium regimes, while excited-state dynamics simulations are computationally demanding and require complex analysis to extract PET times. Here, we employed surface-hopping nonadiabatic excited-state dynamics simulations and statistical rate theories to characterize ultrafast PET in a dimer of stacked adenine nucleobases. We show that the widely used classical Marcus Theory and Fermi's Golden Rule fail to describe ultrafast PET or even reproduce qualitative rate trends. Instead, we propose a chromophore-localized variant of nonadiabatic Rice-Rampsperger-Kassel-Marcus (NA-RRKM) theory, which yields PET timescales that are in excellent agreement with excited-state dynamics simulations.

Synthetic access to the Z-isomer of substituted alkenes is a challenging task due to the thermodynamically disfavored energy profile. Rather than direct synthesis, irradiation in the presence of a photosensitizer can lead to accumulation with a high ratio of Z-isomer. While classical photochemical models can provide a qualitative explanation of this behavior, quantitative insight into the kinetics of the process remain limited. In this study, we investigate the mechanistic aspects of E → Z photocatalyzed isomerization using kinetic arguments based on triplet energy transfer. Using Fermi's golden rule and four-state model, we demonstrated that the rate of catalytic transformation involving the E-alkene is faster, causing its depletion and conversely the accumulation of the Z-alkene. To accomplish this, we utilize the nonorthogonal wave function method, enabling simultaneous study of all pathways, emphasizing the importance of charge transfer (CT) states. The findings of this work provide quantitative validation of photochemical concepts based on electronic structure theory, clarifying how two structurally similar isomers can exhibit such different kinetics, leading to the accumulation of the Z-isomer under light irradiation in the presence of a photosensitizer.

With the rapid development of nanophotonics and cavity quantum electrodynamics, there has been growing interest in how confined electromagnetic fields modify fundamental molecular processes such as electron transfer. In this paper, we revisit the problem of nonadiabatic electron transfer (ET) in confined electromagnetic fields studied in Semenov and Nitzan [J. Chem. Phys. 150, 174122 (2019)] and present a unified rate theory based on Fermi's golden rule. By employing a polaron-transformed Hamiltonian, we derive analytic expressions for the ET rate correlation functions that are valid across all temperature regimes and all cavity mode time scales. In the high-temperature limit, our formalism recovers the Marcus and Marcus-Jortner results, while in the low-temperature limit, it reveals the emergence of the energy gap law. We further extend the theory to include cavity loss by using an effective Brownian oscillator spectral density, which enables closed-form expressions for the ET rate in lossy cavities. As applications, we demonstrate two key cavity-induced phenomena: (i) resonance effects, where the ET rate is strongly enhanced with certain cavity mode frequencies, and (ii) electron-transfer-induced photon emission, arising from the population of cavity photon Fock states during the ET process. These results establish a general framework for understanding how confined electromagnetic fields reshape charge transfer dynamics and suggest novel opportunities for controlling and probing ET reactions in nanophotonic environments.

Hybridization of a molecular exciton with a quantized photon creates a polariton. Despite extensive experimental investigations, the apparent lifetime of the exciton-polariton is not well-understood. We examined the steady-state population dynamics for a Holstein-Tavis-Cumming Hamiltonian to illuminate the long-term polaritonic dynamics and lifetime of the exciton-polariton in an optical cavity. For a realistic description of polariton relaxation, cavity loss and various exciton decay channels are included in the model. We found that in the presence of weak but finite exciton loss, the apparent lifetime of the lower polariton coincides with the out-of-cavity exciton lifetime and is independent of cavity-matter detuning. This is a simple explanation for the experimentally observed lifetimes for exciton polaritons and theoretically justifies the dark state reservoir hypothesis. Furthermore, if the upper polariton is initially populated, the system reaches the steady state very quickly, leading to single-exponential polariton relaxation. Starting from the lower polariton leads to a longer pre-steady-state time period, leading to double-exponential relaxation. Finally, we considered the effect of site orientational disorders and the exciton frequency disorderers. Under the collective limit, the effects of this disorder can be included in Fermi's golden rule population dynamics without explicit sampling. For the exciton energy disorders, numerical calculations are needed. Our theoretical framework is applicable to interpret exciton-polariton experiments, especially related to the measured apparent lifetime of polaritons.

