RESUMO
This paper generalizes very recent and unexpected findings [J. Phys. Chem. A, 2021, 125, 5152-5165] regarding the known "direct- and inverse-electron demand" Diels-Alder mechanisms. Application of bonding evolution theory indicates that the key electron rearrangement associated with significant chemical events (e. g., the breaking/forming processes of bonds) can be characterized via the simplest fold polynomial. For the CC bond formation, neither substituent position nor the type of electronic demand induces a measurable cusp-type signature. As opposed to the case of [4+2] cycloaddition between 1,3-butadiene and ethylene, where the two new CC single bonds occur beyond the transition state (TS) in the activated cases, the first CC bond occurs in the domain of structural stability featuring the TS, whereas the second one remains located in the deactivation path connecting the TS with the cycloadduct.
Assuntos
Elétrons , Reação de CicloadiçãoRESUMO
The electronic rearrangement featuring the photochemically-induced 1,3-cis-butadiene is discussed within a bonding evolution theory (BET) perspective based on the topological analysis of the electron localization function and Thom's catastrophe theory. The process involves the vertical singlet-singlet excitation S0 âS2 , and the subsequent deactivation implying the S2 /S1 and S1 /S0 conical intersection regions. BET results reveal that the new CC bond is finally formed on the S0 surface, as also recently found in the photochemical addition of two ethylenes [Phys. Chem. Chem. Phys. 23, 20598, (2021)].
Assuntos
Elétrons , Teoria Quântica , ButadienosRESUMO
In this work we propose a variant of a classical SIR epidemiological model where pathogens are characterized by a (phenotypic) mutant trait x. Imposing that the trait x mutates according to a random walk process and that it directly influences the epidemiological components of the pathogen, we studied its evolutionary development by interpreting the tenet of maximizing the basic reproductive number of the pathogen as an optimal control problem. Pontryagin's maximum principle was used to identify the possible optimal evolutionary strategies of the pathogen. Qualitatively, three types of optimal evolutionary routes were identified and interpreted in the context of virulence evolution. Each optimal solution imposes a different tradeoff relation among the epidemiological parameters. The results predict (mostly) two kinds of infections: short-lasting mild infections and long-lasting acute infections.
Assuntos
Interações Hospedeiro-Patógeno , Modelos Biológicos , Virulência , Animais , Número Básico de Reprodução/estatística & dados numéricos , Evolução Biológica , Epidemias/estatística & dados numéricos , Fatores Epidemiológicos , Interações entre Hospedeiro e Microrganismos , Interações Hospedeiro-Parasita , Interações Hospedeiro-Patógeno/genética , Interações Hospedeiro-Patógeno/fisiologia , Humanos , Infecções/epidemiologia , Conceitos Matemáticos , Mutação , Virulência/genética , Virulência/fisiologiaRESUMO
The sequence of the electronic flow driving the hydrometallation of acetylene by lithium hydride (and that of the opposite ß-hydride elimination reaction from the alkenyl metal intermediate), was examined within the perspective provided by the bonding evolution theory (BET). The analysis was based on the application of catastrophe theory to the changes of the electron localization function topology along the intrinsic reaction coordinate. The description of the electronic processes occurring on the process was represented in terms of topological structural stability domains (SSDs) and the associated elementary bifurcation catastrophes. Within such a framework of representation, the "evolution" of the system through the different SSDs reveals the key chemical events driving the transformation, including the large polarization effect as a consequence of Pauli repulsion between ions of the positive cationic metal on the hydride domain, the activation of the CC triple bond to attack the cationic center, and the agostic stabilizing interactions involving the hardest cationic metal, followed by the attack of the hydride center. These results contribute to emphasizing the intrinsic value and usefulness of using topological-based approaches and associated tools to increase our knowledge and understanding of the subtleties underlying the electronic flow as nuclei evolve along the reaction coordinate, providing detailed and complementary insights in comparison to other interpretative tool such those based on orbital-based representations, concerning the intimate nature of the electronic rearrangement of key mechanistic processes in chemistry. Graphical abstract The sequence of the electron flow (indicated by letters a and b) along the intrinsic reaction path for the hydrometallation of acetylene by lithium hydride to yield ethenyl lithium via a four-membered transition structure (TS), as determined within the bonding evolution theory to provide the key chemical events driven the changes in the key bonding patterns. Blue arrow Main event on the side HC ≡ CH + LiH â TS, red arrow the TS â HLiC=CH2 pathway, green arrows relative motion of nuclei along the imaginary frequency at the position of TS on the intrinsic reaction coordinate.
RESUMO
Arthur Schopenhauer (1788-1860) is known as the pessimist philosopher and the psychologist of the will. He anticipated some features of cognitive neuroscience, psychoanalysis and evolutionary psychology, but he is relatively unfamiliar to most contemporary mental health professionals. Schopenhauer conceived the will as the universes essence; purposeful human actions are a small part of it. We do not directly perceive the will, but only its phenomena through the Veil of Maya, which, in contemporary terms, refers to the cognitive and perceptual limits imposed by our own biological species. This is why Schopenhauer posits that we have a representation (idea) of the world. We have a direct access to the will by perceiving our bodys desires. The will is insatiable and selfish. Because of these wills features, there is no possibility of collective or global salvation. However, individual or existential salvation may occur by denying the will through a path that includes: 1) an aesthetic experience particularly with the aid of art, that allows contemplation of the ´Platonic Ideas´, lessening desire and promoting knowledge through contemplation,; 2) the ethical experience refers to the insight about the unity of the universe, particularly by realizing the ubiquity of suffering and neediness, and 3) the metaphysical step which promotes compassion and asceticism. These philosophical principles may add to specific psychotherapeutic techniques in expanding the individuals awareness beyond herself/himself, and thus arise and improve the psychological outcome.
Arturo Schopenhauer (1788-1860) es conocido como el filósofo pesimista y como el psicólogo de la voluntad. Schopenhauer anticipó algunos elementos de las neurociencias cognitivas, del psicoanálisis y de la psicología evolutiva, pero es poco conocido por la mayoría de los profesionales de la salud mental contemporáneos. Schopenhauer concibió la voluntad como la esencia del universo; la acción humana voluntaria es una pequeña parte de la voluntad. No percibimos a la voluntad directamente sino a sus fenómenos a través del Velo de Maya, el cual se refiere en términos presentes a los límites cognitivos y perceptuales impuestos por nuestra propia especie biológica. Es por esta razón que Schopenhauer afirmó que nos hacemos una representación (idea) del mundo. Tenemos un acceso directo a la voluntad al percibir los deseos de nuestro cuerpo. La voluntad es insaciable y egoísta. Dadas estas características de la voluntad, no existe la salvación colectiva o global. Sin embargo, es posible la salvación individual, mediante la negación de la voluntad, la cual ocurre a través de un camino que incluye: 1) la experiencia estética, en particular con la ayuda del arte, que permite contemplar las ´Ideas Platónicas´, aplacar el deseo y promover el conocimiento mediante la contemplación; 2) la experiencia ética, la cual se refiere a la toma de conciencia sobre la unidad del universo, en especial al darse cuenta de la ubicuidad del sufrimiento y de la naturaleza menesterosa del ser humano, y; 3) la experiencia metafísica, la cual promueve la compasión y el ascetismo. Estos principios filosóficos pueden agregarse a las técnicas psicoterapéuticas específicas para expandir la conciencia individual más allá de sí mismo (misma), y de esa manera estimular y mejorar la evolución psicológica.