Tddft Derivative Couplings And Other Topics In Quantum Chemistry

Photochemical reactions, which involve both the ground and excited electronic states of a molecule, can promote processes otherwise inaccessible by normal reactions. In general, photochemical reactions may be classified as adiabatic or nonadiabatic depending on whether the reaction takes place on the same adiabatic potential energy surface or not. From research over the last two decades, we now understand that many processes in nature turn out to be nonadiabatic { including charge transfer, electronic excitation quenching, and spin-forbidden transitions. The efficiency of such processes depends critically on the electron-nuclear interaction, which is quantified by the derivative coupling between the two involved states. The first part of the work (chapters 3-6) presented here mainly focuses on understanding the electron-nuclear interaction using the electronic structure theory. Two approaches are developed calculating the derivative couplings between the excited states within the time-dependent density functional theory. The behavior of the derivative couplings around a conical intersection is analyzed for two real molecules: benzaldehyde and protonated formaldamine. The second part of this work (chapters 7-8) focuses on understanding the electron-electron interaction in the framework of Green\u27s function. Detailed working equations are derived for the GW approximation, which is used to calculate the electron attachment/detachment energy, and the Bethe-Salpeter equation, which is used to obtain the electron excitation energies of a system

Normalized Solutions to Nonautonomous Kirchhoff Equation

In this paper, we study the existence of normalized solutions to the following Kirchhoff equation with a perturbation: $$\left\{ \begin{aligned} &-\left(a+b\int _{\mathbb{R}^{N}}\left | \nabla u \right|^{2} dx\right)\Delta u+\lambda u=|u|^{p-2} u+h(x)\left |u\right |^{q-2}u, \quad \text{ in } \mathbb{R}^{N}, \\ &\int_{\mathbb{R}^{N}}\left|u\right|^{2}dx=c, \quad u \in H^{1}(\mathbb{R}^{N}), \end{aligned} \right.$$ where $1\le N\le 3, a,b,c>0, 1\leq q<2$, $\lambda \in \mathbb{R}$. We treat three cases. (i)When $2<p<2+\frac{4}{N},h(x)\ge0$, we obtain the existence of global constraint minimizers. (ii)When $2+\frac{8}{N}<p<2^{*},h(x)\ge0$, we prove the existence of mountain pass solution. (iii)When $2+\frac{8}{N}<p<2^{*},h(x)\leq0$, we establish the existence of bound state solutions.Comment: arXiv admin note: text overlap with arXiv:2301.07926 by other author

COMMUNITY PARTICIPATION IN WASTE MANAGEMENT IN CHANGWON CITY, SOUTH KOREA

Changwon City, located in the southern central region of Gyeongsangnam-do in South Korea, has become a major center of industrial economy in the central region of Gyeongnam. To achieve good waste management can be done by handling: institutional aspects, financial aspects, regulatory aspects (legal), aspects of community participation, and operational technical aspects. The purposes of this research are to find out the participation of the community in Changwon City, South Korea and to investigate the type of management carried out in Changwon City, South Korea. The literature study method uses secondary data from Changwon City, South Korea and several studies on waste management to support and supplement information from the interviews. Government of South Korea adopted the concept of a volume-based waste fee system and collecting the recyclable waste, which is a volume-based waste disposal system, where each citizen has to pay for every plastic waste that will be used. The greater the waste production will need the greater the costs. Communities are required to sort out their waste before putting it in a plastic bag according to the type of waste, especially waste that can still be recycled. Korea has also established an expanded producer responsibility system and recycles its construction waste. Korea's waste information system has resulted in cost savings, promoted transparency, and eliminated illegal waste disposal. The effects of this policy include reducing the production of solid household waste, contributing to the completion of separate disposal, collecting waste and recyclable goods securing the cost of waste treatment from the benefits of the VBWF system and economic utilization

Normalized bound state solutions of fractional Schr\"{o}dinger equations with general potential

In this paper, we study a class of fractional Schr\"{o}dinger equation \begin{equation} \label{eq0} \left\{ \begin{aligned} &(-\Delta)^{s}u=\lambda u+a(x)|u|^{p-2}u,\\ &\int_{\mathbb{R}^{N}}|u|^{2}dx=c^{2},\ u\in H^{s}(\mathbb{R}^{N}), \end{aligned} \right. \end{equation} where $N>2s$, $s\in(0,1)$ and $p\in(2,2+4s/N), c>0$. $a(x)\in C(\mathbb{R}^{N},\mathbb{R})$ is a positive potential function. By using Fixed Point Theorem of Brouwer, barycenter function and variational method, we obtain the existence of normalized bound solutions for the problem

Existence of solutions for a Dirichlet problem with a p-Laplacian

AbstractSome theorems of existence of weak solutions are obtained for p-Laplacian equations with Dirichlet boundary conditions by using a critical point theorem