Azulene's nonradiative decay dynamics and kinetics from its singlet excited-states were studied using mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) combined with trajectory surface-hopping nonadiabatic molecular dynamics (NAMD) and Fermi's golden rule (FGR) rate theory. The NAMD dynamics reproduce experimental observations that the S1 → S0 decay is accelerated and exhibits a crossover from mono- to biexponential kinetics with increasing excess vibrational energy. Minimum-energy-path analyses reveal a continuous S1/S0 conical-intersection seam slightly above the S1 minimum, providing readily accessible funnels. Time-resolved normal-mode projections reveal selective energy funneling into C-C stretching modes at 1272, 1528, and 1692 cm-1. Constructive combinations of the latter two modes appear to promote rapid access to the conical-intersection seam, whereas their beating at ∼ 160 fs imposes a natural limit on the decrease of the decay time upon a further increase of excess energies, suggesting that their interference delays the decay. The FGR rate calculation data for the S1 → S0 transition reaffirm that the nonradiative decay proceeds mainly near or through the conical intersection, rather than via simple nonadiabatic derivative coupling around the minimum of S1. On the other hand, the FGR rates indicate that S2 decays predominantly to S0, as the S2-S1 vibronic coupling is exceptionally weak, which serves as a primary cause for azulene's characteristic anti-Kasha emission.

The rational design of heavy-metal-free photosensitizers (PSs) is essential for advancing fluorescence (FL) imaging and photodynamic therapy (PDT). In this work, we present a systematic quantum-chemical investigation of eight coumarin-based derivatives (C1–C8) to elucidate how molecular structure controls excited-state dynamics. Time-dependent density functional theory (TD-DFT), combined with Fermi's Golden Rule, was applied to compute FL emission, internal conversion (IC), and intersystem crossing (ISC) rate constants, enabling quantitative prediction of FL and triplet quantum yields. The results show that C1, C2 and C6 undergo reduced fluorescence due to partial population of the dark 1TICT state, but maintains both moderate fluorescence and appreciable triplet yield, supporting dual applications in imaging and PDT. The heavy-atom derivative C3 achieves nearly unit triplet quantum yield (ΦT ≈ 1.0), confirming the dominant role of sulfur-enhanced ISC and reactive oxygen species generation. In contrast, C4 and C8 favor fluorescence over ISC, while C5 and C7 exhibit the highest emission efficiency by suppressing both TICT state and ISC process, identifying them as optimal imaging probes. Importantly, Herzberg–Teller vibronic coupling was found to dominate ISC efficiency in heavy-atom-free systems but was negligible in heavy-atom-based analogues. In addition, the large two-photon absorption (TPA) cross sections of C1–C8 provide redshifted excitation windows, thereby overcoming the penetration limitations of one-photon absorption (OPA) and enhancing biomedical applicability. Collectively, these insights establish design principles for tailoring radiative and non-radiative pathways in coumarin scaffolds, enabling the targeted development of multifunctional organic PSs.

Traditional philosophy divides ethics into three major modes: utilitarianism (reward and punishment), deontology (the will of God), and virtue ethics (personal integrity). Daoists firmly support the latter, matching Martin Seligman’s understanding of key virtues and personality strengths. They also insist on ethics of difference and situation, noting that neither two people nor two cases are ever completely alike, thus necessitating adaptation and flexibility. Key virtues are accordingly tolerance and respect, coupled with a strong emphasis on the unique needs of the other person. Thus, the Golden Rule here is “do unto others as they would have us do unto them.” Another major dimension is the notion of freedom: from constraints, toward personal realization, and expressed in political liberty. Rulers should always listen and let go, never be controlling or tyrannical. The key personal relationship, moreover, is that of friendship, where like-minded people come together to join in peace and harmony, always accepting, always supporting, and without any major personal agendas.

The Nonequilibrium Fermi's Golden Rule (NE-FGR) provides a convenient theoretical framework for calculating the charge transfer (CT) rate between a photoexcited bright donor electronic state and a dark acceptor electronic state when the nuclear degrees of freedom start out in a nonequilibrium initial state. In this paper, we show that NE-FGR rates can be significantly modified by placing the molecular system inside an electromagnetic microcavity, even when the coupling with the cavity modes is weak. In this case, cavity-modified NE-FGR rates can also be estimated from the same inputs needed for calculating the cavity-free NE-FGR rates, thereby bypassing the need for an explicit simulation of the molecular system inside the cavity. We also introduce an approximate limit of the cavity-modified NE-FGR, which we denote cavity-modified instantaneous Marcus theory, since it is based on the same assumptions underlying Marcus theory. The utility of the proposed framework for calculating cavity-modified NE-FGR rates is demonstrated by applications to photo-induced CT in the carotenoid-porphyrin-C60 molecular triad dissolved in liquid tetrahydrofuran and the Garg-Onuchic-Ambegaokar model for a CT reaction in the condensed phase.

