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2024 | Book

Molecular Properties via Induced Current Densities

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About this book

This book outlines past and new developments in molecular response theory in terms of static and dynamic-induced current densities and showcases an important step forward in the field of molecular density functions and their topological analysis. The book begins with a general perspective on topics such as classical Hamiltonian, quantum mechanical Hamiltonian, and topological analysis of the electron charge density, followed by an in-depth overview of time-dependent and -independent perturbations, and applications.

In this book, the author presents a completely new approach that allows the interpretation of electric and magnetic properties through origin-independent density functions. Readers will also find examples of how the new origin-independent density functions are useful for rationalizing the chemical behavior of molecules interacting with impinging radiation. The concepts contained within the book are the basis for a deeper understanding of Nuclear magnetic resonance (NMR) and Electron paramagnetic resonance (EPR) spectroscopies, as well as the mechanisms that give rise to electric polarization and optical activity in chiral systems. A basic knowledge of quantum mechanics and ab initio electronic structure calculation methods such as Hartree-Fock and Density Functional Theory is required. Given its breadth, the book provides an important contribution to the field of Quantum Chemical Topology and appeals to students and researchers interested in learning more about the relationship between electrical and magnetic properties, density functions derivable from them and experimental observables.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
To describe the interaction of a molecule with an external field, the concept of molecular response comes into play. Formally, it refers to response theory, namely the calculation of field-induced molecular properties through changes in expectation values [1]. The molecular response can take a variety of forms depending on the perturbing field, which can be electric, magnetic, or both, static or dynamic as in the case of the electromagnetic radiation. For example, in the presence of an electric field (time-independent or time-dependent), the electron cloud is polarized and an induced electric moment (static or dynamic) appears as a consequence of the perturbation. In the case of a magnetic field, electron currents start flowing within the electron cloud, thus providing an induced magnetic moment. Such induced electric and magnetic moments can be measured and may serve in technological applications.
Francesco Ferdinando Summa
Chapter 2. General Definitions
Abstract
We premise that our study of the interaction of a molecule with external electric and magnetic fields is a semi-classical one, i.e., the molecular system is treated at the QM level, while the fields are considered at the classical level. Therefore, we start recalling the basic equations of the classical electromagnetic field theory that will be used in the following. Then the quantum mechanical Hamiltonian in the Born-Oppenheimer approximation, without and with relativistic corrections, will be outlined, together with some of the tools needed for the topological analysis of the scalar field \(\rho (\boldsymbol{r})\), useful also for the analysis of the current density exposed later.
Francesco Ferdinando Summa
Chapter 3. Time-Independent Electron Current Density
Abstract
This chapter has a dual aim. The first is to report the equations defining total electron current density induced by static and uniform magnetic and electric fields in the presence of a spin–orbit coupling interaction, while the second is to show a procedure referred to as CTOCD that provides a solution to the well-known problem of the origin dependence of the non-relativistic computed first-order electron current density vector field.
Francesco Ferdinando Summa
Chapter 4. Time-Dependent Perturbations
Abstract
In this chapter expressions for the polarization charge and current densities induced in the electron cloud of a molecule by a monochromatic plane wave will be briefly recalled using the time-dependent quantum mechanical perturbation theory [1]. The description carried out in this chapter regards closed-shell systems, but it is clear that the discussion here reported can be extended to deal with open-shell systems and relativistic effects.
Francesco Ferdinando Summa
Chapter 5. Implementation of Origin-Independent Dynamic Polarizability Density Within Coupled Cluster Response Theory
Abstract
The implementation of dynamic origin-independent polarizability density at CCSD within the Coupled Cluster response theory approach is shown.
Francesco Ferdinando Summa
Chapter 6. Conclusions and Outlook
Abstract
The general theory of first-order molecular density functions, which are connected to the molecular response to external electric and magnetic fields, has been developed in terms of induced charge and current densities.
Francesco Ferdinando Summa
Metadata
Title
Molecular Properties via Induced Current Densities
Author
Francesco Ferdinando Summa
Copyright Year
2024
Electronic ISBN
978-3-031-60159-0
Print ISBN
978-3-031-60158-3
DOI
https://doi.org/10.1007/978-3-031-60159-0

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