Ultrafast electron dynamics plays a crucial role in understanding the properties of metals, particularly in the context of electron-phonon coupling (EPC). This study focuses on orientation-dependent ultrafast carrier dynamics in single-crystalline platinum films epitaxially grown on AlN-buffered sapphire substrates. Femtosecond time-resolved transient differential reflectance measurements reveal significant variations in the EPC constants across in-plane crystallographic directions, highlighting the influence of lattice symmetry. Theoretical analysis, based on group theory and Fermi's Golden Rule, shows that these ultrafast processes are affected by the symmetry of the platinum lattice, influencing the EPC dynamics. Unlike polycrystalline materials, single-crystalline platinum films exhibit distinct orientation-dependent behaviors, emphasizing the importance of crystallographic orientation in models. These findings provide new insights into ultrafast phenomena in metals and offer valuable perspectives for designing materials with tailored ultrafast properties for technological applications.

Given the need to rethink fiscal rules, seeking a balance that strengthens the fiscal anchor while protecting investment to sustain economic growth, this document addresses the following question: Which fiscal rule is most effective in ensuring fiscal sustainability and credibility in Colombia, while at the same time safe­guarding public investment? To answer this, three rules are evaluated: i) a golden fiscal rule combined with a debt rule, ii) an expenditure rule combined with a debt rule, and iii) a structural net primary balance rule, as defined in Law 2155 of 2021. The analysis is conducted through a Dynamic Stochastic General Equilibrium (DSGE) model calibrated and estimated for Colombia. The results show that the golden rule is more effec­tive in containing the fiscal deficit and public debt as a share of GDP.

This study explored how advanced artificial intelligence technologies, particularly convolutional neural networks (CNNs), can be applied to visual communication design, especially for automated poster layout generation. The study innovatively combined CNN technology with design practices, proposing an object detection model to identify and locate poster elements. This approach improved classification and localization accuracy in complex scenarios, laying the foundation for more efficient and precise automated design tools. The research covered experiment design, CNN application, layout model construction, and optimization processes. Aesthetic principles like the golden ratio and rule of thirds were applied to enhance visual appeal. By integrating these strategies, the study achieved a transition from design logic to computational logic, generating diverse design solutions. It offers new perspectives for artificial-intelligence-assisted visual communication design.

This composition advances a model of integrative religious pluralism as a means of fostering interreligious understanding, wherein distinct traditions retain their particularities while aligning along certain shared metaphysical, ethical, and spiritual axes. The framework holds that three core elements are either implicitly or explicitly shared across the world's religious and spiritual traditions: first, the idea of transcendental unity, in which diverse paths ultimately point toward a common, ineffable ultimate; second, the golden rule of morality, a universal moral principle that calls on us to treat others as we wish to be treated-or at the very least, not to treat others in ways we would not accept ourselves; and third, the overcoming of ego-whether understood as moksha, nirvana, or salvation-as both a soteriological goal and a practical guide for living peacefully with others. Taken together with established scholarships, we aim to argue that these shared insights offer a strong foundation for interreligious dialog and a more harmonious coexistence.

We have investigated the rate of ionization of traps using the proper adiabatic approximation. This rate is usually described by an Arrhenius-type equation in the experimental determination of trap depths from thermoluminescence measurements,R = νe-E/kT where R is the rate of ionization, E is the trap depth, and ν is the frequency factor. Although Eq. 1 has the form of an Arrhenius equation, in the exponent is the trap depth, not the activation barrier, Eb , as in a typical Arrhenius equation. (See Figure 1.)In a typical analysis of glow curves, ν is assumed to be a constant, although a weak temperature dependence is generally indicated by various authors. We have formulated this trap ionization problem using the proper adiabatic approximation for a single configurational coordinate system. In our formulation the nonadiabaticity operator drives the system from the ground state to the excited state nonradiatively. Using a first-order perturbation theory we have obtained the transition rate using the Fermi golden rule. We show that E in the exponent is indeed the trap depth, and that has a weak temperature dependence. We investigated the effect of this temperature dependence on calculating the trap depth from the glow curves. This will be discussed in detail in the presentation. Fig. 1: Adiabatic potentials for the electron in the ground state of the trap and in the excited state following ionization for a single configurational coordinate system. Figure 1

The subject of the study is the system of taxation of legal entities and its impact on key financial indicators of economic activity, including net profit, return on sales and assets. The relevance of the work is determined by the need to find a balance between the fiscal interests of the state and the financial stability of the business. The aim of the work is to identify the structural relationships between the tax burden and the financial results of companies and to develop recommendations for optimizing the tax strategy while observing the «golden rule» of economics. The features of the application of preferential tax regimes and the risks associated with changes in tax legislation are considered. The analysis of the dynamics of the tax burden in various sectors of the economy, including a comparative assessment of the tax burden on businesses in the federal districts of Russia. The tax burden has been calculated through the net return on sales and assets. When calculating the tax burden, it is proposed to use the same method of recognizing revenue and tax liabilities through their accrual under the general taxation system. The high tax burden negatively affects the profitability of companies and reduces their investment attractiveness. An important aspect is the justification for tax optimization, not only to minimize tax liabilities, but also to use the released resources in the development, implementation of technologies and sustainability in the market. The conclusion is made about the impact of the growing tax burden on the reduction of net profit, return on assets and the critical importance of optimizing the tax strategy for sustainable development in the context of annually changing tax legislation.

Introduction. Improving the quality of teaching Russian to Iranian students is an urgent methodological problem due to the intensive development of bilateral relations between Russia and Iran. Teaching Russian to Iranian students should be nationally oriented. The principle of visualization, the "golden rule of didactics," is implemented in Iranian students' work with multilingual texts. The success of Iranian students in learning Russian is achieved through the principle of active communication. The article presents a set of exercises that promote the development of speaking skills, and suggests modern methods of teaching Russian based on visual aids and the use of polycode text. The developed exercises are intended for foreign (Iranian) students who have a Russian language proficiency level of A2-B1 or higher. The purpose of the study is to develop exercises and justify their use in the teaching process of Russian as a foreign language. The proposed set of exercises, based on the principles of active communication, visualization, and ethno-orientation, is recommended for use in the educational process at an Iranian university outside the Russian language environment. The study used methods of analyzing scientific and educational literature on the problems of teaching Russian to Persian-speaking students of a nonphilological profile, as well as scientific observation and generalization of the experience of teaching Russian to Iranian students. The study provides a rationale for using a set of exercises based on visual aids to help students learn Russian. The novelty of the research lies in the refinement of the key concept of a polycode text, in scientific generalization, and in the proposal of a new didactic material based on the principles of visibility, ethno-orientation, active communication, oral advance, and taking into account the ethno-psychological specifics, cognitive, and communicative needs of Iranian students. The practical significance of the research lies in the development of exercises for Iranian students learning Russian, and in the possibility of disseminating the experience of teaching Russian as a foreign language to Persian-speaking students.

An enhancement of fluorescence and anticancer efficiency of coumarin-substituted thiosemicarbazone and its Cu2+ therapeutic sensing.

Abstract In this work, we present a theoretical study of the optical absorption coefficient (OAC) in GaAs/AlGaAs spherical quantum dots (QDs) described by the Kratzer potential. By solving the Schrödinger equation, the quantized energy levels and wave functions of charge carriers are obtained, and an analytical expression for the OAC is derived using Fermi’s golden rule. Numerical calculations reveal discrete absorption peaks whose energies and intensities depend strongly on the quantum states involved, the dot radius, the confinement potential depth, and the temperature. Increasing the dot size leads to a red shift and enhanced absorption, while deeper confinement potentials induce a blue shift and stronger peaks. Temperature mainly reduces the absorption intensity through thermal broadening but leaves the spectral positions unchanged. These results highlight the roles of quantum confinement, dipole selection rules, and carrier distribution in shaping the optical response of semiconductor QDs and provide useful guidelines for tailoring the absorption properties of GaAs/AlGaAs nanostructures for optoelectronic and photonic applications.

Probing electron transfer in catalytic reactions: A Catalysis Golden Rule and the role of non-innocent supports

Many reactions in chemistry and biology involve multiple electronic states, rendering them nonadiabatic in nature. These reactions can be formally described using Fermi's golden rule (FGR) in the weak-coupling limit. Nonadiabatic instanton theory presents a semiclassical approximation to FGR which is directly applicable to molecular systems. However, there are cases where the theory has not yet been formulated. For instance, in many real-world reactions, including spin-crossover or proton-coupled electron transfer, the nonadiabatic crossing occurs near a potential-energy barrier. This scenario gives rise to competing nonadiabatic reaction pathways, some of which involve tunneling through a round-top barrier while simultaneously switching electronic states. To date, no rate theory is available for describing tunneling via these unconventional pathways. Here, we extend instanton theory to model this class of processes, which we term the "nonconvex" regime. Benchmark tests on model systems show that the rates predicted by instanton theory are in excellent agreement with quantum-mechanical FGR calculations. Furthermore, the theory offers new insights into multistep tunneling reactions and the competition between sequential and concerted nonadiabatic tunneling pathways.